List of top Mathematics Questions asked in CUET (UG)

A ladder 25 feet long is leaning against a wall such that it touches 24 feet high window. How far is the foot of the ladder from the wall?

In an A.P., the product of the first term and the second term is 120 and the product of the second term and the third term is 168. Find the tenth term of the A.P. when common difference \(d>0\)

If \(A=\begin{bmatrix} 1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\), \(B=\begin{bmatrix} 1 & -2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\) and AB = I₃, where I₃ is the unit matrix of order 3 × 3, then x + y is equal to :

If \(A=\begin{bmatrix} x & 1 \\ 1 & 0 \end{bmatrix}\)and A = A^-1, then the value of x is :

If x, y, z are different and \(A=\begin{vmatrix} x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{vmatrix}=0\), then the value of xyz is :

If the points (2, -3), (λ, -1) and (0, 4) are collinear, then the value of λ is :

If y = \(10^{10^x}\), then \(\frac{dy}{dx}\) is :

The tangent to the parabola, x² = 2y at the point \((1,\frac{1}{2})\) makes with the x-axis an angle of :

The function f(x) - x³ , x ∈ R has :

If \(f(x)=\begin{cases} 2x+8, & 1\le x\le2 \\ 6x, & 2\lt x \lt4\end{cases}\), then \(\int_1^4f(x)\) is :

The area of the region bounded by the line 2y = 5x +7, x-axis and the lines x - 1 and x -3 is :

The integrating factor of the differential equation (1 +y²)dx - (tan^-1 y - x)dy = 0, is :

The order and the degree of the differential equation
\(\frac{d^2y}{dx^2}=(1+\frac{dy}{dx})^{\frac{1}{2}}\)
respectively are :

Which of the following is correct ?

The corner points of feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy where p, q > 0. The condition on p and q so that, minimum of Z occurs at (3, 0) and (1, 1) is :

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces, and 5 on 1 face is :

If \(P(A)=\frac{3}{10},P(B)=\frac{2}{5}\), and P(A ∪ B) = \(\frac{3}{5}\), then \(P(\frac{B}{A})+P(\frac{A}{B})\) is equal to :

The relation R in the set A = {1, 2, 3, 4} is given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)} is :

If f(x) - 27x³ and g(x) = \((x)^{\frac{1}{3}}\), then gof(x) is :

Principal value of \(\tan^{-1}(\sqrt3)+\tan^{-1}(1)\) is :

The principal value of \(\sin^{-1}(\frac{1}{2})\) is :

If A is an invertible matrix, such that A² - A + I = 0, then the inverse of A is :

The determinant \(\begin{vmatrix} x & \sin\theta & \cos\theta \\ -\sin\theta & -x & 1 \\ \cos\theta & 1 & x \end{vmatrix}\) is :

The value of k for which the matrix \(\begin{pmatrix} 0 & 2 & 4 \\ 2 & 0 & 5 \\ -3 & 5 & 0 \end{pmatrix}\) is a symmetric matrix is given by :

The value of λ for which the matrix \(\begin{pmatrix} 1 & 0 & λ \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{pmatrix}\) is a singular matrix is :