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Nimcet-2025

120 Questions • Previous Year Paper

Question 1

+12-3
What is the general solution of the equation cot θ+tan⁡θ=2\theta +\tan \theta =2 ?
A
θ=nπ+π4\theta =n\pi +\dfrac{\pi }{4}
B
θ=nπ2+π6\theta =\dfrac{n\pi }{2} +\dfrac{\pi }{6}
C
θ=nπ2+π8\theta =\dfrac{n\pi }{2} +\dfrac{\pi }{8}
D
θ=nπ2+π4\theta =\dfrac{n\pi }{2} +\dfrac{\pi }{4}

Question 2

+12-3
Consider the matrix (−1  −1    20        −1      −10          0      −1)\left(\begin{array}{l} {-1{\rm \; }-1{\rm \; \; 2}} \\ {{\rm 0\; \; \; \; -1\; \; \; -1}} \\ {{\rm 0\; \; \; \; \; 0\; \; \; -1}} \end{array}\right) The sum of al the entries of the matrix B19{}^{19} is
A
-163
B
174
C
192
D
11

Question 3

+12-3
The length of the projection of a⃗=2i^+3j^+k^\vec{a}=2\hat{i}+3\hat{j}+\hat{k}on b⃗\vec{b}=2i^+j^+2k^2\hat{i}+\hat{j}+2\hat{k} is equal to:
A
−23\dfrac{-2}{3}
B
13\dfrac{1}{3}
C
23\dfrac{2}{3}
D
−13\dfrac{-1}{3}

Question 4

+12-3
If x, y and z are the three cube roots of 27, then the determinant of the matrix \newline [x    y    zy    z    xz    x    y]\left[\begin{array}{l} {x{\rm \; \; y\; \; z}} \\ {y{\rm \; \; z\; \; x}} \\ {z{\rm \; \; x\; \; y}} \end{array}\right]is
A
(x-y)(x-z)(y-z)
B
-1
C
1
D
0

Question 5

+12-3
Let A and B be two square matrices of same order satisfying A;+5A+=0 and B;+3B+I=0 repectively. Where I is the identity matrix. Then the inverse of C = BA + 2B + 2A + 4I is
A
BA - 3B + A - 3I
B
AB - A + 3B - 3I
C
AB + A + 3B + 3I
D
BA + 3B + A + 3I

Question 6

+12-3
A circle with its center in the first quadrant touches both the coordinate axes and the line. x - y - 2 = 0 Then the area of the circle is
A
π2\frac{\pi }{2}
B
2π\pi
C
π\pi
D
4π\pi

Question 7

+12-3
The scores of students in a national level examination are normally distributed with a mean of 500 and a standard deviation of 100. If the value of the cumulative distribution of the standard normal random variable at 0.5 is 0.691, then the probability that a randomly selected student scored between 450 and 500 is
A
0.591
B
0.091
C
0.191
D
0.391

Question 8

+12-3
Let E and F be two events such that P(E) >\mathrm{>} 0 and P(F) >\mathrm{>} 0 Which one of the following is NOT equivalent to the condition that P(E) =P(E|F)
A
Ec{}^{c} c and F are independent
B
E and F are independent
C
P(Ec{}^{c}) P (Fc{}^{c} ) ≠\ne P(Ec{}^{c} ∩\cap Fc{}^{c})
D
P(F) =P(F{\textbar}E)

Question 9

+12-3
The circle x2+y2+ax+βy+y=0x^{2} +y^{2} +ax+\beta y+y=0is the image of the circle x2+y2−6x−10y+30=0x^{2} +y^{2} -6x-10y+30=0 across the line 3x + y = 2 The value of [α+β+γ]\left[\alpha +\beta +\gamma \right] is (where [.] represents the floor function.)
A
23
B
20
C
21
D
22

Question 10

+12-3
A tower subtends an angle of 30∘{}^\circ at a point on the same level as the foot of the tower. At a second point la meters above the first, the depression of the foot of the tower is 600, What is the horizontal distance of the tower from the point?
A
2h cot 60∘{}^\circ
B
h cot 60∘{}^\circ
C
h tan 60∘{}^\circ
D
2h tan 60∘{}^\circ

Question 11

+12-3
The captains of five cricket teams, including India and Australia, are lined up randomly next to one other for a group photo. What is the probability that the captains of India and Australia will stand next to each other?
A
12\dfrac{1}{2}
B
15\dfrac{1}{5}
C
14\dfrac{1}{4}
D
25\dfrac{2}{5}

Question 12

+12-3
Let A=(5n−4n−1:n∈N)A=\left(5^{n} -4n-1:n\in N\right)and B={16(n−1):n∈N}B=\left\{16\left(n-1\right):n\in N\right\} be sets. Then
A
A⊂\subset B
B
B⊂\subset A
C
A∩\cap B is a finite set
D
neither A⊂\subset B nor B⊂\subset A

Question 13

+12-3
If a⃗\vec{a} and b⃗\vec{b}are two vectors such that |a⃗\vec{a}|=3,| b⃗\vec{b}|=4 and |a⃗+b⃗\vec{a}+\vec{b}|=1, then value of|a⃗−b⃗\vec{a}-\vec{b}|is
A
2
B
1
C
6
D
7

Question 14

+12-3
The value of the integral ∫0π2(1+2cos⁡x)(2+cos⁡x)2\int _{0}^{\frac{\pi }{2} }\dfrac{(1+2\cos x)}{(2+\cos x)^{2} } dx lies in the interval integrate
A
(1,2)
B
(0,1)
C
(-2,-1)
D
(-1,0)

Question 15

+12-3
If a⃗,b⃗\vec{a},\vec{b} and c⃗\vec{c} are three vectors such that a⃗×b⃗=c⃗,a⃗,c⃗=2\vec{a}\times \vec{b}=\vec{c},\vec{a},\vec{c}=2andb⃗,c⃗\vec{b},\vec{c}=1.if|b⃗\vec{b}| then the value of \newline |a⃗\vec{a}| is
A
3
B
2
C
1
D
4

Question 16

+12-3
The obtuse angle between lines 2y = x + 1 and y = 3x + 2 is
A
3π4\dfrac{3\pi }{4}
B
4π5\dfrac{4\pi }{5}
C
5π6\dfrac{5\pi }{6}
D
2π3\dfrac{2\pi }{3}

Question 17

+12-3
Consider the sample space Ω\Omega ={\mathrm{\{} (x, y): x, y ? (1,2,3,4}\mathrm{\}}}\mathrm{\}} where each outcome is equally likely. Let A = {\mathrm{\{}x ≥\ge 2}\mathrm{\}} and B = {\mathrm{\{}y ≥\ge x}\mathrm{\}} be two events. Then which of the following is NOT true?
A
P(A) = 3/4
B
P(A ∩\cap B)= 1/4
C
A and B are not independent
D
P(B) = 3/8

Question 18

+12-3
The slope of the normal line to the curve x=t2{}^{2}+3t-8 and y=2t2{}^{2}-2t-5 at the point (2,-1) is.
A
-5
B
−67-\dfrac{6}{7}
C
227\dfrac{22}{7}
D
−76-\dfrac{7}{6}

Question 19

+12-3
Let x be a positive real number such that x(8log⁡5(x)−24)=5−4.x^{\left(8\log _{5} \left(x\right)-24\right)} =5^{-4} . Then the project of all possible values of x is
A
25
B
125
C
5
D
625

Question 20

+12-3
suppose t1{}_{1},t1{}_{1},t3{}_{3},…{\dots},t55{}_{55} are in AP such that ∑t=018t3l+1=1197\sum _{t=0}^{18}t_{3l+1} =1197and t7{}_{7}+3t22{}_{22}=174 \newline if∑l=19tl2=947b\sum _{l=1}^{9}t_{l}^{2} =947b, then the value of b is
A
2
B
5
C
1
D
3

Question 21

+12-3
If 8x−1=(14)x,8^{x-1} =\left(\dfrac{1}{4} \right)^{x} , then the value of 1log⁡x+14−log⁡x+15+1log⁡1−x4−log⁡1−x5\dfrac{1}{\log _{x+1} 4-\log _{x+1} 5} +\dfrac{1}{\log _{1-x} 4-\log _{1-x} 5} is
A
1
B
2
C
45\dfrac{4}{5}
D
54\dfrac{5}{4}

Question 22

+12-3
A tower subtends angles a, 2a and 3a, respectively at points A, B and C which are lying on a horizontal line through the foot of the tower. Then ABBC\dfrac{AB}{BC} equal to
A
None of these
B
2 + 3cos 3α\alpha
C
2 + cos 3α\alpha
D
1 + 2cos 2α\alpha

Question 23

+12-3
There are 40 female and 20 male students in a class. If the average heights of female and male students are 5.15 feet and 5.66 feet, respectively, then the average height (in feet) of all the students in the class equals
A
5.175
B
5.405
C
5.320
D
5.490

Question 24

+12-3
If a⃗=i^+j^+k⌢,b⃗=2i^−j^+3k⌢\vec{a}=\hat{i}+\hat{j}+\stackrel{\frown}{k},\vec{b}=2\hat{i}-\hat{j}+3\stackrel{\frown}{k} and c⃗=i^−2\vec{c}=\hat{i}-2 then a vector of magnitude 22\sqrt{22} which is parallel to 2a⃗−b⃗+3c⃗2\vec{a}-\vec{b}+3\vec{c}is
A
(i^−4j^+2k⌢)2221\left(\hat{i}-4\hat{j}+2\stackrel{\frown}{k}\right)\sqrt{\frac{22}{21} }
B
3i^−3j^+2k⌢3\hat{i}-3\hat{j}+2\stackrel{\frown}{k}
C
(i^−4j^−2k⌢)2221\left(\hat{i}-4\hat{j}-2\stackrel{\frown}{k}\right)\sqrt{\frac{22}{21} }
D
3i^−3j^−2k⌢3\hat{i}-3\hat{j}-2\stackrel{\frown}{k}

Question 25

+12-3
Let F1 {}_{1\ } F2{}_{2} be the foci of the hyperbola \newline x2a2−y2b2=1,\dfrac{x^{2} }{a^{2} } -\frac{y^{2} }{b^{2} } =1, a >\mathrm{>} 0, b >\mathrm{>} 0 , \newline and let O be the origin. Let M be an arbitrary point on curve C and above X-axis and H be a point on MF1{}_{1} such that \newline MF2⊥F1F2MF^{2} \bot F_{1} F_{2} , MF1⊥OH,MF_{1} \bot OH, \OH∣=OF2\backslash OH|=OF_{2} with λ∈(2/5,3/5),\lambda \in \left(2/5,3/5\right), \newline then the range of the eccentricity e is
A
(1,7/3)\left(1,\sqrt{7/3} \right)
B
(2,3)\left(\sqrt{2} ,\sqrt{3} \right)
C
(3,2)\left(\sqrt{3,} 2\right)
D
(7/3,2)\left(\sqrt{7/3} ,2\right)

Question 26

+12-3
Which one of the following is NOT a correct statement?
A
The variance is expressed in the same units as the units of observation
B
The standard deviation is greater than or equal to the mean deviation (about mean)
C
The sum of squares of deviations is minimum when taken from the mean
D
The value of standard deviation changes by a change of scale

Question 27

+12-3
The number of accident per week in a town follows passion distribution with mean 2.if the probability that there are three accidents in two weeks time is ke−6{}^{-6}, then the value of is .
A
9
B
18
C
36
D
27

Question 28

+12-3
The curve y=x1+xtan⁡xy=\dfrac{x}{1+x\tan x} attains maxima.
A
for some x ∈\in [−2π,π]\left[-2\pi ,\pi \right]
B
at x =-cosx
C
at x = cosx
D
at x =cos x and for some x ∈\in [−2π,π]\left[-2\pi ,\pi \right]

Question 29

+12-3
Number of permutation of the letters of the word of BANGLORE such that the string ANGLE appers ains together in all permutations, is
A
120
B
24
C
720
D
1228

Question 30

+12-3
An airplane, when 4000m high from the ground, passes vertically above another airplane at an instant when the angles of elevation of the two airplanes from the same point on the ground are 60∘{}^\circ and 30∘{}^\circ respectively. Find the vertical distance between the two airplanes.
A
6000/7m
B
1200m
C
8000/7m
D
8000/3m

Question 31

+12-3
The number of 3 digit integers that are multiple of 6 which can be formed by using the digits 1,2,3,4,5,6 without repetition is.
A
20
B
26
C
24
D
22

Question 32

+12-3
what is the value of lim⁡x→∞{\mathop{\lim }\limits_{x\to \infty }} -(x+1) (1ex+1−1)?\left(\frac{1}{ex+1} -1\right)?
A
0
B
-1
C
1
D
Does not exist

Question 33

+12-3
The number of all even integers between 99 and 999 which are not multiple of 3 and 5 is
A
235
B
250
C
245
D
240

Question 34

+12-3
Let a⃗\vec{a}and c⃗\vec{c}be unt vectors such tgat the angle between them is cos⁡−1(14).\cos ^{-1} \left(\dfrac{1}{4} \right).ifb⃗\vec{b}=2c⃗\vec{c}+λ\lambda a⃗\vec{a}where λ\lambda >\mathrm{>}0 and |b⃗\vec{b}|=4, then λ\lambda is equal to
A
3
B
13\dfrac{1}{3}
C
14\dfrac{1}{4}
D
4

Question 35

+12-3
Let g: R→R{\rm R}\to {\rm R}& h: R→R{\rm R}\to {\rm R}, be two function such that h(x)=sgn (g(x)). Then select which of the following is not true ? (R{\rm R}denotes the set of all real numbers , sgn stands for sigum function)
A
h(x)is discontinuous at g(x)=0
B
The domain of h(x) is different from the domain of g(x) at the same point
C
The domn of h(x) is the same as the domain of g(x).
D
The domain of continuity of h(x) equal the domain of continuity of g(x)-{\mathrm{\{}x ∈R,\in {\rm R},g(x)=0}\mathrm{\}}

Question 36

+12-3
the maximum value of sin(x)+sin(x+1) is k cos 12\frac{1}{2} . Then the value of K is.
A
2
B
None of these
C
3
D
1

Question 37

+12-3
The value of ddx∫sin⁡x22sin⁡xet2dt\frac{d}{dx} \smallint _{\sin x^{2} }^{2\sin x} e^{t^{2} } dtat t = π\pi is
A
-2
B
1
C
-1
D
2

Question 38

+12-3
Given the equation x+y=1, x2{}^{2}+y2{}^{2}=2, x5{}^{5}+y5{}^{5}=A. let N be the number of solution pairs (x,y) to this system of equation. Then AN is eqal to
A
192\dfrac{19}{2}
B
192\dfrac{19}{2}
C
3
D
9

Question 39

+12-3
An equilateral triangle is inscribed in the parabola y2{}^{2}=x, one vertex of the triangle is at the vertex of the parabola. The centroid of triangle is
A
(2,0)
B
(1,0)
C
(2,0)\left(\sqrt{2} ,0\right)
D
(3,0)\left(\sqrt{3} ,0\right)

Question 40

+12-3
Number of three digit numbers that can be formed using 0,1,2,3 and 5 where these digit are allowed to repeat any number of times, is equal to
A
115
B
140
C
100
D
125

Question 41

+12-3
If B=sin2{}^{2}y+cos4{}^{4}y,then for all real y
A
1 ≤\le B ≤\le 2
B
34≤B≤1316\dfrac{3}{4} \le B\le \dfrac{13}{16}
C
34≤B≤\dfrac{3}{4} \le B\le 1
D
1316≤B≤\dfrac{13}{16} \le B\le 1

Question 42

+12-3
Let f:R→Rf:{\rm R}\to {\rm R}, be any function defined as f(x)={xasin⁡1xβ,x≠00,x=0α,β∈Rf(x)=\left\{\begin{array}{c} {x^{a} \sin \frac{1}{x^{\beta } } ,x\ne 0} \\ {\begin{array}{cc} {0} & {} \end{array},x=0} \end{array}\alpha ,\beta \in {\rm R}\right. . Which of the following is true ? (R{\rm R}denotes the set of all real numbers)
A
f(x) is continuous at x =10 for only a>\mathrm{>} 0 & β\beta >\mathrm{>}0
B
f(x) is differentiable at x =0 for all α\alpha >\mathrm{>}0 & β\beta >\mathrm{>}0
C
f(x) is continuous at x =0 for all α\alpha >\mathrm{>}0 & β∈R\beta \in {\rm R}
D
f(x) is continuous at x =0 for all α\alpha & β∈R\beta \in {\rm R}

Question 43

+12-3
if cos2{}^{2}(10∘{}^\circ )cos(20∘{}^\circ )cos(40∘{}^\circ )cos(50∘{}^\circ )cos(70∘{}^\circ )=a+316a+\frac{\sqrt{3} }{16} cos(10∘{}^\circ ),then 3a−1{}^{-1}is equal to
A
16
B
64
C
932\frac{9}{32}
D
916\frac{9}{16}

Question 44

+12-3
Let A = {\mathrm{\{}1, 2, 3, ..., 20}\mathrm{\}}. Let RCA x A such that R = {\mathrm{\{}(x, y): y = 2x7}\mathrm{\}}. Then the number of elements in R, is equal to
A
13
B
10
C
7
D
17

Question 45

+12-3
The angels of depression of the top and bottom of an 8m tall building from the top of a multi storied building are 30∘{}^\circ and 45∘{}^\circ respectively . what is the height of the multistoried. Building and the distance the two building ?
A
2(3+3)m,2(3+3)m2\left(3+\sqrt{3} \right)m,2\left(3+\sqrt{3} \right)m
B
2(3−3)m,4(3+3)m2\left(3-\sqrt{3} \right)m,4\left(3+\sqrt{3} \right)m
C
4(3+3)m,4(3+3)m4\left(3+\sqrt{3} \right)m,4\left(3+\sqrt{3} \right)m
D
4(2+2)m,4(2+2)m4\left(2+\sqrt{2} \right)m,4\left(2+\sqrt{2} \right)m

Question 46

+12-3
if α\alpha and β\beta are the roots of the equation x2{}^{2}+ax+b=0,(ab ≠\ne 0) then the quadratic equation with roots 1α3+α\frac{1}{\alpha ^{3} +\alpha } and 1β3+β\frac{1}{\beta ^{3} +\beta } is
A
b(b2+1+a2+2b)x2−(a3+a−3ab)x+1=0b\left(b^{2} +1+a^{2} +2b\right)x^{2} -\left(a^{3} +a-3ab\right)x+1=0
B
b(b2+1+a2−2b)x2+(a3+a−3ab)x+1=0b\left(b^{2} +1+a^{2} -2b\right)x^{2} +\left(a^{3} +a-3ab\right)x+1=0
C
b(b2+1+a2−2b)x2−(a3+a−3ab)x+1=0b\left(b^{2} +1+a^{2} -2b\right)x^{2} -\left(a^{3} +a-3ab\right)x+1=0
D
b(b2+1+a2+2b)x2+(a3−a−3ab)x+1=0b\left(b^{2} +1+a^{2} +2b\right)x^{2} +\left(a^{3} -a-3ab\right)x+1=0

Question 47

+12-3
The area enclosed between the curve y = sinx,y =cos c, 0 ≤\le x ≤\le π2\frac{\pi }{2} is
A
2 (2+1)\left(\sqrt{2} +1\right)
B
(2−1)\left(\sqrt{2} -1\right)
C
(2+1)\left(\sqrt{2} +1\right)
D
2(2−1)2\left(\sqrt{2} -1\right)

Question 48

+12-3
Let a⃗=2i−3j+4k,b⃗=i+2j−k\vec{a}=2i-3j+4k,\vec{b}=i+2j-kand b⃗=i−2j\vec{b}=i-2jand c⃗=3i−j\vec{c}=3i-j+ λk\lambda kbe the co-terminal edges of a parallelopiped whose volum is 5 unit . Then the value λ\lambda is
A
3
B
2
C
1
D
4

Question 49

+12-3
Let the line x4+y2\dfrac{x}{4} +\dfrac{y}{2} =1 meets the x-axis and y-axis at A and b, respectively. M is the midpoint of side AB, and M' is the image of the point M across the line x+y =1 , let the point P lie on the line x+y =1 such the the Δ\Delta ABP is an isosceles triangle with AP=BP. Then the distance between M' and P is
A
273\dfrac{2\sqrt{7} }{3}
B
73\dfrac{\sqrt{7} }{3}
C
253\dfrac{2\sqrt{5} }{3}
D
53\dfrac{\sqrt{5} }{3}

Question 50

+12-3
There are two coins , say blue and red . for blue coin, probability of getting head is 0.99 and for red coin , it is 0.01. One coin is chosen randomly and is tossed. The probability of getting head is
A
1
B
0.5
C
0.98
D
0.02

Question 51

+6-0.5
In a certain code language, the word "REASON" is encoded as TDDQSK. Using the same rule, how is the word PRAYER coded?
A
RQDWIO
B
RQDZCU
C
SSAYDU
D
RTBXCT

Question 52

+6-0.5
A number which, when increased by 15\% becomes 161. What is the original number?
A
135
B
145
C
130
D
140

Question 53

+6-0.5
In a remote research outpost, five scientists (dr. anand dr beena dr. chirag dr.dinesh, and dr. Elango) are studying a rare phenomenon. They communicate through a secure. Text-based system. Over the course of an hour , the following exchange occur: \newline 1. Dr. Anand sends a message to Dr. Beena and Dr. Chirug \newline 2. De Benna replies only to Dr. Anand \newline 3. Dr. Anand sends a reminder message to who did not reply \newline 4. Dr. Chirag sends a message to Dr. Dinesh and De. Elango \newline 5. While replying to De Chirag, Dr. Dinesh accidentally sends a "Reply All \newline 6. Dr. Elangs, having received Dr. Cinag's mensage, sends a message to Dir. Ben \newline At the end of this hour, who has recrowd the most messages directly from other scesitats within the group? (Consider culy sunssages sout within the described hour aud only between the five scieututs mentioned)
A
Dr. Chirag
B
Dr. Dinesh
C
Dr. Beena
D
Dr. Anand

Question 54

+6-0.5
At an IM entrepreneurship summit , two young founders- Karan and Deepak- introduced their startup. In their quirky opening, they said: "The product of our ages is 240. And just like in our startup strategy, twice Deepak's age is 4 year more than Karn's age How old was Deepak two years ago?
A
6 Years
B
8 Years
C
15 Years
D
10 Years

Question 55

+6-0.5
Consider the following statements followed by two conclusions. \newline Statements: 1. Some men are great. 2. Some men are wise \newline Conclusions: 1. Men are either great or wise. 2. Some men are neither great nor wise.
A
Only conclusion 2 is valid
B
Only conclusion 1 is valid
C
Neither of the conclusions is valid.
D
Both the conclusions are valid

Question 56

+6-0.5
In a certain code language, 'SUN' is written as 'RWK' and 'MOON' is written as 'LQLR'. Following the same pattern, how will 'STAR' be written?
A
RVXV
B
RUXV
C
SVXU
D
RUDY

Question 57

+6-0.5
A sum of money was divided into 2 parts in the ratio 2:5. First part was invested for 2 years at the annual interest rate of 20% compounded annually. At what rate of simple interest per annum the second part must be invested for 2 years, so that the interest earned in both cases is the same?
A
10.2%
B
8.8%
C
Cannot be determined
D
9.6%

Question 58

+6-0.5
If a number is increased by 30% and then decreased by 20%, what is the net change?
A
6% decrease
B
6% increase
C
4% increase
D
8% Increase

Question 59

+6-0.5
The percentage change in area of a rectangle by decreasing its length and increasing its breadth by 5\% is
A
0.25% decrease
B
no change
C
2.5% increase
D
0.25% increase

Question 60

+6-0.5
Read definition and all four choices carefully, and find the answer that provides the best example of the given definition. Answer the question solely on the basis of the definition given. \newline Definition: \newline An informal gathering occurs when a group of people get together in a casual, relaxed manner. \newline Which situation below is the best example of an informal gathering?
A
After finding about his promotion, Jeremy and a few coworkers decide to go out for a quick drink after work
B
Mary sends out 25 invitations for the bridal shower she is giving for her sister
C
The book club meets on the first Thursday evening of every month
D
Whenever she eats at the Italian restaurant, Kamalika seems to run into Peter

Question 61

+6-0.5
Which number replaces the question mark? \newline 3, 6, 18, 72, ?, 432
A
216
B
144
C
288
D
360

Question 62

+6-0.5
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30∘\mathrm{{}^\circ} degree and 45∘\mathrm{{}^\circ} respectively. If the lighthouse is 100 m high, the distance between the two ships is
A
173 m
B
273 m
C
200 m
D
300 m

Question 63

+6-0.5
Ten years ago, Ram was twice as old as Shyam. Ten years from now, the ratio of their ages will be 3:2. \newline What is Ram's present age?
A
50
B
60
C
70
D
40

Question 64

+6-0.5
Four people (P.Q.R & S) are standing in a queue. Q is ahead of P. R is between P and S. If S is at the end of the queue, who is at the front of the queue?
A
S
B
Q
C
P
D
R

Question 65

+6-0.5
Average Cost (AC) is defined as the sum of Average Fixed Cost (AFC) and Average Variable Cost (AVC), and dumping is defined as selling a product at a price less than AC but more than AVC A company in India, suddenly, found that the demand for its product "200M has fallen to 60% of the output produced in that financial year. As a result, the company must sell 40% of the produced output in a foreign market. If it decides to "dump" 40% of its output in a neighboring country (by reducing the price by 20%), what would be the objective of its 'dumping strategy, among the following? (The company has set a profit margin of 10% of AC while fh\'{a}ng the price of its product for sale in India) \newline (a) To minimize losses, (b) to maximize profits, (c) to contribute to the recovery of fixed costs, (d) to contribute to the recovery of variable costs
A
(b) and (d)
B
(a) and (c)
C
(a) and (b)
D
(b) and (c)

Question 66

+6-0.5
What comes next in the sequence? \newline 2, 6, 12, 20, 30,____\_\_\_\_
A
36
B
50
C
42
D
56

Question 67

+6-0.5
If 1st January 2022 was a Saturday, what day of the week will 1st January 2023 be?
A
Sunday
B
Monday
C
Wednesday
D
Tuesday

Question 68

+6-0.5
A group of 630 children is arranged in rows for a group photograph. Each row contains three fewer children than the row in front of it. What number of rows is not possible?
A
5
B
3
C
6
D
4

Question 69

+6-0.5
A person walks 8 km north, turns right, walks 4 km, turns right again and walks 6 km. Finally, he turus left and walks 3 km. How far is he from the starting point?
A
8.92 km
B
5.89 km
C
37.62 km
D
6.45 km

Question 70

+6-0.5
Five friends A,B,C,D and E are sitting in a row. The following conditions hold: \newline A is sitting next to B. \newline C is sitting at one of the ends. \newline D is sitting between A and E. \newline E is sitting to the right of D. \newline Who is sitting at the second position?
A
D
B
E
C
C
D
A

Question 71

+6-0.5
Statements: \newline I. The meteorological department predicts deficient rainfall during monsoon season \newline II. The GDP growth estimates have been revised downwards by the government. \newline Choose the correct option:
A
Statement I is the cause and Statement II is the effect
B
Both the statements I and II are effects of independent causes
C
Both the statements I and II are independent causes
D
Both the statements I and II are effects of some common cause

Question 72

+6-0.5
Statement: All engineers are good at math. \newline Conclusion 1: Some people good at math are engineers. \newline Conclusion 2: All people good at math are engineers.
A
Only Conclusion 2 follows
B
Both Conclusions follow
C
Neither follows
D
Only Conclusion 1 follows

Question 73

+6-0.5
Mohan introduced Sarita as the mother of his sister's brother. How is Sarita related to Mohan?
A
Sister
B
Mother
C
Aunt
D
Niece

Question 74

+6-0.5
"In order to be a teacher one must graduate from college. All poets are poor. Some Mathematicians are poets. No college graduate is poor."
A
Some teachers are not Mathematicians
B
Teachers are not poor
C
Poets are not teachers
D
Some Mathematicians are not teachers

Question 75

+6-0.5
Statements: \newline All apples are fruits. \newline All fruits are tasty. \newline Conclusions: \newline All apples are tasty. \newline Some tasty things are apples.
A
Only I follows
B
Only II follows
C
Both follow
D
Neither follows

Question 76

+6-0.5
A remote island has a unique social structure. Individuals are either Truth-tellers' (who always speak the truth) or 'Tricksters' (who always lie). You encounter three \newline inhabitants: X, Y, and Z. \newline X says: "Y is a Trickster." \newline Y says: "Exactly one of us is a Truth-teller:" \newline What can you definitively conclude about Z?
A
The information is insufficient to determine Z's identity
B
Z could be either a Truth-teller or a Trickster
C
Z is a Trickster
D
Z is a Truth-teller

Question 77

+6-0.5
If John's mother's father's granddaughter is Maria, what is Maria's relation to John?
A
Cousin
B
Niece
C
Aunt
D
Sister

Question 78

+6-0.5
If 1 man or 2 women can finish a job in 20 days, how may days will 3 men and women take to finish the same job?
A
6
B
3
C
4
D
5

Question 79

+6-0.5
A research team is studying the effects of three different fertilizers (X, Y, and Z) on the growth of a specific plant species. They have four experimental plots with different fertilizer combinations: \newline * Plot 1: Fertilizer X only \newline * Plot 2: Fertilizer Y only \newline * Plot 3: Fertilizer X and Fertilizer Z only \newline * Plot 4: Fertilizer Y and Fertilizer Z only \newline After a period of observation, they note the following: \newline Plants in plots with Fertilizer X showed significantly increased height compared to a control group (no fertilizer). \newline Plants in plots with Fertilizer Y showed a slightly increased leaf area compared to the control group \newline Plants in Plot 3 (X and 2) showed no significant difference in height compared to the control group \newline Plants in Plot 4 (Y and Z) showed significantly increased height compared to the control group. \newline Based on these observations, which of the following conclusions is best supported?
A
Fertilizer Z enhances the leaf area increase caused by Fertilizer Y.
B
Fertilizer Z has no effect on the growth of this plant species.
C
Fertilizer X is the only fertilizer that significantly increases the height of this plant species.
D
Fertilizer Z inhibits the height growth promoted by Fertilizer X.

Question 80

+6-0.5
A, B, C, D, E, F and Gare travelling in three different vehicles: Swift, Creta, and Nexon There are at least two passengers in each vehicle. Among them, only two are male. There are two engineers, two doctors and three teachers. \newline (i) C is a lady doctor and she does not travel with A and F, who are sisters. \newline (ii) B, a male engineer, travels with only G, a teacher, in a Swift. \newline (ii) Dis a male doctor \newline (iv) Two persons belonging to the same profession do not travel in the same vehicle. \newline (v) A is not an engineer and travels in a Creta. \newline (vi) The pair of sisters A and F travels in the same vehicle \newline What is the profession of F?
A
Teacher
B
Engineer
C
Doctor
D
Data Inadequate

Question 81

+6-0.5
Consider a sequence formed by concatenating the positive integers in increasing order 12345678910111213.. Which among the following is the closest to the 2028th digit in this infinite sequence?
A
4
B
1
C
9
D
7

Question 82

+6-0.5
A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slipa back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 8.00 am, at what time will he first touch a flag at 120 feet from the ground?
A
9 p.m
B
2.5 p.m.
C
6 p.m.
D
8 p.m.

Question 83

+6-0.5
Statements: \newline I. All cakes are ice cream \newline 11. No ice cream is chocolate \newline Conclusions: \newline L Some cakes are chocolate \newline II. No cake is chocolate \newline Choose the correct option:
A
Only conclusion II follows
B
Only conclusion I follow
C
Both conclusion I and conclusion II follows
D
Neither conclusion I nor conclusion II follows

Question 84

+6-0.5
Complete the next series: \newline 2 8 12 \newline 8 40 45 \newline 40 240 246 \newline …{\dots} …{\dots} …{\dots}
A
160,960,967
B
240,1680, 1687
C
200, 1000, 1005
D
48, 288, 295

Question 85

+6-0.5
A two digit miber is such that the product of its digits is 12. If 36 is added to the number, the digits interchange their places. What is the number?
A
24
B
38
C
25
D
26

Question 86

+6-0.5
Which word in the following is the "odd man" out?
A
Promoting
B
Nurturing
C
Pampering
D
Incubating

Question 87

+6-0.5
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
A
11/3
B
7/19
C
3/4
D
8/21

Question 88

+6-0.5
Which number replaces the question mark? 4, 9, 16, 25, ?,49
A
32
B
30
C
36
D
40

Question 89

+6-0.5
How many triangles are there in the figure given below?
Question 89 Image
A
32
B
24
C
21
D
13

Question 90

+6-0.5
What is the next number in each of the following 3 sequences?
Question 90 Image
A
254,968, 3689
B
213, 1534, 7635
C
267, 1823, 6759
D
238, 1846, 6389

Question 91

+6-1.5
Dynamic RAM (DRAM) stores each bit of data in a separate capacitor. Due to leakage, the stored charge tends to dissipate over time and needs to be refreshed periodically. Consider the following statements: \newline P: DRAM requires refreshing because it uses capacitors to store bits. \newline Q: SRAM does not require refreshing because it uses flip-flops instead of capacitors. \newline R: DRAM is faster than SRAM because it needs less frequent access. \newline S: DRAM is more suitable for main memory than SRAM due to its density.
A
P and S are true; Q and R are false.
B
Only P and Q are true; R is false, and S is irrelevant.
C
All statements P, Q, R, and S are true.
D
P, Q, and S are true; R is false.

Question 92

+6-1.5
Given an unsigned 32-bit integerx, which of the following C/C++ expressions correctly toggles m bits starting from position (with the least significant bit at position 0]? \newline Assume: x is the input integer; p is the starting position of the hit range (0-based, LSB at position 0); m is the number of bits to toggle; and No overflow or invalid input conditions occur. \newline Which of the following correctly toggles m bits of x starting from position p?
A
x∧\mathrm{\wedge}((1<\mathrm{<}<\mathrm{<}m)<\mathrm{<}<\mathrm{<}p)
B
x\& ∼\sim (((1<\mathrm{<}<\mathrm{<}m)-1)<\mathrm{<}<\mathrm{<}p)
C
x |((1<\mathrm{<}<\mathrm{<}m)<\mathrm{<}<\mathrm{<}p)
D
x∧\mathrm{\wedge} ∧\mathrm{\wedge} (((1<\mathrm{<}<\mathrm{<}m)-1)<\mathrm{<}<\mathrm{<}p)

Question 93

+6-1.5
Consider a 9-bit representation. Which of the following correctly gives the smallest number that can be represented in: (1) 1's completnent, (ii) 2's complement
A
(i)-255, (ii) -256
B
(i)-256, (ii) -255
C
(i)-256, (ii) -256
D
(i)-255, (ii)-255

Question 94

+6-1.5
Consider the Boolean expression X= (A+b),C‾\overline{\left(A+b\right),C} over two Boolean variables A and B. Which one of the following Boolean expressions is equivalent to the given Boolean expression X?
A
Aˉ.bˉ+Cˉ\bar{A}.\bar{b}+\bar{C}
B
Aˉ.Cˉ+Bˉ.Cˉ\bar{A}.\bar{C}+\bar{B}.\bar{C}
C
Aˉ.+Bˉ.Cˉ\bar{A}.+\bar{B}.\bar{C}
D
Aˉ.Bˉ+C\bar{A}.\bar{B}+C

Question 95

+6-1.5
Consider the Boolean function in a CPU control unit: \newline Y = (A+B.Cˉ).  (Aˉ.B+C)\left(A+B.\bar{C}\right).{\rm \; }\left(\bar{A}.B+C\right)
A
A⋅C+B⋅CˉA\cdot C+B\cdot \bar{C}
B
A⋅C+Aˉ⋅B:CˉA\cdot C+\bar{A}\cdot B:\bar{C}
C
A⋅B+CA\cdot B+C
D
A⋅C+Aˉ⋅B+B⋅CˉA\cdot C+\bar{A}\cdot B+B\cdot \bar{C}

Question 96

+6-1.5
Which of the following secondary storage devices has the fastest access time: Optical Drive, Magnetic Tape Drive, Hard Disk Drive (HDD), Solid State Drive (SDD)?
A
Hard Disk Drive (HDD)
B
Magnetic Tape Drive
C
Optical Drive
D
Solid State Drive (SDD)

Question 97

+6-1.5
Consider a system running under two types of workloads: (a) CPU-intensive jobs, (b) 1/0-intensive jobs. Which of the following statements about the relative performance of Interrupt-driven 1/0 and Programmed 1/0 is correct?
A
Interrupt-driven 1/0 performs better in both CPU-intensive and I/O-intensive workloads because it always reduces CPU involvement.
B
Programmed 1/0 performs better for CPU-intensive jobs, while interrupt-driven 1/0 performs better for 1/0-intensive jobs.
C
Interrupt-driven I/O performs better for CPU-intensive jobs by freeing the CPU, while programmed I/O performs better for I/O-intensive jobs due to tighter control.
D
Programmed I/O performs better in both CPU-intensive and I/O-intensive workloads because it gives the CPU full control.

Question 98

+6-1.5
Given the Boolean expression (AB) backslash (B ->\mathrm{>} C) , which of the following rows in the truth table would have an output of 1 (True)?
A
A = 1 B = 0 C = 1
B
A = 0 B = 0 C = 0
C
A = 1 B = 1 C = 1
D
A = 0 B = 1 C = 0

Question 99

+6-1.5
In an instruction execution pipeline, the earliest that the instruction TLB and data TLB can be accessed are
A
Fetch stage and memory stage respectively
B
Memory stage and execute stage respectively
C
Fetch stage and fetch stage respectively
D
Memory stage and memory stage respectively

Question 100

+6-1.5
Which of the following statements about ASCII and Unicode is correct?
A
ASCII uses 16 bits per character, while Unicode uses only 7 bits.
B
Unicode and ASCII are completely different and share no common characters.
C
ASCII can represent more characters than Unicode because it uses fewer bits per character.
D
Unicode is backward compatible with ASCII and includes all ASCII characters in its encoding.

Question 101

+6-1.5
In the design of a control unit of a processor, two common approaches are used: hardware control and microprogrammed control. Consider the following statements: \newline I. Hardware control units are generally faster but more difficult to modify than microprogrammed control units. \newline II. In a horizontal microprogrammed control unit, each control signal has a separate bit in the control word. \newline III. Vertical microprogramming leads to longer control words but provides greater parallelism. \newline IV. Microprogrammed control units are typically easier to implement and modify than hardware control units.
A
I, III, and IV only
B
I, II, and IV only
C
I, II, III, and IV
D
II, III, and IV only

Question 102

+6-1.5
Suppose that C represents the set of all countries, R represents the set of all countries that have at least one river flowing through it, M represents the set of all countries that have at least one mountain in it, and D represents the set of all countries that have at least one desert in it. It is given that ( R∪\cup M∪\cup D)=C. Which one of the following gives the set of all countries that have either a mountain or a river, but does not have a desert in it? The notation D ∧\mathrm{\wedge} c represents the complement of the set D with respect to the universal set C.
A
( R ∪\cup M)-(R ∩\cap M)
B
(R ∩\cap M) ∩\cap Dc{}^{c}
C
(R ∪\cup M)-(R ∩\cap M ∩\cap D c{}^{c})
D
(R ∪\cup M) ∩\cap Dc{}^{c}

Question 103

+6-1.5
In computer architecture, which of the following correctly matches the fundamental unit used in the CPU, cache, and main memory respectively?
A
CPU→\mathrm{\to} Block, Cache→\mathrm{\to} Page, Memory →\mathrm{\to} Word
B
CPU→\mathrm{\to} Word, Cache→\mathrm{\to} Block, Memory →\mathrm{\to}Page
C
CPU→\mathrm{\to} Page, Cache→\mathrm{\to} Word, Memory→\mathrm{\to} Block
D
CPU→\mathrm{\to} Block, Cache →\mathrm{\to} Word, Memory→\mathrm{\to} Page

Question 104

+6-1.5
Debugger is a program that
A
compiles source code to object code
B
links object code to produce an executable
C
allows to set breakpoints, execute a segment of program and display contents of Register
D
does not allow step by step execution of a segment of program

Question 105

+6-1.5
What is the hexadecimal representation of the decimal number 265
A
0x109
B
0x411
C
0x100001001
D
0x190

Question 106

+6-1.5
What is the equivalent decimal value of the unsigned binary number 10101.10101
A
1125.25
B
51.125
C
21.65625
D
25.375

Question 107

+6-1.5
In 8-bit two's complement arithmetic, compute the result of the following addition: A=10011001, B=11010111. What is the resulting 8-bit binary value?
A
01110001
B
Result is invalid
C
01110000
D
11100100

Question 108

+6-1.5
Match all items in Group 1 with correct options from those given in Group 2
Question 108 Image
A
R - 1 Q - 3 P - 2 S – 4
B
P - 2 Q - 3 R - 4 S - 1
C
Q - 2 P - 1 R - 3 S - 4
D
P - 4 Q - 2 R - 3 s - 1

Question 109

+6-1.5
Which of the following is the CORRECT truth table for the XOR Gate with two binary inputs A and B?
A
Option A Image
B
Option B Image
C
Option C Image
D
Option D Image

Question 110

+6-1.5
Consider a system with a CPU having 6 registers and 32-bit instructions. The maximum possible size of the main memory is 512 KB (1K=210{}^{10}). Each instruction takes two registers and one memory address as operands. Which one of the following correctly gives the maximum possible distinct instructions that can be there in the instruction set of the CPU?
A
1024
B
256
C
64
D
128

Question 111

+4-1
Identify the incorrect sentence based on the usage of the verb:
A
Their understanding of the problem was incorrect
B
They are understanding the problem.
C
It has clear ideas.
D
It's been raining since morning

Question 112

+4-1
The man and the dog________\_\_\_\_\_\_\_\_ appropriate form) (flee) through the forest. (fill in the blank with the most
A
were fleeing
B
flees
C
has fled
D
fleeing

Question 113

+4-1
Study the following sentence: The statue of Christ the Redeemer is located on Rio de Janeiro, the largest city of Brazil. (Which of the following parts of the sentence is grammatically incorrect)
A
The statue of Christ the Redeemer
B
on Rio de Janeiro
C
the largest city of Brazil
D
is located

Question 114

+4-1
After running around the city all day delivering invitations for the wedding, I desperately needed to hit the sack. (Identify the meaning of the underlined phrase):
A
To exercise for fitness
B
To watch television
C
To pack one's bags
D
To go to bed

Question 115

+4-1
Which of the following sentences uses the correct form of the verb "to lay"?
A
She has lain the keys on the counter.
B
She laid the book on the table.
C
She lays on the bed every night.
D
She is laying down for a nap.

Question 116

+4-1
Which of the following statements correctly explains the use of articles in the following sentence: After earning an MBA, Srinivas was able to approach a mathematical problem from both a business and analytical perspective.
A
"An MBA" uses the indefinite article an because it begins with a vowel sound, and "a mathematical problem" uses a because "mathematical" begins with a consonant sound.
B
Both articles are used incorrectly because "an MBA" should use a and "a mathematical problem" should use the.
C
"An MBA" should use a instead, because it refers to a specific degree, and "a mathematical problem" should use the to refer to a specific problem.
D
"An MBA" uses a because MBA is an acronym, and "a mathematical problem" should use the since it is referring to a unique or previously mentioned problem.

Question 117

+4-1
The new iPhone seems to cost everyone not just an arm and a leg, but also a kidney." What does "to cost an arm and a leg" mean?
A
To be very expensive
B
To be very cheap
C
To be very short-lived
D
To be afraid of surgery

Question 118

+4-1
Even though in official statements, the Presidential office has warned against violating the 25th protocol, the government's inaction against the Market group shows the government's tacit approval of the movement. (Choose the antonym of the underlined word):
A
Implicit
B
Undeclared
C
Unvoiced
D
Unequivocal

Question 119

+4-1
What is the synonym of `belligerent'?
A
Peaceful
B
Hostel
C
Bellyful
D
Equanimity

Question 120

+4-1
One of the employees. planning to transfer to another department
A
are
B
is
C
were
D
has
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