List of top Questions asked in CUET (PG)

For x = 3, find the value of \(x^5+x^4-x^3-x^2+x-1.\)

The sides of three solid metallic cubes are 30cm, 40cm and 50cm respectively. Find the side of the new cube formed by melting the three cubes (in cm)

Ankit owes ₹ 42,580 on his credit cards, but he could pay only ₹ 12,580. If the annual rate of compound interest is 10%, then how much will he owe after 4 years?

The percentage of loss when an article is sold at Rs. 50 is the same as that of the profit when it is sold at Rs. 70. Percentage of profit or loss on the article is ___.

Given below are two statements:
If \(z_1\) and \(z_2\) are complex numbers
Statement-1 : \(arg(\frac{z_1} {z_2})=arg(z_1)-arg(z_2)\)
Statement-II : \(|z_1+z_2|^2=|z_1|^2+|z_2|^2-2Re(z_1\bar z_2)\)
In the light of the above statements, choose the correct answer from the options given below.

Match List I with List II

Choose the correct answer from the options given below:

If A = \(\begin{bmatrix}        2 & 3 & 1           \\[0.3em]        0 & -1           & 5 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 & 2 & -1  \\[0.3em]  0 & -1  & 3 \end{bmatrix}\), what is the value of (2A-3B)?

The line integral per unit area along the boundary of small area around a point in vector field \(\overrightarrow A\) is called

If A=\(\begin{bmatrix} 1&0 \\[0.3em] 2&-1 \end{bmatrix}\) B= \(\begin{bmatrix} 3&7 \\[0.3em] 4&8 \end{bmatrix}\) and C = \(\begin{bmatrix} -1&1 \\[0.3em] 0&0 \end{bmatrix}\). The value of A+ (B+C) is

If \(\overrightarrow r\) is the position vector of any point on a surface S that encloses the volume V, then find \(\iint\limits_S\overrightarrow r.d\overrightarrow S\)

Choose the correct sequence of the four statements given below, so that the phrase makes a complete sense:
A. Then the sets of equations connecting both are known as transformation of co-ordinates.
B. We can associate a unique set of co-ordinates.
C. Given a point P in rectangular co-ordinates.
D. Called the curvilinear co-ordinates of P.
Choose the correct answer from the options given below.

A single 6-sided dice is rolled, then the probability of getting an odd number is

In a class of 49 students, the ratio of girls to boys is 4:3. If 4 girls leave the class, the ratio of girls to boys would be

If income of A is 20% more than that of B, then income of B is how much percent less than that of A?

The average of 5 consecutive odd positive integers is 9. Then sum of smallest and greatest number is

If 2.5x=0.05 y, then find the value of \((\frac{y-x}{y+x}).\)

In the neighborhood of z = 1, the function f(z) has a power series expansion of the form f(z) = 1+(1-z)+(1-z)² + .... then f(z) is

A rectangular box open at the top is to have volume of 32 cubic feets. The minimum outer surface area of the box is

The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4 × 4 symmetric positive definite matrix is

The matrix P is the inverse of a matrix Q. If I denotes the identity matrix, which one of the following options is correct?

If the matrices \(\left(\begin{matrix} 1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   -1 & 0 \\   0 & 0  \end{matrix}\right),\left(\begin{matrix}   i & 0 \\   0 & 0  \end{matrix}\right) and \left(\begin{matrix}   -i & 0 \\   0 & 0  \end{matrix}\right)\) form a group with respect to matrix multiplication, then which one of the following statements about the groups, thus formed is correct?

Which of the following are generators of the multiplicative group {(1,2,3,4,5,6), x₇} where x₇ denotes multiplication moduls 7?

The general solution of differential equation \(\frac{d^2y}{dx^2}+9y=sin^3x\) is
(given that c₁ and c₂ are arbitrary constants)

The solution of (x² -√2y) dx + (y² - √2x) dy = 0 is given by

Consider the linear mapping F: R² →R² defined by F(x, y) = (3x+4y, 2x-5y) and following bases of R²: E= {e₁, e₂} = {(1, 0), (0, 1)} and S = {u₁, u₂} = {(1, 2), (2, 3)}. Then the matrix A representing F relative to the basis E is: