List of top Questions asked in CUET (UG)

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 :

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

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 :

If the function \(f(x)=\frac{k \sin x+2\cos x}{\sin x+\cos x}\) is increasing for all values of x, then

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		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 area of the region bounded by |x| + |y| = 1, x ≥ 0 y ≥ 0 is :

The area of the region bounded by the curve \(y=\sqrt{3x+10}\), x-axis and between the lines x = -3 and x = 2 is equal to :

If \(a:b=\frac{2}{3}:\frac{1}{4}\) and \(b:c=\frac{3}{4}:\frac{4}{5}\) then find a : b : c.

A's month salary was ₹40000 and he used to save ₹10000 per month. His salary increased by 25% and expenditure increased by 15%. By what percent his savings increased ?

A borrowed Rs 10000 each from his friends B and C for 2 years. He was supposed to pay compound interest at 10% per annum to B and simple interest 11% per annum to C. Who charged more interest at the end of 2 years and how much more ?

A shopkeeper bought an item for ₹600 and marked on it 50% higher than its cost price. He allowed 20% discount on it. Find his profit percentage.

A and B started a business by investing ₹10,000 and ₹18,000 respectively. After 4 months C joined the business with a capital of ₹12,000. After two more months B left the business his capital. At the end of the year A got a share of ₹7,500 in the profit. What is the total profit earned ?

A shopkeeper marked his goods 40% higher than their cost price and allows 20% discount on every item. Find his net profit percentage.

The difference between length and breadth of a rectangle is 15m. If the perimeter of rectangle is 162 m, then the area of the rectangle (in m²) is