CUET Mathematics 2023 15 June Shift 2 PYQs

Let $A = [a_{ij}]$ be a $2 \times 2$ matrix such that $a_{ij} = \frac{|-3i+j|}{2}$ then $a_{21}$ is :

If $A = \begin{bmatrix} -2 & 6 \\ -5 & -1 \end{bmatrix}$ then $A^{-1}$ is :

The value of $\begin{vmatrix} \sqrt{3}/2 & 1/2 \\ \sqrt{3}/2 & 1/2 \end{vmatrix}$

If A is a square matrix of order 3 such that $|A|=2$, then the value of $|adj(adj A)|$ is :

If $y = \log\left[\frac{x^2}{e^2}\right]$ then value of $\frac{d^2y}{dx^2}$ is :

The condition on a and b, such that for $y = \frac{a}{x} - \frac{b}{x^2}$, $\frac{dy}{dx} = 0$ at $x=1$ is :

The interval in which the function $f(x) = 10 - 6x - 2x^2$ is decreasing is :

Area of the region bounded by the curve $|x| + |y| = 1$ and x-axis is :

The value of the integral $\int_{2}^{4} \frac{x}{x^2+1} dx$ is :

The sum of order and degree of the differential equation $\frac{\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2y}{dx^2}} = p$ is :

The solution of the differential equation $\frac{dy}{dx} = \frac{6}{x^2}$; $y(1) = 3$ is :

The random variable X has a probability distribution P(X) of the following form, where k is some number. $P(X=x) = \begin{cases} k, & \text{if } x=0 \\ 2k, & \text{if } x=1 \\ 3k, & \text{if } x=2 \\ 0, & \text{otherwise} \end{cases}$ Then $P(x \leq 2)$ is :

The mean of the number of heads in a simultaneous toss of three coins is :

For the LPP Maximise $z = x + y$ subject to $x - y \leq -1$, $-x + y \leq 2$, $x, y \geq 0$, $z$ has :

Choose the wrong statement from the following :

Given relation $R = \{(x, y) : y = x + 5, x < 4, x, y \in N\}$. Where N is a set of natural numbers then :

Let $f : R \to R$ defined by $f(x) = 2x^3 - 7$ for $x \in R$. Then : (A) $f$ is one-one function (B) $f$ is many to one function (C) $f$ is bijective function (D) $f$ is into function Choose the correct answer from the options given below :

Match List - I with List - II. | List - I | List - II | |----------|-----------| | (A) Range of $y = \text{cosec}^{-1}x$ | (I) $R - (-1, 1)$ | | (B) Domain of $\sec^{-1}x$ | (II) $(0, \pi)$ | | (C) Domain of $\sin^{-1}x$ | (III) $[-1, 1]$ | | (D) Range of $y = \cot^{-1}x$ | (IV) $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right] - \{0\}$ | Choose the correct answer from the options given below :

Let $\tan^{-1}y = \tan^{-1}x + \tan^{-1}\left(\frac{2x}{1-x^2}\right)$. Then $y$ is :

The value of $2y - 3x$, if $2\begin{bmatrix} x & 5 \\ 7 & y-3 \end{bmatrix} + \begin{bmatrix} 3 & -4 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 7 & 6 \\ 15 & 14 \end{bmatrix}$ is :

Match List - I with List - II. If $A = \begin{vmatrix} 3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2 \end{vmatrix}$ | List - I | List - II | |----------|-----------| | (A) $M_{23}$ | (I) $-17$ | | (B) $A_{32} + a_{13}$ | (II) $-1$ | | (C) A | (III) 0 | | (D) $a_{13}A_{12} + a_{23}A_{22} + a_{33}A_{32}$ | (IV) 12 | Choose the correct answer from the options given below :

The number of square matrices of order 2 using numbers 1 and $-1$ exactly once and the number 0 twice is :

Let $\begin{vmatrix} 3x & -7 \\ 1 & 4 \end{vmatrix} = \begin{vmatrix} 3 & 2 \\ 4 & x \end{vmatrix}$, then value of $x$ is :

The value of the determinant $\begin{vmatrix} a\cos\theta & b\sin\theta & 0 \\ -b\sin\theta & a\cos\theta & 0 \\ 0 & 0 & c \end{vmatrix}$ is :

If the points (2, 1), $(-1, 4)$ and (a, 3) are collinear then the value/(s) of a is/(are) :

The points of discontinuity of the function f defined by $f(x) = \begin{cases} x+2 & x \leq 1 \\ x-2 & 1 < x < 2 \\ 0 & x \geq 2 \end{cases}$ are :

If $\cos y = x\cos(a+y)$, then $\frac{dy}{dx} = $

The value of C which satisfies Rolle's Theorem for $f(x) = \sin^4 x + \cos^4 x$ in $\left[0, \frac{\pi}{2}\right]$. Then C is :

Angle between tangents to the curve $y = x^2 - 5x + 6$ at the points (2, 0) and (3, 0) is :

The rate of change of the area of a circular disc with respect to its circumference when radius is 3 is :

The interval in which the $f(x) = \sin x - \cos x$, $0 \leq x \leq 2\pi$ is strictly decreasing is :

The value of $\int_{0}^{3} |2x - 6| dx$ is :

The integral $\int \frac{dx}{x^2(x^4+1)^{\frac{3}{4}}}$ equals __________.

The area of the shaded portion <img src="https://balti.afterboards.in/0Orw0ReJYISKyt0" width="300px"/> is :

Area of the region bounded by $y = -1$, $y = 2$, $x = y^3$ and $x = 0$ is :

The differential equation whose solution is $Ax^2 + By^2 = 1$ where A and B are arbitrary constant is of : (A) first order and first degree (B) second order and first degree (C) second order and second degree (D) second order Choose the correct answer from the options given below :

Integrating factor of the differential equation $(1 - y^2)\frac{dx}{dy} + xy = ay$ is :

Let $\vec{a} = 4\hat{i} - \hat{j} + 3\hat{k}$ and $\vec{b} = -2\hat{i} + \hat{j} - 2\hat{k}$. Then (A) $\vec{a}$ is a unit vector (B) $\vec{a} \times \vec{b} = -\hat{i} + 2\hat{j} + 2\hat{k}$ (C) $\vec{a}$ and $\vec{b}$ are parallel vectors (D) $\vec{a}$ and $\vec{b}$ are neither parallel nor perpendicular vectors Choose the correct answer from the options given below :

Let $\vec{a}$ and $\vec{b}$ be two unit vectors. If the vectors $\vec{c} = 5\vec{a} - 4\vec{b}$ and $\vec{d} = \vec{a} + 2\vec{b}$ are perpendicular to each other, then the angle between $\vec{a}$ and $\vec{b}$ is :

The equation of plane which cuts equal intercepts of unit length on the coordinate axes is :

If the straight lines $x = 1 + s$, $y = -3 - \lambda s$, $z = 1 + \lambda s$ and $x = \frac{t}{2}$, $y = 1 + t$, $z = 2 - t$ with parameters $s$ and $t$ respectively, are coplanar, then $\lambda$ is equal to :

Match List - I with List - II. | List - I | List - II | |----------|-----------| | (A) The common region determined by all the constraints of LPP is called | (I) objective function | | (B) Minimize $z = c_1x_1 + c_2x_2 + ..... + c_nx_n$ is | (II) convex set | | (C) A solution that also satisfies the non-negative restrictions of a LPP is called | (III) feasible region | | (D) The set of all feasible solutions of a LPP is a | (IV) feasible solution | Choose the correct answer from the options given below :

If corner points of a feasible region are (0, 0), (2, 0), $\left(\frac{20}{19}, \frac{45}{19}\right)$ and (0, 3), then (A) Maximum value of $z = 5x + 3y$ is 10 (B) Minimum value of $z = 5x + 3y$ is 0 (C) Maximum value of $z = 5x + 3y$ is $\frac{235}{19}$ and minimum value is 0 (D) Maximum value of $z = 5x + 3y$ is 10 and minimum value is 0 Choose the correct answer from the options given below :

If in a binomial distribution $n = 4$, $P(X=0) = \frac{16}{81}$, then $P(X=4)$ equals :

A and B throw a die alternatively till one of them gets a number more than 4 and wins the game. Then the probability of winning the game by B, if A starts first :

The inverse of the function $f : R \to R$ given by $f(x) = 2x + 7$ is :

If $f(x) = \begin{cases} \frac{x^2 - 9}{x - 3}, & x \neq 3 \\ 5, & x = 3 \end{cases}$ then $f(x)$ :

The integral $\int_{0}^{1} x(1-x)^n dx$ is equal to :

The set of value of $x$ for which the angle between the $\vec{a} = 2x^2\hat{i} + 4x\hat{j} + \hat{k}$ and $\vec{b} = 7\hat{i} - 2\hat{j} + x\hat{k}$ is obtuse is :

The shortest distance between the lines $\frac{x+3}{1} = \frac{y-2}{2} = \frac{z+4}{3}$ and $\frac{x+3}{-3} = \frac{y+7}{2} = \frac{z-6}{4}$ is :