CUET Mathematics 2025 22 May Shift 1 PYQs

The function $f(x) = x^2e^{-2x}$ increases on

The minimum value of $Z = 2x + y$ subjected to $x + y \geq 10, 2x + 3y \leq 26, x, y \geq 0$ is

If A is a square matrix and I is an identity matrix of same order such that $A^2 = A$, then $(I + A)^3 - 8I$ is equal to

$\int \frac{x}{(x-1)(x-2)} dx$ is equal to ( where $C$ is a constant of integration)

If $A = \begin{bmatrix} a & a & a \\ o & a & a \\ o & o & a \end{bmatrix}$, then $|adj A|$ is equal to

The function $f(x) = \frac{-3}{4}x^4 - 8x^3 - \frac{45}{2}x^2 + 163$ has a local maxima at

Let A be a non-singular square matrix of order 3 and $|adj A| = 5$ then $|A|$ is equal to

Let $x = t^2, y = t^3$. Then $\frac{d^2y}{dx^2}$ is equal to

Match **List-I** with **List-II** | List-I | List-II | |---|---| | **Differential Equation** | **Degree** | | (A) $xy\frac{d^2y}{dx^2} + x\left(\frac{dy}{dx}\right)^2 - y\frac{dy}{dx} = 0$ | (I) 3 | | (B) $\frac{d^2y}{dx^2} + \log\left(\frac{dy}{dx}\right) = 0$ | (II) 1 | | (C) $\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^3 + \frac{dy}{dx} + 1 = 0$ | (III) not defined | | (D) $2x^2\left(\frac{d^2y}{dx^2}\right)^3 - 5\left(\frac{dy}{dx}\right)^3 + y = 0$ | (IV) 2 | Choose the correct answer from the options given below:

Area (in sq. units) of the region bounded by the curve $y^2 = 4x$, y-axis and the line $y = 3$ is

Let X denotes the number of doublets obtained in 3 throws of a pair of dice. Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) $P(X = 0)$ | (I) $\frac{1}{216}$ | | (B) $P(X = 1)$ | (II) $\frac{15}{216}$ | | (C) $P(X = 2)$ | (III) $\frac{75}{216}$ | | (D) $P(X = 3)$ | (IV) $\frac{125}{216}$ | Choose the correct answer from the options given below:

The corner points of the bounded feasible region determined by the system of linear inequalities are $(0,0)$, $(4,0)$, $(2,4)$ and $(0,5)$. If maximum value of $z = ax + by$, where $a,b > 0$, occurs at both $(2,4)$ and $(4,0)$ then

$\int_0^1 x e^x dx$ is equal to

If a matrix has 8 elements then the possible order(s) it may have (A) $8 \times 1$ (B) $5 \times 3$ (C) $6 \times 2$ (D) $2 \times 4$ Choose the correct answer from the options given below:

The solution of the differential equation $\frac{dr}{dt} = -rt, r(0) = r_0$ is

The solution set of the inequation $4x + 3y > 5$ is

If $\begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix} \begin{bmatrix} 3 & 5 \\ -1 & 3 \end{bmatrix} = \begin{bmatrix} m & 14 \\ 2 & n \end{bmatrix}$, then $m + n$ is equal to

If n is the sample size of the population, then degree of freedom in t-distribution is

For the given five values $16, 25, 19, 34, 46$, the three years moving averages are

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

A machine costing ₹ 1,00,000 has a useful life of 5 years. The estimated scrap value is ₹ 20,000. Using straight line method the annual depreciation is

Five dice are thrown simultaneously. If the occurrence of an even number in a single dice is considered a success, then the probability of at most 3 successes is

The differential equation of the family of curves $y = Ae^{3x} + Be^{-3 x}$, where $a$ and $\beta$ are arbitrary constants, is

The derivative of $(\log x)^x$ with respect to $\log x$ is

Kavya takes a personal loan of ₹ 10,00,000 at the rate of 12% per annum for 5 years, then the EMI by using flat rate method is

The demand function for a certain product is represented by the equation: $p = 20 + 5x - 3x^2$, where $x$ is the number of units demanded and $p$ is the price per unit (in Rs.), then the marginal revenue when 2 units are sold is:

The Value of $\int_1^3 |2x - 1|dx$ equal to

The term of the perpetuity is

Which one of the following statement is **incorrect** about sinking fund?

The sale of ice creams is higher in summer than in winter is an example of

The following data are from a simple random sample: $6, 8, 11, 9, 15, 17$, then the point estimate of the population mean is

Pipe A can fill a tank in 24 hours and pipe B in 32 hours. If both the pipes are opened in an empty tank at the same time, then the time taken to fill the tank is:

The unit's digit in $13^{61}$ is

Consider the following hypothesis test: $H_0: \mu \leq 16$ $H_a: \mu > 16$ A sample of 25 provided a sample mean $\bar{x} = 17$ and a sample standard deviation $s = 3.5$, then the value of the test statistic in $t$-test is:

The equation of the tangent line to the curve $y = x^2 - 2x + 5$ which is parallel to the line $4x - y + 1 = 0$ is

If X is a random variable with probability distribution as given below: | X | 0 | 1 | 2 | 3 | |---|---|---|---|---| | P(X) | k | 2k | k | 3k | Then, the variance of the distribution is

A random variable X has the following probability distribution: | X | -2 | -1 | 0 | 1 | 2 | 3 | |---|---|---|---|---|---|---| | P(X) | 0.1 | 0.2 | k | 0.3 | 2k | 0.1 | then which of the following are TRUE? (A) $k=0.1$ (B) $P(X < 1) = 0.4$ (C) $P(X < 2) = 0.7$ (D) $P(0 < X < 3) = 0.5$ Choose the correct answer from the options given below:

If $\frac{1}{x^2} - \frac{1}{x} > 0$, then $x$ lies in the interval

If A and B are symmetric matrices of the same order, then which one of the following is true?

The integral $\int e^x\left(\frac{x-1}{2x^2}\right)dx$ is equal to

For what value of $k$, the following system have a unique solution? (where $\mathbb{R}$ is set of real numbers) $x + y + z = 1$ $2x + 3y + 4z = 3$ $x - y + kz = 5$

Which one of the following statement is not correct?

Consider the following data: | Year (X) | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | |---|---|---|---|---|---|---|---| | Profit (₹) (y) | 114 | 130 | 126 | 144 | 138 | 156 | 164 | The equation of straight line trend by using least square method is $y = 138.86 + 7.64 (x - 2007)$, then the trend values for the year 2004 is

The minimum value of $z = 3x + 2y$ subjected to the constraints $2x + y \geq 7, x + 2y \geq 8, x, y \geq 0$ is

If $A = \begin{bmatrix} 7 & 3 \\ 5 & -7 \end{bmatrix}$ be such that $A^{-1} = kA$, then $k$ equals

In what ratio must pulses at ₹72 per kg be mixed with pulses ₹90 per kg so that the mixture be worth ₹80 per kg?

Two runners A and B complete a 150 meters race in 24 seconds and 36 seconds respectively. By how many meters will A defeat B?

The number of all possible matrices of order $2 \times2$ with each entry $0, 1$ or $2$ are.

A man rows 24 km upstream in 6 hours and 36 km downstream in 6 hours each time, then the speed of the boat in the still water is

Match **List-I** with **List-II** | List-I | List-II | |---|---| | **Function** | **Increasing on the interval** | | (A) $f(x) = -x^2 - 2x + 1$ | (I) $(-\infty, -1)$ | | (B) $f(x) = x^2 + 1$ | (II) $(1, \infty)$ | | (C) $f(x) = x^2 - 2x + 3$ | (III) $(-\infty, 0)$ | | (D) $f(x) = -x^2$ | (IV) $(0, \infty)$ | Choose the correct answer from the options given below: