List of top Mathematics Questions asked in CUET (UG)

If \([A]_{3 \times 2} [B]_{x \times y} = [C]_{3 \times 1}\), then \( x \) and \( y \) are:

If A is a square matrix of order 4 and |A| = 4, then |2A| will be:

If $A$ and $B$ are symmetric matrices of the same order, then $AB - BA$ is:

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

The second-order derivative of which of the following functions is $5^x$?

Evaluate the integral $\int_0^1 \frac{a - bx^2}{(a + bx^2)^2} , dx$:

Evaluate the integral $\int \frac{\pi}{x^n + 1 - x} , dx$:

A die is rolled thrice. What is the probability of getting a number greater than $4$ in the first and second throws and a number less than $4$ in the third throw?

The area of the region bounded by the lines $x + 2y = 12$, $x = 2$, $x = 6$, and the $x$-axis is:

If $t = e^{2x}$ and $y = \ln(t^2)$, then $\frac{d^2 y}{dx^2}$ is:

If the solution of the differential equation \[ \frac{dy}{dx} = \frac{ax + 3}{2y + 5} \] represents a circle, then $a$ is equal to:

The minimum value of \(x^2 + \frac{1}{x}\) is:

The particular solution of the differential equation \((y - x^2) dy = (1 - x^3) dx\) with \(y(0) = 1\), is:

The integrating factor of the differential equation \[ (y \log_e y) \frac{dx}{dy} + x = 2 \log_e y \] is:

If \[ y = \frac{1}{\sqrt{1 - 4 \sin^2 x \cos^2 x}}, \] then $\frac{dy}{dx}$ is:

The degree and order of the differential equation \[ \left( \frac{d^2 y}{dx^2} \right)^{\frac{4}{5}} = 10 \frac{dy}{dx} + 2 \] are:

Let \( f : \mathbb{R} \to \mathbb{R} \) be defined as \( f(x) = 10 - x^2 \), then:

If \( x = at^4 \) and \( y = 2at^2 \), then \( \frac{d^2y}{dx^2} \) is equal to:

Let \( A \) and \( B \) be two independent events such that \( P(A) = \frac{3}{5} \) and \( P(B) = \frac{4}{9} \).

Choose the correct answer from the options given below :

The ratio in which a grocer must mix two varieties of tea worth ₹60 per kg and ₹65 per kg so that by selling the mixture at ₹68.20 per kg, he may gain 10% is:

For \[ f(x) = \int \frac{e^x}{\sqrt{4 - e^{2x}}} \, dx, \] if the point $\left(0, \frac{\pi}{2}\right)$ satisfies $y = f(x)$, then the constant of integration of the given integral is:

The value of \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{dx}{1 + \tan^{18}x}\) is:

Let \( f(x) = x^3 - 6x^2 + 12x - 3 \), then at \( x = 2 \), \( f(x) \) has:

The area of the parallelogram, whose adjacent sides are given by the vectors \(\vec{a} = 2\hat{i} - \hat{j} + 5\hat{k}\) and \(\vec{b} = 2\hat{i} + \hat{j} + 2\hat{k}\), is:

The value of \( \lambda \) for which the lines \(\frac{2 - x}{3} = \frac{3 - 4y}{5} = \frac{z - 2}{3}\) and  \(\frac{x - 2}{-3} = \frac{2y - 4}{3} = \frac{2 - z}{\lambda}\) are perpendicular is: