Nimcet-2019

Question 1

+12-3

Number of real solutions of the equation

\sin \left(e^{x} \right)=5^{x} +5^{-x}

is

A

0

B

1

C

2

D

infinitely many

Question 2

+12-3

A force of 78 grams acts at the point (2,3,5). The direction ratios of the line of action being 2,2,1. The magnitude of its moment about the line joining the origin to the point (12,3,4) is

A

24

B

136

C

36

D

0

Question 3

+12-3

The value of non-zero scalars 𝛼 and 𝛽such that for all vectors

\vec{a}

and

\vec{b}

such that

\alpha \left(\vec{a}+2\vec{b}-\beta \vec{a}\left(4\vec{b}-\vec{a}\right)\right)=0

is

A

\alpha =2,\beta =1

B

\alpha =-2,\beta =-3

C

\alpha =1,\beta =3

D

\alpha =-2,\beta =3

Question 4

+12-3

In a beauty contest, half the number of experts voted for Mr. A and two third voted for Mr. B . 10 voted for both and 6 did not for either. How many experts were there in all?

A

18

B

36

C

24

D

NOT

Question 5

+12-3

The mean of 5 observation is 5 and their variance is 124. If three of the observations are 1, 2, 6, then the mean deviation from the mean of the data is

A

2.5

B

2.6

C

2.8

D

2.4

Question 6

+12-3

If A

\mathrm{>}

0, B

\mathrm{>}

0 and

A+B=\frac{\pi }{6}

then the minimum value of tanA+tanB is

A

\sqrt{3} -\sqrt{2}

B

4-2\sqrt{3}

C

\frac{2}{\sqrt{3} }

D

2-\sqrt{3}

Question 7

+12-3

A computer producing factory has only two plants 𝑇1 and 𝑇2. Plant 𝑇1 produces 20% and plant 𝑇2 produces 80% of the total computers produced. 7% of the computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective given that it is produced in plant 𝑇1) = 10P(computer turns out to be defective given that it is produced in plant 𝑇2) . A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant 𝑇2 is

A

36/73

B

47/79

C

78/93

D

75/83

Question 8

+12-3

If

|z|<\sqrt{3} -1

then

|z^{2} +2z\cos \alpha |

is

A

less than 2

B

\sqrt{3} +1

C

\sqrt{3} -1

D

NOT

Question 9

+12-3

Number of onto (surjective) functions from A to B if n(A)=6 and n(B)=3, is

A

2

{}^{6}

-2

B

3

{}^{6}

-3

C

340

D

540

Question 10

+12-3

The sum of infinite terms of a decreasing GP is equal to the greatest value of the function

f\left(x\right)=x^{3} +3x-9

in the interval [

\mathrm{-}

2,3] and the difference between the first two terms is 𝑓′(0). Then the common ratio of GP is

A

-2/3

B

4/3

C

2/3

D

-4/3

Question 11

+12-3

{\mathop{\lim }\limits_{x\to 3}} \frac{\sqrt{3x} -3}{\sqrt{2x-4} -\sqrt{2} }

is equal to

A

\sqrt{3}

B

\frac{\sqrt{3} }{2}

C

\frac{1}{2\sqrt{2} }

D

\frac{1}{\sqrt{2} }

Question 12

+12-3

The curve satisfying the differential equation 𝑦𝑑𝑥− (𝑥+3𝑦2) 𝑑𝑦=0 and passing through the point (1,1) also passes through the point

A

(1/4,1/2)

B

(1/4,-1/2)

C

(-1/3,1/3)

D

(1/3,-1/3)

Question 13

+12-3

If all the words, with or without meaning, are written using the letters of the word QUEEN add are arranged as in English Dictionary, then the position of the word QUEEN is

A

47

{}^{th}

B

44

{}^{th}

C

45

{}^{th}

D

46

{}^{th}

Question 14

+12-3

The integral

\int \sqrt{1+2\cot x\left(\cos ecx+\cot x\right)} dx

\left(0<x<\frac{\pi }{2} \right)

is equal to

A

2\log \left(\sin \frac{x}{2} \right)+C

B

2\log \left(\cos \frac{x}{2} \right)+C

C

4\log \left(\cos \frac{x}{2} \right)+C

D

4\log \left(\sin \frac{x}{2} \right)+C

Question 15

+12-3

The tangent at the point (2,

\mathrm{-}

2) to the curve

x^{2} y^{2} -2x=4\left(1-y\right)

does not pass through the point

A

(-2,-7)

B

(-4,-9)

C

(4,1/3)

D

(8,5)

Question 16

+12-3

Let P(x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x-1 and it leaves remainder 6 when divided by x+1 , then

A

p(-2)=11

B

p(2)=11

C

p(2)=19

D

p(-2)=19

Question 17

+12-3

The median AD of

\Delta

ABC is bisected at E and BE is extended to meet the side AC in F. The AF : FC =

A

1:3

B

2:1

C

1:2

D

3:1

Question 18

+12-3

In a parallelogram ABCD, P is the midpoint of AD. Also, BP and AC intersect at Q. Then AQ : QC =

A

1:3

B

3:1

C

2:1

D

1:2

Question 19

+12-3

The equation of the circle passing through the point (4,6) and whose diameters are along 𝑥+2𝑦−5=0 and 3𝑥−𝑦−1=0 is

A

x^{2} +y^{2} -2x-6y-20=0

B

x^{2} +y^{2} -6x-2y-20=0

C

x^{2} +y^{2} -2x-4y-20=0

D

x^{2} +y^{2} -4x-2y-20=0

Question 20

+12-3

If S and S

\mathrm{\prime}

are foci of the ellipse

\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } =1

, B is the end of the minor axis and BSS' is an equilateral triangle, then the eccentricity of the ellipse is

A

1/2

B

1/3

C

1/4

D

1/5

Question 21

+12-3

The position vectors of the vertices a,b,c of a tetrahedron ABCD are

\hat{i}+\hat{j}+\hat{k}

,

\hat{i}

and 3

\hat{i}

respectively and the altitude for the vertex D to the opposite face ABC meets the face at E. If the length of ED is 4 and the volume of tetrahedron is

\frac{2\sqrt{2} }{3}

, then the length of DE is

A

1

B

2

C

3

D

4

Question 22

+12-3

Equation of the tangent from the point (3, −1) to the ellipse 2x

{}^{2}

+ 9y

{}^{2}

= 3 is

A

2x-3y-3=0

B

2x+3y-3=0

C

2x+y-3=0

D

NOT

Question 23

+12-3

If

\int _{\log 2}^{x}\frac{1}{\sqrt{e^{x} -1} } dx=\frac{\pi }{6}

then x=

A

log2

B

2 log2

C

3 log2

D

4 log2

Question 24

+12-3

If

\int \cos x\cos 2x\cos 5xdx=A_{1} \sin 2x+A_{2} \sin 4x+A_{3} \sin 6x+A_{4} \sin 8x+c

then the values of A

{}_{1}

, A

{}_{2}

, A

{}_{3}

, A

{}_{4}

are

A

A_{1} =\frac{1}{2} ,A_{2} =\frac{1}{4} ,A_{3} =\frac{1}{6} ,A_{4} =\frac{1}{8}

B

A_{1} =\frac{1}{8} ,A_{2} =\frac{1}{16} ,A_{3} =\frac{1}{24} ,A_{4} =\frac{1}{32}

C

A_{1} =\frac{1}{6} ,A_{2} =\frac{1}{12} ,A_{3} =\frac{1}{18} ,A_{4} =\frac{1}{24}

D

A_{1} =\frac{1}{4} ,A_{2} =\frac{1}{8} ,A_{3} =\frac{1}{12} ,A_{4} =\frac{1}{16}

Question 25

+12-3

If x is real, then the minimum value of

\frac{x^{2} -x+1}{x^{2} +x+1}

is

A

1/2

B

2

C

3

D

1/3

Question 26

+12-3

Let

f\left(x\right)=\left\{\begin{array}{c} {\cos \left[x\right],x\ge 0} \\ {|x|+a,x<0} \end{array}\right.

where [x] denotes G.I.F. If f should be continuous at x=0, then a must be

A

0

B

1

C

2

D

-1

Question 27

+12-3

Suppose that A

{}_{1}

,A

{}_{2}

,

{\dots}

.A

{}_{30}

are 30 sets each having 5 elements and B

{}_{1}

,B

{}_{2}

,

{\dots}

.B

{}_{n}

sets such that

\bigcup _{i=1}^{30}A_{i} = \bigcup _{j=1}^{n}B_{j} =S.

If each element of S belongs to exactly ten of the A

{}_{i}

's and exactly nine of the B

{}_{j}

's, then n is

A

15

B

30

C

40

D

45

Question 28

+12-3

In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Also, the total number of games played by the men among themselves exceeded by 66 the number of games that the men played against the women. Then the total number of players in the tournament is

A

13

B

11

C

9

D

7

Question 29

+12-3

\vec{a}

and

\vec{b}

are non-zero non-collinear vectors such that

|\vec{a}|=2

,

\vec{a}.\vec{b}=1

and the angle between

\vec{a}

and

\vec{b}

is

\frac{\pi }{3}

. If

\vec{r}

is any vector satisfying

\vec{r}.\vec{a}=2,\vec{r}.\vec{b}=8

,

\left(\vec{r}+2\vec{a}-10\vec{b}\right).\left(\vec{a}\times \vec{b}\right)=6

and-

\vec{r}+2\vec{a}-10\vec{b}=\lambda \left(\vec{a}\times \vec{b}\right)

then

\lambda

is

A

1/2

B

2

C

\frac{4}{\sqrt{3} }

D

3

Question 30

+12-3

If

\sin ^{2} x\tan x+\cos ^{2} x\cot x-\sin 2x=1+\tan x+\cot x,

x\in \left(0,\pi \right)

then x=

A

\frac{3\pi }{12} ,\frac{5\pi }{12}

B

\frac{5\pi }{12} ,\frac{7\pi }{12}

C

\frac{7\pi }{12} ,\frac{11\pi }{12}

D

\frac{7\pi }{12} ,\frac{9\pi }{12}

Question 31

+12-3

Let s be the set { 𝑎 ∈ 𝑍+ ∶ 𝑎 ≤ 100 }. If the equation[tan2𝑥]-tan𝑥-𝑎 = 0 has real roots (where [.] is the greatest integer function), then the number of elements is S is

A

10

B

8

C

9

D

0

Question 32

+12-3

If

\sum _{i=1}^{n}X_{i} =80

and

\sum _{i=1}^{n}X^{2} {}_{i} =400

then a possible value of n among the following is

A

9

B

12

C

15

D

18

Question 33

+12-3

If the mean deviation 1, 1+d, 1+2d,

{\dots}

, 1+100d from their mean is 255, then d is equal to

A

10.1

B

10.2

C

10.3

D

10.4

Question 34

+12-3

If a man purchases a raffle ticket, he can win a first prize of Rs.5,000 or a second prize of Rs.2,000 with probabilities 0.001 and 0.003respectively. What should be a fair price to pay for the ticket?

A

Rs 11

B

Rs 15

C

Rs 2000

D

NOT

Question 35

+12-3

Let U and V be two events of a sample space S and P(A) denote the probability of an event A. Which of the following statements is true?

A

If P(U)=P(V) the U=V

B

If P(U)=0 then U

{}^{c}

=S

C

If

U\cap V=\phi

then U and V are independent

D

If U and V are independent, then so are U

{}^{c}

and V

{}^{c}

Question 36

+12-3

If a and b are greatest values of

{}^{2n} C_{r}

and

{}^{2n-1} C_{r}

respectively, then

A

a=2b

B

b=2a

C

a=b

D

a

{}^{2}

=2b

{}^{2}

Question 37

+12-3

If

\left(1+x-2x^{2} \right)^{6} =1+a_{1} x+a_{2} x^{2} +...+a_{12} x^{12}

, then the value of

a_{2} +a_{4} +...+a_{12}

is

A

29

B

30

C

31

D

32

Question 38

+12-3

If x , 2x + 2, 3x + 3 are the first three terms of a geometric progression, then 4

{}^{th}

term in the geometric progression is

A

-13.5

B

13.5

C

-27

D

27

Question 39

+12-3

If a, b, c are in GP and log 𝑎 − log 2𝑏, log 2𝑏 − log 3𝑐 and log 3𝑐 − log 𝑎 are in AP, then a, b, c are the lengths of the sides of a triangle which is

A

Acute angled

B

Obtuse angled

C

Right angled

D

Equilateral

Question 40

+12-3

Solution set of inequality

\log _{3} \left(x+2\right)\left(x+4\right)+\log _{1/3} \left(x+2\right)<\frac{1}{2} \log _{\sqrt{3} } 7

is

A

(-2,-1)

B

(-2,3)

C

(-1,3)

D

\left(3,\infty \right)

Question 41

+12-3

If

a,a_{1} ,a_{2} ,...,a_{2n-1} ,b

are in AP,

a,b_{1} ,b_{2} ,...,b_{2n-1} ,b

are in GP and

a,c_{1} ,c_{2} ,...,c_{2n-1} ,b

are in HP, where a, b are positive, then the equation

a_{n} x^{2} -b_{n} x+c_{n} =0

has its roots

A

Real and equal

B

Real and unequal

C

Imaginary

D

One real and one imaginary

Question 42

+12-3

Let 𝑓(𝑥) be a polynomial satisfying f(0)=2, f'(0)=3 and 𝑓′′(x)=𝑓(𝑥). Then f(4) is equal to

A

\frac{5\left(e^{8} -1\right)}{2e^{4} }

B

\frac{5e^{8} -1}{2e^{4} }

C

\frac{2e^{4} }{5e^{8} -1}

D

\frac{2e^{4} }{5\left(e^{8} +1\right)}

Question 43

+12-3

if x, y, z are distinct real numbers and

\left|\begin{array}{ccc} {x} & {x^{2} } & {2+x^{3} } \\ {y} & {y^{2} } & {2+y^{3} } \\ {z} & {z^{2} } & {2+z^{3} } \end{array}\right|=0

then xyz=

A

1

B

-1

C

2

D

-2

Question 44

+12-3

Let 𝑥𝑖 , 𝑖 = 1,2,

{\dots}

, n be n observations and 𝑤𝑖 = 𝑝𝑥𝑖 + 𝑘, 𝑖 = 1,2,

{\dots}

, n where p and k are constants. If the mean of 𝑥𝑖′𝑠 is 48 and standard deviation is 12, whereas the mean of wi’s is 55 and standard deviation is 15, then the value of p and k should be

A

p=1.25, k=-5

B

p=-1.25, k=5

C

p=2.5, k=-5

D

p=25, k=5

Question 45

+12-3

A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of eleven steps, he is one step away from the starting point is

A

462(0.34)5

B

462(0.04)5

C

462(0.14)5

D

462(0.24)5

Question 46

+12-3

Two numbers a and b are chosen at random from a set of first 30 natural numbers, then the probability that a

{}^{2}

-b

{}^{2}

is divisible by 3 is

A

47/87

B

15/87

C

12/87

D

9/87

Question 47

+12-3

If

\Delta =a^{2} -\left(b-c\right)^{2}

where

\Delta

is the area of the

\Delta ABC

then tanA equals

A

15/16

B

8/15

C

8/17

D

½

Question 48

+12-3

A particle P starts from the point

z_{0} =1+2i

, where

i=\sqrt{-1}

. It moves first horizontally away from the origin by 5 units and then vertically away from origin by 3 units to reach a point 𝑧1. From z

{}_{1}

the particle moves 2 units in the direction of the vector i + j and, then it moves through an angle π/2 in an anticlockwise direction on a circle with centre at origin, to reach a point z

{}_{2}

. The point z

{}_{2}

is given by

A

6+7i

B

-7+6i

C

7+6i

D

-6+7i

Question 49

+12-3

Let

f:{\rm R}\to {\rm R}

be defined by

f\left(x\right)=\left\{\begin{array}{c} {x\sin \left(\frac{1}{x} \right),x>0} \\ {0,{\rm \; \; \; \; \; \; \; \; \; }x\le 0} \end{array}\right.

then

A

f is neither continuous nor differentiable at 0

B

f is continuous and differentiable at 0

C

f is continuous but not differentiable at 0

D

f is not continuous but differentiable at 0

Question 50

+12-3

For the two circles

x^{2} +y^{2} =16

and

x^{2} +y^{2} -2y=0

there is/are

A

One pair of common tangents

B

Two pair of common tangents

C

Three common tangents

D

No common tangents

Question 51

+6-1.5

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is

A

123

B

127

C

235

D

305

Question 52

+6-1.5

Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?

A

495

B

550

C

1045

D

2475

Question 53

+6-1.5

Decide which of the give conclusions logically follow from the given statements:

\newline

\textbf{Statements:}

\newline

All suns are moons.

\newline

Some moons are planets.

\newline

\textbf{Conclusions:}

\newline

I. All moons are suns.

\newline

II.At least some moons are planets.

A

Either conclusion I or II is true

B

Neither conclusion I nor II is true

C

Both conclusion I or II is true

D

Only conclusion II is true

Question 54

+6-1.5

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is

A

72m

B

54m

C

50m

D

45m

Question 55

+6-1.5

A clock is set right at 5 AM. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4th day?

A

11:15 PM

B

11:00 PM

C

12:00 PM

D

12:30 PM

Question 56

+6-1.5

The number of solid spheres, each of diameter 3 cm that could be moulded to form a solid metal cylinder of height 54cm and diameter 4 cm is?

A

16

B

24

C

36

D

48

Question 57

+6-1.5

The integers 34041 and 32506, when divided by a 3 - digit integer n, leave the same remainder. What can be the value of n?

A

289

B

307

C

367

D

493

Question 58

+6-1.5

Twelve classmates A, B, C, D, E, F, G, H I, J, K and L are sitting on a square table with 3 persons on each side. ABC and GJK are sitting on opposite sides. A and L are adjacent to each other. K is sitting diagonally to C.

Question: If G and E are facing C and H respectively, the neighbors of K are

A

J and H

B

J and E

C

H and J

D

H and E

Question 59

+6-1.5

Twelve classmates A, B, C, D, E, F, G, H I, J, K and L are sitting on a square table with 3 persons on each side. ABC and GJK are sitting on opposite sides. A and L are adjacent to each other. K is sitting diagonally to C.

Question:If H is sitting between L and F, then he will be facing

A

D

B

E

C

G

D

I

Question 60

+6-1.5

Twelve classmates A, B, C, D, E, F, G, H I, J, K and L are sitting on a square table with 3 persons on each side. ABC and GJK are sitting on opposite sides. A and L are adjacent to each other. K is sitting diagonally to C.

Question: If F is sitting between D and E, who is sitting to the left of K?

A

H

B

I

C

H or I

D

NOT

Question 61

+6-1.5

A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the actual price price were his was the listed price of the article?

A

100%

B

80%

C

75%

D

66%

Question 62

+6-1.5

What pair comes next in the following sequence 99, 90, 83, 78, ...

A

71,69

B

69,57

C

67,59

D

69,63

Question 63

+6-1.5

Using only 2, 5, 10, 25 and 50 paise coins, the smallest number of coins required to pay exactly 79 paise, 66 paise and Re 1.01 to three different persons is

A

17

B

20

C

34

D

18

Question 64

+6-1.5

The number that comes next in the series 1, 2, 3, 6, 11, 20, 37, 68,...

A

105

B

124

C

125

D

126

Question 65

+6-1.5

1.All chickens are birds.

\newline

2.Some chickens are hens.

\newline

3.Female birds lay eggs.

\newline

If the above three statements are facts, which of the following statement must also be a fact?

\newline

I.All birds lay eggs.

\newline

II.Hens are birds.

\newline

III.Some chickens are not hens.

A

II Only

B

II and III only

C

I, II and III

D

None of the statements

Question 66

+6-1.5

In a family of six persons, there are people from three generations. Each person has separate profession and also they like different colours. There are two couples in the family. Rohan is a CA and his wife neither is a doctor nor likes green colour. Engineer likes red colour and his wife is a teacher. Mohini is mother-in-law of Savita and she likes orange colour. Deepak is grandfather of Titu and Titu, who is a principal, likes black colour. Nerru is grand-daughter of Mohini and she likes blue colour. Nerru's mother likes white colour. Savita is a

A

Doctor

B

Teacher

C

housewife

D

NOT

Question 67

+6-1.5

How many 4 - digit numbers that can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

A

216

B

60

C

24

D

25

Question 68

+6-1.5

A team must be selected from ten probable's - A, B, C, D, E, F, G, H, I and J. Of these, A, C, E and J are forwards, B, G and H are point guards and D, F and I are defenders. The team must have at least one forward, one point guard and one defender. If the team includes J, it must also include F. The team must include E or B, but not both. If the team includes G, it must also include F. The team must include exactly one among C, G and I. C and F cannot be members of the same team. D and H cannot be members of the same team. The team must include both A and D or neither of them. There is no restriction on the number of members in the team. What could be the maximum size of the team that includes G?

A

4

B

5

C

6

D

more than 6

Question 69

+6-1.5

There are eight poets, namely, A, B, C, D, E, F, G and H in respect of whom questions are being asked in the examination. The first four are ancient poets and the last four are modern poets. The question on ancient and modern poets is being asked in alternate years. Those who like W also like V, those who like S like R also. The examiner who sets question is not likely to ask question on S because he has written an article on him. But he likes S. Last year a question was asked on U. Considering these facts, on whom the question is most likely to be asked this year ?

A

Q

B

R

C

S

D

V

Question 70

+6-1.5

A dealer offers sells half of the eggs that he has and another half an egg to Anurag. Then he sells half of the balance eggs and another half an egg to Deepak. Then he sells half of the balance eggs and another half an egg to Sivani. In the end he is left with just 7 eggs and he claims that he never broke an egg. How many eggs did he start with?

A

65

B

63

C

67

D

69

Question 71

+6-1.5

In a certain language, if the word 'BASKET' is coded as 'UFLTBC', then how is the word 'SIMPLE' coded in that language?

A

FMQNJT

B

FMQGNJ

C

FMQNJH

D

MFNQTJ

Question 72

+6-1.5

Each of A, B and C is a different digit among 1 to 9. How many different values of the sum of A, B and C are possible, if

ABA\times AA=ACCA?

A

1

B

3

C

7

D

8

Question 73

+6-1.5

John, Johny and Janardan participated in a race and each won a different medal among Gold, Silver and Bronze, not necessarily in that order. Each person among them gives two replies to any question, one of which is true and the other is false (in any order). When asked about the details of the medals obtained by them, the following were their replies:

\newline

John: I won the Gold medal. Johny won the Bronze medal.

\newline

Johny: John won the Silver medal. I won the Gold medal.

\newline

Janardan: Johny won the Silver medal. I won the Gold medal.

\newline

Which among the following is the correct order of the persons who won the Gold medal, the Silver medal and the Bronze medal respectively?

A

John, Johny, Janardan

B

Janardan, John, Johny

C

Johny, Janardan, John

D

Janardan, Johny, John

Question 74

+6-1.5

Each of the five people K, L, M, P and Q is of a different weight. It is known that the number of people heavier than P is the same as the number of people lighter than Q. L is the heaviest and K is not the lightest. Who is the lightest?

A

M

B

L

C

Q

D

P

Question 75

+6-1.5

How many positive numbers less than 10,000 are such that the product of their digits is 210?

A

36

B

42

C

48

D

54

Question 76

+6-1.5

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. Read both statements and Give the answer (U) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

\newline

Give the answer (V) if the data in statement I alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

\newline

Give the answer (W) if the data either in Statement I or in Statement II alone are sufficient to the answer of the question. Give the answer (X) if the data in both statements I and II together are not sufficient to answer the question. Give the answer (Y) if the data in both statements I and II together are are necessary to answer the question.

Question:How will long it take to empty the tank if both the inlet pipe P1 and the outlet pipe P2 are opened simultaneously?

\newline

(i)𝑃1 can fill the tank in 16 minutes.

\newline

(ii) 𝑃2 can empty the full tank in 8 minutes.

A

X

B

U

C

Y

D

V

Question 77

+6-1.5

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. Read both statements and Give the answer (U) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

\newline

Give the answer (V) if the data in statement I alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

\newline

Give the answer (W) if the data either in Statement I or in Statement II alone are sufficient to the answer of the question. Give the answer (X) if the data in both statements I and II together are not sufficient to answer the question. Give the answer (Y) if the data in both statements I and II together are are necessary to answer the question.

Question:How much time will the leak take to empty the full cistern?

\newline

(i) The cistern is normally filled in 9 hours.

\newline

(ii) It takes one hour more than the usual time to fill the cistern because of a leak in the bottom.

A

V

B

U

C

X

D

Y

Question 78

+6-1.5

Wrong number in the series 7, 8, 18, 57, 228, 1165, 6996

A

228

B

18

C

57

D

28

Question 79

+6-1.5

\newline

A, B, C, D, E, and F are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. There are only two married couples in the group. The lawyer is married to D, who is a housewife. No woman in the group is either an engineer or an accountant. C, the accountant, is married to F, who is a professor. A is married to a housewife. E is not a housewife.

Question: How many members of the group are males?

A

2

B

3

C

4

D

Cant be determined

Question 80

+6-1.5

\newline

A, B, C, D, E, and F are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. There are only two married couples in the group. The lawyer is married to D, who is a housewife. No woman in the group is either an engineer or an accountant. C, the accountant, is married to F, who is a professor. A is married to a housewife. E is not a housewife.

Question:What is E's profession?

A

Accountant

B

Lawyer

C

Professor

D

Engineer

Question 81

+6-1.5

Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes?

A

2.5 kg

B

2.4 kg

C

2 kg

D

10 kg

Question 82

+6-1.5

Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls, and more girls than families. Then the minimum possible number of families in the locality is

A

4

B

3

C

2

D

5

Question 83

+6-1.5

Two liquids A and B are in the ratio 5:1 in container 1 and in the ratio 1:3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1:1?

A

2:3

B

4:3

C

3:2

D

3:4

Question 84

+6-1.5

Some friends planned to contribute equally to jointly buy a CD player. However, two of them decided to withdraw at the last minute. As a result, each of the others had to shell out one rupee more than what they had planned for. If the price (in Rs.) of the CD player is an integer between 1000 and 1100, find the number of friends who actually contributed?

A

44

B

23

C

21

D

46

Question 85

+6-1.5

If the points 𝑃(𝑎2,𝑎) lie in the region corresponding to the acute angle between the lines and then

A

𝑎 ∈ (2,6)

B

𝑎 ∈ (4,6)

C

𝑎 ∈ (2,4)

D

𝑎 ∈ (10,14)

Question 86

+6-1.5

Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at 50kmph towards Baroda situated 100 km away. At 7.00 am Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7:30 am Mr. Shah, the traffic controller at Baroda realizes that both trains are running on the same track. How much time does he have to avert a head-on collision between the two trains?

A

15 min

B

20 min

C

25 min

D

30 min

Question 87

+6-1.5

Study the information carefully and answer the questions given below:

\newline

If we arrange the alphabets in the word "RATE" in the English alphabetical order, word "AERT" is formed. Then the third alphabet from the left in this word is "R". similarly, from the word "OPEN" we get - "ENOP" and the third alphabet from the left is "O". From the word "CHEF" we get - "CEFH" the third alphabet from the left "F". From the word "TOY" we get - "OTY" and the third alphabet from the left is "Y". If we use all these letters, then a meaningful English word "FORTY" can be formed. Now find which of the following word set DOES NOT give a meaningful word in the similar way.

A

SAME, ROOM, BEST, AUTO

B

GOAT, PEST, WATT, ARMY

C

MALE, FIND, LOST, THAT

D

JUMP, LIME, DUMB, SOME

Question 88

+6-1.5

If 137 + 276 = 435, how much is 731 + 672 = ?

A

534

B

1403

C

1623

D

1531

Question 89

+6-1.5

Statement-I : Out of total of 200 readers, 100 read Indian Express, 120 read Times of India and 50 read Hindu.

\newline

Statement -II : Out of a total of 200 readers, 100 read Indian Express, 120 reads Times of India and 50 read neither.

\newline

How many people (from the group surveyed) read both Indian Express and Times of India?

A

The statement can be answered with the help of statement II, alone.

B

Both, statement I and statement II are needed to answer the question.

C

The question can be answered with the help of statement I alone.

D

The question cannot be answered even with the help of both the statements.

Question 90

+6-1.5

Which number replaces the question mark in the figure given below?

A

11

B

6

C

3

D

21

Question 91

+4-1

\textbf{Read the following passage and answer questions }

\newline

I have, myself, full confidence that if all do their duty, if nothing is neglected, and if the best arrangements are made, as they are being made, we shall prove ourselves once again able to defend our Island home, to ride out the storm of war, and to outlive the menace of tyranny, if necessary for years, if necessary, alone. At any rate, that is what we are going to try to do. That is the resolve of His Majesty's Government-every man of them.

\newline

That is the will of the parliament of our nation. The British Empire and the French Republic, linked together in their cause and in their need, will defend to the death their native soil, aiding each other like good comrades to the utmost of their strength. Even though large tracts of Europe and many old and famous States have fallen or may fall into the grip of the Gestapo and all the odious apparatus of Nazi rule, we shall not flag or fail.

\newline

We shall go on to the end, we shall fight in France, we shall fight on the seas and oceans, we shall fight with growing confidence and growing strength in the air, we shall defend our Island, whatever the cost may be, we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender, and even if, which I do not for a moment believe, this island or a large part of it were subjugated and starving, then our Empire beyond the seas, armed and guarded by the British Fleet, would carry on the struggle, until, in God's good time, the New World, with all its power and might, steps forth to the rescue and the liberation of the old."

Question:"That is the resolve of His Majesty's Government." What is their resolve?

A

Surrender to the Nazis

B

Negotiate with the Nazis

C

Run away from the Nazis

D

Fight the Nazis

Question 92

+4-1

\textbf{Read the following passage and answer questions }

\newline

I have, myself, full confidence that if all do their duty, if nothing is neglected, and if the best arrangements are made, as they are being made, we shall prove ourselves once again able to defend our Island home, to ride out the storm of war, and to outlive the menace of tyranny, if necessary for years, if necessary, alone. At any rate, that is what we are going to try to do. That is the resolve of His Majesty's Government-every man of them.

\newline

That is the will of the parliament of our nation. The British Empire and the French Republic, linked together in their cause and in their need, will defend to the death their native soil, aiding each other like good comrades to the utmost of their strength. Even though large tracts of Europe and many old and famous States have fallen or may fall into the grip of the Gestapo and all the odious apparatus of Nazi rule, we shall not flag or fail.

\newline

We shall go on to the end, we shall fight in France, we shall fight on the seas and oceans, we shall fight with growing confidence and growing strength in the air, we shall defend our Island, whatever the cost may be, we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender, and even if, which I do not for a moment believe, this island or a large part of it were subjugated and starving, then our Empire beyond the seas, armed and guarded by the British Fleet, would carry on the struggle, until, in God's good time, the New World, with all its power and might, steps forth to the rescue and the liberation of the old."

Question:What does subjugate mean?

A

Surrender

B

compare

C

control

D

abandon

Question 93

+4-1

\textbf{Read the following passage and answer questions }

\newline

I have, myself, full confidence that if all do their duty, if nothing is neglected, and if the best arrangements are made, as they are being made, we shall prove ourselves once again able to defend our Island home, to ride out the storm of war, and to outlive the menace of tyranny, if necessary for years, if necessary, alone. At any rate, that is what we are going to try to do. That is the resolve of His Majesty's Government-every man of them.

\newline

That is the will of the parliament of our nation. The British Empire and the French Republic, linked together in their cause and in their need, will defend to the death their native soil, aiding each other like good comrades to the utmost of their strength. Even though large tracts of Europe and many old and famous States have fallen or may fall into the grip of the Gestapo and all the odious apparatus of Nazi rule, we shall not flag or fail.

\newline

We shall go on to the end, we shall fight in France, we shall fight on the seas and oceans, we shall fight with growing confidence and growing strength in the air, we shall defend our Island, whatever the cost may be, we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender, and even if, which I do not for a moment believe, this island or a large part of it were subjugated and starving, then our Empire beyond the seas, armed and guarded by the British Fleet, would carry on the struggle, until, in God's good time, the New World, with all its power and might, steps forth to the rescue and the liberation of the old."

Question:What does the term ride out the storm mean?

A

Handle a crisis successfully

B

Hide from storm

C

Hide in some place where one cannot be found.

D

Ride on a boat at the time of storm

Question 94

+4-1

Use the appropriate phrasal verb and complete the sentence given below. The new system in education is aimed at

\_\_\_\_\_\_\_\_\_\_\_

the differences between rich and poor.

A

Goof around

B

Evening Out

C

Glossing Over

D

Give Over

Question 95

+4-1

There are two blanks in the sentences given below. From the pairs of word given below the sentences, choose the pair that fills the blank most appropriately. Private companies supplying 'breakfast cereals' have started

\_\_\_\_\_\_\_\_

in agriculture in poorer countries. This has

\_\_\_\_\_\_\_\_\_

the spectre of land grabs and political conflicts.

A

Spending ... intensified

B

Dealing ... inflated

C

Ploughing ... increased

D

Investing ... raised

Question 96

+4-1

Select the most suitable synonym for the underlined word in the sentence. All the members of organization expressed implacable opposition to the move.

A

Indignant

B

Adamant

C

Unified

D

Quixotic

Question 97

+4-1

In the sentence given below, a part of sentence is underlined. Four different ways of phrasing the underlined part are indicated as four choices. Choose the best alternative and mark its corresponding letter as your answer. A nation is built not be legislation but by the stirrings in the heart of the people.

A

By legislation and by inspiration

B

Not by laws but by the excitement of the people

C

By law and by inciting the people

D

More by the passions in the hearts of the people than by laws

Question 98

+4-1

Pick the most appropriate substitute to the capitalized word in the following sequence. The weapon inspector's report was not expected to provide INCONTROVERTIBLE evidence of weapons of mass destruction.

A

Conclusive

B

Disputable

C

Inconvenient

D

Indecisive

Question 99

+4-1

The word PIN is used in four different ways. Choose the option in which the usage of the word is incorrect or inappropriate?

A

She combed her heir backward and secured it with a pin.

B

Jack managed to grab the thief and pin him against the wall until the police arrived on the scene.

C

It is imprudent to pin your hopes on someone to help you out of his situation.

D

You can't pin the blame at anyone without verifying facts.

Question 100

+4-1

Select the most suitable antonym from the given choices for the word: "SANGFROID".

A

Equanimity

B

steadiness

C

Aplomb

D

Turbulence

Question 101

+4-1

Select the most suitable synonym from the given choices for the word: "ANTEDILUVIAN".

A

Recluse

B

Maverick

C

Archaic

D

Bellicose

Question 102

+4-1

Select a word from the given alternatives which has the same meaning as the underlined word: He has a propensity for getting into debt.

A

Tendency

B

Aptitude

C

Characteristics

D

Quality

Question 103

+4-1

Choose one of the words that is most nearly same as meaning of the given word Indemnify.

A

Insure

B

Compensate for loss

C

Assure

D

Sue for damages

Question 104

+4-1

Which of the following is the correct passive of the sentence, ``JOHN HAS EATEN THE APPLES??"

A

The apples are being eaten by John.

B

The apples are eaten by John.

C

The apples have been eaten by John.

D

The apples will be eaten by John.

Question 105

+4-1

Fill in the blanks choosing the correct adjective: The phoenix is a

\_\_\_\_\_\_

Bird.

A

Mythical

B

Ethical

C

Natural

D

Carnivorous

Question 106

+4-1

In the following a part of the sentence is underlined. Four different ways of phrasing the underlined part are indicated below. Chose the best alternative among the four choices given. When he entered the house, it was in sixes and sevens.

A

It was six O'clock when he entered the house

B

Inmates were eulogized when he entered

C

House was in pandemonium

D

House wad blissful

Question 107

+4-1

Identify the word that means "To try to achieve something is difficult circumstances despite a setbacks".

A

Persuade

B

persevere

C

picturesque

D

perspective

Question 108

+4-1

Extreme old age when a man behaves like a child.

A

Imbecility

B

senility

C

dotage

D

superannuation

Question 109

+4-1

Anne had to pay everything because as usual, Peter

\_\_\_\_\_\_\_\_\_\_

his wallet at home.

A

Had left

B

was leaving

C

left

D

leave

Question 110

+4-1

\textbf{ }

Choose the phrasal verb to replace the explanation in brackets. "We must (be quick)

\_\_\_\_\_\_\_\_

or we'll be late for school".

A

Act up

B

Hurry up

C

Fasten on

D

Speed in

Question 111

+8-2

In an 8 bit representation of computer system the decimal number 47 has to be subtracted from 38 and the result in binary 2's complement is

\_\_\_\_\_\_\_\_\_

A

11110111

B

10001001

C

11111001

D

11110001

Question 112

+8-2

How many Boolean expressions can be be formed with 3 Boolean variables?

A

16

B

1024

C

32

D

256

Question 113

+8-2

Which of the following represents (𝐷4)

{}_{16}

?

A

(4E)

{}_{16}

-(5B)

{}_{16\ }

B

(14E)

{}_{16}

- (7A)

{}_{16\ }

C

(15C)

{}_{16}

- (6D)

{}_{16\ }

{}_{\ \ \ }

{}_{\ }

D

(1E4)

{}_{16}

-(A7)

{}_{16\ }

Question 114

+8-2

The base (or radix) of the number system such that the following equation holds 312/20 = 131.1 is

A

3

B

4

C

5

D

6

Question 115

+8-2

If N is a 16-bit signed integer, then 2's complement representation of N is (F87B)

{}_{16}

. The 2's complement representation of 8*N is

A

(𝐶3𝐷8)16

B

(187B)

{}_{16\ }

C

(F878)

{}_{16\ }

D

(987B)

{}_{16\ }

Question 116

+8-2

For the circuit shown below, the complement of the output

A

0

B

X

C

X'

D

1

Question 117

+8-2

If the 2's complement representation of a number is (011010)

{}_{2}

, what is its equivalent hexadecimal representation?

A

(110)16

B

(1A)16

C

(16)16

D

(26)16

Question 118

+8-2

If we can generate a maximum of 4 Boolean functions using n Boolean variables, what will be minimum value of n?

A

65536

B

16

C

1

D

4

Question 119

+8-2

With 4-bit 2's complement arithmetic, which of the following addition will result in overflow?

A

1111+1101

B

0110+0110

C

1101+0101

D

0101+1011

Question 120

+8-2

\textbf{ }

In IEEE single precision floating point representation, exponent is represented in

\_\_\_

A

8 bit Sign - magnitude representation

B

8 bit 2's complement representation

C

Biases exponent representation with a bias value 127

D

Biases exponent representation with a bias value 128

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