Keam 2026 21st April Question Paper Question Paper with Solutions | KEAM Mock Test | JeeMate

Q 1MathematicsSection A • MCQsets and relations

+4 / -1

Let $R$ be a relation in $\mathbb{N}$ defined by $\{(x,y): x+3y=10, x,y \in \mathbb{N}\}$ . Then the range of $R$ is

A

\{1,2,3,4\}

B

\{2,3,4\}

C

\{1,3,4\}

D

\{1,2,3\}

E

\{1,3\}

Q 2MathematicsSection A • MCQfunctions

+4 / -1

The domain of $f(x) = \dfrac{x^2+1}{x^2+x+1}$ is

A

\mathbb{R}

B

\mathbb{R}-\{2\}

C

\mathbb{R}-\{1\}

D

\mathbb{R}-\{0\}

E

\mathbb{R}-\{1,-1\}

Q 3MathematicsSection A • MCQsets and relations

+4 / -1

Let $A$ and $B$ be two sets having 3 and 2 elements respectively. Then the number of subsets of $A \times B$ having at least three elements is

A

24

B

52

C

42

D

64

E

60

Q 4MathematicsSection A • MCQsets and relations

+4 / -1

The number of elements in the set $\{(x,y): 2x^2+3y^2=35, x,y \in \mathbb{Z}\}$ , where $\mathbb{Z}$ is the set of all integers, is

A

4

B

6

C

16

D

12

E

8

Q 5MathematicsSection A • MCQcomplex numbers

+4 / -1

If $|z+4| = 2|z+1|$ , where $z$ is a complex number, then $|z|$ is equal to

A

0

B

2

C

4

D

8

E

16

Q 6MathematicsSection A • MCQcomplex numbers

+4 / -1

If $z(3-i) = 2+i$ , then $z^2 =$

A

\dfrac{i}{2}

B

\dfrac{-i}{2}

C

\dfrac{1}{2}

D

\dfrac{-1}{2}

E

\dfrac{1+i}{2}

Q 7MathematicsSection A • MCQcomplex numbers

+4 / -1

The imaginary part of $\dfrac{1-i\sqrt{3}}{1+i\sqrt{3}}$ is

A

\dfrac{-1}{2}

B

\dfrac{1}{2}

C

\dfrac{\sqrt{3}}{2}

D

\dfrac{-\sqrt{3}}{2}

E

\dfrac{\sqrt{3}}{4}

Q 8MathematicsSection A • MCQcomplex numbers

+4 / -1

The sum of $i^2 + i^4 + \ldots$ upto 25 terms is equal to

A

0

B

i

C

-i

D

1

E

-1

Q 9MathematicsSection A • MCQsequences and series

+4 / -1

In a geometric progression of positive terms, if any term is equal to the sum of the next two terms, then the common ratio of the geometric progression is equal to

A

\dfrac{\sqrt{5}+1}{2}

B

\dfrac{\sqrt{5}-1}{2}

C

\dfrac{\sqrt{5}-1}{4}

D

\dfrac{\sqrt{5}+1}{4}

E

\dfrac{\sqrt{5}}{2}

Q 10MathematicsSection A • MCQsequences and series

+4 / -1

A geometric progression has an even number of terms. If the sum of all terms is five times the sum of all odd terms, then the common ratio is equal to

A

4

B

\dfrac{2}{5}

C

2

D

\dfrac{1}{5}

E

\dfrac{4}{5}

Q 11MathematicsSection A • MCQsequences and series

+4 / -1

If $a,b,c$ are three unequal numbers such that $a,b,c$ are in arithmetic progression and $b-a, c-b, a$ are in geometric progression, then $a:b:c$ is

A

3:4:5

B

1:2:3

C

1:3:2

D

2:1:3

E

1:4:3

Q 12MathematicsSection A • MCQsequences and series

+4 / -1

If three geometric means are inserted between 2 and 32, then the three numbers are

A

4,6,8

B

6,8,10

C

4,8,32

D

4,6,12

E

4,8,16

Q 13MathematicsSection A • MCQpermutations and combinations

+4 / -1

If $\dfrac{{}^nP_{r-1}}{a} = \dfrac{{}^nP_r}{b} = \dfrac{{}^nP_{r+1}}{c}$ , then

A

c^2 = b(a+c)

B

b^2 = a(a+b)

C

b^2 = a(b+c)

D

a^2 = b(a+c)

E

a^2 = c(a+b)

Q 14MathematicsSection A • MCQpermutations and combinations

+4 / -1

The number of ways in which we can choose a committee from 3 men and 6 women so that the committee includes at least two men and exactly twice as many women as men is

A

35

B

42

C

46

D

52

E

55

Q 15MathematicsSection A • MCQbinomial theorem

+4 / -1

If $\dfrac{1}{8!} + \dfrac{1}{9!} = \dfrac{x}{12!}$ , then the value of $x$ is equal to

A

100

B

80

C

90

D

72

E

120

Q 16MathematicsSection A • MCQpermutations and combinations

+4 / -1

There are two women participants in a badminton tournament. The number of games the men played between themselves exceeds by 12 the number of games they played with women. If each player played one game with each other, then the number of men in the tournament was

A

4

B

6

C

7

D

8

E

10

Q 17MathematicsSection A • MCQbinomial theorem

+4 / -1

If the 17th and 18th term in the expansion of $(2+x)^{50}$ are equal, then the value of $x$ is equal to

A

1

B

2

C

4

D

6

E

8

Q 18MathematicsSection A • MCQfunctions

+4 / -1

Let $f(x) = \begin{vmatrix} x & 1 \\ \sin 2\pi x & 2x^2 \end{vmatrix}$ . If $f(x)$ is an odd function, $f(-x) = g(x)$ and $\lambda f(1) g(1) = 4$ , then the value of $\lambda$ is equal to

A

1

B

-4

C

0

D

4

E

-1

Q 19MathematicsSection A • MCQmatrices and determinants

+4 / -1

The value of the determinant of the inverse of the matrix $\begin{bmatrix} -4 & -5 \\ 2 & 2 \end{bmatrix}$ is

A

\dfrac{1}{4}

B

\dfrac{1}{2}

C

\dfrac{-1}{4}

D

1

E

2

Q 20MathematicsSection A • MCQmatrices and determinants

+4 / -1

If $A = \begin{bmatrix} 3 & \lambda-3 \\ -1 & 1 \end{bmatrix}$ , $B = \begin{bmatrix} 3 & 2 \\ 2 & 1 \end{bmatrix}$ and $AB = \begin{bmatrix} 7 & 1 \\ -1 & -1 \end{bmatrix}$ , then $\lambda$ is equal to

A

2

B

4

C

6

D

7

E

8

Q 21MathematicsSection A • MCQmatrices and determinants

+4 / -1

If $A = \begin{bmatrix} 1 & 1 \\ 0 & i \end{bmatrix}$ and $A^{42} = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ , then $a+d$ is equal to

A

0

B

i

C

-i

D

1

E

-1

Q 22MathematicsSection A • MCQquadratic equations

+4 / -1

If $(x-1)(x^2-5x+7) < (x-1)$ , then $x$ belongs to

A

(-\infty,-1)\cup(2,3)

B

(-\infty,-1]\cup[2,3]

C

(-\infty,1)\cup(2,3)

D

(-\infty,1)\cup[2,3)

E

(-\infty,1)\cup(2,3]

Q 23MathematicsSection A • MCQquadratic equations

+4 / -1

The solution set of $\left|x+\dfrac{1}{x}\right| > 2$ is

A

\mathbb{R}

B

\mathbb{R}-\{0\}

C

\mathbb{R}-\{1,-1\}

D

\mathbb{R}-\{-1\}

E

\mathbb{R}-\{-1,0,1\}

Q 24MathematicsSection A • MCQtrigonometric ratios and identities

+4 / -1

Let $L$ be an arc of a circle which subtends $45^\circ$ at the centre. If the radius of circle is 4 cm, then the length of the $L$ in centimeter is

A

\dfrac{\pi}{6}

B

\pi

C

\dfrac{\pi}{4}

D

\dfrac{\pi}{2}

E

\dfrac{\pi}{3}

Q 25MathematicsSection A • MCQmatrices and determinants

+4 / -1

If $A = \begin{bmatrix} 1 & \sin\theta & 1 \\ -\sin\theta & 1 & \sin\theta \\ -1 & -\sin\theta & 1 \end{bmatrix}$ , $(0 \le \theta \le 2\pi)$ , then the minimum value of $|A|$ is

A

2

B

0

C

1

D

-1

E

4

Q 26MathematicsSection A • MCQtrigonometric equations

+4 / -1

If $\tan\left(\dfrac{\pi}{4}+\theta\right) = \dfrac{1}{2}$ , then the value of $\sin 2\theta$ is

A

\dfrac{-1}{5}

B

\dfrac{2}{5}

C

\dfrac{-3}{5}

D

\dfrac{4}{5}

E

1

Q 27MathematicsSection A • MCQtrigonometric ratios and identities

+4 / -1

If $1+\cos x = \alpha$ , $0 \le x \le \dfrac{\pi}{2}$ , then $\sin\dfrac{x}{2}$ is equal to

A

\sqrt{\dfrac{2+\alpha}{2}}

B

\sqrt{\dfrac{2-\alpha}{2}}

C

\sqrt{2-\dfrac{\alpha}{2}}

D

\sqrt{\dfrac{1+\alpha}{2}}

E

\sqrt{\dfrac{1-\alpha}{2}}

Q 28MathematicsSection A • MCQinverse trigonometric functions

+4 / -1

The value of $\cos^{-1}\left(\dfrac{-\sqrt{3}}{2}\right) + \sin^{-1}\left(\dfrac{1}{2}\right)$ is equal to

A

\dfrac{\pi}{3}

B

\dfrac{\pi}{4}

C

\dfrac{\pi}{6}

D

\dfrac{\pi}{2}

E

\pi

Q 29MathematicsSection A • MCQinverse trigonometric functions

+4 / -1

The value of $2\tan^{-1}\left(\dfrac{1}{3}\right) + \cot^{-1}\left(\dfrac{3}{4}\right) =$

A

\dfrac{\pi}{3}

B

\dfrac{2\pi}{3}

C

\dfrac{\pi}{4}

D

\dfrac{\pi}{6}

E

\dfrac{\pi}{2}

Q 30MathematicsSection A • MCQinverse trigonometric functions

+4 / -1

If $\alpha$ and $\beta$ are respectively the minimum and maximum values of $\dfrac{\pi^2}{8} + 2\left(\sin^{-1}x - \dfrac{\pi}{4}\right)^2$ , then $\dfrac{\beta}{\alpha} =$

A

10

B

4

C

6

D

2

E

12

Q 31MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

If the points $(3,-2),(a,2),(8,8)$ are collinear, then the value of $a$ is

A

0

B

2

C

4

D

5

E

6

Q 32MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

If the slope of the line joining the points $(3,4)$ and $(-2,a)$ is equal to $\dfrac{-2}{5}$ , then the value of $a$ is equal to

A

0

B

2

C

3

D

4

E

6

Q 33MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

The distance of the point $P(1,-3)$ from the line $2y-3x=4$ is

A

\sqrt{13}

units

B

13 units

C

7 units

D

\sqrt{7}

units

E

2\sqrt{13}

units

Q 34MathematicsSection A • MCQparabola

+4 / -1

The line $x-1=0$ is the directrix of the parabola, $y^2-kx+8=0$ . Then, the values of $k$ are

A

8,4

B

8,-4

C

-8,-4

D

8

E

-8,4

Q 35MathematicsSection A • MCQparabola

+4 / -1

The length of the latus rectum of $x^2=-9y$ is equal to

A

9 units

B

\dfrac{3}{2}

units

C

4 units

D

3 units

E

\dfrac{9}{4}

units

Q 36MathematicsSection A • MCQcircle

+4 / -1

The centre and radius of the circle $x^2+y^2-2x+4y=8$ respectively are

A

(1,2),\sqrt{13}

B

(-1,2),\sqrt{13}

C

(-1,-1),\sqrt{13}

D

(1,-2),\sqrt{13}

E

(2,1),\sqrt{13}

Q 37MathematicsSection A • MCQellipse

+4 / -1

If the length of the major axis of an ellipse is thrice the length of the minor axis, then its eccentricity is equal to

A

\dfrac{2\sqrt{2}}{3}

B

\dfrac{\sqrt{2}}{\sqrt{3}}

C

\dfrac{1}{2}

D

\dfrac{1}{\sqrt{2}}

E

\dfrac{1}{2\sqrt{2}}

Q 38MathematicsSection A • MCQvector algebra

+4 / -1

Let $\vec{a},\vec{b},\vec{c}$ be such that $\vec{a}+\vec{b}+\vec{c}=\vec{0}$ . If $|\vec{a}|=3, |\vec{b}|=4, |\vec{c}|=5$ , then $|\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}| =$

A

20

B

24

C

25

D

30

E

35

Q 39MathematicsSection A • MCQvector algebra

+4 / -1

If $\theta$ is the angle between two vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}|=7, |\vec{b}|=1$ and $|\vec{a}\times\vec{b}|^2 = k^2 - (\vec{a}.\vec{b})^2$ , then the value(s) of $k$ is/are

A

5

B

-5

C

3

D

-3

E

\pm 7

Q 40MathematicsSection A • MCQvector algebra

+4 / -1

If $O$ is the origin and $C$ is the midpoint of $A(-2,1)$ and $B(4,-3)$ , then $\vec{OC}$ is

A

\hat{i}+\hat{j}

B

-\hat{i}-\hat{j}

C

\dfrac{1}{2}\hat{i}+\dfrac{1}{2}\hat{j}

D

\hat{i}-\hat{j}

E

-\hat{i}+\hat{j}

Q 41MathematicsSection A • MCQvector algebra

+4 / -1

If $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ , then the projection of $\vec{a}$ on $\vec{b}$ is

A

\sqrt{3}

B

\dfrac{1}{\sqrt{3}}

C

\dfrac{-1}{\sqrt{3}}

D

-\sqrt{3}

E

\dfrac{1}{3}

Q 42MathematicsSection A • MCQ3d geometry

+4 / -1

If the lines $\dfrac{2x-1}{2}=\dfrac{3-y}{1}=\dfrac{z-1}{3}$ and $\dfrac{x+3}{2}=\dfrac{y+2}{5}=\dfrac{z+1}{a}$ are perpendicular to each other, then the value of $a$ is equal to

A

\dfrac{1}{4}

B

\dfrac{3}{4}

C

\dfrac{1}{2}

D

2

E

1

Q 43MathematicsSection A • MCQ3d geometry

+4 / -1

The equation of straight line passing through $(a,b,c)$ and parallel to $x$ -axis is

A

\dfrac{x-a}{a}=\dfrac{y-b}{0}=\dfrac{z-c}{0}

B

\dfrac{x-a}{0}=\dfrac{y-b}{1}=\dfrac{z-c}{1}

C

\dfrac{x-a}{1}=\dfrac{y-b}{0}=\dfrac{z-c}{1}

D

\dfrac{x-a}{1}=\dfrac{y-b}{1}=\dfrac{z-c}{1}

E

\dfrac{x-a}{0}=\dfrac{y-b}{1}=\dfrac{z-c}{0}

Q 44MathematicsSection A • MCQ3d geometry

+4 / -1

The equation of a line passing through the point $(1,-2,3)$ and equally inclined to the axes are

A

x+1=y-2=z+3

B

x+1=y-2=z-3

C

x-1=y-2=z+3

D

x-1=y+2=z+3

E

x-1=y+2=z-3

Q 45MathematicsSection A • MCQ3d geometry

+4 / -1

The vector equation of the straight line $\dfrac{x-2}{3}=\dfrac{y+1}{2}=\dfrac{z-3}{2}$ is

A

(2\hat{i}-\hat{j}-3\hat{k}) + \mu(3\hat{i}-2\hat{j}-2\hat{k})

B

(2\hat{i}-\hat{j}+3\hat{k}) + \mu(3\hat{i}+2\hat{j}+2\hat{k})

, where

\mu

is a scalar.

C

(3\hat{i}-2\hat{j}-2\hat{k}) + \mu(2\hat{i}-\hat{j}-3\hat{k})

, where

\mu

is a scalar.

D

(3\hat{i}+2\hat{j}+2\hat{k}) + \mu(2\hat{i}-\hat{j}+3\hat{k})

, where

\mu

is a scalar.

E

(3\hat{i}+2\hat{j}+2\hat{k}) + \mu(2\hat{i}+\hat{j}+3\hat{k})

, where

\mu

is a scalar.

Q 46MathematicsSection A • MCQprobability

+4 / -1

A dice is thrown three times. If the first thrown is five, the probability of getting 14 as the sum is

A

\dfrac{1}{9}

B

\dfrac{1}{3}

C

\dfrac{2}{9}

D

\dfrac{2}{3}

E

\dfrac{1}{5}

Q 47MathematicsSection A • MCQstatistics

+4 / -1

If the variance of $1,2,3,\ldots,n$ is 10, then the value of $n$ is

A

5

B

9

C

11

D

13

E

15

Q 48MathematicsSection A • MCQprobability

+4 / -1

If $P(A)=\dfrac{1}{4}, P(B)=\dfrac{1}{5}$ and $P(A\cap B)=\dfrac{1}{8}$ , then $P(A'/B') =$ ( $A'$ and $B'$ denote the complements of A and B respectively)

A

\dfrac{27}{32}

B

\dfrac{23}{32}

C

\dfrac{25}{32}

D

\dfrac{21}{32}

E

\dfrac{29}{32}

Q 49MathematicsSection A • MCQstatistics

+4 / -1

We have two data sets each of size 5. The variances are 4 and 5 and the corresponding means are 2 and 4 respectively. Then the variance of the combined data set is

A

\dfrac{1}{2}

B

\dfrac{5}{2}

C

6

D

\dfrac{11}{2}

E

\dfrac{13}{2}

Q 50MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

The value of $\lim_{x\to 5}\left(\dfrac{25-x^2}{4-\sqrt{x^2-9}}\right)$ is

A

32

B

16

C

8

D

4

E

0

Q 51MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

The value of $\lim_{x\to 0}\dfrac{\sqrt{1-\cos 2x}}{|x|}$ is equal to

A

-2

B

-\sqrt{2}

C

\sqrt{2}

D

1

E

2

Q 52MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

The positive integer $n$ , such that $\lim_{x\to 3}\dfrac{x^n-3^n}{x-3}=108$

A

3

B

12

C

6

D

9

E

4

Q 53MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

Let $\lim_{x\to a} f(x)g(x)=16$ and $\lim_{x\to a}\dfrac{f(x)}{g(x)}=4$ . If both $\lim_{x\to a}f(x)$ and $\lim_{x\to a}g(x)$ exist, then $\lim_{x\to a}f[(x)+g(x)] =$

A

\pm 10

B

-16

C

\pm 2

D

16

E

\pm 4

Q 54MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

If $f(1)=2; f'(1)=1$ , then $\lim_{x\to 1}\left[\dfrac{xf(1)-f(x)}{x-1}\right] =$

A

0

B

-2

C

-1

D

2

E

1

Q 55MathematicsSection A • MCQdifferentiation

+4 / -1

Let $f(x)$ and $g(x)$ be twice differentiable functions defined on $[0,2]$ such that $f''(x)-g''(x)=0, f'(1)=4, g'(1)=2, f(2)=9, g(2)=3$ . At $x=3/2, f(x)-g(x) =$

A

2

B

3

C

5

D

8

E

10

Q 56MathematicsSection A • MCQdifferentiation

+4 / -1

If $y=\log\left(\sqrt{\dfrac{x-1}{x+2}}\right)$ , then $\dfrac{dy}{dx}=$

A

\dfrac{1}{2(x-1)(x+2)}

B

\dfrac{3}{2(x-1)(x+2)}

C

\dfrac{3}{(x-1)(x+2)}

D

\dfrac{1}{(x-1)(x+2)}

E

\dfrac{1}{3(x-1)(x+2)}

Q 57MathematicsSection A • MCQdifferentiation

+4 / -1

If $y=3^x+e^x+x^x+x^3$ , then $\dfrac{dy}{dx}$ at $x=3$ is equal to

A

e^3+27\log_e 3+54

B

e^3+27\log_e 3+27

C

e^3+54\log_e 3+27

D

e^3+54\log_e 3+54

E

e^3+54\log_e 3+54

Q 58MathematicsSection A • MCQdifferentiation

+4 / -1

If $y=\sin x + e^x$ , then $\dfrac{d^2x}{dy^2}$ is equal to

A

\dfrac{e^x-\sin x}{(\cos x+e^x)^2}

B

\dfrac{e^x+\sin x}{(\cos x+e^x)^2}

C

\dfrac{e^x-\sin x}{(\cos x+e^x)^3}

D

\dfrac{\sin x-e^x}{(\cos x+e^x)^2}

E

\dfrac{\sin x-e^x}{(\cos x+e^x)^3}

Q 59MathematicsSection A • MCQdifferentiation

+4 / -1

If $y=\log_{10}x+\log_e x$ , then $\dfrac{dy}{dx}$ is equal to

A

\dfrac{1-\log_{10}e}{x}

B

\dfrac{1+\log_e 10}{x}

C

x+\log_{10}e

D

x+\log_e 10

E

\dfrac{1}{x}\left[\dfrac{1}{\log_e 10}+1\right]

Q 60MathematicsSection A • MCQapplication of derivatives

+4 / -1

The function $f(x)=x^4-2x^2$ is strictly increasing on

A

(-2,0)

and

[1,\infty)

B

[-1,0]

and

[2,\infty)

C

[-1,0]

and

[1,\infty)

D

(-2,0]

and

[0,\infty)

E

[-2,0]

and

(1,\infty)

Q 61MathematicsSection A • MCQapplication of derivatives

+4 / -1

If the rate of increase of the radius of circle 5 cm/sec, then the rate of increase of its area when the radius is 20 cms, will be

A

10\pi\ cm^2/sec

B

20\pi\ cm^2/sec

C

100\pi\ cm^2/sec

D

200\pi\ cm^2/sec

E

400\pi\ cm^2/sec

Q 62MathematicsSection A • MCQapplication of derivatives

+4 / -1

If the function $f(x)=x^2+ax+1$ is increasing on $[1,2]$ , then $a$ is greater than or equal to

A

-2

B

-5

C

-4

D

-7

E

-3

Q 63MathematicsSection A • MCQapplication of derivatives

+4 / -1

The absolute maximum value of the function $f(x)=x^3-3x+2$ in $[0,2]$ is

A

0

B

1

C

2

D

3

E

4

Q 64MathematicsSection A • MCQindefinite integration

+4 / -1

If $\int \left(3t^2\sin\left(\dfrac{1}{t}\right)-t\cos\left(\dfrac{1}{t}\right)\right)dt = f(t)\sin\left(\dfrac{1}{t}\right)+c$ , then $f(2)$ is equal to

A

-2

B

2

C

4

D

8

E

16

Q 65MathematicsSection A • MCQindefinite integration

+4 / -1

If $\int \dfrac{2^{1/x}}{x^2}dx = k\,2^{1/x}+c$ , then $k$ is equal to

A

\dfrac{1}{\log 2}

B

\log 4

C

\dfrac{1}{\log 3}

D

\dfrac{-1}{\log 3}

E

\dfrac{-1}{\log 2}

Q 66MathematicsSection A • MCQindefinite integration

+4 / -1

$\int e^x\left(\dfrac{1-\sin x}{1-\cos x}\right)dx =$

A

e^x\cot x + C

B

-e^x\cot x + C

C

e^x\cot\dfrac{x}{2} + C

D

-e^x\cot\dfrac{x}{2} + C

E

2e^x\cot\dfrac{x}{2} + C

Q 67MathematicsSection A • MCQindefinite integration

+4 / -1

If $u=\int e^x\cos x\, dx, v=\int e^x\sin x\, dx$ , then $u+v =$

A

-u'+C

B

u'+C

C

-v'+C

D

v'+C

E

2v'+C

Q 68MathematicsSection A • MCQindefinite integration

+4 / -1

$\int \sin^3 x\, e^{\log\cos x}\, dx =$

A

\dfrac{\cos^4 x}{4}+C

B

\dfrac{-\cos^4 x}{4}+C

C

\dfrac{x\cos^4 x}{4}+C

D

\dfrac{\sin^4 x}{4}+C

E

\dfrac{-\sin^4 x}{4}+C

Q 69MathematicsSection A • MCQdefinite integration

+4 / -1

If $\int_a^b x^3\,dx=0$ and $\int_a^b x^2\,dx=\dfrac{2}{3}$ , then the values of $a$ and $b$ respectively are

A

1 and 1

B

0 and 1

C

1 and -1

D

-1 and 0

E

-1 and 1

Q 70MathematicsSection A • MCQdefinite integration

+4 / -1

$\int_{\pi/6}^{\pi/3} \dfrac{dx}{1+\sqrt{\tan x}} =$

A

\dfrac{\pi}{6}

B

\dfrac{\pi}{4}

C

\dfrac{\pi}{3}

D

\dfrac{\pi}{12}

E

\dfrac{\pi}{2}

Q 71MathematicsSection A • MCQarea under the curves

+4 / -1

The area of the region bounded by the lines, $y=x+2, x=0, x=1$ and $y=0$ is

A

2 sq.units

B

\dfrac{5}{2}

sq.units

C

\dfrac{9}{2}

sq.units

D

9 sq.units

E

12 sq.units

Q 72MathematicsSection A • MCQdefinite integration

+4 / -1

$\int_0^{\pi/4} \sqrt{1+\sin 2x}\, dx =$

A

1

B

\sqrt{2}+1

C

\sqrt{2}-1

D

1-\sqrt{2}

E

-\sqrt{2}

Q 73MathematicsSection A • MCQdifferential equations

+4 / -1

The solution of $(e^y+1)\cos x\, dx + e^y\sin x\, dy = 0$ is

A

(e^y+1)\sin x = C

B

(e^y+1)=C\sin x

C

e^y=C\sin x

D

(e^y-1)\sin x = C

E

(e^y+1)\cos x = C

Q 74MathematicsSection A • MCQdifferential equations

+4 / -1

The function $y=be^x+ae^{-x}$ , $a$ and $b$ are constants, is a solution of

A

y''+y=0

B

y''-y=0

C

y''+x=0

D

y''-2y=0

E

y''+xy=0

Q 75MathematicsSection A • MCQlinear programming

+4 / -1

Which one of the following point is not in a feasible region bounded by the inequalities $x\le 4, y\le 6, x+y\le 6, x\ge 0, y\ge 0$

A

(0,0)

B

(4,0)

C

(4,2)

D

(0,6)

E

(6,0)

Q 76PhysicsSection A • MCQunits and measurements

+4 / -1

A physical quantity that has the same dimensions as those of Boltzmann constant is

A

energy

B

bulk modulus

C

power

D

gas constant R

E

thermal conductivity

Q 77PhysicsSection A • MCQunits and measurements

+4 / -1

Taking into consideration of significant figures, in the conversion relation $2.0\ ms^{-2} = X\ km\, h^{-2}$ , the value of $X$ is

A

2.6\times 10^4

B

2.592\times 10^4

C

2\times 10^4

D

2.592\times 10^5

E

2.60\times 10^5

Q 78PhysicsSection A • MCQmotion in a plane

+4 / -1

A body starts moving from the origin along a straight line at a speed of $20\ kmh^{-1}$ for 1 hour. Then it turns perpendicular to its path and moves with the same velocity for 30 minutes. Then the magnitude of its displacement is

A

10 km

B

20 km

C

10\sqrt{5}

km

D

10\sqrt{2}

km

E

20\sqrt{5}

km

Q 79PhysicsSection A • MCQcircular motion

+4 / -1

If the angular speed of a particle moving in a circular path of radius 1.2 m is increased from $2\ rads^{-1}$ to $4\ rads^{-1}$ keeping its radius constant, then its linear speed is increased by

A

1.6\ ms^{-1}

B

2.4\ ms^{-1}

C

3.6\ ms^{-1}

D

4.8\ ms^{-1}

E

6\ ms^{-1}

Q 80PhysicsSection A • MCQmotion in a plane

+4 / -1

If the position vector of a particle is $\vec{r}=2t\hat{i}+\sqrt{3}t^2\hat{j}+5\hat{k}$ with $\vec{r}$ in $m$ and $t$ in $s$ , then at $t=1s$ the angle made by the velocity vector with $x$ -axis is

A

30^\circ

B

45^\circ

C

60^\circ

D

120^\circ

E

90^\circ

Q 81PhysicsSection A • MCQlaws of motion

+4 / -1

If the maximum acceleration of a moving platform to keep a box of mass 5 kg on it without sliding is $3\ ms^{-1}$ , then the static friction between the box and floor of the platform is $(g=10\ ms^{-2})$

A

0.15

B

0.25

C

0.30

D

0.35

E

0.4

Q 82PhysicsSection A • MCQlaws of motion

+4 / -1

If 10 identical silver coins each of mass $m$ are placed one over the other, then force on the $6^{th}$ coin from the bottom is

A

10 mg

B

8 mg

C

6 mg

D

4 mg

E

zero

Q 83PhysicsSection A • MCQcenter of mass

+4 / -1

A body initially at rest breaks up into two pieces of masses $M$ and $3M$ and move with a total kinetic energy of $E$ , then the kinetic energy of the piece of mass $M$ is

A

\dfrac{3E}{4}

B

\dfrac{E}{4}

C

\dfrac{2E}{3}

D

\dfrac{E}{3}

E

\dfrac{E}{2}

Q 84PhysicsSection A • MCQwork energy and power

+4 / -1

If a proton, a deuteron and an $\alpha$ -particle have the same speed, then the kinetic energy is

A

same for all particles

B

the lowest for proton

C

the highest for deuteron

D

same for proton and deuteron

E

the lowest for

\alpha

-particle

Q 85PhysicsSection A • MCQrotational motion

+4 / -1

The moment of inertia of a system of two masses 2 kg and 4 kg lying in the $x$ - $y$ plane at distances, 2 m and 4 m, respectively from the origin about the $z$ -axis is (in $kgm^2$ )

A

36

B

48

C

64

D

72

E

80

Q 86PhysicsSection A • MCQrotational motion

+4 / -1

A swimmer jumps from a height is able to increase the number of loops made in air by

A

stretching his legs outwards

B

decreasing angular velocity

C

by stretching his arms

D

by pulling his legs and arms inward

E

by pulling his legs inward and stretching his arms outward

Q 87PhysicsSection A • MCQgravitation

+4 / -1

The ratio of the weights of an object of mass m at a height $R$ and $2R$ from the surface of earth is ( $R$ is the radius of earth)

A

4:9

B

1:1

C

9:4

D

1:2

E

4:1

Q 88PhysicsSection A • MCQgravitation

+4 / -1

If the magnitude of gravitational potential energy of an object of mass 200 kg at a height of $3.6\times 10^6 m$ from the earth surface is $6\times 10^6 J$ , then its value at a height of $5.6\times 10^6 m$ is (Radius of earth is $6.4\times 10^6 m$ )

A

5\times 10^6 J

B

4\times 10^6 J

C

3\times 10^6 J

D

2\times 10^6 J

E

10^6 J

Q 89PhysicsSection A • MCQelasticity

+4 / -1

The force required to increase the length of a thin copper wire of cross-sectional area $0.1\ cm^2$ by 0.1% is (Young's modulus of copper is $11\times 10^{10}\ Nm^{-2}$ )

A

550 N

B

11\times 10^4 N

C

10.5\times 10^3 N

D

1100 N

E

5.5\times 10^3 N

Q 90PhysicsSection A • MCQfluid mechanics

+4 / -1

If a huge tank has a small side hole at a depth of 2 m from the surface of water, then the velocity of water flowing through the hole is $(g=10\ ms^{-2})$

A

2\sqrt{5}\ ms^{-1}

B

2\sqrt{10}\ ms^{-1}

C

\sqrt{10}\ ms^{-1}

D

4\sqrt{10}\ ms^{-1}

E

4\sqrt{5}\ ms^{-1}

Q 91PhysicsSection A • MCQthermal properties of matter

+4 / -1

Lakes and ponds freeze at the top surface with water below. This phenomenon is due to

A

high pressure at their bottom

B

low pressure at their bottom

C

the maximum density of water at

4^\circ C

D

the maximum density of water at

0^\circ C

E

elevation of freezing point of water

Q 92PhysicsSection A • MCQkinetic theory of gases

+4 / -1

If the temperature of 2 moles of krypton gas is increased from $-11^\\circ C$ to $89^\\circ C$ at constant volume, then (specific heat at constant volume of krypton is $C_V$ )

A

work done on the gas is not zero

B

internal energy is not changed

C

work is done by the gas

D

amount of heat added is

200\,C_V

E

internal energy is increased by

100\,C_V

Q 93PhysicsSection A • MCQheat and thermodynamics

+4 / -1

If an ideal heat engine with an efficiency of 40% rejects heat at $27^\\circ C$ , then it should have absorbed heat at

A

377^\circ C

B

500^\circ C

C

227^\circ C

D

427^\circ C

E

460^\circ C

Q 94PhysicsSection A • MCQkinetic theory of gases

+4 / -1

Two perfect monoatomic gases at temperatures 300 K and 410 K are mixed without any loss of heat. If $10^{24}$ and $10^{23}$ are the number of molecules in the respective gases, then the temperature of the mixture is

A

340 K

B

310 K

C

360 K

D

350 K

E

370 K

Q 95PhysicsSection A • MCQkinetic theory of gases

+4 / -1

If the temperature $T$ of oxygen molecule is raised to $9T$ , then its root mean square speed $v$ is increased to

A

3v

B

2v

C

\sqrt{2}v

D

\sqrt{3}v

E

\sqrt{\dfrac{3}{2}}v

Q 96PhysicsSection A • MCQsimple harmonic motion

+4 / -1

For a particle executing simple harmonic motion with amplitude $A$ and time period $T$ along $x$ -axis, the time taken by the particle to move from $x=0$ to $x=A$ is

A

\dfrac{T}{2}

B

\dfrac{T}{3}

C

\dfrac{T}{4}

D

\dfrac{T}{8}

E

\dfrac{T}{6}

Q 97PhysicsSection A • MCQwaves

+4 / -1

With Laplace correction in Newton's formula for the velocity of sound in gases, the velocity of sound in monoatomic gas at STP is

A

\sqrt{\dfrac{7P}{5\rho}}

B

\sqrt{\dfrac{5P}{3\rho}}

C

\sqrt{\dfrac{2P}{2\rho}}

D

\sqrt{\dfrac{7P}{2\rho}}

E

\sqrt{\dfrac{P}{\rho}}

Q 98PhysicsSection A • MCQelectrostatics

+4 / -1

A, B and C are three points in space forming an equilateral triangle of side 10 cm. If a point charge $8\ \mu C$ is placed at A, then the work done in moving a unit charge from B to C is

A

zero

B

720 J

C

7200 J

D

360 J

E

3600 J

Q 99PhysicsSection A • MCQcapacitor

+4 / -1

Three capacitors A, B, C with respective capacitance of $1\mu F$ , $2\mu F$ and $3\mu F$ are connected as shown. For a given voltage source $V$ connected across them, the combination that can store the maximum energy is

qImage--capacitor-electromagnetism-Jeemate

A

Capacitor A alone in one branch, in parallel with capacitors B and C connected in series in the other branch

B

Capacitors A and C connected in parallel with each other, and this combination connected in parallel with capacitor B

C

Capacitors A, B and C all connected in series

D

Capacitors A and B connected in series in one branch, in parallel with capacitor C alone in the other branch

E

Capacitors A, B and C all connected in parallel with each other

Q 100PhysicsSection A • MCQelectrostatics

+4 / -1

The equipotential surface of a system of two point charge $5\ \mu C$ and $-5\ \mu C$ at points A and B separated by 80 cm is a plane perpendicular to the line connecting A and B at

A

0.4 m from A

B

0.6 m from A

C

0.5 m from A

D

0.6 m from B

E

0.5 m from B

Q 101PhysicsSection A • MCQelectrostatics

+4 / -1

If an infinitely long uniformly charged wire produces an electric field of intensity $E$ at a distance of $d$ from it, then the linear charge density $\lambda$ of the wire is

A

\pi\epsilon_0 Ed

B

\dfrac{\pi}{2}\epsilon_0 Ed

C

\dfrac{1}{2}\epsilon_0 Ed

D

2\pi\epsilon_0 Ed

E

\epsilon_0 Ed

Q 102PhysicsSection A • MCQcurrent electricity

+4 / -1

The ratio of the rate of flow of electrons through three resistors connected in parallel to a voltage source $V$ is $3:2:1$ , then the ratio of their respective resistance values is

A

1:1:1

B

6:3:2

C

2:3:6

D

9:4:1

E

\sqrt{6}:\sqrt{4}:\sqrt{2}

Q 103PhysicsSection A • MCQcurrent electricity

+4 / -1

The ratio of the heat produced in a $2\Omega$ and a $4\Omega$ resistor connected in series with a voltage source of 12 V is

A

2:1

B

1:4

C

4:1

D

1:2

E

1:8

Q 104PhysicsSection A • MCQcurrent electricity

+4 / -1

Three cells of 3 V, 4 V and 4 V with respective internal resistances $0.5\Omega$ , $0.75\Omega$ and $0.75\Omega$ are connected in series to a resistor of $4\Omega$ . Then the current in the circuit is

qImage--current-electricity-electromagnetism-Jeemate

A

1 A

B

0.5 A

C

0.25 A

D

0.75 A

E

0.67 A

Q 105PhysicsSection A • MCQmoving charges and magnetism

+4 / -1

If a current carrying circular loop is suspended in a uniform magnetic field $B$ , then

A

a couple will act on the loop

B

the loop will start to rotate

C

areal vector of the loop will be set in the direction of

B

D

areal vector of the loop will be perpendicular to the direction of

B

E

loop will be deflected away from the field

B

Q 106PhysicsSection A • MCQmagnetism and matter

+4 / -1

In a uniform magnetic field $B$ , a bar magnet of magnetic moment $M$ is kept suspended at an angle of $60^\\circ$ with respect to $B$ . The work done to turn it from $60^\\circ$ to $90^\\circ$ with respect to the field is

A

MB

B

\sqrt{2}MB

C

0

D

2MB

E

\dfrac{MB}{2}

Q 107PhysicsSection A • MCQmoving charges and magnetism

+4 / -1

The flow of current of 2A through a straight solenoid of length 2 m produces a magnetic field of $2\pi\times 10^{-4}T$ at its centre. Then the number of turns in the solenoid is

A

600

B

500

C

3500

D

5000

E

700

Q 108PhysicsSection A • MCQmoving charges and magnetism

+4 / -1

A wire of length 4 m carrying a current of 1 A is bent to form a circular loop. The magnetic moment of the loop (in $Am^2$ ) is

A

\dfrac{4}{\pi^2}

B

\dfrac{2}{\pi^2}

C

\dfrac{2}{\pi}

D

\dfrac{4}{\pi}

E

4\pi

Q 109PhysicsSection A • MCQelectromagnetic induction

+4 / -1

The plane of a circular loop of area $150\ cm^2$ is perpendicular to a uniform magnetic field of 0.5 T. If the loop is turned such that its plane is in the direction of the field in 0.5 s, then the induced $emf$ produced is

A

25 mV

B

10 mV

C

2.5 mV

D

15 mV

E

7.5 mV

Q 110PhysicsSection A • MCQalternating current

+4 / -1

Two identical transformers A and B each with $\dfrac{N_p}{N_s}=2$ are connected such that the secondary output obtained from A is given as the primary input voltage for B. If the primary ac voltage of A is 200 V, then the secondary voltage from B is

A

100 V

B

200 V

C

50 V

D

400 V

E

500 V

Q 111PhysicsSection A • MCQelectromagnetic waves

+4 / -1

Microwaves are

A

used in radio and television communications

B

having frequency range from 54 MHz to 890 MHz

C

short wavelength radio waves

D

produced by hot bodies and molecules

E

absorbed by ordinary glass

Q 112PhysicsSection A • MCQray optics

+4 / -1

An object placed at 10 cm in front of a concave mirror of focal length of 8 cm gives image of magnification of

A

4

B

6

C

8

D

2

E

10

Q 113PhysicsSection A • MCQray optics

+4 / -1

The magnifying power of a telescope of length 76 cm in the normal adjustment is 75. Then the focal lengths of the objective and eyepiece lenses are, respectively,

A

50 cm, 25 cm

B

70 cm, 5 cm

C

75 cm, 1 cm

D

73 cm, 2 cm

E

60 cm, 15 cm

Q 114PhysicsSection A • MCQwave optics

+4 / -1

The fringe width obtained in a given Young's double slit experimental set up for red light, blue light and green light are, respectively, $\beta_R, \beta_B$ and $\beta_G$ . Then

A

\beta_B > \beta_R

B

\beta_R > \beta_G

C

\beta_G > \beta_R

D

\beta_B > \beta_R

E

\beta_R = \beta_B = \beta_G

Q 115PhysicsSection A • MCQdual nature of radiation

+4 / -1

If the de Broglie wavelength associated with an electron is 0.1227 nm, then its accelerating potential is

A

64 V

B

200 V

C

100 V

D

160 V

E

36 V

Q 116PhysicsSection A • MCQdual nature of radiation

+4 / -1

If a radiation of energy 5.2 eV falls on the photosensitive surfaces of Mo and Ni, they emit photoelectrons with maximum kinetic energy of 0.5 eV and 1 eV, respectively. Then the work function of

A

Mo is 2.6 eV

B

Ni is 6.2 eV

C

Mo is 6.2 eV

D

Ni is 4.2 eV

E

Mo is 4.2 eV

Q 117PhysicsSection A • MCQatoms and nuclei

+4 / -1

If a radioactive parent nucleus ${}^{236}_{94}X$ emits two alpha particles and two $\beta$ particles successively to reach the daughter nucleus ${}^a_bY$ , then the values of $a$ and $b$ are

A

224 and 90

B

220 and 94

C

228 and 92

D

230 and 92

E

226 and 92

Q 118PhysicsSection A • MCQatoms and nuclei

+4 / -1

The difference in magnitudes of angular momentum of the electrons revolving in $5^{th}$ Bohr's orbit and $3^{rd}$ Bohr's orbit of hydrogen atom is

A

\dfrac{2h}{\pi}

B

\dfrac{h}{\pi}

C

\dfrac{h}{2\pi}

D

\dfrac{3h}{2\pi}

E

\dfrac{5h}{2\pi}

Q 119PhysicsSection A • MCQsemiconductor devices and logic gates

+4 / -1

Intrinsic semiconductors Ge or Si doped with

A

indium becomes an n-type semiconductor

B

antimony becomes a p-type semiconductor

C

phosphorus becomes a n-type semiconductor

D

boron becomes a n-type semiconductor

E

arsenic becomes a p-type semiconductor

Q 120PhysicsSection A • MCQsemiconductor devices and logic gates

+4 / -1

Four ideal diodes D1, D2, D3, D4 are connected in a circuit with three $500\Omega$ resistors and a 10 V battery as shown in the figure. Then the current drawn from the battery is

qImage--semiconductor-devices-and-logic-gates-modern-physics-Jeemate

A

zero

B

10 mA

C

100 mA

D

50 mA

E

20 mA

Q 121ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

The empirical formula of a metal oxide which has 54% metal (M) and 46% oxygen (O) is (Atomic mass of M = 27 amu and O = 16 amu)

A

M_3O_2

B

MO_2

C

M_2O_3

D

M_2O_5

E

M_2O

Q 122ChemistrySection A • MCQatomic structure

+4 / -1

The threshold wavelength of a metal is 6000 $A^\circ$ . The work function of the metal is ( $h = 6.62\times 10^{-34}\ Js$ )

A

3.31\times 10^{19} J

B

3.31\times 10^{-19} J

C

13.2\times 10^{-19} J

D

13.2\times 10^{19} J

E

1.5\times 10^{-19} J

Q 123ChemistrySection A • MCQatomic structure

+4 / -1

The radius of the first orbit He $^+$ is

A

52.9 pm

B

13.24 pm

C

211.6 pm

D

105.8 pm

E

26.45 pm

Q 124ChemistrySection A • MCQatomic structure

+4 / -1

In Mosley experiment, the X-ray spectrum is obtained by plotting

A

square root of frequency vs atomic mass

B

square root of frequency vs atomic number

C

square of frequency vs atomic mass

D

square root of wavelength vs atomic number

E

square root of wavelength vs atomic mass

Q 125ChemistrySection A • MCQperiodic classification of elements

+4 / -1

Which of the following elements have the highest and the lowest first ionization enthalpy? (i) Be (ii) B (iii) C (iv) N (v) O

A

(ii) and (iv)

B

(i) and (v)

C

(i) and (iii)

D

(ii) and (iii)

E

(i) and (ii)

Q 126ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The correct increasing order of dipole moment of the following molecules is $NF_3, CHCl_3, NH_3, H_2O$

A

NF_3 < CHCl_3 < NH_3 < H_2O

B

NF_3 < CHCl_3 < H_2O < NH_3

C

H_2O < NF_3 < CHCl_3 < NH_3

D

CHCl_3 < NF_3 < H_2O < NH_3

E

NH_3 < NF_3 < CHCl_3 < H_2O

Q 127ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

The number of bonding pairs and lone pairs of electrons in $BrF_5$ molecule are respectively

A

4 and 2

B

3 and 2

C

4 and 1

D

5 and 1

E

3 and 1

Q 128ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

Which of the following bond has highest mean bond enthalpy?

A

N=N

B

O=O

C

N≡N

D

C≡C

E

C≡O

Q 129ChemistrySection A • MCQthermodynamics

+4 / -1

The correct increasing order of enthalpy of fusion of $\Delta_{fus}H^\circ$ (in kJ mol $^{-1}$ ) of the following compounds is $CH_3COCH_3, CCl_4, C_6H_6$

A

CH_3COCH_3 < CCl_4 < C_6H_6

B

CH_3COCH_3 < C_6H_6 < CCl_4

C

CCl_4 < C_6H_6 < CH_3COCH_3

D

CCl_4 < CH_3COCH_3 < C_6H_6

E

C_6H_6 < CH_3COCH_3 < CCl_4

Q 130ChemistrySection A • MCQionic equilibrium

+4 / -1

The solubility product, $K_{sp}$ of a sparingly soluble salt, $AX_2$ , is $3.2\times 10^{-14}\ mol^3 lit^{-3}$ . Its solubility is

A

4\times 10^{-3}\ mol\, lit^{-1}

B

2\times 10^{-2}\ mol\, lit^{-1}

C

2\times 10^{-5}\ mol\, lit^{-1}

D

8\times 10^{-4}\ mol\, lit^{-1}

E

2\times 10^{-3}\ mol\, lit^{-1}

Q 131ChemistrySection A • MCQionic equilibrium

+4 / -1

Match the correct pH value with the following substances: (a) Milk of magnesia (b) Black coffee (c) Egg white (d) Milk with (i) pH = 6.8 (ii) pH = 7.8 (iii) pH = 5 (iv) pH = 10

A

(a)-(iv), (b)-(ii), (c)-(i), (d)-(ii)

B

(a)-(iv), (b)-(ii), (c)-(iii), (d)-(i)

C

(a)-(i), (b)-(iv), (c)-(iii), (d)-(ii)

D

(a)-(i), (b)-(iii), (c)-(ii), (d)-(iv)

E

(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

Q 132ChemistrySection A • MCQelectrochemistry

+4 / -1

The $\Delta_rG^\circ$ of the galvanic cell in which the following cell reaction takes place, $2Cr_{(s)}+3Cd^{2+}_{(aq)} \to 2Cr^{3+}_{(aq)}+3Cd_{(s)}$ , is ( $E^\circ_{Cr^{3+}/Cr}=-0.74\ V$ and $E^\circ_{Cd^{2+}/Cd}=-0.40\ V$ )

A

-196.86\ kJ\,mol^{-1}

B

+196.86\ kJ\,mol^{-1}

C

-96.50\ kJ\,mol^{-1}

D

+96.50\ kJ\,mol^{-1}

E

+98.12\ kJ\,mol^{-1}

Q 133ChemistrySection A • MCQelectrochemistry

+4 / -1

The molar conductivity of a weak mono basic acid, HA at 298 K is $70\ Scm^2mol^{-1}$ . What is the percentage ionisation of HA at 298 K? [At infinite dilution $\lambda_{H^+}=340\ Scm^2mol^{-1}$ and $\lambda_{A^-}=80\ Scm^2mol^{-1}$ ]

A

8.35%

B

16.7%

C

20%

D

32.5%

E

15.3%

Q 134ChemistrySection A • MCQp block elements

+4 / -1

The percentage of helium present in air used by scuba divers is

A

56.2%

B

11.7%

C

32.1%

D

19.7%

E

21.5%

Q 135ChemistrySection A • MCQchemical kinetics

+4 / -1

A first order reaction follows the equation $k=(4\times 10^{10}\ s^{-1})e^{-2000/T}$ . The value of $E_a$ for the reaction is about ( $R=8.314\ JK^{-1}mol^{-1}$ )

A

17.4\ kJ\,mol^{-1}

B

18.5\ kJ\,mol^{-1}

C

17.5\ kJ\,mol^{-1}

D

16.6\ kJ\,mol^{-1}

E

17.8\ kJ\,mol^{-1}

Q 136ChemistrySection A • MCQchemical kinetics

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In a pseudo first order reaction, the following results were obtained: Time/s: 0,10,20,30,40,50,60; [A]/mol lit $^{-1}$ : 0.65,0.55,0.46,0.38,0.26,0.2,0.13. Average rate of the reaction between 20 and 40 seconds is

A

0.01\ mol\,lit^{-1}s^{-1}

B

0.02\ mol\,lit^{-1}s^{-1}

C

0.001\ mol\,lit^{-1}s^{-1}

D

0.1\ mol\,lit^{-1}s^{-1}

E

0.04\ mol\,lit^{-1}s^{-1}

Q 137ChemistrySection A • MCQd and f block elements

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Which of the following compound of manganese is a mixed oxide?

A

MnO

B

Mn_3O_4

C

Mn_2O_3

D

MnO_2

E

Mn_2O_7

Q 138ChemistrySection A • MCQcoordination compounds

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The formula of Pentaamminecarbonatocobalt(III)chloride is

A

[Co(NH_3)_5(CO)]Cl_2

B

[Co(NH_3)_5(CO_3)]Cl

C

[Co(NH_3)_5(CO)_3]Cl_2

D

[Co(NH_3)_5(CO_3)]Cl_2

E

[Co(NH_3)_5(CO_3)]Cl_3

Q 139ChemistrySection A • MCQcoordination compounds

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The correct increasing order of wavelength of absorption of the following complexes is (i) $[CoCl(NH_3)_5]^{2+}$ (ii) $[Co(NH_3)_5(H_2O)]^{3+}$ (iii) $[Co(NH_3)_6]^{3+}$ (iv) $[Co(CN)_6]^{3-}$

A

(i) < (ii) < (iii) < (iv)

B

(i) < (ii) < (iv) < (iii)

C

(ii) < (i) < (iv) < (iii)

D

(iv) < (iii) < (ii) < (i)

E

(iv) < (i) < (ii) < (iii)

Q 140ChemistrySection A • MCQsalt analysis

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When sodium fusion extract is treated with sodium nitroprusside, the appearance of violet colour is due to the formation of

A

[Fe(CN)_5NO]^{2-}

B

[Fe(CN)_5NO]^{2+}

C

[Fe(CN)_5NOS]^{4-}

D

[Fe(CN)_5NOS]^{2-}

E

[Fe(CN)_5NOS]^{2+}

Q 141ChemistrySection A • MCQhydrocarbons

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Which of the following gives 2-methylbutane on hydrogenation? (i) 2-methylbut-1-ene (ii) 3-methylbut-1-yne (iii) 2-methylbut-2-ene (iv) 3-methylbut-1-ene (v) pent-2-ene

A

(i) and (iii)

B

(ii), (iii), (iv)

C

(ii), (iii), (v)

D

(i), (ii), (v)

E

(i), (iii), (iv)

Q 142ChemistrySection A • MCQhydrocarbons

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An alkene, $C_3H_6$ (X), on treatment with HBr in presence of peroxide gives (Y). The compound (Y) on treatment with $AgNO_2$ in ethanol gives (Z). The compounds (X), (Y) and (Z) are respectively

A

propene, 1-bromopropane, 1-nitropropane

B

propene, 2-bromopropane, 2-nitropropane

C

propene, 2-bromopropane, 1-nitropropane

D

propyne, 1-bromopropane, 1-nitropropane

E

propene, 1,2-dibromopropane, 1,2-dinitropropane

Q 143ChemistrySection A • MCQhaloalkanes and haloarenes

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The reaction $CH_3Br + AgF \to CH_3F + AgBr$ is termed as

A

Stephen reaction

B

Swarts reaction

C

Sandmeyer reaction

D

Kolbe's reaction

E

Riemer-Tiemann reaction

Q 144ChemistrySection A • MCQalcohols phenols and ethers

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When 2-methylbutan-2-ol is treated with Lucas reagent con.HCl and $ZnCl_2$ at room temperature, the product obtained is

A

2-chlorobutane

B

2-chloro-2-methylbutane

C

1-chlorobutane

D

1-chloropentane

E

2-chloro-2-methylbutene

Q 145ChemistrySection A • MCQalcohols phenols and ethers

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The relative ease of dehydration of the following alcohols is (i) Propan-2-ol (ii) Propan-1-ol (iii) 2-Methylpropan-2-ol

A

(iii) > (ii) > (i)

B

(ii) > (i) > (iii)

C

(ii) > (iii) > (i)

D

(i) > (ii) > (iii)

E

(iii) > (i) > (ii)

Q 146ChemistrySection A • MCQaldehydes ketones and carboxylic acids

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Which of the following is a commercial method of manufacture of benzaldehyde?

A

Hydrogenation of benzoylchloride with Pd/BaSO4 as catalyst.

B

Oxidation of toluene with chromyl chloride followed by hydrolysis

C

Toluene is treated with Cr2O3 in acetic anhydride followed by hydrolysis

D

Side chain chlorination of toluene followed by hydrolysis.

E

Benzene is treated with CO and HCl in the presence of anhydrous AlCl3.

Q 147ChemistrySection A • MCQaldehydes ketones and carboxylic acids

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Vigorous oxidation of n-propylbenzene with alkaline potassium permanganate (KMnO4-KOH/ $\Delta$ ) followed by hydrolysis gives

A

phenol

B

phenyl acetic acid

C

phenyl propionic acid

D

benzaldehyde

E

benzoic acid

Q 148ChemistrySection A • MCQcompounds containing nitrogen

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The descending order of basic strength of the following amines is (i) N-Methylbenzenamine (ii) N,N'-Dimethylbenzenamine (iii) Benzenamine (iv) Phenylmethanamine

A

(i) > (ii) > (iv) > (iii)

B

(iv) > (i) > (ii) > (iii)

C

(iv) > (ii) > (i) > (iii)

D

(iv) > (iii) > (ii) > (i)

E

(i) > (iv) > (ii) > (iii)

Q 149ChemistrySection A • MCQcompounds containing nitrogen

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Benzene diazoniumchloride on treatment with HCl in the presence of copper powder gives chlorobenzene. This reaction is termed as

A

Sandmeyer reaction

B

Gatterman reaction

C

Stephen reaction

D

Gatterman Koch reaction

E

Etard reaction

Q 150ChemistrySection A • MCQbiomolecules

+4 / -1

Which of the following statements are true about sucrose? (i) It is a dissacharide (ii) It is a reducing sugar (iii) It is laevorotatory (iv) Sucrose on hydrolysis gives equimolar mixture of D(+) glucose and D-(-)fructose. (v) In sucrose, two monosacharides are held together by a glycosidic linkage

A

(i), (ii), (iii)

B

(i), (ii), (v)

C

(ii), (iii), (v)

D

(i), (iii), (v)

E

(i), (iv), (v)

KEAM 2026 21st April Question Paper with Solutions