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"/>

If the equation of a floor of a room is given by $x + y - z + 4 = 0$ and the equation of roof is given by $x + y - z + 5 = 0$. Then, the height of the room is :

$5^{100} (\mod 9) =$

An asset costing Rs. 50,000 has a useful life of 4 years. The estimated scrap value is Rs. 10,000. By using linear depreciation method, the book value at the end of the second year is :

Rahul can run 34.4 m in the given time as Amit runs 50 m. By how much distance Rahul is away from Amit at the winning point, in a two km race ?

The minimum value of $ax + by$, where $xy = c^2$ and a, b, c are positive, is :

A company intends to create a sinking fund to replace at the end of 20$^{th}$ year assets costing Rs. 2,50,000. Then the value of the amount to be retained out of profits every year if the interest rate is 5% is : [Given $(1.05)^{20} = 2.6532$]

Using simple average of relatives method, the price index for 2011, taking 2001 as base year, was found to be 127. If $\Sigma p_0 = 263$, then x and y from the following data are : | Commodities | A | B | C | D | E | F | |---|---|---|---|---|---|---| | Prices (in Rs.) in 2001 | 80 | 70 | x | 20 | 18 | 25 | | Prices (in Rs.) in 2011 | 100 | 87.50 | 61 | 22 | y | 32.50 |

The present value of a perpetuity of Rs. 2,500 payable at the end of each year, if money is worth 10% compounded annually, is :

Match List - I with List - II. Given that $\Sigma p_0 q_0 = 150$, $\Sigma p_0 q_1 = 80$, $\Sigma p_1 q_0 = 240$, $\Sigma p_1 q_1 = 200$. | List - I | List - II | |---|---| | (A) Laspeyre's index | (I) 160 | | (B) Paasche's index | (II) 200 | | (C) Fesher's index | (III) 205 | | (D) Dorbish and Bowley's | (IV) 250 | Choose the correct answer from the options given below :

Let A be a square matrix. Then, (A) $A + A^T$ is a symmetric matrix (B) $A - A^T$ is a skew-symmetric matrix (C) $AA^T$ is a skew-symmetric matrix (D) $A^T A$ is a symmetric matrix Choose the correct answer from the options given below :

Let $f : R \to R$ be defined such that $f(x) = 16x^2 - 16x + 12$ (A) Maximum value of $f(x)$ is 8 (B) Minimum value of $f(x)$ is 8 (C) Minimum value of $f(x)$ is 16 (D) No maximum value of $f(x)$ Choose the correct answer from the options given below :

If $C(x) = ax^2 - bx - c$ represents the total cost function then the slope of the tangent to the marginal cost curve at the point $(x, y)$ is :

The demand function of a monopolist is given by $p = 1500 - 2x - x^2$, then value of marginal revenue when $x = 20$ is :

The EMI (in Rs.) under the flat rate on a loan of Rs. 6,00,000 with 20% annual interest for 5 years is :

Corner points of the feasible region for an LPP are : (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let $z = 4x + 6y$ be the objective function. Then, Max z $-$ Min z is equal to :

Match List - I with List - II. | List - I (Functions) | List - II (Maximum value) | |---|---| | (A) $f(x) = -x^2, x \in (-\infty, \infty)$ | (I) 8 | | (B) $f(x) = -x^2 + 1, x \in (-\infty, \infty)$ | (II) 7 | | (C) $f(x) = x + 1, x \in [0, 6]$ | (III) 1 | | (D) $f(x) = x^3, x \in [0, 2]$ | (IV) 0 | Choose the correct answer from the options given below :

The present value of a perpetuity of Rs. 6,240 payable at the beginning of each year, if money is worth 10% effective, is :

The effective rate that is equivalent to a nominal rate of 12% compounded quarterly is :

The objective function $z = 4x + 3y$ can be maximised subject to the constraints $3x + 4y \leq 24$, $8x + 6y \leq 48$, $x \leq 5$, $y \leq 6$, $x \geq 0$, $y \geq 0$ :

Pipes A and B can fill a tank in 5 hours and 6 hours respectively. Another Pipe can empty the full tank in 30 hours. If all three pipes are opened together, then the tank will be filled in :

If $x^3 + y^3 = xy$, then $\frac{dy}{dx}$ is equal to :

The set of positive integers less than 50 forming the equivalence class of 6 modulo 9 is given by :

A company has issued a bond having a face value of Rs. 10,000 paying annual dividends at 8.5%. The bond will be redeemed at par at the end of 10 years, then the purchase price of this bond if the investor wishes a yield rate of 8% is : [Given $(1.08)^{-10} = 0.46319349$]

A container contains 50 litres of milk. From this container 10 litres of milk was taken out and replaced by water. This process is repeated two more times. How much milk is now left in the container ?

Mr. Ram took a loan of Rs. 4,00,000 at 10% annual interest rate and paid Rs. 20,000 as monthly instalment under flat rate system. What is the term of the loan ?

If $-\frac{1}{3x - 5} \leq 0$, then :

Which of the following statements are correct ? (A) $\text{var}(aX + b) = a^2 \text{var}(X)$ (B) $\text{var}(X) = E(X^2) - \{E(X)\}^2$ (C) $E(aX + b) = aE(X) + b$ (D) $E(X) = \sum_{i=1}^{n} p_i x_i^2$ Choose the correct answer from the options given below :

In binomial distribution with $n = 10$ and $P = \frac{1}{3}$, the probability of the event that unequal number of failures and successes occur is :

The standard deviation of a sampling distribution of a statistic is also known as :

The probability distribution of a random variable X is given below : | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.1 | 0.25 | 0.3 | 0.2 | 0.15 | Then, $\text{Var}\left(\frac{X}{2}\right)$ is :

If the matrix $A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix}$ satisfies the equation $A^T A = I_3$, then $x^2 + y^2 + z^2$ is :

A motor boat goes 20 km downstream and comes back to the starting point in 6 hours. If the speed of the boat in still water is 12 km/h, then the speed of the stream is :

If $x = 6t^2$, $y = \frac{6}{t^2}$, then $\frac{d^2 y}{dx^2}$ is equal to :

If X has a Poisson distribution such that $P(X = 1) = P(X = 2)$ then $P(X = 3)$ is :

Consider the following hypothesis test : $\mu_o : \mu \leq 26$ $\mu_a : \mu > 26$ A sample of 36 is provided with a sample mean of 25.75. The population standard deviation is 3. The value of the test statistic is :

The maximum value of $Z = 3x + 4y$ subjected to the constraints $3x + 7y \leq 21$, $5x + 2y \leq 10$; $x, y \geq 0$ is :