CUET Mathematics 2023 30 May Shift 3 PYQs

If $\begin{vmatrix} 3x & 4 \\ 7 & x \end{vmatrix} = \begin{vmatrix} 6 & 3 \\ 2 & 1 \end{vmatrix}$ then :

Given $A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} x & y \\ 1 & 4 \end{bmatrix}$, If $A = B$, then $x$ and $y$ are :

The feasible region for a LPP is shown in the given figure. The maximum value of $z = 2x + 5y$ is :<img src="https://balti.afterboards.in/fjQTz13IBfFlQGM" width="400px"/>

Match List - I with List - II. Match the integrating factors : | List - I (Differential Equation) | List - II (Integrating factor) | |---|---| | (A) $\frac{dy}{dx} + 3y = e^{-2x}$ | (I) $\frac{1}{x}$ | | (B) $x\frac{dy}{dx} + y = 3x^2$ | (II) $e^{-x}$ | | (C) $x\frac{dy}{dx} - y = 3x^2$ | (III) $x$ | | (D) $\frac{dy}{dx} - y = x$ | (IV) $e^{3x}$ | Choose the correct answer from the options given below :

The area enclosed between $y^2 = 4x$, $x = 1$, $x = 4$ in first quadrant is :

If the probability distribution of a random variable X is as given below : | X | -1 | 0 | 1 | 2 | 3 | |---|---|---|---|---|---| | P(X) | K | $\frac{1}{5}$ | 2K | $\frac{3}{10}$ | K | Then the value of K is :

The sum of the products of elements of any row with the cofactors of corresponding elements is equal to :

If order of matrix A is $m \times p$ and order of matrix B is $p \times n$, then what is the order of matrix AB ?

If $x = a\left(t - \frac{1}{t}\right)$, $y = b\left(t + \frac{1}{t}\right)$, then $\frac{dy}{dx} =$

$\int \left(x + \frac{1}{x}\right)^2 dx$ equals :

The slope of the tangent to the curve $x = at^2$, $y = 2at$ at 't' is :

If m and n are respectively the order and degree of the differential equation : $\left(\frac{d^2 y}{dx^2}\right)^5 + 6 \frac{\left(\frac{d^2 y}{dx^2}\right)^3}{\frac{d^3 y}{dx^3}} + \frac{d^3 y}{dx^3} = x^2 + 5$, then :

If the function $f(x) = x^4 - 62x^2 + ax + 9$ attains its local maximum value at $x = 1$, then a is equal to :

The mean number of heads in two tosses of a coin is :

In a Linear Programming problem, the objective function is always :

If matrix $A = \begin{bmatrix} 3 & x \\ y & 0 \end{bmatrix}$ and $A' = A$, then :

Relation R on Real Numbers is defined as $R = \{(a, b) : a \leq b\}$. The relation is :

If A and B are invertible matrices of order 3, $|A| = 2$ and $|(AB)^{-1}| = -\frac{1}{6}$, then the value of $|B|$ is :

The degree of the differential equation $\left[1 + \left(\frac{dy}{dx}\right)\right]^3 = \left(\frac{d^2 y}{dx^2}\right)^2$ is :

The vector equation of the line joining the points $(-2, -3, -4)$ and $(1, -2, 4)$ is :

Which of the following statements are correct ? (A) If $f : R \to R$ then $f(x) = |x|$ is continuous everywhere. (B) If $f : R \to R$ then $f(x) = |x|$ is continuous everywhere but not differentiable at $x = 0$. (C) Let $f : R - \{0\} \to R$ then $f(x) = \frac{1}{x}$ is continuous everywhere. (D) Let $f : R \to R$ then $f(x) = |x - 1| + |x - 2|$ is continuous everywhere but not differentiable at exactly 2 points. (E) If $f : R \to R$ then $f(x) = \cot x$ is continuous everywhere. Choose the correct answer from the options given below :

Let $A = \begin{bmatrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ \lambda & 2 & -3 \end{bmatrix}$. If $A^{-1}$ does not exist, then $\lambda =$

If $f(x) = \begin{cases} \frac{k\cos x}{\pi - 2x}, & x \neq \frac{\pi}{2} \\ 3, & x = \frac{\pi}{2} \end{cases}$ is continuous at $x = \frac{\pi}{2}$, then k is :

Match List - I with List - II. | List - I | List - II | |---|---| | (A) If A and B are mutually exclusive events, then $P(A \cup B) =$ | (I) $\frac{P(A \cap B)}{P(B)}, P(B) \neq 0$ | | (B) If A and B are independent events, then $P(A \cap B) =$ | (II) $\frac{P(A \cap B)}{P(A)}, P(A) \neq 0$ | | (C) If A and B are two events of a sample space of an experiment, then $P(A/B) =$ | (III) $P(A) \cdot P(B)$ | | (D) If A and B are two events of a sample space of an experiment, then $P(B/A) =$ | (IV) $P(A) + P(B)$ | Choose the correct answer from the options given below :

In $\triangle ABC$ :<img src="https://balti.afterboards.in/DZjDM0ROyzDP3kj" width="300px"/> (A) $\vec{AB} + \vec{BC} + \vec{CA} = \vec{O}$ (B) $\vec{AB} + \vec{BC} - \vec{AC} = \vec{O}$ (C) $\vec{AB} + \vec{BC} - \vec{CA} = \vec{O}$ (D) $\vec{AB} - \vec{CB} + \vec{CA} = \vec{O}$ (E) $\vec{AB} - \vec{CB} - \vec{CA} = \vec{O}$ Choose the correct answer from the options given below :

Area of the region bounded by the curve $y = \cos x$ and x-axis between $x = 0$ and $x = \pi$ is :

If a, b and c are all different from zero and $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = 0$, then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ is :

The area enclosed between the curve $y = x^2 + 2$ and x-axis between $x = 0$ and $x = 3$ is :

If $|\vec{a}| = 3$ and $|\vec{b}| = 4$, then a value of $\lambda$ for which $\vec{a} + \lambda \vec{b}$ and $\vec{a} - \lambda \vec{b}$ are perpendicular is :

If $A = \begin{bmatrix} 1 & -2 & 3 \\ -4 & 2 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -2 \\ 3 & -4 \\ 2 & 4 \end{bmatrix}$ then product AB is :

The variance of number of heads in three tosses of a coin is :

The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is $z = 4x + 3y$. Compare the quantity in Column - A and Column - B. | Column - A | Column - B | |---|---| | Maximum value of z | 350 |

The interval in which the function $f(x) = 2x^3 - 3x^2 - 36x + 7$ is strictly decreasing is :

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$, then $A^2 - 5A + 7I =$

$\int \frac{\sqrt{\tan x}}{\sin x \cos x} dx$ equals :

Solution of differential equation $x dy - y dx = 0$ respresents :

The corner points of the feasible region determined by the following system of linear inequalities : $2x + y \leq 10$, $x + 3y \leq 15$, $x, y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z = px + qy$, where $p, q > 0$ condition on p and q so that maximum of z occurs at both (3, 4) and (0, 5) is :

The two curves $x^3 - 3xy^2 + 15 = 0$ and $3x^2 y - y^3 + 17 = 0$ :

The derivative of $\sec(\tan \sqrt{x})$ with respect to x is :

The angle between the two planes $x + y - z = 3$ and $3x + 2y + z = 5$ is :

If $\sin^{-1} x + \sin^{-1} y = \frac{2\pi}{3}$, then the value of $\cos^{-1} x + \cos^{-1} y$ is :

The maximum value of $(\sin x)(\cos x)$ is :

$\int e^x \sec x (1 + \tan x) dx$ equals :

Which of the following graphs represent a function ?

Let $a \leq \tan^{-1} x + \cot^{-1} x + \sin^{-1} x \leq b$. If $\alpha$ and $\beta$ denote the minimum and maximum possible values of a and b respectively, then :

If a set P contains 5 elements and the set Q contains 8 elements, then the number of one-one functions from A to B is :

The equation of tangent to the curve given by $x = a\sin^3 t$, $y = b\cos^3 t$ at a point where $t = \frac{\pi}{2}$ is :

The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is $\theta = 60°$, is :

Which of the following regions will represent the shaded area in the given figure ?<img src="https://balti.afterboards.in/WldIj2j494JVyIl" width="400px"/>