CUET Mathematics 2025 3 June Shift 2 PYQs

Which of the following functions has a local minima at $x = 0$? (A) $f(x) = x^3$ (B) $f(x) = |x|$ (C) $f(x) = x^2$ (D) $f(x) = x^{-2}$ Choose the correct answer from the options given below:

If A be a square matrix of order 3 such that $|A| = 2$, then $|adj(2A)|$ is equal to

Which of the following terms are associated with a linear programming problem? (A) Constraints (B) Independent events (C) Feasible region (D) Objective function Choose the correct answer from the options given below:

If A is an invertible matrix, then which of the following statement(s) is/are TRUE? (A) $|A^{-1}| = |A|$ (B) $(A^{-1})^{-1} = A$ (C) $A^{-1} = \frac{adj A}{|A|}$ (D) $(A^T)^{-1} = (A^{-1})^T$ Choose the correct answer from the options given below:

If A and B are symmetric matrices, then AB - BA is

$\int_0^a \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a-x}} dx$ is equal to

The general solution of the differential equation $\frac{dy}{dx} = -4xy^2$ is given by

If $x = at^2, y = 2at$; then $\frac{d^2y}{dx^2}$ is equal to

Assume A, B and C are matrices of order $m \times n$, $n \times 3$ and $3 \times q$ respectively. The restrictions on $_{m,n}$ and $_q$ so that $AB + BC$ is defined are

The area (in sq. units) of the region bounded by $y = -1, y = 2, x = y^3$ and $x = 0$ is equal to

Function $f(x) = x^x, x > 0$ decreases on the interval

Let X denotes the number of heads in a simultaneous toss of three coins, then $P(0 < X < 3)$ is

If $z = 3x + 4y$ be the objective function of a of a linear programming problem (LPP) and (3, 1), (2, 4), (0, 4), (5, 0) be corner points of the bounded feasible region. Then the maximum value of objective function is

Match List-I with List-II | List-I | List-II | |------------|-------------| | (A) Degree of this differential equation $\frac{d^4y}{dx^4} + 2\log_e\left(\frac{d^3y}{dx^3}\right) = 0$ | (I) 1 | | (B) Order of this differential equation $e^{\left(\frac{dy}{dx}\right)^3} + 3y\left(\frac{d^2y}{dx^2}\right)^3 = 0$ | (II) 4 | | (C) Degree of $\frac{d^4y}{dx^4} + \left(\frac{dy}{dx}\right)^2 = 0$ | (III) not defined | | (D) Order of the differential equation $2\frac{d^4y}{dx^4} + \left(\frac{d^2y}{dx^2}\right)^5 = 0$ | (IV) 2 | Choose the correct answer from the options given below:

$\int_0^8 (x^{\frac{2}{3}} + 1) dx$ is equal to

The length of a rectangle is decreasing at the rate of 4 cm/minute and the width is increasing at the rate of 3 cm/minute, then the rate of change of the perimeter is

The cost of type 1 rice is Rs. 20 per kg and type 2 rice is Rs. 30 per kg. If both Type 1 and Type 2 are mixed in the ratio 2:3, then the price per kg of the mixed variety is

Ram invested Rs.20,000 in a mutual fund in the year 2012. The value of the mutual fund increased to Rs.32,000 in the year 2017, then the compound annual growth rate of his investment is (Given that $(1.6)^{\frac{1}{5}} = 1.098$)

In a kilometer race, A beats B by 50 meters or by 5 seconds, then the time taken by A to complete the race is

Mr. Vishnu has an initial investment of Rs.80,000 in an investment plan. After 3 years, it has grown to Rs.1,00,000, then his rate of return is

Which of the following statements are TRUE? (A) The variable t of t-distribution ranges from $-\infty$ to $\infty$. (B) The probability curve of the t-distribution is symmetric about the line $t=0$ (C) The variance of the t-distribution is greater than one. (D) As the number of degrees of freedom decreases, the t-distribution curve moves closer to the standard normal probability curve. Choose the correct answer from the options given below:

The value of $\int_2^4 \frac{x}{x^2 + 1} dx$ is equal to

For the following data: | | Size | Mean | Standard deviation | |---|---|---|---| | Sample 1 | 4 | 40 | 8 | | Sample 2 | 5 | 50 | 10 | The sample statistic t follows t-distribution with 'm' degrees of freedom, then m is equal to

The break-even point is the level of production where

If the matrix $A = \begin{bmatrix} x & 2 & y \\ -2 & 0 & 3 \\ -1 & z & 0 \end{bmatrix}$ is skew-symmetric, then the value of $2x - 3y + 5z$ is equal to

If X is a random variable and $a$, $b$ are real numbers, then which of the following statements are true? (A) $Var(aX+b) = a^2 Var(X)$ (B) $E(aX+b)= a E(X) + b$ (C) $E(aX+b)= a E(X) - E(b)$ (D) $Var(aX+b)= a Var(X) + b$ Choose the correct answer from the options given below:

The corner points of the bounded feasible region determined by the system of linear constraints are $(0,8)$, $(4,4)$, $(12,12)$, $(0,20)$. Let $z = px + qy$, where $p, q > 0$. Condition on $p$ and $q$ so that the maximum of $z$ occurs at both the points $(12,12)$, $(0,20)$ is

If $(t_1, y_1)$, $(t_2, y_2)$,......,$(t_n, y_n)$ denote the time series and $y_t$ are the trend values of the variables $y$, then

Choose the correct statement about Sinking Fund?

The least non-negative remainder, when $5^{61}$ is divided by 7, is

Choose the correct statement about CAGR(compound annual growth rate)?

If the system of equations $kx + y + z = 0$, $x + ky - z = 0$, $x - y + z = 0$ has a non-zero solution, then the possible values of $k$ are:

If $A$ is a square matrix such that $A^2 = A$ and $I$ is the identity matrix of the same order as $A$, then $(I + 2A)^2 - 5A$ is equal to

A machine costing Rs.2,00,000 has a useful life of 5 years.The estimated scrap value is Rs.20,000. By using straight line method, the annual depreciation is

A random variable X has the following probability distribution: | X | 0 | 1 | 2 | |---|---|---|---| | P(X) | 1/4 | 1/2 | 1/4 | then, which of the following is correct?

A man rows downstream 30 km and upstream 20 km. If he takes 5 hours to cover each distance, then the speed of stream is

Pipe A and B can fill a tank in 20 hours and 25 hours respectively, and pipe C can empty the full tank in 40 hours.If all the pipes are opened together, then how much time will be needed to make the tank full?

The point which provides the optimal solution of the linear programming problem maximize $z = 21x + 35y$ $3x + 2y \leq 30$ $4x + 5y \leq 60$ $x \geq 0, y \geq 0$ has the coordinates

If $A = \begin{bmatrix} 5 & 2 \\ 4 & 3 \end{bmatrix}$ is a given matrix, then which of the following statements are correct? (A) $|A| = 7$ (B) minor of $3 = -5$ (C) co-factor of $2 = -4$ (D) $adj(A) = \begin{bmatrix} 3 & -2 \\ -4 & 5 \end{bmatrix}$ Choose the correct answer from the options given below:

The following data are from a random sample: 5,8,10,7,10,14, then the point estimate of the population standard deviation is

For the given five values, 16,25,19,34,43, the three year moving averages are

The binomial distribution for which the mean is 5 and variance 4, is

The sum of the order and degree of the differential equation representing the family of curves $y = mx + m^4$, where m is arbitrary constant, is

Assuming the same rate of change continues for the following data: | Year (x) | 2019 | 2020 | 2021 | 2022 | 2023 | |---|---|---|---|---|---| | Profit(in Percentage) (y) | 38 | 40 | 65 | 72 | 69 | The equation of the straight line trend using the least square method is:

Which of the following statements are TRUE? (A) The sales of woolen clothes, gold, silver etc. exhibit seasonal trends. (B) The price of stocks in the share market repeats after a definite time interval. (C) The rise and fall of the share market is an example of a cyclic trend. (D) The rise in prices before festivals is an example of a irregular trend. Choose the correct answer from the options given below:

The curve $y = f(x)$ is normal probability curve, then which of the following statements are correct? (A) mean, median and mode of the distribution coincide. (B) the area bounded by the curve $y = f(x)$ and $x$-axis is one unit. (C) The curve is symmetrical about the line $x = \mu$, where $\mu$ is the mean. (D) $y$-axis is an asymptote to the curve. Choose the correct answer from the options given below:

The two positive numbers whose sum is 16 and the sum of whose squares is minimum then the positive numbers are:

If $A = \begin{bmatrix} 3 & 2a \\ 1 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 3 \\ b & 5 \end{bmatrix}$ both are singular matrices, then $a + b$ is equal to

The demand for a certain product is represented by the function $p = 150 + 10x - x^2$ (in Rs.) where $x$ is the number of units demanded and $p$ is the price per unit, then the value of marginal revenue, when 10 units are sold is

If $\frac{3x - 5}{6} + 8 \geq 4 + \frac{2x}{3}$, then