List of top Questions asked in CUET (UG)

If y = Asinx + Bcosx, Where A and B are constants, then \(\frac{d^2y}{dx^2}\) is equal to :

The slope of the normal to the curve y = 2x² + 3sinx at x = 0, is :

For fencing of flower bed with 100 cm long wire in the form of circular sector, the maximum area of the flower bed is :

Match List I with List II

List I (Functions)		List II (Derivatives)
A.	f(x)=sin-1x	I.	\(\frac{1}{1+x^2}\), x ∈ R
B.	f(x)=tan-1x	II.	\(\frac{1}{\sqrt{1-x^2}}\), x ∈ (-1, 1)
C.	f(x)=cos-1x	III.	\(-\frac{1}{\sqrt{1-x^2}}\), x ∈ (-1, 1)
D.	f(x)=sin-1x	IV.	\(-\frac{1}{1+x^2}\), x ∈ R

Choose the correct answer from the options given below :

Match List I with List II

List I		List II
A.	\(\int\limits^{\frac{\pi}{2}}_0\frac{\sin^{\frac{7}{2}}x}{\sin^{\frac{7}{2}}+\cos^{\frac{7}{2}}}dx\)	I.	\(\frac{\pi}{4}-\frac{1}{2}\)
B.	\(\int\limits_0^{\pi}\frac{x\sin x}{1+\cos^2x}dx\)	II.	0
C.	\(\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}x\cos x\ dx\)	III.	\(\frac{\pi}{4}\)
D.	\(\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sin^2x\ dx\)	IV.	\(\frac{\pi^2}{4}\)

Choose the correct answer from the options given below :

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 :

The value of the determinant \(\begin{vmatrix} x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1 \end{vmatrix}\) 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 :

If the order of a matrix A is 2 × 3, the order of matrix B is 3 × 4 and the order of matrix C is 3 × 4, then the order of the matrix (A, B).C^T 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 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 :

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

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 :

The function f(x) - x³ , x ∈ R has :

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

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

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 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 ?

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 :