Latest Current Affairs 14 May 2021

CURRENT AFFAIRS
14 May 2021

NATIONAL NEWS:

 

A) Experts point to contradiction in Indias push for IPR waiver on Covid-19 vaccines.

Public health advocates and intellectual property rights experts point to a contradiction in Indias global push for suspension of intellectual property protection with its stand in the Supreme Court that bringing Covid-19 vaccines under a statutory regime will be counter-productive at this stage. India, along with South Africa, had initiated a proposal for the temporary waiver of certain provisions in the Agreement on Trade-Related Aspects of Intellectual Property Rights (TRIPS) to facilitate fair, affordable and universal access to Covid-19 vaccines and medicines, especially for developing countries. The October 2020 communication to the TRIPS Council of the World Trade Organisation (WTO) referred to several reports about intellectual property rights hindering or potentially hindering timely provisioning of affordable medical products to patients. The two countries had highlighted that some WTO Members had carried out urgent legal amendments to their national patent laws to expedite the process of issuing compulsory/government use licences. Internationally, there is an urgent call for global solidarity, and the unhindered global sharing of technology and know-how in order that rapid responses for the handling of COVID-19 can be put in place on a real-time basis, they stressed in October last year. The United States has recently conveyed its support for an intellectual property waiver for Covid-19 vaccines. However, experts point to an affidavit filed by the Centre in the Supreme Court on May 9, 2021, which shows the government taking a different stand in favour of protection of intellectual property rights. Any exercise of statutory powers either under the Patents Act, 1970 read with TRIPS Agreement and Doha Declaration or in any other way can only prove to be counter-productive at this stage, the Centre has said in the affidavit. The government assures that it is very actively engaging itself with global organisations at a diplomatic level to find out a solution in the best possible interest of India.

B) Overseas Citizens of India, stung by Home Ministry notification, plan to take battle to Supreme Court.

The Home Ministrys March 4 order that required professional Overseas Citizens of India (OCIs) such as journalists, engineers and researchers to notify the Ministry about their activities in India has left them in the lurch. A portal that was to come up for the purpose is not operational yet. A Ministry official said it was delayed as several officials in the Ministrys foreigners division tested positive for Covid-19 in the past month. A director rank official, A. Radharani, succumbed to the virus last week. The official said the OCIs could intimate the Foreigners Regional Registration Office (FRRO) through e-mail till the portal is activated. Rajanna Sreedhara, president of Association of Resident OCI and Families (AROCIF), said that they were planning to challenge the Ministrys notification in the Supreme Court as they believed it was discriminatory. On March 4, the Ministry issued a gazette notification that OCI cardholders could claim only NRI (Non-Resident Indian) quota seats in educational institutions. It specified that OCIs could only pursue the following professions doctors, dentists, nurses and pharmacists, advocates, architects and chartered accountants, the rest would require special permission. OCIs are of Indian origin but hold foreign passports. India does not allow dual citizenship but provides certain benefits under Section 7B(I) of the Citizenship Act, 1955 to the OCIs. So far, 37.72 lakh OCI Cards are said to have been issued. The notification said that OCIs shall be required to obtain a special permission or a special permit from the competent authority or the FRRO or the Indian mission to undertake research, missionary or Tabligh or mountaineering or journalistic activities or internship in any foreign diplomatic missions. The notification does not mention IT professionals, a large number of OCIs are engineers; so will they have to apply for employment visa? It says permission required to conduct research…this will place undue burden on scientific, pharmaceutical, medical, biotechnology and other research fields, Sreedhara said.

C) Doctors in rural Unnao resign en masse, alleging harassment by administration over Covid-19 work.

More than a dozen doctors posted in rural hospitals in the Unnao district of Uttar Pradesh collectively resigned, alleging harassment and misbehaviour by administrative officials. Sixteen doctors, posted at community health centres and primary health centres submitted their resignation letters to the chief medical officer (CMO) of the district on Wednesday. Speaking to the media, one of them said that while their teams would work on the field from noon to 4-5 p.m., isolating Covid-19 positive cases in their home, distributing medicine and carrying out sampling, the local SDM would summon them after that seeking a report of their work. The doctors would have to drive back several km to the tehsil from their place of work just to prove that they are working, said the doctor. Despite continuously working, it has been made to appear like we are not working and that due to this, the Covid-19 situation is going out of control, he said. The doctors also alleged that they were not provided sufficient drug supply from the government and often faced verbal harassment at the hands of the CMO and the CMS. If the field teams were unable to trace down patients because of submission of wrong phone numbers and addresses, they should not be held responsible for it, said the doctors.

D) India resists community transmission tag despite soaring cases.

Despite adding the highest number of cases in the world every day, India continues to label itself as a country with no community transmission (CT), opting instead for the lower, less serious classification called cluster of cases, according to the latest weekly report by the World Health Organisation (WHO) on May 11. Countries such as the United States, Brazil, United Kingdom, France and a perusal of the list of over 190 countries suggest the majority have all labelled themselves as being in community transmission. Among the 10 countries with the most number of confirmed cases, only Italy and Russia do not label themselves as being in community transmission. Both countries have been on a declining trajectory for at least a month and together contribute less than 20,000 cases a day  about 5% of Indias daily numbers. India, since the beginning of the pandemic has never marked itself as being in community transition. Broadly, CT is when new cases in the last 14 days cant be traced to those who have an international travel history, when cases cant be linked to specific cluster.

E) Priyanka Gandhi demands judicial probe into bodies in Ganga.

Congress general secretary Priyanka Gandhi Vadra on Thursday said the situation in Uttar Pradesh is inhuman and criminal and demanded a judicial probe headed by a High Court judge into the several instances of bodies found floating in the Ganga in many parts of the State. What is happening in U.P. is inhuman and criminal. The government is busy image-building while people are suffering unimaginably. There must be an immediate judicial enquiry headed by a High Court judge into these events, tweeted Vadra, who is the Congress general secretary in-charge of U.P. The Unnao district authorities meanwhile ordered an inquiry over fresh reports of bodies being found buried on the banks of the Ganga in the Bighapur Patan tehsil area. There were also reports of bodies floating in the river in Ballia and other places of U.P. and Bihar. Bodies are floating in the Ganga in Ballia and Ghazipur. Reports are coming in of mass burials on the banks of the river in Unnao. Official numbers from cities like Lucknow, Gorakhpur, Jhansi and Kanpur appear to be grossly under-reported, the Congress leader said in another tweet.

F) Put FCRA on hold to ease relief flow, Nasscom plea to PM.

India’s IT industry body Nasscom has urged Prime Minister Narendra Modi to grant emergency use authorisation for all WHO-approved vaccines in view of domestic vaccine shortages, and temporarily relax stringent Foreign Contribution Regulation Act (FCRA) norms to ease the flow of overseas COVID-19 relief into the country. Newscom’s missive to the PM listed three critical asks to enable industry to act faster to help the country navigate the second wave. Many countries and global companies are providing aid to India and are helping the healthcare infrastructure deal with the surge. However, the amended provisions of the FCRA Act 2020 are proving to be a deterrent, the letter to the PM said. On May 3, the government permitted imports without GST levies for pandemic relief material donated from abroad for free distribution in the country, delegating States to certify the entities that will receive such imports. However, no exemption has been granted from the FCRA norms that require domestic entities receiving foreign aid to get an approval from the Ministry of Home Affairs. Given the humanitarian crisis, we would request the government to grant a temporary waiver to the FCRA Act and the 2020 amendments. This will enable NGOs to transfer funds between FCRA-approved NGOs and non-FCRA approved NGOs, it said. The amendments flagged by Nasscom prohibit entities receiving foreign contributions from transferring those to any other person, so even entities registered under the FCRA for providing healthcare support, are unable to pass on the relief material to patients or smaller NGOs.

G) PM Modi is missing along with vaccines and oxygen, tweets Rahul Gandhi.

Prime Minister Narendra Modi is also missing along with vaccine, oxygen and medicines, former Congress president Rahul Gandhi said on Thursday. In a tweet, Gandhi said, Prime Minister is also missing along with vaccine, oxygen and medicines. Among the things that remains include the Central Vista, goods and services tax (GST) on medicines, and photographs of the Prime Minister here and there, the Congress leader tweeted. Several Congress leaders also countered the government on vaccine shortage after Urban Development Minister Hardeep Singh Puri had blamed Congress leaders for raising doubts about Bharat Biotechs Covaxin being given approval without the phase three clinical trial data. Where is the Vaccine ? NDA/BJP Ministers are desperately trying to deflect attention from their Criminal mishandling of Pandemic by Goebbelinaly (sic) blaming opposition for fuelling vaccine hesitancy. FOCUS ON DOING SOME WORK FOR A CHANGE, Lok Sabha member Manish Tewari tweeted by tagging a news report about 100 vaccination centres in Delhi closing down owing to a vaccine shortage. His colleague, Shashi Tharoor, who was specifically named by Puri in a tweet, asked if the vaccine shortage in the country was because of his tweet. Let me keep it simple: 1. Is the vaccine shortage because of Congress tweets? 2. Did GOI fail to order enough vaccines because of my tweets? 3. Is differential pricing in May the result of my pointing out on Jan 3 that that Phase 3 trials of Covaxin were not complete @HardeepSPuri, asked Tharoor.

INTERNATIONAL NEWS 

A) Riyadh frees Bin Laden patriarch. 

Saudi Arabia has released construction magnate Bakr bin Laden, more than three years after his detention in a purge of the kingdoms elite that upended his vast business empire, sources told AFP. The former chairman of the Bin Laden Group, Saudi biggest construction company, was reunited last week with his family in the Red Sea city of Jeddah after being freed from an undisclosed detention site, two people close to his family said. Mr. Bakr, 70, a half-brother of the late Al-Qaeda leader Osama bin Laden, was not reachable for Mr. Bakr and two other siblings, Saad and Saleh, were snared in a November 2017 purge that saw hundreds of royals, tycoons and Ministers locked up for months in Riyadhs Ritz-Carlton hotel, then widely dubbed a fivestar prison. The unprecedented crackdown, which rattled private investors just as the kingdom sought to lure capital to help diversify the economy, was described by the government as an anti-corruption measure.

B) Mohamed Nasheed flown to Germany for treatment.

Maldivian leader Mohamed Nasheed was on Thursday flown to Germany for treatment, a week after surviving an assassination attempt in capital Male that left him critically injured. Following the May 6 terror attack, as Maldives police described the bomb explosion, doctors in a Male hospital performed complex surgeries on the Parliamentary Speaker and former President, to remove shrapnel from his liver, lungs and abdomen. He was discharged from hospital on Thursday, and medically evacuated to Germany with high security, local media reported. In the first tweet from his account since the explosion, Mr. Nasheed said in the local Dhivehi language: A special thanks to the health sector of the Maldives. By the grace of Allah, I will stay the course to deliver good governance that you all seek. Eid Mubarak to everyone! Linking the blast to religious extremists, the police arrested three persons allegedly involved in the deliberate act of terror. The Maldivess Parliamentary Committee on National Security Services is probing the security breach that led to the attack on the former President. In a statement condemning the attempted assassination, South Asians for Human Rights (SAHR), a regional network of human rights defenders, said the incident evoked popular unresolved murders and disappearances in past linked to extremist groups, such as the murder of blogger Yameen Rasheed in 2017, and MP Afrasheem Ali in 2012, and the 2014 disappearance [subsequently declared murder] of journalist Ahmed Rilwan Abdulla. The network urged President Ibrahim Mohamed Solihs government to probe the incidents and bring perpetrators to justice. Ahmed Shaheed, United Nations special rapporteur on freedom of religion or belief, who formerly served as Foreign Minister of the Maldives, said it is important to carefully conceptualise the May 6 attack.

Maths 10th Previous Year Question Paper 2015 (CBSE)

Maths

SET-I

Section – A

Q.1. If the quadratic equation px2– 2√5px + 15 = 0 has two equal roots, then find the value of p.

Answer. The given quadratic equation can be written as px2– 2√5px + 15 = 0

a = p, b = -2√5p, c = 15

For equal roots, D = 0

D = b2 – 4ac

0 = (– 2√5p)2 – 4 ×p × 15

0 = 4 ×5p2 – 60p

0 = 20p2 – 60p

p = 60p / 20p = 3 

∴ p = 3

 

Q.2. In Figure 1, a tower AB is 20 m high and BC, its shadow on the ground, is 20-√3 m long. Find the Sun’s altitude.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-1

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-12
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-13

 

Q.3. Two different dices are tossed together. Find the probability that the product of the two numbers on the top of the dice is 6.

Answer. Total outcomes = 6n = 62 = 36

Possible outcomes having the product of the two numbers on the top of the dice as 6 are (3 × 2, 2 × 3, 6 × 1, 1 × 6), i.e., 4

P(Product of two numbers is 6) = 4/36 = 1/9 

Q.4. In Figure 2, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT = 60°, find ∠PRQ.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-2

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-15

Section – B

Q.5. In Figure 3, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120°, then prove that OR = PR + RQ.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-3

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-16
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-17

 

Q.6. In Figure 4, a triangle ABC is drawn to circumscribe a circle of radius 3 cm, such that the segments BD and DC are respectively of lengths 6 cm and 9 cm. If the area of ∆ABC is 54 cm2, then find the lengths of sides AB and AC.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-4

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-18

 

Q.7. Solve the following quadratic equation for x: 4x2 + 4bx -(a2 – b2) = 0

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-19

 

Q.8. In an AP, if S5+ S7 = 167 and S10 = 235, then find the AP, where Sn denotes the sum of its first n terms.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-20
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-21

 

Q.9. The points A(4,7), B(p,3) and C(7,3) are the vertices of a right triangle, right-angled at B. Find the value of p.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-22

 

Q.10. Find the relation between x and y if the points A(x, y), B(-5, 7) and C(-4, 5) are collinear.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-23

Section – C

Q.11. The 14th term of an AP is twice its 8th term. If its 6th term is -8, then find the sum of its first 20 terms.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-24
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-25

 

Q.12. Solve for x: cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-6

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-26

 

Q.13. The angle of elevation of an aeroplane from a point A on the ground is 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of 1500 √3 m, find the speed of the plane in km/hr.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-27

 

Q.14. If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = 3/5 AB, where P lies on the line segment AB.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-28

 

Q.15. The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is 1/4. The probability of selecting a blue ball at random from the same jar is 1/3 . If the jar contains 10 orange balls, find the total number of balls in the jar.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-29

 

Q.16. Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60°. Also find the area of the corresponding major segment. [Use π = 22/7 ]

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-30

 

Q.17. Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m, and the canvas to be used costs Rs 100 per sq. m, find the amount, the associations will have to pay. [Use π = 22/7 ] What values are shown by these associations?

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-31
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-32

 

Q.18. A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-33

 

Q.19. A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs 5 per 100 sq. cm. [Use π = 3.14]

Answer. Let the side of cuboidal block (a) = 10cm

Let the  radius of hemisphere be r

Side of cube = Diameter of hemisphere

Largest possible diameter of hemisphere = 10cm

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-35

 

Q.20. 504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area. [Use π = 22/7 ]

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-36

Section – D

Q.21. The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-37
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-38

Q.22. Find the 60th term of the AP 8,10,12,…, if it has a total of 60 terms and hence find the sum of its last 10 terms.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-67

Q.23. A train travels at a certain average speed for a distance of 54 km and then travels a . distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-39

Q.24. Prove that the lengths of the tangents drawn from an external point to a circle are equal.

Answer. Given : Let circle be with centre O and P be a point outside circle PQ and PR are two tangents to circle intersecting at point Q and R respectively

To Prove : Lengths of tangents are equal i.e. PQ = PR

Construction:  Join OQ, OR and OP

Proof: As PQ is a tangent OQ⊥PQ [Tangent at any point of circle is perpendicular to the radius through point of contact]

So, ∠OQP = 90°

Hence ΔOQP is right triangle.

 

Q.25. Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-40
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-41

 

Q.26. Construct a ∆ABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°. Construct another ∆AB’C’ similar to ∆ABC with base AB’ = 8 cm.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-42

 

Q.27. At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30°. The angle of depression of the reflection of the cloud in the lake, at A is 60°. Find the distance of the cloud from A.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-43
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-44

 

Q.28. A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is

(i) a card of spade or an ace. (ii) a black king.

(iii) neither a jack nor a king. (iv) either a king or a queen.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-45

 

Q.29. Find the values of k so. that the area of the triangle with vertices (1, -1), (-4, 2k) and (-k, -5) is 24 sq. units.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-46

 

Q.30. In Figure 5, PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flower beds (shaded parts).

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-7

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-47
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-48

Q.31. From each end of a solid metal cylinder, metal was scooped out in hemispherical form of same diameter. The height of the cylinder is 10 cm and its base is of radius 4.2 cm. The rest of the cylinder is melted and converted into a cylindrical wire of 1.4 cm thickness. Find the length of the wire. [Use π = 22/7 ]

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-49

SET II

Q.10. If A(4, 3), B(-l, y) and C(3, 4) are the vertices of a right triangle ABC, right-angled at A, then find the value of y.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-50

Q.18. All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if the area of the circle is 1256 cm2. [Use π= 3.14]

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-51

Q.19. Solve for x:cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-8

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-52

Q.20. The 16th term of an AP is five times its third term. If its 10th term is 41, then find the sum of its first fifteen terms.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-53
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-54

Q.28. A bus travels at a certain average speed for a distance of 75 km and then travels a distance of 90 km at an average speed of 10 km/h more than the first speed. If it takes 3 hours to complete the total journey, find its first speed.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-55

Q.29. Prove that the tangent at any point of a circle is perpendicular to the radius through the I point of contact.

Answer. Given : Let circle be with centre O and P be a point outside circle PQ and PR are two tangents to circle intersecting at point Q and R respectively

To Prove : Lengths of tangents are equal i.e. PQ = PR

Construction:  Join OQ, OR and OP

Proof: As PQ is a tangent OQ⊥PQ [Tangent at any point of circle is perpendicular to the radius through point of contact]

So, ∠OQP = 90°

Hence ΔOQP is right triangle

Q.30. Construct a right triangle ABC with AB = 6 cm, BC = 8 cm and ∠B = 90°. Draw BD, the perpendicular from B on AC. Draw the circle through B, C and D and construct the tangents from A to this circle.

Answer. 

cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2014-16
cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2014-17

Q.31. Find the values of k so that the area of the triangle with vertices (k + 1, 1), (4, -3) and (7, -k) is 6 sq. units.

Answer.A(k + 1, 1), B(4, -3) and C(7, -k)

Area of ΔABC = ½ [x1 (y2y3) + x2 (y3y1) + x3 (y1y2)]

6 = ½ [(k+1)(-3 + k) + 4(-k-1) + 7(1+3)]

12 = [-3k + k2 -3 + k-4k-4 + 28]

12 = [ k2 -6k + 21]

⇒  k2 -6k + 21-12    ⇒  k2 -6k + 9

⇒ k2 -3k -3k + 9      ⇒ k(k-3)-3(k-3) = 0

⇒ k-3 = 0 ⇒ k-3 = 0

⇒ k = 3 ⇒ k = 3

Solving get k = 3

SET III

Q.10. Solve the following quadratic equation for x:  x2 – 2ax – (4b2 – a2) = 0

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-58

Q.18. The 13th term of an AP is four times its 3rd term. If its fifth term is 16, then find the sum of its first ten terms.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-59

Q.19. Find the coordinates of a point P on the line segment joining A(1, 2) and B(6, 7) such that AP=2/5 AB.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-60
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-61

Q.20. A bag contains, white, black and red balls only. A ball is drawn at random from the bag. If the probability of getting a white ball is 3/10 and that of a black ball is 2/5, then find the probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-62

Q.28. A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-63
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-64

Q .29. Arithmetic Progressions, 12,19,… has 50 terms. Find its last term. Hence find the sum of its last 15 terms.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-65

Q.30. Construct a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60°. Now construct another triangle whose sides are 5/7 times the corresponding sides of ∆ABC.

Answer. 

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2011-21
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2011-22

Q.31. Find the values of k for which the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2015-66

Maths 10th Previous Year Question Paper 2016 (CBSE)

Maths

SET-I

Section – A

Q.1. In Fig. 1, PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°. Find ∠PCA.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-1

Answer.

∠ACB = 90°            …………..[Angle in the semi-circle

In ΔABC, ∠CAB + ∠ACB + ∠CBA = 180°

30° + 90° + ∠CBA = 180°

∠CBA = 180° – 30° – 90° = 60° [Angle-sum-property of a Δ]

∠PCA = ∠CBA       ………….[Angle in the alternate Segment]

∴ ∠PCA = 60°

 

Q. 2. For what value of k will k + 9, 2k – 1 and 2k + 7 are the consecutive terms of an A.P.?

Answer. As we know, a2 – a1 = a3 -a2

2k -1-(k+9) = 2k +7 – (2k -1)

2k -1- k – 9 = 2k +7 – 2k + 1

k – 10 = 8 

∴ k = 8 + 10 = 18

 

Q 3. A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.

Answer.

Let AC be the ladder

Cos60° = AB/AC

½ = 2.5/AC

∴  Length of ladder, AC = 5cm

 

Q. 4. A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.

Answer.

S = 52

P (neither a red card nor a queen)

= 1 – P(red card or a queen)

= 1- [(26+4-2)/52]  [red cards = 26, Queen = 4, Red queen = 2]

= 1 – 28/52 = 24/52 = 6/13

 

Section-B

Q. 5. If -5 is a root of the quadratic equation 2×2+ px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.

Answer. 2x2 + px – 15 = 0

Since (-5) is a root of the given equation

∴ 2(-5)2 + p(-5) – 15 = 0

=  2(25) – 5p – 15 = 0

=  50 – 15 = 5p 

=  35 = 5p

=  p = 7 ——(i)

     p(x2+x) + k   px2 + px + k = 0

Here, a = p, b = p, c = k

D = 0                (Roots are equal)

       b2 – 4ac = 0      , (p)2 – 4(p)k = 0

(7)2 – 4(7)k = 0

49 – 28k = 0

∴ k = 49/28 = 7/4

 

Q. 6. Let P and Q be the points of trisection of the line segment joining the points A (2, -2) and B (-7, 4) such that P is nearer to A. Find the coordinates of P and Q.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-20
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-21

 

Q. 7. In Fig. 2, a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that: AB + CD = BC + DA.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-2

Answer.

AP = AS

BP = BQ

CR = CQ

DR = DS

[∴ Tangents drawn from an external point are equal in length]

By adding (i) to (iv)

(AP + BP) + (CR + DR) = AS + BQ + CQ + DS

AB + CD = (BQ + CQ) + (AS + DS)

∴ AB + CD = BC + AD (Hence Proved)

 

Q. 8. Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right angled isosceles triangle.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-23

 

Q. 9. The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term.

Answer. Let 1st term = a,  Common difference = d

a4 = 0 ⇒ a + 3d ⇒ a = -3d          …………(i)

a25 = a + 24d ⇒ -3d + 24d = 21d ….[From (i)

3(a11) = 3(a + 10d) ⇒ 3(-3d + 10d) =21d ….[From (i)

From above, a25 = 3(a11) (Hence proved)

 

Q. 10. In Fig. 3, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP = 2r, show that ∠OTS = ∠OST = 30°.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-3

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-26

Section – C

Q 11. In Fig. 4, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. (Take π = 3.14)

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-4

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-27

 

Q 12. In Fig. 5, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at the rate of Rs 500/sq. metre. (Use π = 22/7 )

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-5

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-28
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-29

 

Q 13. If the point P(x, y) is equidistant from the points A (a + b,b – a) and B(a -b,a + b), prove that bx = ay.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-30

 

Q 14. In Fig. 6, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC = 40°. (Use π= 22/7 )

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-6

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-31

 

Q 15. If the ratio of the sum of first n terms of two A.P’s is (7n + 1) : (4n + 27), find the ratio of their mth terms.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-32
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-33

 

Q 16. Solve for x:

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-7

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-34

 

Q 17. A conical vessel, with bash radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (Use π= 22/7)

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-35

 

Q 18. A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 3 (5/9) cm. Find the diameter of the cylindrical vessel.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-36
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-37

 

Q 19. A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Find the distance of the hill from the ship and the height of the hill.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-38

 

Q 20. Three different coins are tossed together. Find the probability of getting (i) exactly two heads (ii) at least two heads (ii) at least two tails.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-39
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-40

Section  – D

Q 21. Due to heavy floods in a State, thousands were rendered homeless. 50 schools collectively offered to the State Government to provide place and the canvas for 1,500 tents to be fixed by the Government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 m and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs Rs 120 per sq. m, find the amount shared by each school to set up the tents. What value is generated by the above problem? (Use π= 22/7)

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-41
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-42

 

Q 22. Prove that the lengths of the tangents drawn from an external point to a circle are equal.

Answer. Given : Let circle be with centre O and P be a point outside circle PQ and PR are two tangents to circle intersecting at point Q and R respectively

To Prove : Lengths of tangents are equal i.e. PQ = PR

Construction:  Join OQ, OR and OP

Proof: As PQ is a tangent OQ⊥PQ [Tangent at any point of circle is perpendicular to the radius through point of contact]

So, ∠OQP = 90°

Hence ΔOQP is right triangle

 

Q. 23. Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60° to each other.

Answer. 

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2013-16

 

Q 24. In Fig. 7, two equal circles, with centres O and O’, touch each other at X. OO’ produced meets the circle with centre O’ at A. AC is tangent to the circle with centre O, at the point C. O’D is perpendicular to AC. Find the value of DO’/CO.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-8

Answer. Given: two equal circles, with centres O and O’, touch each other at point X. OO’ is produced to meet the circle with centre O’ at A. AC is tangent to the circle with centre O, at the point C. O’D is perpendicular to AC.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-43

 

Q 25. Solve for x:

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-9

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-44

 

Q 26. The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of tower is 45°. Find the height of the tower PQ and the distance PX. (Use √3= 1.73)

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-45
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-46
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-47

 

Q 27. The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses preceding the house numbered X is equal to sum of the numbers of houses following X.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-48
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-49

 

Q 28. In Fig. 8, the vertices of ∆ABC are A(4, 6), B(l, 5) and C(7, 2). A line segment DE is drawn to intersect the sides AB and AC at D and E respectively such that AD/AB= AE/AC= 1/3 .Calculate the area of ∆ADE and Calculate the area compare it with area of ∆ABC.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-10

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-50
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-51

 

Q 29. A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that the product of x and y is less than 16.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-52

 

Q 30. In Fig. 9, is shown a sector OAP of a circle with centre O, containing ∠θ. AB is perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is r :

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-11
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-12

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-53

 

Q 31. A motor boat whose speed is 24 km/h in still water takes 1 hr more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-54

 

SET II

Q 10.Solve for x:

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-13

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-55

 

Q 18. The digits of a positive number of three digits are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-56
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-57

 

Q 19. If the roots of the quadratic equation (a – b)x2 + (b – c)x + (c – a) = 0 are equal, prove that 2a = b + c.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-58

 

Q 20. From a pack of 52 playing cards, Jacks, Queens and Kings of red colour are removed. From the remaining, a card is drawn at random. Find the probability that drawn card is: (i) a black King (ii) a card of red colour (iii) a card of black colour

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-59

 

Q 28. Draw an isosceles ∆ABC in which BC = 5.5 cm and altitude AL = 3 cm. Then construct another triangle whose sides are 3/4 of the corresponding sides of ∆ABC.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-60

 

Q 29. Prove that the tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.

Answer. Given: XY is a tangent at point P to the circle with centre O.

To prove: OP⏊XY

Construction: Take a point Q on XY other than P and join OQ.

Proof: If point Q lies inside the circle, then XY will become a secant and not a tangent to the circle.

∴ OQ > OP

This happen with every point on the line XY except the point P.

OP is the shortest of all the distances of the point O to the points of XY

∴ OP⏊XY

 

Q 30. As observed from the top of a lighthouse, 100 m high above sea level, the angles of depression of a ship, sailing directly towards it, changes from 30° to 60°. Find the distance travelled by the ship during the period of observation. (Use √3 = 1.73)

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-61

 

Q 31. A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find the length and breadth of the rectangular park.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-62
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-63

SET III

Q 10. Solve for x:

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-14

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-64

 

Q 18. There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card (i) is divisible by 9 and is a perfect square (ii) is a prime number greater than 80.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-65

 

Q 19. Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Find the numbers.

Answer. Let three consecutive natural numbers are x, x+1,x+2

According to the question, (x+1)2 -[(x+2)2x2 ] = 60

x2+1+2x -[x2+4+4xx2 ] = 60

x2 + 1 + 2xx2– 4 – 4x + x2 = 60

x2 – 2x – 63 = 0

x2 – 9x +7x – 63 = 0

x(x –9) + 7(x – 9) = 0

⇒ (x –9)(x + 7) = 0

x –9 = 0 , x = 9

x + 7 = 0 , x = -7

Natural No’s can not be -ve, ∴ x = 9

∴ Numbers are 9, 10, 11

 

Q 20. The sums of first n terms of three arithmetic progressions are S1, S2 and S3 respectively. The first term of each A.P. is 1 and their common differences are 1, 2 and 3 respectively. Prove that S1+ S3 = 2S2.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-67

 

Q 28. Two pipes running together can fill a tank in 11 (1/9) minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-68
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-69

 

Q 29. From a point on the ground, the angle of elevation of the top of a tower is observed to be 60°. From a point 40 m vertically above the first point of observation, the angle of elevation of the top of the tower is 30°. Find the height of the tower and its horizontal distance from the point of observation.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-70
cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-71

 

Q 30. Draw a triangle with sides 5 cm, 6 cm and 7 cm. Then draw another triangle whose sides are 4/5 of the corresponding sides of first triangle.

Answer.

cbse-previous-year-question-papers-class-10-maths-sa2-outside-delhi-2016-72

 

Q 31. A number x is selected at random from the numbers 1, 4, 9, 16 and another number y is selected at random from the numbers 1, 2, 3, 4. Find the probability that the value of xy is more than 16.

Answer. x can be any one of 1,4,9, or 16, i.e. 4 ways y can be any one of 1,2,3 or 4 ways

 Total number of cases of xy = 4×4 = 16 ways

Number of cases, where product is more than 16 

(9,2)(9,3)(9,4)(16,2)(16,3)(16,4) i.e. 6 ways

9×2 = 18 9×3 = 27

9×4 = 36 16×2 = 32

16×3 = 48 16×4 = 64

{18,27,36,32,48,64}

∴ Required Probability = 6/16 = 3/8

CDS(I) Exam 2016 English Previous Year Paper

CDS(I) 2016 English

SENTENCE IMPROVEMENT 

Directions for the following 20 (twenty) items : 

Look at the underlined part of each sentence. Below each sentence are given three possible substitutions for the underlined part. If one of them (a), (b) or (c) is better than the underlined part, indicate your response on the Answer Sheet against the corresponding letter (a), (b) or (c). If none of the substitutions improves the sentence, indicate (d) as your response on the Answer Sheet. Thus a “No improvement” response will be signified by the letter (d). 

Q 1. The police accused him for theft. 

(a) with 

(b) in 

(c) of 

(d) No improvement  

 

Q 2. He wanted that I left immediately. 

(a) I may leave 

(b) me to leave 

(c) I leave 

(d) No improvement

 

Q 3. This is to certify that I know Mr. J. Mathews since 1970. 

(a) am knowing 

(b) had known 

(c) have known 

(d) No improvement

 

Q 4. They took away everything that belonged to him. 

(a) that had been belonging 

(b) that belong 

(c) that has been belonging 

(d) No improvement

 

Q 5. It was the mother of the girl of whose voice I had recognised. 

(a) whose voice 

(b) the voice of who 

(c) voice whose 

(d) No improvement

 

Q 6. The Executive Council is consisted of ten members

(a) consists of 

(b) comprises of 

(c) constituted of 

(d) No improvement.

 

Q 7.The maid was laying the table for dinner. 

(a) setting up

(b) lying 

(c) sorting out 

(d) No improvement 

 

Q 8. We have so arranged the matters and one of us is always on duty. 

(a) that one of us 

(b) so that one of us 

(c) such that one of us 

(d) No improvement 

 

Q 9. Hardly have we got into the forest when it began to rain. 

(a) Hardly we got 

(b) We had hardly got 

(c) We had got hard 

(d) No improvement

 

Q 10. Each time he felt tired he lied down. 

(a) lies 

(b) lays 

(c) lay 

(d) No improvement

 

Q 11. Though it was raining, but I went out. 

(a) but yet I 

(b) 1 

(c) however I 

(d) No improvement

 

Q 12. There is no chance of success unless you do not work hard. 

(a) unless you work 

(b) until your working 

(c) until you do not work 

(d) No improvement

 

Q 13. She has grown too old to do little work. 

(a) some 

(b) any 

(c) a little 

(d) No improvement

 

Q 14. No one enjoys to deceive his family. 

 (a) deceiving 

(b) for deceiving 

(c) deceive 

(d) No improvement 

 

Q 15. Have you ever saw the flower of a pumpkin plant? 

(a) see 

(b) seeing 

(c) seen 

(d) No improvement 

 

Q 16. It is an ancient, historical place and it once belongs to the Pandavas. 

(a) belonged 

(b) belonging 

(c) belong 

(d) No improvement 

 

Q 17. Since we were knowing the correct route, we did not worry at all. 

(a) knew 

(b) have known 

(c) know 

(d) No improvement 

 

Q 18. Our country can progress when only people work hard. 

(a) when people only work hard 

(b) when people work hard only 

(c) only when people work hard 

(d) No improvement 

 

Q 19. Wake me up when father will come. 

(a) comes 

(b) will have come 

(c) came 

(d) No improvement

 

Q 20. Do take an umbrella with you lest you do not get wet. 

(a) lest you should get wet 

(b) lest you should not get wet 

(c) lest you might not get wet 

(d) No improvement 

 

ORDERING OF WORDS IN A SENTENCE 

Directions for the following 15 (fifteen) items : 

Each of the following items in this section consists of a sentence the parts of which have been jumbled. These parts have been labelled P, Q, R and S. Given below each sentence are four sequences namely (a), (b), (c) and (d). You are required to rearrange the jumbled parts of the sentence and mark your response accordingly. 

Q 21. that it would affect the investigation process (P) / they refused (Q)/ of these raids saying (R)/ to divulge the venues(S) 

The proper sequence should be 

(a) PQRS 

(b) SRPQ 

(c) QSRP

(d) RPQS 

 

Q 22. that he already has (P) / buying things (Q) / that rich man (R) / goes on (S)   

The proper sequence should be 

(a) PSQR 

(b) RSQP 

(c) SQRP 

(d) RPQS 

 

Q 23. the police commissioner rushed (P) / the crowd (Q) / to control (R) / the police force (S) 

The proper sequence should be 

(a) QRSP 

(b) PQRS 

(c) PSRQ 

(d) RSPQ 

 

Q 24. my brother (P) / to attend his friend’s wedding (Q) / is going to Chennai (R) /  tomorrow (S)

The proper sequence should be 

(a) PSQR 

(b) QPSR 

(c) ROPS 

(d) PRSQ 

 

Q 25. quickly (P) / he gave orders (Q) / to catch the thief (R) / to his men (S) 

The proper sequence should be 

(a) SPRQ 

(b) QSRP 

(c) PSRQ

(d) RSPP 

 

Q 26. to give a definition(P) /  if I were (Q) / I would begin (R) /  like this (S)  

The proper sequence should be 

(a) QPRS 

(b) PQRS 

(c) SRQP 

(d) RSPQ 

 

Q 27. deserve all honour in society (P) / in doing their job well (Q) / men of conscience who take pride (R) /  whatever its nature (S) 

The proper sequence should be 

(a) RQSP 

(b) QRPS 

(c) PRSQ 

(d) SPQR 

 

Q 28. while some live (P) / to eat and drink (Q) / many do not have enough (R) /  in luxury (S) 

The proper sequence should be 

(a) PSRQ 

(b) PRSQ 

(c) SPOR 

(d) RISP 

 

Q 29. I believed then /  that no matter (P) / one should always find some time for exercise (Q) / and I believe even now (R) / the amount of work one has (S) 

The proper sequence should be 

(a) PROS 

(b) PSRQ 

(c) RPQS 

(d) RPSQ 

 

Q 30. I wonder (P) / whenever I decide to go to the cinema  (Q) / with my scooter  (R) / why I always have trouble (S)  

The proper sequence should be 

(a) QSPR 

(b) QRSP 

(c) PSRQ

(d) PRSO 

 

Q 31. The bird-catcher / by means of snares  (P) / knew all the birds of the forest (Q) / by the hundred  (R) / and was accustomed to capturing the winged creatures (S)

The proper sequence should be 

(a) QPSR 

(b) QSRP 

(C) PQSR 

(d) PROS 

 

Q 32. Man is / a biological being (P) /  his physical and material needs  (Q) /  confined to  (R) / not merely 

 

The proper sequence should be 

(a) RSPQ 

(b) SRP 

(c) RPSQ 

(d) SPRQ 

 

Q 33. A gang of robbers / while they were fast asleep  (P) / entered the village (Q) /  and stole the property of the villagers (R) /  at night (S) 

 

The proper sequence should be 

(a) QSRP 

(b) SQPR 

(c) SPOR 

(d) QPSR 

 

Q 34. The opposition members  (P) / the ruling of the Speaker (Q) / to protest against  (R) /of the Parliament. (S) / walked out 

The proper sequence should be 

(a) SPQR

 (b) QRPS

 (c) RSPQ 

(d) SRQP 

 

Q 35. When /  (P) / a boy saved her  (P) / by a speeding car (R) / at the risk of his life (S) /a little girl was about to be run over 

 

 The proper sequence should be 

(a) SPRO 

(b) RSQP 

(c) SQPR 

(d) QPSR 

 

ORDERING OF SENTENCES 

Directions for the following 10 (ten) items : 

In the following items each passage consists of six sentences. The first and the sixth sentence are given in the beginning as Sl and S6. The middle four sentences in each have been removed and jumbled up. These are labelled P, Q, R and S. You are required to find out the proper sequence of the four sentences and mark your response accordingly on the Answer Sheet. 

Q 36. S1 : Once upon a time there was a king who had a wonderfully nice garden. 

S6: In the trees lived a nightingale that sang so sweetly that all who passed by stood still and listened. 

P : In the middle of the garden there was a lovely forest with tall trees and deep lakes. 

Q : In this garden were to be seen the most wonderful flowers with silver bells tied to them. 

R: The garden was so large that even the gardener himself did not know where it began and where it ended. 

S: These bells always sounded so that nobody should pass by without noticing the flowers. 

The proper sequence should be 

(a) QPRS

(b) SPQR 

(c) QSRP

 (d) QPSR 

 

Q 37. S1 : One of the first things the learning of a new language teaches you is that language comes from the region of the unconscious. 

S6: The test of how much you know is : how much can you say without having to think how you are going . : to say it ? 

P: What is often meant by “thinking in a language” is really the ability to use it without thinking about it. 

Q: We grown-up people have to filter it through our minds – a much more laborious process. 

R: That is why children learn a new language so effortlessly: it comes straight from their instincts. 

S : But we cannot say that we know a language, or know what we have studied of it, until we can use it instinctively. 

The proper sequence should be 

(a) SQRP 

(b) RPSQ 

(c) PQSR 

(d) RQSP

 

Q 38. S1 : For seventeen years she led a sheltered life in the convent. 

S6: Two years later she left the Loreto Convent where she had spent many happy and useful years. 

P: Her heart went out to the people living there. 

Q : In 1946 she asked for permission to work in the slums.

R: Then one day, while she was returning from an errand, she saw the slums of Calcutta. 

S : She felt she had found her second vocation, her real calling. 

The proper sequence should be

(a) PRSQ 

(b) RPSQ

(c) RPQS 

(d) QRPS

 

Q 39. SI : Good memory is so common that we regard a man who does not possess it as eccentric.

S6: She wheeled away the perambu lator, picturing to herself his terror when he would come out and find the baby gone. 

P:I have heard of a father who, having offered to take the baby out in a perambulator, was tempted by the sunny morning to pause on his journey and slip into a public house for a glass of beer. 

Q: A little later, his wife had to do some shopping which took her past the public house where to her horror, she discovered her sleeping baby. 

R: Leaving the perambulator outside, he disappeared into the drink shop. 

S : Indignant at her husband’s behaviour, she decided to teach him a lesson. 

The proper sequence should be 

(a) PQRS 

(b) PRQS 

(c) PSQR 

(d) PQSR

 

Q 40. Sl : Human ways of life have steadily changed. 

S6: Even if we try to do nothing, we cannot prevent change. 

P: Ancient Egypt – Greece – the Roman Empire – the Dark Ages and the Middle Ages – the Renaissance – the age of modern science and of modern nations one has succeeded the other; the history has never stood still.

Q : About ten thousand years ago, man I lived entirely by hunting

R: A settled civilized life only began when agriculture was discovered.

S : From that time to this, civilization has always been changing. 

The proper sequence should be 

(a) QRSP 

(b) QPSR 

(c) QSRP 

(d) PRSQ

 

Q 41. Sl : In our youth we are apt to think that applause and publicity constitute success. 

 

S6: So let us be initiated into the mysteries of maturity and be taught how to resist and spurn the lure of hollow shows. 

P : The man who values the applause more than his own effort has not outgrown his youth. 

Q : It is our achievement or work which wins lasting rewards. 

R : But these are only the trappings, the ephemeral illusions. 

S : One should concentrate on one’s work knowing that applause will come unsought. 

The proper sequence should be

(a) SRQP 

(b) PSRQ 

(c) QPSR 

(d) RQPS

 

Q 42. S1: My office sent an urgent email asking me to return. 

S6: It was evening before I could sit and write to my parents that I would be joining them soon. 

P: I immediately replied requesting a few days of grace as I had to book the return passage, pack and attend sundry matters before winding up my establishment here. 

Q : On the way, I went to the laundry and made sure I would get my clothes in time. 

R : Then I rushed to the bank, collected all my money and made reserva tions for my return journey. 

S : From the shop next to it, I bought a couple of trunks to dump my books and other odd articles so that I could send them away in advance.

The proper sequence should be

(a) PQRS 

(b) PRQS 

(C) PRSQ 

(d) PSRQ

 

Q 43. S1: Wordsworth knew the behaviour of owls in the night better than most of us know the ways of black birds in day time. 

S6: His great poetry owes much to the night. 

P : Out of school there were no restrictions on the hours he kept. 

Q : No poet ever had happier school days. 

R : He would skate by the light of the stars, snare woodcocks at dead of night, watch the sunrise after a long ramble.

S: Throughout life he was an inveterate walker by night.

The proper sequence should be 

(a) Q P R S 

(b) P SQR 

(c) QRPS 

(d) SQPR

 

Q 44. Sl : Science has already conferred an immense boon on mankind by the growth of medicine.

S6: The general death rate in 1948 (10.8) was the lowest ever recorded up to that date. 

P : It has continued ever since and is still continuing 

Q : In the eighteenth century people expected most of their children to die before they were grown up. 

R : In 1920 the infant mortality rate in England and Wales was 80 per thousand; in 1948 it was 34 per thousand. 

S : Improvement began at the start of the nineteenth century, chiefly owing to vaccination. 

The proper sequence should be 

(a) PQRS 

(b) RPQS 

(c) QPRS 

(d) PRQS

 

Q 45. SI : The young traveller gazed out into the dismal country with a face of mingled repulsion and interest. 

S6: He quickly restored it to his secret pocket. 

P: At intervals he drew from his pocket a bulky letter to which he referred, and on the margins of which he scribbled some notes.

R : From the back of his waist he produced something which one would hardly have expected to find in the possession of so mild mannered a man. 

Q : It was a navy revolver of the largest size. 

S : As he turned it slantwise to the light, the glint upon the rims of the copper shells within the drum showed that it was fully loaded.

The proper sequence should be 

(a) RPQS 

(b) QSPR 

(c) SQRP 

(d) PQSR

 

FILL IN THE BLANK 

Directions for the following 10 (ten) items : 

Each of the following sentences in this section has a blank space and four words are given after each sentence. Select whichever word you consider most appropriate for the blank space and indicate your response on the Answer Sheet accordingly. 

Q 46. The mounting pressure was so over whelming that he ultimately to her _________ wish. 

(a) yielded in 

(b) gave in

(c) cowed in

(d) agreed in

 

Q 47. Authority _________ when it is not supported by the moral purity of its user. 

(a) prevails

(b) entails

(c) crumbles

(d) waits

 

Q 48. In a developing country like India some industries will have to be brought within public_________ and control, for other wise rapid growth of the economy may be impossible. 

(a) perspective

(b) hegemony

(c) observation

(d) ownership

 

Q 49. Gandhiji conceived of the idea of channelizing the powerful currents of the united mass movement so as to give the utmost impetus to the national for independence. 

(a) struggle 

(b) conflict 

(c) onslaught 

(d) march 

 

Q 50. Because of his _________habits, he could not save much money. 

(a) extravagant 

(b) frugal 

(c) unsavoury 

(d) bad 

 

Q 51. Socrates was _________  of spreading discontent among young men of Athens and of trying to destroy their faith in the old gods. 

(a) rebuked 

(b) disparaged 

(c) accused 

(d) demonised 

 

Q 52. The robbers fell _________  amongst themselves over the sharing of the loot. 

(a) out

(b) through

(c) off

(d) across

 

Q 54. Speeding and blocking are traffic offences which lead to _________  accidents. 

(a) troublesome 

(b) final 

(c) great 

(d) gruesome 

 

Q 53. A really sophisticated person would never be  _________  enough to think that he is always right.

(a) reverent

(b) naive

(c) articulate

(d) humble

 

Q 55. Creative people are often  _________  with their own uniqueness. 

(a) obsessed 

(b) deranged 

(c) unbalanced 

(d) dissatisfied 

 

SELECTING WORDS 

Directions for the following 20 (twenty) items : 

In the following passage at certain points you are given a choice of three words marked (a), (b) and (c), one of which fits the meaning of the passage. Choose the best word out of the three. Mark the letter, viz., (a), (b) or (c), relating to this word on your Answer Sheet. Examples K and L have been solved for you. 

The K was in the school in Simla. L was home sick. 

K. (a) boy (b) horse (c) dog

L. (a) She (b) It (c) He

Explanation : Out of the list given in item K, only, ‘boy’ is the correct answer because usually, a boy, and not a horse or a dog, attends school. So ‘(a)’ is to be marked on the Answer Sheet for item K. A boy is usually referred to as “he’, so for item L, (c)’ is the correct answer. Notice that to solve the first item K you have to read the rest of the sentence and then see what fits best. 

I was engaged in many activities and I wanted a proper reconciliation between my activity and thought. Thought without  (56)  is undeveloped thought. Action action without (57) is folly. Of course we (58) act on some impulse or (59) urge. If suddenly you throw (60) no brick at me and my (61) goes up in front to (62) myself, it is an automatic, (63) action and not a result (64) deliberate thought. Our living is (65) by a series of automatic (66) from morning till night. Anything (67) do outside that common range of (68) however, has to be (69) by some measure of thinking. (70) more action and thought are (71) and integrated, the more effective (72) become and the happier you (73). There will then be no (74) between a wish to do something and (75) to act. 

Q 56. (a) wish  (b) action (c) idea

Q 57. (a) thought (b) wish (c) idea

Q 58. (a) never (b) belatedly (c) sometimes

Q 59. (a) peaceful (b) uncontrollable (c) indisputable

Q 60. (a) no (b) an  (c) a

Q 61. (a) hand (b) wrist (c) finger

Q 62. (a)stimulate myself it is an automatic (b)rescue (c)protect

Q 63. (a)uncontrollable action (b) instinctive(c)impulsive

Q 64. (a)to deliberate thought our living is  (b) in (c)of 

Q 65. (a)made by a series  (b)conditioned (c)developed

Q 66. (a)thoughts from morning till night anything (b)actions (c)wishes

Q 67. (a)we do outside that  (b) I (c) they 

Q 68. (a)thoughts however has to be  (b)ideas (c)actions

Q 69. (a)proceeded by some measure  (b) preceded (c)followed 

Q 70. (a)some more action and thought are  (b) If (c)  The 

Q 71. (a)developed and integrated the  (b) allied (c) hostile 

Q 72. (a) they become and the happier you (b)thoughts  (c)we

Q 73. (a)appear There will then  (b) develop (c)grow 

Q 74. (a) reconciliation become and the happier you (b) conflict (c)inflict 

Q 75. (a)inability to act  (b) probability (c)plausibility 

 

SPOTTING ERRORS 

Directions for the following 15 (fifteen) items : 

Each question in this section has a sentence with three underlined parts labelled (a), (b) and (c). Read each sentence to find out whether there is any error in any underlined part and indicate your response in the Answer Sheet against the corresponding letter i.e., (a) or (b) or (c). If you find no error, your response should be indicated as (d). 

Q 76. (a) This hardly won freedom /(b) should not be lost /(c)  so soon/(d) No error. 

Q 77.(a) I tried to meet the person /(b) whom you said /(c) was looking for me  /(d) No error. 

 

Q 78.(a) We looked after the thief, /(b) but he was nowhere /(c) to be found /(d) No error. 

Q 79. (a) I hoped that the train  /(b) will arrive on time, /(c) but it did not. /(d) No error. 

Q 80.(a) Their all belongings  /(b) were lost  /(c)in the fire. /(d)No error. 

Q 81.(a)He was in the temper /(b) and refused /(c)to discuss the matter again. /(d) No error. 

Q 82.(a) The decorations in your house  /(b)are similar /(c) to his house./(d) No error. 

Q 83.(a) Despite of the increase in air fares, /(b) most people still prefer /(c) to travel by plane./(d) No error. 

Q 84 .(a) He told the boys that /(b) bif they worked hard, /(c)they will surely passs. /(d) Noerror. 

Q 85. (a) I shall write /(b) to you  /(c) when I shall reach Chennai./(d)No error. 

Q 86. (a) Neither of these two documents /(b)support your claim /(c)on the property./(d) No error. 

Q 87.(a) He is school teacher,  /(b)but all his sons /(c) are doctors. /(d)No error. 

Q 88.(a) His grandfather /(b)had told to smoke /(c) was a bad habit. /(d) No error.

Q 89.(a)  My book, which /(b)I gave it to you yesterday,/(c)is very interesting./(d) Noerror. 

Q 90.(a) I am entirely agreeing with you, /(b)but I regret ,/(c) I can’t help you. /(d)No error.   

 

COMPREHENSION 

Directions for the 21 (twenty one) items which follow : 

In this section you have six short passages. After each passage, you will find some questions based on the passage. First, read a passage and answer the questions based on it. You are required to select your answers based on the contents of the passage and opinion of the author only. 

Passage 1 

To avoid the various foolish opinions to which mankind is prone, no superhuman brain is required. A few simple rules will keep you, not from all errors, but from silly errors. 

If the matter is one that can be settled by observation, make the observation yourself. Aristotle could have avoided the mistake of thinking that women have fewer teeth than men, by the simple device of asking Mrs. Aristotle to keep her mouth open while he counted. Thinking that you know, when in fact you do not, is a bad mistake to which we are all prone. I believe myself that hedgehogs eat black beetles, because I have been told that they do; but if I were writing a book on the habits of hedgehogs, I should not commit myself until I had seen one enjoying this diet. Aristotle, however, was less cautious. Ancient and medieval writers knew all about unicorns and salamanders; not one of them thought it necessary to avoid dogmatic statements about them because he had never seen one of them. 

Q 91. The writer believes that 

(a) most people could avoid making foolish mistakes if they were clever 

(b) through observation we could avoid making many mistakes

(c) Aristotle made many mistakes because he was not observant

(d) All errors are caused by our own error in thinking 

 

Q 92. With reference to the passage, which one of the following is the correct statement ? 

(a) Aristotle was able to avoid the mistake of thinking that women have fewer teeth than men 

(b) Aristotle thought women have fewer teeth than men 

(c) Aristotle proved that women have fewer teeth by counting his wife’s teeth 

(d) Aristotle may have thought that women have fewer teeth because he never had a wife

 

Q 93. The writer says that if he was writing a book on hedgehogs 

(a) he would maintain that they eat black beetles because he had been told so 

(b) he would first observe their eating habits 

(c) he would think it unnecessary to verify that they ate black beetles

(d) he would make the statement that they ate black beetles and later verify it

 

Q 94. The writer is of the opinion that 

(a) unicorns and salamanders were observed by ancient and medieval writers but were unknown to modern writers 

(b) ancient and medieval writers wrote authoritatively about unicorns and salamanders though they had never seen them 

(c) unicorns and salamanders do not exist 

(d) only those who had observed the habits of unicorns and salamanders wrote about them 

 

Q 95. A ‘dogmatic statement’ in the context means a statement which is 

(a) convincing 

(b) proved 

(c) unquestionable 

(d) doubtful 

 

Passage 2 

Since I had nothing better to do, I decided to go to the market to buy a few handkerchiefs, the old ones had done vanishing trick. On the way I met an old friend of mine and I took him to a nearby restaurant for tea and snacks. Afterwards I went to the shop and selected a dozen handkerchiefs. I pulled out my purse to make the payment, and discovered that it was empty; I then realized that it was not my purse, it was a different purse altogether. How that happened is still a source of wonder to me and I refuse to believe that it was the work of my good old friend, for it was his purse that I held in my hand. 

Q 96. The man could not buy the handkerchiefs because 

(a) he did not like the handkerchiefs 

(b) his friend did not allow him to buy them 

(c) the shop did not have any handkerchiefs 

(d) he had no money in the purse 

 

Q 97. When he tried to take out the purse, he discovered that 

(a) it was not there 

(b) it was lost 

(c) it was a new purse 

(d) it was his friend’s purse

 

Passage 3 

A profound terror, increased still by the darkness, the silence and his waking images, froze his heart within him. He almost felt his hair stand on end, when by straining his eyes to their utmost, he perceived through the shadows two faint yellow lights. At first he attributed these lights to the reflection of his own pupils, but soon the vivid brilliance of the night aided him gradually to distinguish the objects around him in the cave, and he beheld a huge animal lying but two steps from him. 

Q 98. The opening of the passage suggests that 

(a) darkness, silence and waking images added to his already being in pro found terror 

(b) a profound terror increased the waking images in his frozen heart

(c) the person was frightened by darkness and silence

(d) a profound terror was caused in him by the silence and darkness of the night

 

Q 99. When he perceived through the shadows two faint lights, 

(a) he experienced a great strain

(b) he felt his hair stand upright

(c) his eyes felt strained to their utmost 

(d) his pupils dilated

 

Q 100. The person in the story the person was frightened by darkness and silence 

(a) imagined that he saw an animal 

(b) could not recognize the animal 

(c) saw the animal by chance

(d) expected to see the animal

 

Passage 4 

We are tempted to assume that technological progress is real progress and that material success is the criterion of civilization. If the Eastern people become fascinated by machines and techniques and use them, as Western nations do, to build huge industrial organizations and large military establishments, they will get involved in power politics and drift into the danger of death. Scientific and technological civilization brings great opportunities and great rewards but also great risks and temptations. Science and technology are neither good nor bad. They are not to be tabooed but tamed and assigned their proper place. They become dangerous only if they become idols. 

Q 101. According to the author, people think that real progress lies in 

(a) material success and technological growth 

(b) imitating Western nations 

(c) having large industries and political power 

(d) taking risks and facing temptations

 

Q 102. According to the author, science and technology should be 

(a) tabooed and eliminated from life

(b) used in a controlled and careful manner 

(c) encouraged and liberally used 

(d) made compulsory in education

 

Q 103. From the passage one gathers that the Eastern people must 

(a) appreciate scientific achievements 

(b) build huge industrial organizations 

(c) avoid being controlled by machines and techniques of industrial produc tion 

(d) be fascinated by machines

 

Q 104. According to the author, science and technology are 

(a) totally harmless 

(b) extremely dangerous

(c) to be treated as idols

(d) useful, if they are not worshipped blindly 

 

Passage 5 

It is not luck but labour that makes men. Luck, says an American writer, is ever waiting for something to turn up; labour with keen eyes and strong will always turns up something. Luck lies in bed and wishes the postman would bring him news of a legacy; labour turns out at six and with busy pen and ringing hammer lays the foundation of competence. Luck whines, labour watches. Luck relies on chance; labour on character. Luck slips downwards to self-indulgence; labour strides upwards and aspires to independence. The conviction, therefore, is extending that diligence is the mother of good luck; in other words, that a man’s success in life will be proportionate to his efforts, to his industry, to his attention to small things. 

Q 105. Which one of the following statements sums up the meaning of the passage ? 

(a) Luck waits without exertion but labour exerts without waiting

(b) Luck waits and complains without working while labour achieves success although it complains

(c) Luck often ends in defeat but labour produces luck

(d) Luck is self-indulgent but labour is selfless

 

Q 106. Which one of the following statements is true about the passage ?

(a) Luck is necessary for success

(b) Success depends on hard work and attention to details

(c) Expectation of good luck always meets with disappointment

(d) Success is exactly proportionate to hard work only

 

Q 107.“ ___________labour turns out at six and with busy pen and ringing hammer lays the foundation of competence.” This statement means 

(a) hard work of all kinds makes people efficient and skilled

(b) the labour lays the foundation of the building 

(c) the writer and the labourer are the true eyes of the society 

(d) there is no worker who works so hard as the labourer who begins his day at six in the morning 

 

Passage 6 

The avowed purpose of the exact sciences is to establish complete intellectual control over experience in terms of precise rules which can be formally set out and empirically tested. Could that ideal be fully achieved, all truth and all error could henceforth be ascribed to an exact theory of the universe, while we who accept this theory would be relieved of any occasion for exercising our personal judgement. We should only have to follow the rules faithfully. Classical mechanics approaches this ideal so closely that it is often thought to have achieved it. But this leaves out of account the element of personal judgement involved in applying the formulae of mechanics to the facts of experience. 

Q 108. The purpose of the exact sciences is to 

(a) form opinions about our experience

(b) formulate principles which will help us to exercise our personal judgement

(c) assert our intellectual superiority 

(d) make formal and testable rules which can help verify experience

 

Q 109. An exact theory of the universe is 

(a) not desirable 

(b) improbable 

(c) possible 

(d) yet to be made

 

Q 110. In exact sciences 

(a) personal judgements are set aside in favour of a mechanical theory 

(b) one does not find answers to all questions and problems 

(c) one reposes faith in actual experience 

(d) one interprets the universe according to one’s wish 

 

Q 111. Classical mechanics 

(a) has formulated precise rules based on experience Cape

(b) has gained intellectual control over the world

(c) has formulated an exact theory of the universe

(d) just falls short of achieving intel lectual control over experience

 

SYNONYMS 

Directions for the following 9 (nine) items : 

Each item in this section consists of a word in capital letters followed by four words or groups of words. Select the word or groups of words that is most similar in meaning to the word in capital letters. 

Q 112. AMBIGUOUS

(a) contrasting 

(b) connivance

 (c) vague 

(d) wilful

 

Q 113. ELUCIDATE 

(a) clarify 

(b) calculate 

(c) summarise 

(d) update

 

Q 114. MONOTONOUS 

(a) dreary

(b) dreadful 

(c) single-minded 

(d) monologue

 

Q 115. KINDLE 

(a) make fun of 

(b) excite 

(c) very kind

(d) kind-hearted

 

Q 116. PALATIAL 

(a) very clean 

(b) very special 

(c) sense of taste 

(d) magnificent 

 

Q 117. TACTFUL 

(a) diplomatic 

(b) indifferent 

(c) intelligent 

(d) deceitful 

 

Q 118. VORACIOUS 

(a) very bad 

(b) insatiable 

(c) stingy 

(d) malicious 

 

Q 119. STRICTURE 

(a) strictness 

(b) stinging 

(c) discipline 

(d) censure 

 

Q 120. OBEISANCE 

(a) homage 

(b) pilgrimage 

(c) subjugation 

(d) obligation 

Maths 10th Previous Year Question Paper 2017 (CBSE)

Maths

Section – A

Q.1. What is the common difference of an A.P. in which a21 – a7 = 84 ?

Solution: Given, a21 – a7 = 84

⇒ (a + 20d) – (a + 6d) = 84

⇒ a + 20d – a – 6d = 84

⇒ 20d – 6d = 84

⇒ 14d = 84

Hence common difference = 6

 

Q. 2.If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP.

Solution: Given, ∠APB = 60°

∠APO = 30°

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q2

In right angle ΔOAP,

OP/OA = cosec 30°

⇒ OP/a = 2

⇒ OP = 2a.

Q. 3.If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is the angle of elevation of the sun?]

Solution: In ΔABC,

tan θ = AB/ BC

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q3

⇒ tan θ = 30/10√3 = √3

⇒ tan θ = tan 60°

⇒ θ = 60°

Hence angle of elevation is 60°.

 

Q. 4. The probability of selecting a rotten apple randomly from a heap of 900 apples is 0-18. What is the number of rotten apples in the heap? 

Solution: Total apples = 900

P(E) = 0.18

No. of rotten apples / Total No. of apples = 0.18

No. of rotten apples / 900 = 0.18

No. of rotten apples = 900 × 0.18 = 162

Section – B

Q. 5. Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other. 

Solution: Given equation is px2 – 14x + 8 = 0

Let one root = α

then other root = 6α

Sum of roots = -b/a

α+6α=-(-14)/p

7α=14/p or α= 2/p   ……….(1)

Product of roots = c/a

(α)(6α)=8/p

2=8/p  ……….(2)

Putting value of α from eq. (i),

⇒6×(2/p)2 = 8/p

⇒6×4/p2 = 8/p

⇒24p = 8p2

⇒8p2-24p = 0

⇒8p(p-3) = 0

⇒ Either 8p = 0

p = 0

or        (p-3) = 0

p = 3

For p=0, given condition is not satisfied

ஃ p=3

 

Q 6.Which term of the progression 20, 19¼  , 18½ , 17 ¾, … is the first negative term ? 

Solution: Given, A.P. is 20, 19¼  , 18½ , 17 ¾, …

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q6

 

Q. 7. Prove that the tangents drawn at the endpoints of a chord of a circle make equal angles with the chord.

Solution: Given, a circle of radius OA and centred at O with chord AB and tangents PQ & RS are drawn from point A and B respectively.

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q7

Draw OM ⊥ AB, and join OA and OB.

In ∆OAM and ∆OMB,

OA = OB (Radii)

OM = OM (Common)

∠OMA = ∠OMB (Each 90°)

∆OAM = ∆OMB (By R.H.S. Congurency)

∠OAM = ∠OBM (C.PC.T.)

Also, ∠OAP = ∠OBR = 90° (Line joining point of contact of tangent to centre is perpendicular on it)

On addition,

∠OAM + ∠OAP = ∠OBM + ∠OBR

⇒ ∠PAB = ∠RBA

⇒ ∠PAQ – ∠PAB = ∠RBS – ∠RBA

⇒ ∠QAB = ∠SBA

Hence Proved

 

Q. 8. A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA 

Solution: Given, a quad. ABCD and a circle touch its all four sides at P, Q, R, and S respectively.

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q8

To prove: AB + CD = BC + DA

Now, L.H.S. = AB + CD

= AP + PB + CR + RD

= AS + BQ + CQ + DS (Tangents from same external point are always equal)

= (AS + SD) + (BQ + QC)

= AD + BC

= R.H.S.

Hence Proved.

 

Q 9.A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the coordinates of P and Q. 

Solution: Let co-ordinate of P (0, y)

Co-ordinate of Q (x, 0)

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q9

 

Q. 10.If the distances of P(x, y), from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y. 

Solution: Given, PA = PB

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q10

⇒ x2 + 25 – 10x + y2 + 1 – 2y = x2 + 1 + 2x + y2 + 25 – 10y

⇒ -10x – 2y = 2x – 10y

⇒ -10x – 2x = -10y + 2y

⇒ 12x = 8y

⇒ 3x = 2y

Hence Proved.

Section – C

Q 11. If ad ≠ bc, then prove that the equation (a2 +b2) x2 + 2 (ac + bd) x +  (c2 + d2) = 0 has no real roots. 

Solution: Given, ad ≠ bc

(a2 + b2) x2 + 2(ac + bd)x + (c2 + d2) = 0

D = b2 – 4ac

= [2(ac + bd)]2 – 4 (a2 + b2) (c2 + d2)]

= 4[a2c2 + b2d2 + 2abcd] – 4(a2c2 + a2d2 + b2c2 + b2d2)

= 4[a2c2 + b2d2 + 2abcd – a2c2 – a2d2 – b2c2 – b2d2]

= 4[-a2d2 – b2c2 + 2abcd]

= -4[a2d2 + b2c2 – 2abcd]

= -4[ad – bc]2

D is negative

Hence given equation has no real roots.

 

Q 12.The first term of an A.E is 5, the last term is 45 and the sum of all its terms is 400. Find the number of terms and the common difference of the A.P. 

Solution: Given, a = 5, an = 45, Sn = 400

We have, Sn = ⇒ 400 = n/2 [5 + 45]

⇒ 400 = n/2 [50]

⇒ 25n = 400

⇒ n = 16

Now, an = a + (n – 1) d

⇒ 45 = 5 + (16 – 1)d

⇒ 45 – 5 = 15d

⇒ 15d = 40

⇒ d = 8/3

So n = 16 and d = 8/3

 

Q 13.On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower. 

Solution:

Let height AB of tower = h  m.

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q13
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q13.1

 

Q14. A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag. 

Solution: Given, no. of white balls = 15

Let no. of black balls = x

Total balls = (15 + x)

According to the question,

P(Blackball) = 3 × P(White ball)

⇒ x/15+x = 3 × 15/15+x

⇒ x = 45

No. of black balls in bag = 45

 

Q 15.In what ratio does the point (2411, y) the line segment joining the points P(2, -2) and Q(3, 7) ? Also, find the value of y. 

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q15

Solution: Let point R divides PQ in the ratio k : 1

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q15.1
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q15.2

Q 16. Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semi-circle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region. 

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q16

Solution: Given, radius of large semi-circle = 4.5 cm

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q16.1

Q17. In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region. [Use π = 227]

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q17

Solution: Angle for shaded region = 360° – 60° = 300°

Area of shaded region

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q17.1

 

Q 18.Water in a canal, 5-4 m wide and 1.8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation ? 

Solution: Width of canal = 5.4 m

Depth of canal = 1.8 m

Length of water in canal for 1 hr = 25 km = 25000 m

Volume of water flown out from canal in 1 hr = l × b × h = 5.4 × 1.8 × 25000 = 243000 m3

Volume of water for 40 min = 243000 × 40 60 = 162000 m3

Area to be irrigated with 10 cm standing water in field = Volume/ Height

= (162000×100)/10  m2

= 1620000 m2

= 162 hectare

 

Q 19.The slant height of a frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum. 

Solution: Slant height of frustum ‘l’ = 4 cm

Perimeter of upper top = 18 cm

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q19

Q 20. The dimensions of a solid iron cuboid are 4.4 m × 2.6 m × 1.0 m. It is melted and recast into hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe. 

Solution:  Inner radius of pipe ‘r’ = 30 cm 

The thickness of pipe = 5 cm

Outer radius ‘R’ = 30 + 5 = 35 cm

Now, Volume of hollow pipe = Volume of Cuboid

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q20

Section – D

Q. 21.Solve for x:

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q21

Solution:

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q21.1

Q 22.Two taps running together can fill a tank in 3 1/13  hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank ? 

Solution: Let tank fill by one tap = x hrs

other tap = (x + 3) hrs

Together they fill by (3) 1/13 = 40/13 hrs

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q22

Either x – 5 = 0 or 13x + 24 = 0

x = 5, x = -24/13 (Rejected)

One tap fill the tank in 5 hrs

So other tap fill the tank in 5 + 3 = 8 hrs

 

Q 23.If the ratio of the sum of the first n terms of two A.P.S is (7n + 1) : (4n + 27), then find the ratio of their 9th terms. 

Solution:

Ratio of the sum of first n terms of two A.P.s are

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q23

Hence ratio of 9th terms of two A.P.s is 24 : 19

 

Q 24.Prove that the lengths of two tangents drawn from an external point to a circle are equal. 

Solution: Given, a circle with centre O and external point P. |

Two tangents PA and PB are drawn.

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q24

To Prove: PA = PB

Construction: Join radius OA and OB also join O to P.

Proof: In ∆OAP and ∆OBP,

OA = OB (Radii)

∠A = ∠B (Each 90°)

OP = OP (Common)

∆AOP = ∆BOP (RHS cong.)

PA = PB [By C.PC.T.]

Hence Proved.

 

Q 25.In the given figure, XY and XY are two parallel tangents to a circle with centre O and another tangent AB with a point of contact C, is intersecting XY at A and X’Y’ at B. Prove that ∠AOB = 90°. 

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q25

Solution: Given, XX’ & YY’ are parallel.

Tangent AB is another tangent which touches the circle at C.

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q25.1

To prove: ∠AOB = 90°

Construction: Join OC.

Proof: In ∆OPA and ∆OCA,

OP = OC (Radii)

∠OPA = ∠OCA (Radius ⊥ Tangent)

OA = OA (Common)

∆OPA = ∆OCA (CPCT)

∠1 = ∠2 …(i)

Similarly, ∆OQB = ∆OCB

∠3 = ∠4 …(ii)

Also, POQ is a diameter of circle

∠POQ = 180° (Straight angle)

∠1 + ∠2 + ∠3 + ∠4 = 180°

From eq. (i) and (ii),

∠2 + ∠2 + ∠3 + ∠3 = 180°

⇒ 2(∠2 + ∠3) = 180°

⇒ ∠2 + ∠3 = 90°

Hence, ∠AOB = 90°

Hence Proved.

 

Q 26.Construct a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are 3 4  times the corresponding sides of the ∆ABC. 

Solution: BC = 7 cm, ∠B = 45°, ∠A = 105°

∠C = 180 ° – (∠B + ∠A) = 180° – (45° + 105°) = 180° – 150° = 30°

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q26

Steps of construction:

  1. Draw a line segment BC = 7 cm.
  2. Draw an angle 45° at B and 30° at C. They intersect at A.
  3. Draw an acute angle at B.
  4. Divide angle ray in 4 equal parts as B1, B2, B3 and B4.
  5. Join B4 to C.
  6. From By draw a line parallel to B4C intersecting BC at C’.
  7. Draw another line parallel to CA from C’ intersecting AB ray at A.
    Hence, ∆A’BC’ is required triangle such that ∆A’BC’ ~ ∆ABC with A’B = ¾ AB

 

Q 27. An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are 45° and 60° respectively. Find the width of the river. [Use √3 = 1.732] 

Solution: Let aeroplane is at A, 300 m high from a river. C and D are opposite banks of river.

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q27

Q 28. If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear, then find the value of k. 

Solution: Since A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear points, so area of triangle = 0.

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q28
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q28.1

 

Q. 29. Two different dice are thrown together. Find the probability that the numbers obtained have

(i) even sum, and

(ii) even product. 

Solution: When two different dice are thrown together

Total outcomes = 6 × 6 = 36

(i) For even sum: Favourable outcomes are

(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6),

(3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6),

(5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6)

No. of favourable outcomes = 18

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q29

(ii) For even product: Favourable outcomes are

(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).

No. of favourable outcomes = 27

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q29.1

Q. 30. In the given figure, ABCD is a rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q30

Solution: Area of Shaded region = Area of a rectangle – Area of a semi-circle

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q30.1

 

Q. 31.In a rain-water harvesting system, the rainwater from a roof of 22 m × 20 m drains into a cylindrical tank having a diameter of base 2 m and height 35 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.

Solution: Volume of water collected in system = Volume of a cylindrical tank

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set I Q31

Set II

Note: Except for the following questions, all the remaining questions have been asked in previous sets.

Section – B

Q. 10.Which term of the A.P. 8, 14, 20, 26,… will be 72 more than its 41st term? 

Solution: A.P. is 8, 14, 20, 26,….

a = 8, d = 14 – 8 = 6

Let an = a41 + 72

a + (n – 1)d = a + 40d + 72

⇒ (n – 1) 6 = 40 × 6 + 72 = 240 + 72 = 312

⇒ n – 1 = 52

⇒ n = 52 + 1 = 53rd term

Section – C

Q. 18.From a solid right circular cylinder of height 24 cm and radius 0.7 cm, a right circular cone of the same height and same radius is cut out. Find the total surface area of the remaining solid.

Solution: Given, Height of cylinder ‘h’ = 2.4 cm,

Radius of base ‘r’ = 0.7 cm

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q18
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q18.1

 

Q. 19.If the 10th term of an A.E is 52 and the 17th term is 20 more than the 13th term, find the A.P. 

Solution: Given, a10 = 52;

a17 = a13 + 20

⇒ a + 16d = a + 12d + 20

⇒ 16d = 12d + 20

⇒ 4d = 20

⇒ d = 5

Also, a + 9d = 52

⇒ a + 9 × 5 = 52

⇒ a + 45 = 52

⇒ a = 7

Therefore A.E = 7, 12, 17, 22, 27,….

 

Q. 20. If the roots of the equation (c^2 – ab) x^2 – 2(a^2 – bc) x + b^2 – ac = 0 in x are equal, then show that either a = 0 or a^3 + b^3 + c^3 = 3abc.

Solution:

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q20

Section – D

Q. 28. Solve for x:

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q28

Solution:CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q28.1

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q28.2

Q 29.A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less on the journey. Find the original speed of the train.

Solution: Let original speed of train = x km/hr

Increased speed of train = (x + 5) km/hr

Distance = 300 km

According to the question,

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q29

Q 30.A man observes a car from the top of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from 30° to 45° in 12 minutes, find the time taken by the car now to reach the tower.

Solution: Let AB is a tower, the car is at point D at 30° and goes to C at 45° in 12 minutes.

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q30
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q30.1

Q. 31.In the given figure, ΔABC is a right-angled triangle in which ∠A is 90°. Semi-circles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q31

Solution: In right ΔBAC, by Pythagoras theorem,

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q31.1
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set II Q31.2

Set III

Note: Except for the following questions, all the remaining questions have been asked in previous sets.

Section – B

Q. 10.For what value of n, are the terms of two A.Ps 63, 65, 67,…. and 3, 10, 17,…. equal ? 

Solution:1st A.P. is 63, 65, 67,…

a = 63, d = 65 – 63 = 2

an = a + (n – 1 )d = 63 + (n – 1) 2 = 63 + 2n – 2 = 61 + 2n

2nd A.E is 3, 10, 17,…

a = 3, d = 10 – 3 = 7

an = a + (n – 1 )d = 3 + (n – 1) 7 = 3 + 7n – 7 = 7n – 4

According to question,

61 + 2n = 7n – 4

⇒ 61 + 4 = 7n – 2n

⇒ 65 = 5n

⇒ n = 13

Hence, 13th term of both A.P. is equal.

Section – C

Q. 18.A toy is in the form of a cone of radius 3-5 cm mounted on a hemisphere of the same radius on its circular face. The total height of the toy is 15*5 cm. Find the total surface area of the toy. 

Solution: Given, radius of base ‘r’ = 3.5 cm

Total height of toy = 15.5 cm

Height of cone ‘h’ = 15.5 – 3.5 = 12 cm

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q18
CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q18.1

Q. 19.How many terms of an A.E 9, 17, 25,… must be taken to give a sum of 636? 

Solution: A.P. is 9, 17, 25,….,

Sn = 636

a = 9, d = 17 – 9 = 8

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q19

Q. 20. If the roots of the equation (a2 + b2) x2 – 2 (ac + bd) x + (c2 + d2) = 0 are equal, prove that a/b = c/d

Solution:

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q20

Section – D

Q. 28.Solve for x:

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q28

Solution:

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q28.1

Q. 29. A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days, how many days will B take to finish it? 

Solution: Let B can finish a work in x days

so, A can finish work in (x – 6) days

Together they finish work in 4 days

Now,

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q29

⇒ 4 (2x – 6) = x2 – 6x

⇒ 8x – 24 = x2 – 6x

⇒ x2 – 14x + 24 = 0

⇒ x2 – 12x – 2x + 24 = 0

⇒ x(x – 12) – 2(x – 12) = 0

⇒ (x – 12) (x – 2) = 0

Either x – 12 = 0 or x – 2 = 0

x = 12 or x = 2 (Rejected)

B can finish work in 12 days

A can finish work in 6 days.

 

Q. 30.From the top of a tower, 100 m high, a man observes two cars on the opposite sides of the tower and in a same straight line with its base, with angles of depression 30° and 45°. Find the distance between cars.

[Take √3 = 1.732]

Solution: Let AB is a tower.

Cars are at point C and D respectively

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q30

Distance between two cars = x + y = 173.2 + 100 = 273.2 m

 

Q. 31.In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region.

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q31

Solution: Given, C (O, OB) with AC = 24 cm AB = 7 cm and ∠BOD = 90°

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Set III Q31.1

∠CAB = 90° (Angle in semi-circle)

Using pythagoras theorem in ∆CAB,

BC2 = AC2 + AB2 = (24)2 + (7)2 = 576 + 49 = 625

⇒ BC = 25 cm

Radius of circle = OB = OD = OC = 25/2cm

Area of shaded region = Area of semi-circle with diamieter BC – Area of ∆CAB + Area of sector BOD

Latest Current Affairs 13 May 2021

CURRENT AFFAIRS
13 May 2021

NATIONAL NEWS:

A) Opposition parties urge Modi to start free, universal vaccination.

In a joint letter to Prime Minister Narendra Modi, 12 Opposition parties have urged the government to immediately begin a free, universal mass vaccination campaign across the country as the Covid-19 pandemic has assumed unprecedented dimensions of a human catastrophe. This is the second joint letter by the opposition parties in less than ten days to the government. In an earlier letter on May 3, the parties had asked the government to ensure uninterrupted supply of medical oxygen and free vaccinations. The signatories of the letter include Chief Ministers Mamata Banerjee, M K Stalin, Uddhav Thackeray and Hemant Soren. Congress president Sonia Gandhi, JD(S) leader H D Deve Gowda, NCP patriarch Sharad Pawar, Samajwadi Party leader Akhilesh Yadav, National Conference leader Dr. Farooq Abdullah, RJD leader Tejashwi Yadav, CPI general secretary D Raja and CPI(M) general secretary Sitaram Yechury are the other signatories. The parties complained that all their previous attempts to draw the government’s attention, both independently and jointly, had come to naught. Without going into all the acts of commission and omission by the Central government that have brought the country to such a tragic pass, we are of the firm opinion that the following measures must be undertaken on a war footing by your government, they said. The government should procure vaccines centrally from all available sources global and domestic. Immediately begin a free, universal mass vaccination campaign across the country. Invoke compulsory licensing to expand domestic vaccine production, they noted. The budgetary allocation of Rs 35,000 crore for vaccines should be immediately spent, the parties said. As of now, only close to Rs. 5,000 crore had been spent.

B) Covid-19 catastrophe was preventable, says independent panel of experts. 

The catastrophic scale of the Covid-19 pandemic could have been prevented but a toxic cocktail of dithering and poor coordination meant the warning signs went unheeded, independent global panel concluded on Wednesday. The Independent Panel for Pandemic Preparedness and Response (IPPPR) said a series of bad decisions has allowed Covid-19 to kill at least 3.3 million people so far and devastate the global economy. Institutions failed to protect people and science-denying leaders eroded public trust in health interventions, the IPPPR said in its long-awaited final report. Early responses to the outbreak detected in Wuhan, China in December 2019 lacked urgency, with February 2020 a costly lost month as countries failed to heed the alarm, said the panel. To tackle the current pandemic, it called on the richest countries to donate a billion vaccine doses to the poorest. And the panel also called on the world’s wealthiest nations to fund new organisations dedicated to preparing for the next pandemic. The report was requested by World Health Organization (WHO) member states last May. The panel was jointly chaired by former New Zealand Prime Minister Helen Clark and former Liberian President Ellen Johnson Sirleaf, a 2011 Nobel Peace Prize laureate. The report, ‘Covid-19: Make it the Last Pandemic’, argued that the global alarm system needed overhauling to prevent a similar catastrophe. Poor strategic choices, unwillingness to tackle inequalities and an uncoordinated system created a toxic cocktail which allowed the pandemic to turn into a catastrophic human crisis, the report said. The threat of a pandemic had been overlooked and countries were woefully unprepared to deal with one, the report found. The panel did not spare the WHO, saying it could have declared the situation a Public Health Emergency of International Concern (PHEIC) its highest level of alarm on January 22, 2020. Instead, it waited eight more days before doing so. The panel also proposed an overhaul of the WHO to give it greater control over its funding and more authority for its leadership.

C) Health Ministry claims WHO doesn’t mention any ‘Indian variant’ though it does, using the scientific name.

The World Health Organisation (WHO) has not associated the term ‘Indian Variant’ with the B.1.617 variant of the coronavirus in its 32-page document, according to the Health Ministry. In fact, the word ‘Indian’ has not been used in its report on the matter, noted a release issued by the Ministry on Wednesday. It added that some reports had covered the news of classifying B.1.617 as a variant of global concern and termed the B.1.617 strain of the coronavirus as an Indian Variant. This release, however, seems to be willfully mixing up two different issues: it is certainly inappropriate to link the nomenclature of any variant with a particular nation, and it has been pointed out by many that it is not right to speak of the ‘Wuhan virus’ or the ‘U.K. variant’, etc. But that doesn’t mean that B.1.617 did not originate in India, or that it is not most widely prevalent in India, or that it is not a ‘Variant of Concern’. The Indian variant, B.1.617 and its family of related coronaviruses have been categorised as a Variant of Concern (VOC) by WHO, a classification which will now prompt greater international scrutiny of those who test positive overseas. 

D) Ivermectin still being used in India despite WHO recommendation against it.

Though it continues to be listed in India as a possible treatment option for mild Covid-19 patients under home isolation, Ivermectin, according to the World Health Organisation’s recent direction, is not recommended for general use. This orally-administered drug is included in India’s revised national Covid-19 treatment protocol for people with mild infection even though its maker has now clarified that there is no evidence of its efficacy against the viral disease. Safety and efficacy are important when using any drug for a new indication. WHO recommends against use of ‘Ivermectin’ for COVID-19 except within clinical trials, Soumya Swaminathan, WHO’s chief scientist, tweeted earlier this week. Indian physicians who continue to use this drug state that it is an approved anti-parasitic agent. It has shown, in laboratory settings, to inhibit SARS-COV2 replication. It may be effective for the management of early onset, mild Covid-19 for adult patients. In a clinical setting, it is observed that there is an early viral clearance in patients who are put on Ivermectin. There are no severe adverse effects noted in patients with non-severe Covid-19, said Vighnesh Naidu Y, consultant physician, Yashoda Hospitals, Hyderabad.

E) Justice Chandrachud tests positive for Covid-19.

Supreme Court judge Justice D.Y. Chandrachud, who was leading the Bench hearing cases on Covid-19 management, has tested positive for the virus. A crucial hearing on the COVID issue is listed before a three-judge Bench of Justices Chandrachud, L. Nageswara Rao and S. Ravindra Bhat for hearing on Thursday. Justice Chandrachud’s Bench had in the previous hearing constituted a National Task Force to scientifically study and recommend a foolproof mechanism for allocation of oxygen to States. Justice Chandrachud had made it clear to the Centre that the Supreme Court would not remain a mute spectator to a national calamity. The Covid-19 cases, which were initially being heard by a Bench led by former CJI Justice S.A. Bobde, was shifted to a Bench led by Justice Chandrachud following Justice Bobde’s retirement.

F) Gautam Navlakha denied bail again.

The Supreme Court on Wednesday refused bail to activist Gautam Navlakha in the Bhima Koregaon violence case. A Bench led by Justice U.U. Lalit had reserved the case for judgment on March 26. The case was listed on Wednesday. Justice K.M. Joseph pronounced the verdict, saying Navlakha’s period of house arrest cannot be counted as custody and, hence, he was not eligible for statutory bail. The Bench had heard arguments raised by senior advocate Kapil Sibal and advocates Nitya Ramakrishnan and Shadan Farasat for grant of default bail to Navlakha under Section 167(2) of the Code of Criminal Procedure read with Section 43(D)(2) of the Unlawful Activities Prevention Act. Navlakha challenged the dismissal of his bail plea by the Bombay High Court on February 8. The High Court had upheld the NIA court verdict denying him bail despite the petitioner spending more than 90 days in custody.

G) Covid Watch: Numbers and Developments.

The number of reported coronavirus cases from India stood at 2,35,63,982 with the death toll at 2,56,607. The head of the main Indian health agency responding to the coronavirus has said districts reporting a high number of infections should remain locked down for another six to eight weeks to control the spread of the rampaging disease. Balram Bhargava, head of the Indian Council of Medical Research (ICMR), said in an interview that lockdown restrictions should remain in place in all districts where the rate of infection is above 10% of those tested. Currently, three-fourths of India’s 718 districts have what is known as a test-positivity rate above 10%, including major cities like New Delhi, Mumbai and the tech hub of Bengaluru. Dr. Bhargava’s comments are the first time a senior government official has outlined how long lockdowns, which already encompass large parts of country, need to continue to rein in the crisis in India. Prime Minister Narendra Modi’s government has shied away from imposing a nationwide lockdown because of the economic impact and has left it to State governments. The high positivity districts should remain (shut). If they come to 5% from 10% (positivity rate), we can open them, but that has to happen. That won’t happen in six-eight weeks, clearly, Dr. Bhargava said in an interview at the New Delhi headquarters of the ICMR, the country’s top medical research body. Referring to the capital, one of India’s hardest hit cities, where the positivity rate reached around 35% but has now fallen to about 17%, Dr. Bhargava said: If Delhi is opened tomorrow, it will be a disaster.

INTERNATIONAL NEWS 

A) Taliban seizes district on outskirts of Kabul. 

The Taliban has seized a district from the Afghan government forces on the outskirts of Kabul, ahead of a three day ceasefire agreed between the warring sides, officials said. Nerkh district is around 40 kilometres from the Afghan capital in the neighbouring Wardak province, which has long been used by militants as a gateway to reach Kabul. Violence has soared since May 1 when the U.S. military began formally withdrawing its last remaining troops, as peace efforts between the Taliban and the Afghan government have stalled. Security and defence forces made a tactical retreat from the police headquarters of Nerkh district, Interior Ministry spokesman Tareq Arian said. Zabihullah Mujahid, a spokesman for the Taliban, said the insurgents captured the area on Tuesday, adding that fighters seized the police headquarters and an army base. The Defence Ministry on Wednesday said it would launch an offensive to win back the district, home to more than 60,000 people. Commando reinforcements are on their way, said Fawad Aman, a spokesman for the Defence Ministry. Large swathes of Wardak and neighbouring Logar province have been controlled or contested years the Talban fighters. The main highway that connects Kabul to southern Kandahar province the former Taliban stronghold and the scene of intense fighting in recent weeks through the district. Taliban fighters have been enriching major urban centres, spurring speculation that the militants are waiting for the U.S. to withdraw before launching all other assaults cities.

B) India opened up too early, says U.S. President’s top medical adviser Dr Anthony Fauci.

India made the incorrect assumption that it was finished with the Covid-19 pandemic and opened up prematurely, and that’s what has left the country in such dire straits, America’s top infectious diseases expert Dr. Anthony Fauci told Senators. India has been severely affected by the unprecedented second wave of the coronavirus and hospitals in several States are reeling under the shortage of health workers, vaccines, oxygen, drugs and beds. The reason that India is in such dire straits now is that they had an original surge and made the incorrect assumption that they were finished with it, and what happened, they opened up prematurely and wound up having a surge right now that we’re all very well aware of is extremely devastating, Dr. Fauci told the Senate Health, Education, Labour and Pensions Committee during a hearing on Tuesday on the Covid-19 response. Dr. Fauci, who is the Director of the U.S. National Institute of Allergy and Infectious Diseases (NIAID), is also the chief medical advisor to President Joe Biden. Chairing the hearing, Senator Patty Murray said that the surge of Covid-19 that is devastating India is a painful reminder really that the U.S. can’t end the pandemic here until it ends it everywhere. India’s outbreak underscores the need for a robust public health infrastructure in the U.S. to respond appropriately to this pandemic and future outbreaks as well, Senator Murray said as she asked Dr. Fauci what can the U.S. learn from India’s outbreak.

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