**SSC CGL 4th March 2020 Shift-1 **

**General Intelligence and Reasoning**

**Instructions **

For the following questions answer them individually

**Q. 1 Select the figure that can replace the question mark (?) in the following series. **

**Answer: **A.

**Explanation: **next figure,

∴ The correct answer is option A.

**Q. 2 Four words have been given, out of which three are alike in some manner, while one is different. Select the odd word. **

**A. **Righteousness

**B. **Virtue

**C. **Conduct

**D. **Probity

**Answer: **C.

**Explanation: **Except ‘conduct’ remaining all have the same meaning.

∴ The correct answer is option C.

**Q. 3 How many triangles are present in the given figure? **

**A. **26

**B. **28

**C. **22

**D. **30

**Answer: **C.

**Explanation: **

Number of triangles in ABFE = 10

Number of triangles in EFCD = 10

And 2 triangles are AFD and CEB

Total number of triangle = 10 + 10 + 2 = 22

∴ The correct answer is option C.

**Q. 4 Study the given pattern carefully and select the number that can replace the question mark (?) in it.**

**A. **200

**B. **196

**C. **199

**D. **169

**Answer: **C.

**Explanation:**

(7)^{2} + 4 = 49 + 4 = 53

(11)^{2} + 6 = 121 + 6 = 127

(14)^{2} + 3 = 196 + 3 = 199

∴ The correct answer is option C.

**Q. 5 In a certain code language, LARVAE is coded as 3-1-9-4-1-5. How will INSECT be coded as in that language? **

**A. **9-4-8-4-6-7

**B. **3-4-8-2-6-8

**C. **9-4-8-2-6-7

**D. **9-5-10-5-3-2

**Answer: **D.

**Explanation: **

L(12) = 1 + 2 = 3

A(1) = 1

R(18) = 1 + 8 = 9

V(22) = 2 + 2 = 4

A(1) = 1

E(5)= 5

Similarly,

I(9)= 9

N(14) = 1 + 4 = 5

S(19) = 1 + 9 = 10

E(5) = 5

C(3)= 3

T(20) = 2 + 0 = 2

‘INSECT’ is coded as 9-5-10-5-3-2.

∴ The correct answer is option D.

**Q. 6 Select the letter-cluster that can replace the question mark (?) in the following series. DAC, GWH,JSM, MOR, ? **

**A. **QKV

**B. **PKW

**C. **QJW

**D. **PJV

**Answer: **B.

**Explanation: **

So, next letter cluster = PKW

∴ The correct answer is option B.

**Q. 7 Select the number that can replace the question mark (?) in the following series. 17, 20, 15, 22, 13, ? **

**A. **2

**B. **22

**C. **4

**D. **24

**Answer: **D.

**Explanation: **

The series follows as pattern,

17 + 3 = 20

20 – 5 = 15

15 + 7 = 22

22 – 9 = 13

**13 + 11 = 24 **

∴ The correct answer is option D.

**Q. 8 Select the option in which the numbers are related in the same way as are the numbers in the given set. (109, 114, 139) **

**A. **(419, 424, 439)

**B. **(268, 302, 237)

**C. **(579, 534, 549)

**D. **(313, 318, 343)

**Answer: **D.

**Explanation: **

In (109, 114, 139),

109 + 5 = 114

114 + 5^{2} = 114 + 25 = 139

Similarly,

In (313, 318, 343),

313 + 5 = 318

318 + 5^{2} = 318 + 25 = 343

∴ The correct answer is option D.

**Q. 9 Which two signs should be interchanged to make the given equation correct? **

**225 + 5 × 3 ÷ 5 − 7 = 133**

**A. **−*and*×

**B. **+*and*÷

**C. **+*and*×

**D. **−*and*÷

**Answer: **B.

**Explanation: **

225 + 5 × 3 ÷ 5 − 7 = 133

From the option B,

225 ÷ 5 × 3 + 5 − 7 = 133

45 × 3 + 5 − 7 = 133

135 + 5 − 7 = 133

133 =133

∴ The correct answer is option B.

**Q. 10 The given Venn diagram represents artists in a circus: **

**The triangle represents clowns, the circle represents acrobats, the rectangle represents males and the square represents ringmasters. The numbers given in the diagram represent the number of persons in that particular category. **

**How many male clowns are also ringmasters, but NOT acrobats? **

**A. **15

**B. **5

**C. **17

**D. **11

**Answer: **C.

**Explanation: **

Number of male clowns which are ringmasters, but NOT acrobats = 17

∴ The correct answer is option C.

**Q. 11 Arsh is Shivam’s father and Dhruvis the son of Bimla. Eshwar is the father ofArsh. If Shivam is the brother of Dhruv, how is Bimla related to Eshwar? **

**A. **Wife

**B. **Daughter-in-law

**C. **Mother

**D. **Sister-in-law

**Answer: **B.

**Explanation: **

In the diagram, the square and circle shows the male and females respectively. Vertical lines show the son/father, horizontal line sow the brother/sister and double horizontal lines show the couple.

From the diagram,

Bimla is daughter-in-law of Eshwar.

**Q. 12 Select the option in which the words share the same relationship as that shared by the given pair of words. Hive : Bee **

**A. **Burrow : Hare

**B. **Sty : Dog

**C. **Eyrie : Bear

**D. **Stable : Cow

**Answer: **A.

**Explanation: **

Bee lives in hive similarly,

Hare lives in burrow.

∴ The correct answer is option A.

**Q. 13 Select the correct combination of mathematical signs to sequentially replace the * signs, to balance the following equation. **

**(12 * 7 * 6) * 13 * 6**

**A. ×, −, ÷, =**

**B. ÷, −, =, ×**

**C. −, ÷, ×, =**

**D. ×, =, ÷, −**

**Answer: **A.

**Explanation: **

(12 * 7 * 6) * 13 * 6

From the option A,

(12×7− 6)÷ 13 = 6

78÷ 13 = 6

6 = 6

∴ The correct answer is option A.

**Q. 14 In a certain code language, STRAIGHT is written as TSARGITH. How will THURSDAY be written as in that language? **

**A. **UHTDRSYA

**B. **HTRUDSYA

**C. **HTRUDSAY

**D. **AYSDURTH

**Answer: **B.

**Explanation: **

Similarly,

∴ The correct answer is option B.

**Q. 15 Select the option figure in which the given figure is embedded (rotation is NOT allowed).**

**Answer: **D.

**Explanation: **

The following answer figure contains question figure,

∴ The correct answer is option D.

**Q. 16 Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: **

**1. Some cars are rockets. **

**2. All rockets are engines. **

**Conclusions: **

**I. Some engines are rockets. **

**II. Some engines are cars. **

**A. **Neither conclusion I norII follows.

**B. **Only conclusion II follows.

**C. **Only conclusion I follows.

**D. **Both conclusions I and II follow.

**Answer: **D.

**Explanation: **

From the Venn diagram,

Both conclusions I and II follow.

∴ The correct answer is option D.

**Q. 17 Arrange the following words in the order in which they appear in an English dictionary. **

**1. Gemlike **

**2. Geminate **

**3. Gemmier **

**4. Geminal **

**5. Gemini **

**A. **4, 3, 2, 1, 5

**B. **3, 5, 4, 1, 2

**C. **4, 5, 2, 1, 3

**D. **4, 2, 5, 1, 3

**Answer: **D.

**Explanation: **

Word according to English dictionary,

Geminal, Geminate, Gemini, Gemlike, Gemmier

∴ The correct answer is option D.

**Q. 18 Which of the option figures is the exact mirror image of the given figure when the mirror is held at the right side? **

**Answer: **A.

**Explanation: **

Mirror image =

∴ The correct answer is option A.

**Q. 19 Select the option that is related to the third word in the same way as the second word is related to the first word. **

**Jackal : Howl:: Rain : ? **

**A. **Hustle

**B. **Thunder

**C. **Patter

**D. **Drops

**Answer: **C.

**Explanation: **

As howl is related to the jackal similarly, patter is related to the rain.

∴ The correct answer is option C.

**Q. 20 Select the set of letters that when sequentially placed in the blanks of the given letter series will complete the series.**

**_swws_wwws_swwww_sss **

**A. **w, s, w, s

**B. **w, s, s, s

**C. **w, w, s, s

**D. **w, s, s, w

**Answer: **B.

**Explanation: **

**w**/s/ww/s**s**/www/s**s**s/wwww/**s**sss

∴ The correct answer is option B.

**Q. 21 Four letter-clusters have been given, out of which three are alike in some manner, while one is different. Select the odd letter-cluster. **

**A. **YXW

**B. **FGH

**C. **NML

**D. **TSR

**Answer: **B.

**Explanation: **

Except ‘FGH’ remaining all letter-clusters are in decreasing order.

∴ The correct answer is option B.

**Q. 22 Select the box that CANNOT be formed by folding the given unfolded box. **

**Answer: **B.

**Explanation: **

From the unfolded box,

Opposite side of a = c

Opposite side of f = d

Opposite side of b = e

∴ The correct answer is option B.

**Q. 23 A recent survey of married couples in Indian metro cities showed that 20% of the couples have only one child, 45% of the remaining couples have two children, and the rest of the couples have three or more children. What is the percentage of couples with three or more children? **

**A. **56%

**B. **44%

**C. **42%

**D. **35%

**Answer: **B.

**Explanation: **

Let the total couple be 100.

Couple with one child = 20

Remaining couples = 100 – 20 = 80

Couple with two child = 45% of the remaining = (80×45) /100 = 36

Couples with three or more children = 80 – 36 = 44%

**Q. 24 The sequence of folding a piece of paper and the manner in which the folded paper has been cut is shown in the following figures. How would this paper look when unfolded? **

**Answer: **B.

**Explanation: **

Look of the paper when unfolded –

∴ The correct answer is option B.

**Q. 25 Select the option that is related to the third number in the same way as the second number is related to the first number and the sixth number is related to the fifth number. **

**52 : 221 :: 20 : ? :: 64 : 272 **

**A. **85

**B. **84

**C. **255

**D. **170

**Answer: **A.

**Explanation: **

52×4 + ^{52}/4 = 208 + 13 = 221

64 ×4 + ^{64}/4= 256 + 16 = 272

Similarly,

20×4 + ^{20}/4 = 80 + 5 = 85

∴ The correct answer is option A.

**General Awareness **

**Instructions **

For the following questions answer them individually

**Q. 26 The ________ lake in Gujarat was an artificial reservoir built during the rule of the Mauryas. **

**A. **Pushkar

**B. **Sudarshana

**C. **Loktak

**D. **Lonar

**Answer: **B.

**Q. 27 _________ was the capital of Magadha before the 4th century BCE. **

**A. **Varanasi

**B. **Mathura

**C. **Rajagaha

**D. **Pataliputra

**Answer: **C.

**Q. 28 Which of the following is NOT a folk dance belonging to the union territory of Jammu and Kashmir? **

**A. **Hafiza

**B. **Dhumal

**C. **Dangi

**D. **Rouf

**Answer: **C.

**Q. 29 Lt. General _______ took charge as the Chief of Army Staff on 31 December 2019. **

**A. **Bipin Rawat

**B. **Manoj Mukund Naravane

**C. **Ravendra Pal Singh

**D. **Anil Chauhan

**Answer: **B.

**Q. 30 The Harshacharita is a biography of Harshavardhana, the ruler of Kannauj, composed in Sanskrit by his court poet, _______. **

**A. **Jinsena

**B. **Dandin

**C. **Kamban

**D. **Banabhatta

**Answer: **D.

**Q. 31 In biological terms, _______ is a relationship between two organisms in which one organism benefits and the other is unaffected. **

**A. **Amensalism

**B. **Commensalism

**C. **Parasitism

**D. **Mutualism

**Answer: **B.

**Q. 32 The 14th Dalai Lama resides in _______. **

**A.** Shillong

**B. **Kalimpong

**C. **Dharamsala

**D. **Gangtok

**Answer: **C.

**Q. 33 According to the United Nations’ World Economic Situation and Prospects Report, 2019, the Indian economy is expected to expand by _____ in 2020. **

**A. **7.1%

**B. **7.6%

**C. **7.8%

**D. **7.2%

**Answer: **A.

**Q. 34 In the 4th century BCE, the capital of Magadha was shifted to ________. **

**A. **Panipat

**B. **Varanasi

**C. **Mathura

**D. **Pataliputra

**Answer: **D.

**Q. 35 Article 17 of the Constitution of India deals with the abolition of ________. **

**A. **untouchability

**B. **slavery

**C. **titles

**D. **sati

**Answer: **A.

**Q. 36 In April 2019, scientists in ________ produced the world’s first 3D. printed heart using human tissue. **

**A. **Croatia

**B. **Kenya

**C. **Ethiopia

**D. **Israel

**Answer: **D.

**Q. 37 The Vedic Civilization in India flourished along the river__________. **

**A. **Tapi

**B. **Narmada

**C. **Saraswati

**D. **Godavari

**Answer: **C.

**Q. 38 _______ expansion makes the Eiffel Tower taller during summers. **

**A. **Thermal

**B. **Chemical

**C. **Gravitational

**D. **Gradient

**Answer: **A.

**Q. 39 King Harshavardhana ascended the throne of Thaneshwar and Kannauj on the death of his brother, ________. **

**A. **Rajyavardhana

**B. **Suryavardhana

**C. **Indravardhana

**D. **Chandravardhana

**Answer: **A.

**Q. 40 Who was the President of the World Bank Group as of January, 2020? **

**A. **Paul Wolfowitz

**B. **David Malpass

**C. **Robert Zoellick

**D. **Jim Yong Kim

**Answer: **B.

**Q. 41 Who among the following is an Indian Olympic archer and Padma Shri winner? **

**A. **Bajrang Punia

**B. **Balbir Singh Dosanjh

**C. **Limba Ram

**D. **Kidambi Srikanth

**Answer: **C.

**Q. 42 In May 2019, the International Monetary Fund agreed to bail out ________ with a fund of $6 billion. **

**A. **India

**B. **Bangladesh

**C. **Nepal

**D. **Pakistan

**Answer: **D.

**Q. 43 Planetary scientists call the thin gaseous envelope around the Moon as the _______. **

**A. **lunar exosphere

**B. **lunar thermosphere

**C. **lunar stratosphere

**D. **lunar endosphere

**Answer: **A.

**Q. 44 The major component of modern Olympic gold medals is ________. **

**A. **Gold

**B. **Silver

**C. **Copper

**D. **Bronze

**Answer: **B.

**Q. 45 The Gol Gumbad (Gumbaz) of ________ is the mausoleum of Muhammad Adil Shah. **

**A. **Bijapur

**B. **Allahabad

**C. **Delhi

**D. **Agra

**Answer: **A.

**Q. 46 Private ownership of the means of production is a feature of a _______ economy. **

**A. **dual

**B. **mixed

**C. **socialist

**D. **capitalist

**Answer: **D.

**Q. 47 Xerophthalmia is caused due to the deficiency of vitamin ________. **

**A. **D

**B. **C

**C. **A

**D. **K

**Answer: **C.

**Q. 48 The Biraja Temple, the Rajarani Temple and the Samaleswari Temple are all located in ________. **

**A. **Kerala

**B. **Assam

**C. **Odisha

**D. **Tamil Nadu

**Answer: **C.

**Q. 49 Which Article of the Indian Constitution prohibits discrimination on the grounds of religion, race, caste, sex and place of birth? **

**A. **Article 19

**B. **Article 23

**C. **Article 25

**D. **Article 15

**Answer: **D.

**Q. 50 Asia’s largest wholesale spice market is located in _______. **

**A. **Bengaluru

**B. **Ahmedabad

**C. **Kolkata

**D. **Delhi

**Answer: **D.

**Quantitative Aptitude **

**Instructions **

For the following questions answer them individually

**Q. 51 In **△*ABC*, ∠*A *= 90^{∘}**, M is the midpoint of ***BC*** and ***D*** is a point on ***BC*** such that ***AD *⊥ *BC***. If ***AB *= 7 **cm and ***AC *= 24**cm, then ***AD *: *AM*** is equal to: **

**A. **32 : 43

**B. **24 : 25

**C. **336 : 625

**D. **168 : 275

**Answer: **C.

**Explanation: **

By triplet 7-24-25,

BC = 25 cm

M is the midpoint of BC so,

*BM = BC /2*

BM = 25/2 = 12.5 cm

By property,

AM = BM = 12.5 cm

*AD *⊥ *BC *so,

BC × AD = AC × AB

25 ×*AD *= 7 × 24

AD = 168/25 = 6.72

AD : AM = 6.72 : 12.5 = 336 : 625

**Q. 52 **O**n simplification,**** is equal to: **

**A. **4

**B. **1

**C. ½ **

**D. ¼ **

**Answer: A.**

**Explanation:**

**Q. 53 If 5***x + *^{1}*/3x = 4***, then what is the value of 9***x*^{2}** + **^{1}**/25***x*^{2}**? **

**A. **174/125

**B. **119/25

**C. **144/125

**D. **114/25

**Answer: D. **

**Explanation: **

**Q. 54 The given table represents the number of computers sold by four dealers A, B, C and D during the first six months of 2016. Study the table carefully and answer the question that follows. **

**The total number of computers sold by dealer A. during February to June is what percentage more than the total number of computers sold by all the dealers in June? (Correct to one decimal place) **

**A. **25.3

**B. **21.2

**C. **24.4

**D. **17.5

**Answer: **B.

**Explanation: **

The total number of computers sold by dealer A. during February to June = 94 + 85 + 108 + 98 + 95 = 480 Total number of computers sold by all the dealers in June = 95 + 108 + 102 + 91 = 396

Required percentage (480−396)/396 × 100= 84/396 × 100= 21.2%

**Q. 55 The average of twelve numbers is 45.5. The average of the first four numbers is 41.5 and that of the next five numbers is 48. The **10^{th }**number is 4 more than the **11^{th }**number and 9 more than the **12^{th }**number. What is the average of the **10^{th }**and **11^{th }**numbers? **

**A. **47

**B. **47.8

**C. **46

**D. **46.6

**Answer: **D.

**Explanation: **

The average of 12 numbers = 45.5

Sum of 12 numbers = average × *numbers *= 45.5 × 12= 546

The average of the first four numbers = 41.5

Sum of first four numbers = 41.5×4 = 166

The average of next five numbers = 48

Sum of next five numbers = 48×5 = 240

Sum of the first 9 numbers = sum of first four numbers + sum of next five numbers = 166 + 240 = 406 10th number = 4 + 11th number —(1)

10th number = 9 + 12th number —(2)

Sum of the first 9 numbers +10th number + 11th number + 12th number = 546 406 + 10th number + 10th number – 4 + 10th number – 9 = 546

3×10th number = 546 – 406 + 4 + 9

3×10th number = 153

10th number = 51

From eq(1),

11th number = 10th number – 4 = 51 – 4 = 47

12th number = 10th number – 9 = 51 – 9 = 42

The average of the 10* ^{th }*and 12

**Q. 56 The value of (**tan 30^{0} cosec 60^{0} +tan 60^{0} sec 30^{0} **) / (**sin^{2} 30^{0} +4 cot^{2} 45^{0} −sec^{2} 60^{0}**) is: **

**A. **2/3

**B. **32/99

**C. **8/3** **

**D. **32/3

**Answer: **D.

**Explanation: **

**Q. 57 Sonu saves 15% of her income. If her income increases by 20% and she still saves the same amount as before, then what is the percentage increase in her expenditure? (correct to one decimal place) **

**A. **23.5

**B. **22.8

**C. **23.8

**D. **242

**Answer: **A.

**Explanation: **

Let the initial income of Sonu be Rs.100.

saving = 15%

Expenditure = 100 – 15 = 85%

Saving = 100 -85 = Rs.15

Expenditure = 85% of 100 = Rs.85

Income after increment = 100 ×120/100= Rs.120

Saving = 15

Expenditure = 120 – 15 = 105

Increment in expenditure = 105 – 85 = Rs.20

Percentage Increment in expenditure =20/85×100 = 23.52%

**Q. 58 When 732 is divided by a positive integer x, the remainder is 12. How many values of x are there? **

**A. **19

**B. **18

**C. **20

**D. **16

**Answer: **C.

**Explanation: **

Number which fully divide by a positive integer x = number – remainder = 732 -12 = 720

720 is fully divide by positive integer x.

Factor of 720 = 1×2×3×4×5×6

Total factor = (4 + 1).(2 + 1).(1 + 1) = 5.3.2 = 30

We combine these factors which are more than 12 and maximum 720 because the remainder is 12. Combination lees than 13 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12

Number of combination lees than 13 = 10

Number of values of x = 30 – 10 = 20

**Q. 59 The circumference of the base of a conical tent is 66 m.If the height of the tent is 36 m, what is the area (in m**^{2}** ) of the canvas used in making the tent?(Take ***π *= 22/7 **) **

**A. **1237.5

**B. **1171.5

**C. **1254

**D. **1155

**Answer: **A.

**Explanation: **

The circumference of the base of a conical tent = 66 m

2*πr *= 66

*r* =(66×7)/(2×22) = 21/2 m

*h* = 36 m

*l* =√(*r*^{2}+*h*^{2})

*l* =√((21/2)^{2}+36^{2}) = √(441/4+1296) = 75/2=37.5

Area of canvas = *πrl*= 22/7×21/2×37.5=1237.5 sqm

**Q. 60 If a + b + c = 11, ab + bc + ca = 3 and abc = —135, then what is the value of ***a*^{3 }+ *b*^{3 }+ *c*^{3} **? **

**A. **827

**B. **929

**C. **823

**D. **925

**Answer: **A.

**Explanation: **

*a*^{3 }+ *b*^{3 }+ *c*^{3}

=> (*a *+ *b *+ *c*)[(*a *+ *b *+ *c*)^{2 }− 3(*ab *+ *bc *+ *ac*)] + 3*abc *

=> (11)[(11)^{2 }− 3(3)] + 3 × (−135)

=>(11)[112] − 405

=> 1132 – 405 = 827

**Q. 61 In **△*ABC*, *AB *= *AC***. A circle drawn through B touches AC at D and intersect AB at P. If D is the mid point of AC and AP 2.5 cm, then AB is equal to: **

**A. **9 cm

**B. **10 cm

**C. **7.5 cm

**D. **12.5 cm

**Answer: **B.

**Explanation: **

Given D is midpoint of AC so,

AD= AC/2

But also given AC = AB

AD= AB/2 = —-(1)

AD is a tangent and APB is a secant. So the tangent secant theorem can be applied, *AD*^{2 }= *AP *× *AB *

(AB/2 )^{2} = 2.5 × *AB *

*AB*^{2}/4 = 2.5 × *AB*

AB = 10 cm

**Q. 62 If **5 sin^{2} *θ *+ 14 cos *θ *= 13,0^{∘ }< *θ *< 90^{∘}**, then what is the value of **(sec *θ*+cot *θ*)*/*(cosec *θ*+tan *θ*)**? **

**A. **40/29

**B. **32/27

**C. **21/28

**D. **9/8

**Answer : A.**

**Explanation:**

5 sin^{2} θ +14 cos θ = 13

5 (1-cos^{2} θ) +14 cos θ = 13

−5cos^{2}θ + 14 cos θ = 8

5cos^{2}θ − 10 cos θ − 4 cos θ + 8 = 0

5cosθ(cos θ − 2) − 4 (cos θ − 2) = 0

(5cosθ − 4)(cos θ − 2) = 0

(cos θ − 2) (it is not possible)

For 0^{∘ }< *θ *< 90^{∘}

(5cosθ − 4) = 0

cosθ = ⅘

by triplet 3-4-5,

sin θ = ⅗

Now

**Q. 63 The value of ****is: **

**A. **8 ½

**B. **24

**C. **25 ½

**D. **26

**Answer: **C.

**Explanation: **

**Q. 64 If 2x + 1, x + 2, 2 and 5 are in proportion, then what is the mean proportional between 3.5(1 – x) and 8(1 + x)? **

**A. **5.5

**B. **5.25

**C. **4.25

**D. **4.5

**Answer: **B.

**Explanation: **

2x + 1, x + 2, 2 and 5 are in proportion. So,

(2*x*+1)/(*x*+2) =2/5

(2x + 1) ×5 = (*x *+ 2) × 2

10*x *+ 5 = 2*x *+ 4

8x = -1

x = -1/8

Mean proportional between 3.5(1 – x) and 8(1 + x)

Numbers = 3.5(1 + 1/8) and 8(1 -1/8) = 31.5/8 and 7

Mean proportional =√(31.5/8 × 7) =√27.5625 = 5.25

**Q. 65 ABCD is a cyclic quadrilateral in which AB = 16.5 cm, BC = x cm, CD = 11 cm, AD = 19.8 cm, and BD is bisected by AC at O. What is the value of x ? **

**A. **12.8 cm

**B. **12.4 cm

**C. **13.2 cm

**D. **13.8 cm

**Answer: **C.

**Explanation: **

ABCD is a cyclic quadrilateral in which AB = 16.5 cm

BC = x cm

CD = 11 cm

AD = 19.8 cm

By the property,

AB⋅BC = AD⋅DC

16.5 × *x = *19.8 × 11

16.5 × *x *= 217.8

x = 217.8/16.5 = 13.2 cm

**Q. 66 In **△*ABC*, ∠*B *= 68^{∘ }**and **∠*C *= 32^{∘}**. Sides AB and AC are produced to points D and E, respectively. The bisectors of **∠*DBC ***and** ∠*BCE ***meet at F. What is the measure of **∠*BFC***? **

**A. **39^{∘}

**B. **65^{∘}

**C. **55^{∘}

**D. **50^{∘}

**Answer: **D.

**Explanation: **

From the angle bisector property,

∠*BFC *= 90° − ∠*A/2*

In △*ABC *,

∠*A *+ ∠*B *+ ∠*C *= 180°

∠*A *= 180° − 32° − 68° = 80°

∠*BFC *= 90° − 80°/2

∠*BFC *= 50°

**Q. 67 A trader allows a discount of 18% on the marked price of an article. How much percentage above the cost price must he mark it so as to get a profit of 6.6%? **

**A. **30

**B. **24

**C. **28

**D. **25

**Answer: **A.

**Explanation: **

Let the cost price be Rs.100.

Profit = 6.6% = 6.6

Selling price = 100 + 6.6 = Rs.106.6

Discount = 18%

Let the marked price be 100%

Selling price = 100 – 18 = 82%

106.6 = 82%

100%(marked price) =106.6/82 × 100 = 130

Percentage above the cost price must he mark =(130−100)/100 ×100 = 30%

**Q. 68 The given table represents the number of computers sold by four dealers A, B, C and D during the first six months of 2016. Study the table carefully and answer the question that follows. **

**The total number of computers sold by dealer B. in April, May and June is what percentage of the total number of computers sold by all the dealers in February and April? **

**A. **48 ^{5}/_{7}

**B. **43 ^{6}/_{7}

**C. **38 ^{3}/_{8}

**D. **50 ^{7}/_{8}

**Answer: **C.

**Explanation: **

The total number of computers sold by dealer B. in April, May and June = 97 + 102 + 108 = 307

The total number of computers sold by all the dealers in February and April = 94 + 96 + 104 + 106 + 108 + 97 + 99 + 96 = 800

Required percentage =307/800×100=38 ^{3}/_{8}%

**Q. 69 A boat can go 3 km upstream and 5 km downstream in 55 minutes. It can also go 4 km upstream and 9 km downstream in 1 hour 25 minutes. In how much time(in hours) will it go 43.2 km downstream? **

**A. **3.6

**B. **4.4

**C.** 5.4

**D. **4.8

**Answer: **A.

**Explanation: **

Let the speed of stream be u and speed of boat be v.

Speed in upstream = v – u

Speed in downstream = v + u

A boat can go 3 km upstream and 5 km downstream in 55 minutes so,

^{3}/(v−u) + ^{5}/(v+u) =1+ ^{25}/60

Boat can go 4 km upstream and 9 km downstream in 1 hour 25 minutes

^{4}/(v−u) + ^{9}/(v+u) =^{55}/60

^{4}/(v−u) + ^{9}/(v+u) =^{85}/60

^{1}/(v−u) = x

^{1}/(v+u) = y

3x + 5y = 11/12 ………….(1)

4x + 9y = 17/12 …………(2)

eq(1) multiply by 4 and eq(2) multiply by 3,

12x + 20y = 44/12 ………….(3)

12x + 27y = 51/12 …………(4)

From eq (3) and (4),

7y =7/12

y=1/12

From eq(1),

3x + 5(1/12) = 11/12

3x = 6/12

x = ⅙

^{1}/(v−u) = ⅙

v-u = 6 ………….(5)

^{1}/(v+u) = 1/12

v+u = 12 ………….(6)

Speed in downstream = u + v = 12 km/hr

Time taken by boat = 43.6/12 = 3.63 hr

**Q. 70 What is the compound interest on a sum of ₹12,000 for **2⅝ **years at 8% p.a., when the interest is compounded annually? (nearest to a rupee) **

**A. **₹2,642

**B. **₹2,697

**C. **₹2,712

**D. **₹2,654

**Answer: **B.

**Explanation: **

Time =2⅝ years = 2 + ⅝years

We find the interest for the first 5/8 year by simple interest

Simple interest =*prt /100 *

p = 12000

r = 8%

Simple interest =(12000×8×⅝ )/100 = 600

Now,

p = 12000 + 600 = 12600

Compound interest = p(1 + *r*/100)^{t} − p

= 12600 (1 + *8*/100)^{2}− 12600

=12600 × 108/100 ×108/100 – 12600

= 14696.64 – 12600 = 2096.64 ≈ Rs.2097

Total interest = 2097 + 600 = Rs.2697

**Q. 71 If **sec *θ *− tan *θ *= ^{x}*/y *(0 < x <y) **and **0^{∘ }< *θ *< 90^{∘}**, then **sin *θ ***is equal to: **

**A. **(*x** ^{2}* +

**B. **(*x** ^{2}* +

**C. ***(y** ^{2}* −

**D. ***2xy / *(*x** ^{2}* +

**Answer: **C.

**Explanation: **

sec *θ *− tan *θ *= ^{x}*/y *—(1)

1/(sec *θ *− tan *θ*) = ^{y}*/x*

sec^{2} *θ *− tan^{2} *θ*/(sec *θ *− tan *θ*) = ^{y}*/x*

^{(sec }^{θ }^{− tan }^{θ)(}^{sec }^{θ }^{+ tan }* ^{θ)}*/(sec

(sec *θ *+ tan *θ*) = ^{y}*/x *—(2)

From eq(1) and (2),

(sec *θ *– tan *θ*)+(sec *θ *+ tan *θ*) = ^{x}*/y + *^{y}*/x*

*2 sec θ = (x*^{2}*+y*^{2}*)/ xy*

*sec θ = x*^{2}*+y*^{2}* / 2xy*

*cos θ = 2xy / x*^{2}*+y*^{2}* *

Base = 2xy

Hypotenuses = {x^{2} + y^{2}}

By Pythagoras,

(p)^{2} + (2xy)^{2} = (x^{2} + y^{2} )^{2}

(p)^{2} = x^{4} + y^{4} + 2x^{2}y^{2} – 4x^{2}y^{2}

(p)^{2} = x^{4} + y^{4} – 2x^{2}y^{2}

(p)^{2} = (x^{2} – y^{2})^{2}

p = x^{2} – y^{2} = y^{2}– x^{2}

sin *θ *= *p*/*h *=(y^{2}– x^{2})/(x^{2} + y^{2})

**Q. 72 A person buys 5 tables and 9 chairs for ₹15,400. Hesells the tables at 10% profit and chairs at 20% profit. If his total profit on selling all the tables and chairs is ₹2,080, what is the cost price of 3 chairs? **

**A. **₹1,800

**B. **₹1,740

**C. **₹1,860

**D. **₹1,890

**Answer: **A.

**Explanation: **

Let the price of 9 chairs be x.

Price of 5 tables = 15400 – x

He sells the tables at 10% profit and chairs at 20% profit.

Total profit = 2080

(15400 – x) (10/100) + x(20/100) = 2080

15400 – x + 2x = 20800

x = 5400

Price of 9 chairs = 5400

Price of 3 chairs = 5400/3 = Rs.1800

**Instructions **

The given table represents the number of computers sold by four dealers A, B, C and D during the first six months of 2016. Study the table carefully and answer the question that follows.

**Q. 73 The number of months, in which the number of computers sold by dealer B. was less than the average number of computers sold by dealer C. over six months, was: **

**A. **4

**B. **3

**C. **5

**D. **2

**Answer: **A.

**Explanation: **

Average number of computers sold by dealer C over six months = total number of computer/6 =(95+104+100+99+100+102)/6 = 600/6 =100

The number of months, in which the number of computers sold by dealer B was less than the average number of computers sold by dealer C over six months, was 4(January, feb, march, April)

**Q. 74 What is the ratio of the total number of computers sold by dealer A. in February, April and May to the total number of computers sold by dealer D. in March, May and June? **

**A. **10 : 9

**B. **6 : 5

**C. **15 : 13

**D. **20 : 27

**Answer: **A.

**Explanation: **

The total number of computers sold by dealer A. in February, April and May = 94 + 108 + 98 = 300

The total number of computers sold by dealer D. in March, May and June = 90 + 89 + 91 = 270

Ratio of the total number of computers sold by dealer A. in February, April and May to the total number of computers sold by dealer D. in March, May and June = 300 : 270

= 10 : 9

**Instructions **

For the following questions answer them individually

**Q. 75 A can complete a certain work in 30 days. B. is 25% more efficient than A and C is 20% more efficient than B They all worked together for 3 days. B alone will complete the remaining work in: **

**A. **18 days

**B. **12 days

**C. **20 days

**D. **15 days

**Answer: **D.

**Explanation: **

Let the efficiency of A. be x.

Efficiency of B. = 25% more efficient than A = 1.25x

Efficiency of C = 20% more efficient than B = 1.25*x *× 120/100= 1.5x

Efficiency ratio of A, B and C = x: 1.25x : 1.5x = 4 : 5 : 6

Total work = efficiency×time = 4×30 = 120 units

3 days work = (4 + 5 + 6)×3 =15× 3 = 45 units

Remaining work = 120 – 45 = 75 units

Time taken to complete work by B. = 75/5 = 15 days

**English Comprehension **

**Instructions **

For the following questions answer them individually

**Q. 76 Select the correct active form of the given sentence. **

**This beautiful story was written by Maya. **

**A. **Maya was writing this beautiful story.

**B. **Maya writes this beautiful story.

**C. **Maya is writing this beautiful story.

**D. **Maya wrote this beautiful story.

**Answer: **D.

**Q. 77 Select the wrongly spelt word. **

**A. **Compromise

**B. **Consumation

**C. **Competence

**D. **Chronology

**Answer: **B.

**Q. 78 Select the most appropriate meaning of the given idiom. **

**Back to square one **

**A. **Draw a square

**B. **Neglect something

**C. **Move ahead

**D. **Come to the original point

**Answer: **D.

**Q. 79 Select the wrongly spelt word. **

**A. **Turmoil

**B. **Tresure

**C. **Truthful

**D. **Tamarind

**Answer: **B.

**Q. 80 Select the antonym of the given word. **

**LIBERTY **

**A. **Independence

**B. **Deliverance

**C. **Convenience

**D. **Dependence

**Answer: **D.

**Q. 81 Select the most appropriate word to substitute the underlined word of the given sentence. If substitution is not required select ‘No improvement’. **

**To fight on the battlefield for the sake of one’s country needs ****a great strongness.**** **

**A. **the greatest strongness

**B. **a lots of strength

**C. **No improvement

**D. **great courage

**Answer: **D.

**Instructions **

In the following passage some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank.

**Comprehension: **

‘A stitch in time saves nine’. This wise saying suggests that an (1)______ action taken on time to rectify an error rules (2)______ the possibility of accumulation of such errors and future (3)______ . Wisdom therefore lies in correcting the error as soon as it is (4)______. There is no point-in allowing the (5)______ to grow and then take hasty actions to set things right.

**Q. 82 Select the most appropriate option for blank no. 1 **

**A. **superficial

**B. **wrong

**C. **appropriate

**D. **opposite

**Answer: **C.

**Q. 83 Select the most appropriate option for blank no. 2 **

**A. **in

**B. **at

**C. **out

**D. **for

**Answer: **C.

**Q. 84 Select the most appropriate option for blank no. 3 **

**A. **qualities

**B. **facilities

**C. **damages

**D. **advantages

**Answer: **C.

**Q. 85 Select the most appropriate option for blank no. 4 **

**A. **discovered

**B. **managed

**C. **proposed

**D. **invented

**Answer: **A.

**Q. 86 Select the most appropriate option for blank no. 5 **

**A. **parody

**B. **remedy

**C. **malady

**D. **melody

**Answer: **C.

**Instructions **

For the following questions answer them individually

**Q. 87 Select one word for the following group of words. **

**Open refusal to obey orders **

**A. **Defiance

**B. **Compliance

**C. **Obedience

**D. **Adherence

**Answer: **A.

**Q. 88 Select the synonym of the given word. **

**PREVENT **

**A. **Construct

**B. **Provoke

**C. **Allow

**D. **Avert

**Answer: **D.

**Q. 89 Select one word for the following group of words. **

**Morals that govern one’s behavior **

**A. **Intuition

**B.** Attitude

**C. **Psychology

**D. **Ethics

**Answer: **D.

**Q. 90 Select the antonym of the given word. **

**BROAD **

**A. **Long

**B. **Narrow

**C. **Wide

**D. **Large

**Answer: **B.

**Instructions **

Given below are four jumbled sentences. Out of the given options pick the one that gives their correct order.

**Q. 91 **

**A. Eventually, she overcame adversities and achieved success. **

**B. She engaged herself in ‘earn while you learn’, finance scheme in her college. **

**C. She needed financial support to complete her graduation. **

**D. Rama was a very poor girl. **

**A. **ADCB

**B. **ABCD

**C. **DCBA

**D. **CBDA

**Answer: **C.

**Q. 92 **

**A. “We are going to the market,” declared Reetu and Geetu. **

**B. “Where are you going?” the father asked. **

**C. “Take your umbrella, it is going to rain,” the mother said. **

**D. “Yes, definitely. We will,” replied the two. **

**A. **ABDC.

**B. **DCAB.

**C. **BCDA.

**D. **BACD.

**Answer: **D.

**Instructions **

For the following questions answer them individually

**Q. 93 In the sentence identify the segment which contains the grammatical error. The boy which stole the money was caught by the police. **

**A. **was caught

**B. **stole the money

**C. **by the police

**D. **The boy which

**Answer: **D.

**Q. 94 Select the most appropriate meaning of the given idiom. **

**Dead heat **

**A. **A. strong heat wave

**B. **Strong opposition to one’s ideas

**C. **A deadly blast of hot air

**D. **Close contest that ends in a tie

**Answer: **D.

**Q. 95 In the sentence identify the segment which contains the grammatical error. **

**Saraswati college has maintained its reputation as one of the best colleges in the country. **

**A. **Saraswati college has maintained

**B. **one of the best college

**C. **in the country

**D. **its reputation as

**Answer: **B.

**Q. 96 Select the most appropriate word to fill in the blank. **

**She ______ on paying the bill at the restaurant. **

**A. **offered

**B. **suggested

**C. **insisted

**D. **requested

**Answer: **C.

**Q. 97 Select the most appropriate segment to substitute the underlined segment of the given sentence. If substitution is not required select ‘no improvement’. **

**The animal ****resembled with**** a cat. **

**A. **No improvement

**B. **resembled by

**C. **resembled

**D. **resembled to

**Answer: **C.

**Q. 98 Select the most appropriate word to fill in the blank. **

**The groom stood before the ______ for the wedding ceremony at the church. **

**A. **alter

**B. **atlas

**C. **altar

**D. **attic

**Answer: **C.

**Q. 99 Select the correct direct form of the given sentence. **

**The teacher commanded the students not to shout. **

**A. **The teacher said to the student, “You should not shout.”

**B. **The teacher told to the students, “You must not shout.”

**C. **The teacher said to the students, “Don’t shout.”

**D. **The teacher says to the students, “Do not shout.”

**Answer: **C

**Q. 100 Select the synonym of the given word. **

**REVERE **

**A. **Repeat

**B. **Respect

**C. **Condemn

**D. **Enjoy

**Answer: **B.

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