CUET Mathematics 2022 PYQs25 May Shift 1. Free, no login required.

Q1:

Algebra > Matrices & Determinants

Easy

common

If A is a square matrix of order 3, B = kA and |B| = $x$|A| then,

$x = 2k$

$x = k^2$

$x = k^3$

$x = 3k$

Correct Answer

Option 3

Correct Answer

Explanation

Q2:

Calculus > Application of Integrals

Easy

common

The area enclosed by the ellipse $\frac{x^2}{9^2} + \frac{y^2}{6^2} = 1$ is:

$15\pi$

$54\pi$

$18\pi$

$\frac{3}{2}\pi$

Correct Answer

Option 2

Correct Answer

Explanation

Q3:

Algebra > Linear Programming

Easy

common

The programming problem Max $Z = 2x + 3y$ subject to the conditions $0 \leq x \leq 3, 0 \leq y \leq 4$ is :

not an LPP

an LPP, with unbounded feasible region and no solution

an LPP, and Max $Z = 18$, at $x = 3, y = 4$

an LPP, and Max $Z = 12$, at $x = 0, y = 4$

Correct Answer

Option 3

Correct Answer

Explanation

Q4:

Calculus > Differential Equations

Easy

common

The differential equation $\frac{dy}{dx} + \frac{x}{y} = 0$, represents the family of curves:

$x^2 - y^2 = C$

$\frac{x}{y} = C$

$xy = C$

$x^2 + y^2 = C$

Correct Answer

Option 4

Correct Answer

Explanation

Q5:

Calculus > Application of Derivatives

Easy

common

Match List I with List II | LIST I | LIST II | |---|---| | A. Maximum value of $f(x) = -\lvert x+1 \rvert + 3$ | I. 6 | | B. Minimum value of $f(x) = (2x-1)^2 + 5$ | II. 5 | | C. Maximum value of $f(x) = 6 - x^2$ | III. no maximum value | | D. Maximum value of $f(x) = x^3 + 1$ | IV. 3 | Choose the correct answer from the options given below:

A-IV, B-II, C-I, D-III

A-III, B-IV, C-I, D-II

A-I, B-II, C-III, D-IV

A-II, B-III, C-IV, D-I

Correct Answer

Option 1

Correct Answer

Explanation

Q6:

Algebra > Probability

Easy

common

In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Then, E (X) is :

$\frac{7}{10}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{7}{11}$

Correct Answer

Option 1

Correct Answer

Explanation

Q7:

Calculus > Integrals

Easy

common

$\int_{0}^{1.5} [x] dx$, where $[x]$ denotes the greatest integer function $\leq x$, is equal to :

$\frac{1}{4}$

$\frac{1}{2}$

$1$

$0$

Correct Answer

Option 2

Correct Answer

Explanation

Q8:

Algebra > Linear Programming

Easy

common

The solution of a LPP with basic feasible solutions (0, 0), (10, 0), (0, 20), (10, 15) and objective function Max $Z = 2x + 3y$ is :

$x = 0, y = 20$, Max $Z = 60$

$x = 10, y = 15$, Max $Z = 65$

$x = 10, y = 20$, Max $Z = 70$

$x = 15, y = 10$, Max $Z = 60$

Correct Answer

Option 2

Correct Answer

Explanation

Q9:

Calculus > Differential Equations

Easy

common

The degree of the differential equation $\left(1 + \frac{dy}{dx}\right)^4 = \left(\frac{d^2y}{dx^2}\right)^2$ is:

Correct Answer

Option 3

Correct Answer

Explanation

Q10:

Calculus > Continuity & Differentiability

Easy

common

If $y = \frac{1}{x+1}$, then $\frac{d^2y}{dx^2}$ at $x = 2$ is:

$\frac{2}{9}$

$\frac{3}{2}$

$\frac{2}{27}$

$\frac{3}{8}$

Correct Answer

Option 3

Correct Answer

Explanation

Q11:

Algebra > Matrices & Determinants

Easy

common

If matrix A is of order $2 \times 3$ and B of order $3 \times 2$, then

AB, BA both are defined and are equal

AB is defined but BA is not defined

AB is not defined but BA is defined

AB, BA are defined but are not equal

Correct Answer

Option 4

Correct Answer

Explanation

Q12:

Algebra > Matrices & Determinants

Easy

common

The matrix $A = \begin{bmatrix} 0 & 1 & -3 \\ -1 & 0 & 0 \\ 3 & 0 & 0 \end{bmatrix}$ is a

Diagonal matrix

Symmetric matrix

Skew-symmetric matrix

Scalar matrix

Correct Answer

Option 3

Correct Answer

Explanation

Q13:

Calculus > Application of Derivatives

Medium

common

If $f(x) = \frac{1}{1-x}$, then for $x > 1, f(x)$ is:

decreasing

constant

increasing

neither decreasing nor increasing

Correct Answer

Option 3

Correct Answer

Explanation

Q14:

Algebra > Probability

Easy

common

In a box containing 100 bulbs, 10 are defective. Then the probability, that out of a sample of 5 bulbs none is defective, is:

$10^{-1}$

$\left(\frac{1}{2}\right)^5$

$\left(\frac{9}{10}\right)^5$

$\left(\frac{9}{10}\right)$

Correct Answer

Option 3

Correct Answer

Explanation

Q15:

Algebra > Matrices & Determinants

Easy

common

If $\begin{vmatrix} 2 & 3-x \\ x & 1 \end{vmatrix} = 0$, then the values of $x$ are:

1 and 3

1 and 2

2 and 3

3 and 0

Correct Answer

Option 2

Correct Answer

Explanation

Q16:

Algebra > Relations & Functions

Easy

core

Let A = {1,2,3}. Consider the relation R = {(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}. Then R is

reflexive only

reflexive and transitive

symmetric and transitive

neither symmetric nor transitive

Correct Answer

Option 2

Correct Answer

Explanation

Q17:

Algebra > Relations & Functions

Medium

core

A manufacturer can sell $x$ items at a price of Rs $3x+5$ each. The cost price of $x$ items is Rs $x^2 + 5x$. If x is the number of items she should sell to get no profit and no loss, then:

$x = 10$

$x = 30$

$x = 0$

$x = -10$

Correct Answer

Option 3

Correct Answer

Explanation

Q18:

Geometry > 3D Geometry

Medium

core

The angle between the line $\frac{x+2}{3} = \frac{y-3}{2} = \frac{z+5}{6}$ and the plane $2x + 10y - 11z = 5$ is:

$\cos^{-1}\left(\frac{8}{21}\right)$

$\sin^{-1}\left(\frac{8}{21}\right)$

$\cos^{-1}\left(\frac{21}{82}\right)$

$\sin^{-1}\left(\frac{21}{82}\right)$

Correct Answer

Option 2

Correct Answer

Explanation

Q19:

Calculus > Differential Equations

Easy

core

Solution of $\frac{dy}{dx} = (1+x^2)(1+y^2)$ is:

$\tan^{-1} y = x + \frac{x^3}{3} + c$

$\tan^{-1} y = x - \frac{x^3}{3} + c$

$\tan^{-1} y = x^2 + \frac{x^3}{3} + c$

$\tan^{-1} y = x^2 - \frac{x^3}{3} + c$

Correct Answer

Option 1

Correct Answer

Explanation

Q20:

Algebra > Matrices & Determinants

Medium

core

If the matrix $A = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$, then $A^2$ is equal to:

$\begin{bmatrix} \cos 2\theta & \sin 2\theta \\ -\sin 2\theta & \cos 2\theta \end{bmatrix}$

$\begin{bmatrix} \cos^2\theta & \sin^2\theta \\ -\sin^2\theta & \cos^2\theta \end{bmatrix}$

$\begin{bmatrix} \cos\theta^2 & \sin\theta^2 \\ -\sin\theta^2 & \cos\theta^2 \end{bmatrix}$

$\begin{bmatrix} \cos\theta+\sin\theta & \cos\theta-\sin\theta \\ \sin\theta-\cos\theta & \cos\theta+\sin\theta \end{bmatrix}$

Correct Answer

Option 1

Correct Answer

Explanation

Q21:

Calculus > Differential Equations

Medium

core

Particular solution of the differential equation $\log\left(\frac{dy}{dx}\right) = x + y$, given that when $x = 0, y = 0$ is:

$e^x + e^{-y} = 2$

$e^{-x} + e^y = 2$

$e^x + e^y = 2$

$e^{-x} + e^{-y} = 2$

Correct Answer

Option 1

Correct Answer

Explanation

Q22:

Algebra > Linear Programming

Medium

core

The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are :<img src="https://balti.afterboards.in/uuDFz7SlhIgJEH7" width="400px"/>

$x + y \geq 50$ $2x + y \leq 80$ $x, y \geq 0$

$x + y \leq 50$ $2x + y \geq 80$ $x, y \geq 0$

$x + y \leq 50$ $2x + y \leq 80$ $x, y \geq 0$

$x + y \geq 50$ $2x + y \geq 80$ $x, y \geq 0$

Correct Answer

Option 3

Correct Answer

Explanation

Q23:

Calculus > Continuity & Differentiability

Medium

core

The derivative of $\sin(\tan^{-1} e^{2x})$ with respect to $x$ is:

$\frac{2e^{2x} \sin(\tan^{-1} e^{2x})}{1 + e^{4x}}$

$\frac{2e^{2x} \cos(\tan^{-1} e^{2x})}{1 + e^{4x}}$

$\frac{2e^{2x} \sin(\tan^{-1} e^{2x})}{1 + e^{x^2}}$

$\frac{2e^{2x} \cos(\tan^{-1} e^{2x})}{1 + e^{2x}}$

Correct Answer

Option 2

Correct Answer

Explanation

Q24:

Calculus > Application of Derivatives

Easy

core

The approximate volume of a cube of side a meters on increasing the side by 4% is:

$1.04 a^3$ m$^3$

$1.004 a^3$ m$^3$

$1.12 a^3$ m$^3$

$1.12 a^2$ m$^3$

Correct Answer

Option 3

Correct Answer

Explanation

Q25:

Algebra > Linear Programming

Medium

core

The feasible region of an LPP Max $Z = 3x + 2y$ subject to $x \geq 0, y \geq 0, x - 2y \leq 3$ is:

Bounded in first quadrant but has no solution

Unbounded in first quadrant but has a solution

Unbounded in first quadrant and has no solution

Bounded and has a solution $x = 0, y = 0, Z = 0$

Correct Answer

Option 3

Correct Answer

Explanation

Q26:

Algebra > Probability

Easy

core

Two dice are thrown simultaneously. If X denotes the number of sixes, then the variance of X is:

$\frac{5}{18}$

$\frac{7}{18}$

$\frac{1}{3}$

$\frac{2}{3}$

Correct Answer

Option 1

Correct Answer

Explanation

Q27:

Calculus > Application of Integrals

Medium

core

The area of the region bounded by the parabola $y^2 = 4ax$ and its latus rectum is:

$\frac{4a^2}{3}$ sq. units

$\frac{8a^2}{3}$ sq. units

$\frac{2a^2}{3}$ sq. units

$\frac{9a^2}{5}$ sq. units

Correct Answer

Option 2

Correct Answer

Explanation

Q28:

Geometry > Trigonometry

Medium

core

Match List I with List II | LIST I | LIST II | |---|---| | A. $\sin^{-1} x + \cos^{-1} x, x \in [-1,1]$ | I. $-\frac{\pi}{2}$ | | B. $\tan^{-1} \sqrt{3} - \cot^{-1}(-\sqrt{3})$ | II. $-\frac{\pi}{6}$ | | C. $\cos^{-1}\left(\cos\frac{13\pi}{6}\right)$ | III. $\frac{\pi}{2}$ | | D. $\sin^{-1}\left(-\frac{1}{2}\right)$ | IV. $\frac{\pi}{6}$ | Choose the correct answer from the options given below:

A-III, B-I, C-IV, D-II

A-IV, B-I, C-II, D-III

A-II, B-III, C-IV, D-I

A-I, B-II, C-III, D-IV

Correct Answer

Option 1

Correct Answer

Explanation

Q29:

Algebra > Matrices & Determinants

Medium

core

If the matrix $A = \begin{bmatrix} 0 & x+y & 1 \\ 3 & z & 2 \\ x-y & -2 & 0 \end{bmatrix}$ is skew-symmetric, then :

$x = 2, y = 1, z = 0$

$x = 2, y = 2, z = 0$

$x = -2, y = -1, z = 0$

$x = -2, y = -1, z = -1$

Correct Answer

Option 3

Correct Answer

Explanation

Q30:

Geometry > 3D Geometry

Hard

core

A. Equation of the line passing through the point (1, 2, 3) and parallel to the vector $3\hat{i} + 2\hat{j} - 2\hat{k}$ is $\frac{x-1}{3} = \frac{y-2}{2} = \frac{y-3}{-2}$. B. Equation of line passing through (1, 2, 3) and parallel to the line given by $\frac{x+3}{3} = \frac{4-y}{5} = \frac{z+8}{6}$ is $\frac{x-1}{3} = \frac{y-2}{5} = \frac{z+3}{6}$. C. Equation of line passing through the origin and (5, -2, 3) is $\frac{x}{5} = \frac{y}{-2} = \frac{z}{3}$. D. Equation of plane passing through the point (1, 2, 3) and perpendicular to the line with direction ratio's 2, 3, -1 is $2(x-1)+3(y-2)-1(z-3) = 0$. E. Equation of plane with intercepts 2, 3 and 4 on x, y and z-axis respectively is $2x + 3y + 4z = 1$. Choose the correct answer from the options given below:

A, E only

A, C, D only

C, D, E only

E only

Correct Answer

Option 2

Correct Answer

Explanation

Q31:

Algebra > Relations & Functions

Easy

core

If $f: R \to R$ is defined by $f(x) = \sin x + x$, then $f(f(x))$ is:

$2\sin x + 2x$

$\sin^2 x + x^2$

$\sin(\sin x + x) + \sin x + x$

$\sin^2 x + 2\sin x + x$

Correct Answer

Option 3

Correct Answer

Explanation

Q32:

Algebra > Matrices & Determinants

Medium

core

If $A = \begin{bmatrix} \cos\theta & \sin\theta & 0 \\ -\sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and B is a square matrix of order 3, then |AB| is equal to:

$|B|^2$

$|B|$

$\sin^2\theta |B|$

$\cos^2\theta |B|$

Correct Answer

Option 2

Correct Answer

Explanation

Q33:

Algebra > Vector Algebra

Medium

core

Match List I with List II | LIST I | LIST II | |---|---| | A. The area of parallelogram determined by vectors $2\hat{i}$ and $3\hat{j}$ | I. 2 | | B. The value of $(\hat{i} \times \hat{j}) \cdot \hat{k} + (\hat{j} \times \hat{k}) \cdot \hat{i}$ | II. 4 | | C. The value of a for which the vectors $2\hat{i} - 3\hat{j} + 4\hat{k}$ and $a\hat{i} - 6\hat{j} + 8\hat{k}$ are collinear. | III. 0 | | D. The value of $\lambda$ for which the vectors $2\hat{i} + \hat{j} + \hat{k}$ and $2\hat{i} - 4\hat{j} + \lambda\hat{k}$ are perpendicular | IV. 6 | Choose the correct answer from the options given below:

A-I, B-II, C-III, D-IV

A-II, B-I, C-III, D-IV

A-III, B-IV, C-II, D-I

A-IV, B-I, C-II, D-III

Correct Answer

Option 4

Correct Answer

Explanation

Q34:

Algebra > Matrices & Determinants

Easy

core

If three points $A(a_1, b_1), B(a_2, b_2)$ and $C(a_3, b_3)$ are collinear and $D = \begin{vmatrix} a_1 & b_1 & 1 \\ a_2 & b_2 & 1 \\ a_3 & b_3 & 1 \end{vmatrix}$, then:

$D = 0$

$D = \pm 1$

$D^2 = 0$ or $1$

$D = (a_1 + a_2 + a_3) - (b_1 + b_2 + b_3)$

Correct Answer

Option 1

Correct Answer

Explanation

Q35:

Calculus > Application of Integrals

Easy

core

The area of the region bounded by the lines $x = 2y + 3, x = 0, y = 1$ and $y = -1$ is:

4 sq. units

6 sq. units

8 sq. units

$\frac{3}{2}$ sq. units

Correct Answer

Option 2

Correct Answer

Explanation

Q36:

Calculus > Integrals

Hard

core

$\int \left(\frac{1+x+x^2}{1+x^2}\right) e^{\tan^{-1} x} dx =$

$x + e^{\tan^{-1} x} + c$

$e^{\tan^{-1} x} - x + c$

$e^{\tan^{-1} x} + c$

$x e^{\tan^{-1} x} + c$

Correct Answer

Option 4

Correct Answer

Explanation

Q37:

Geometry > Trigonometry

Easy

core

Value of $\frac{e^{\sin(\tan^{-1} x + \cot^{-1} x)}}{e^{\sin(\sin^{-1} x + \cos^{-1} x)}}, x \in [-1, 1]$, is:

$0$

$\frac{\pi}{2}$

$1$

$-\frac{\pi}{2}$

Correct Answer

Option 3

Correct Answer

Explanation

Q38:

Calculus > Continuity & Differentiability

Hard

core

If $\sqrt{1-x^2} + \sqrt{1-y^2} = a(x-y)$, then $\frac{dy}{dx} =$

$\sqrt{\frac{1-x^2}{1-y^2}}$

$\sqrt{\frac{1-y^2}{1-x^2}}$

$\sqrt{\frac{1-x^2}{1+y^2}}$

$\sqrt{\frac{1+x^2}{1-y^2}}$

Correct Answer

Option 2

Correct Answer

Explanation

Q39:

Algebra > Matrices & Determinants

Easy

core

If A is a square matrix of order 3, then |adj A| is equal to:

$|A|$

$|A|^2$

$|A|^3$

$3|A|$

Correct Answer

Option 2

Correct Answer

Explanation

Q40:

Calculus > Application of Derivatives

Medium

core

The maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 27$ is:

Correct Answer

Option 2

Correct Answer

Explanation

Q41:

Calculus > Integrals

Hard

core

Match List I with List II | LIST I | LIST II | |---|---| | A. $\int \frac{\sin x}{1 + \cos x} \, dx$ | I. $e^{\tan^{-1} x} + C$ | | B. $\int \frac{1}{1 - \tan x} \, dx$ | II. $\log(\log x + 1) + C$ | | C. $\int \frac{e^{\tan^{-1} x}}{1 + x^2} \, dx$ | III. $-\log\lvert 1+\cos x \rvert + C$ | | D. $\int \frac{1}{x + x \log x} \, dx$ | IV. $\frac{x}{2} - \frac{1}{2}\log\lvert \cos x - \sin x \rvert + C$ | Choose the correct answer from the options given below:

A-II, B-III, C-IV, D-I

A-III, B-IV, C-I, D-II

A-I, B-II, C-III, D-IV

A-IV, B-I, C-III, D-II

Correct Answer

Option 2

Correct Answer

Explanation

Q42:

Calculus > Continuity & Differentiability

Medium

core

The function $f(x) = \frac{x-1}{x(x^2-1)}, x \neq 1, f(1) = 1$, is discontinuous at

Exactly one point

Exactly two points

Exactly three points

No point

Correct Answer

Option 3

Correct Answer

Explanation

Q43:

Algebra > Probability

Easy

core

Probabilities to solve a specific problem by A, B and C are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. Probability that at least one will solve the problem is:

$\frac{1}{24}$

$\frac{1}{4}$

$\frac{23}{24}$

$\frac{3}{4}$

Correct Answer

Option 4

Correct Answer

Explanation

Q44:

Algebra > Matrices & Determinants

Easy

core

Which of the following statements is NOT CORRECT.

A row matrix has only one row.

A diagonal matrix has all diagonal elements equal to zero.

A symmetric matrix is a square matrix satisfying certain conditions.

A skew-symmetric matrix has all diagonal elements equal to zero.

Correct Answer

Option 2

Correct Answer

Explanation

Q45:

Geometry > 3D Geometry

Easy

core

If a line makes angles 90 degree, 60 degree and $\theta$ with $x, y$ and $z$ axis respectively, where $\theta$ is acute, then value of $\theta$ is:

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

Correct Answer

Option 1

Correct Answer

Explanation

Q46:

Algebra > Relations & Functions

Easy

core

The range of the function $f(x) = \frac{1}{3 - \sin 4x}$ is:

$\left[\frac{1}{4}, \frac{1}{2}\right]$

$\left[\frac{1}{2}, 1\right]$

$\left[\frac{1}{4}, \frac{3}{4}\right]$

$\left[\frac{1}{2}, \frac{3}{4}\right]$

Correct Answer

Option 1

Correct Answer

Explanation

Q47:

Calculus > Application of Derivatives

Medium

core

The equation of the tangent, to the curve $y = x^2 - 2x - 3$ which is perpendicular to the line $x + 2y + 3 = 0$, is

$4x - 2y = 7$

$2x - y = 7$

$2x - y = 5$

$4x - 2y = 5$

Correct Answer

Option 2

Correct Answer

Explanation

Q48:

Calculus > Differential Equations

Medium

core

The solution of the differentiable equation $2x\frac{dy}{dx} + y = 14x^3, x > 0$, is

$y = 2x^3 + c x^{\frac{1}{2}}$

$y = x^3 + c x^{\frac{1}{2}}$

$y = 2x^3 + c x^{-\frac{1}{2}}$

$y = x^3 + c x^{-\frac{1}{2}}$

Correct Answer

Option 3

Correct Answer

Explanation

Q49:

Algebra > Vector Algebra

Medium

core

Let the vectors $\vec{a} = \hat{i} - 3\hat{j} + 2\hat{k}, \vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ and $\vec{c} = 3\hat{i} + 5\hat{j} - 2\lambda\hat{k}$ be coplanar. Then $\lambda$ is equal to

$-1$

$1$

$-2$

$2$

Correct Answer

Option 4

Correct Answer

Explanation

Q50:

Algebra > Probability

Medium

core

A coin is tossed 7 times. The probability of getting at least 4 heads is:

$\frac{5}{8}$

$\frac{3}{4}$

$\frac{1}{4}$

$\frac{1}{2}$

Correct Answer

Option 4

Correct Answer

Explanation

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