CUET Mathematics 2022 25 May Shift 1 PYQs

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

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

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

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

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:

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 :

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

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 :

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

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

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

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

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

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

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

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

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:

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:

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

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

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

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"/>

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

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

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

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

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

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:

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

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:

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

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:

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:

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:

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

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

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

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

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

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

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:

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

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:

Which of the following statements is NOT CORRECT.

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:

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

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

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

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

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