List of top Mathematics Questions asked in CUET (PG)

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

If P(x) is a polynomial of degree 10 with leading coefficient as 11 and having (x-1), (x-2), (x-3),...(x-10) as factor, then the coefficient of x⁹ in P(x) 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?

Function f(x)=(x+1)^cotx is continuous at x = 0, then the value of f(0) is

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:

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

If λ₁,λ₂,λ₃ are the given values of the matrix \(\begin{bmatrix}   -2 & 2 & -3 \\   2 & 1 & -6 \\ -1 & -2 & 0 \end{bmatrix}\), then λ₁²+λ₂²+λ₃² is equal to

The dimension of the general solution space W of the homogeneous system
x₁+2x₂-3x₃+2x₄-4x₅=0
2x₁+4x₂-5x₃+x₄-6x₅ = 0
5x₁+10x₂-13x₃+4x₄-16x₅= 0

If A=\(\begin{bmatrix} 1 & 2 & 0 & -1\\   2 & 6 & -3 & -3\\  3 & 10 & -6 & -5 \end{bmatrix}\), then which one of the following is true?

Find the sum of two consecutive numbers in which four times are first number is 12 more than the thrice of the second number

If f is twice differentiable function such that f''(x) = - f(x) and f'(x) = g(x), h(x) = [f(x)]²+[g(x)]² and h(5)=11, then h(10) =

The equation of the bisector of the acute angle between the lines 3x-4y+7=0 and 12x+5y-2=0

If \(x^2\frac{d^2y}{dx^2}-2x\frac{dy}{dx}-4y=x^4\), then particular integral (P.I) of the given differential equation is

Let f(z) = u + iv be an analytic function, where u = x³-3xy² +3x² -3y², then the imaginary part v of f(z) is

The order of 16 in \((\mathbb{Z}_{24}, +_{24})\) is:

Which one of the following is correct :-

A beam is supported at its ends by supporters which are 12 meters apart. Since the load is concentrated at its centre, there is a deflection of 3 cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection 1 cm?

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

The tangent to the hyperbola x²-y² = 3 are parallel to the straight line 2x + y +8=0 points are

The number of common tangents that can be drawn to the circle x²+y²-4x-6y-3=0 and x²+y²+2x+2y+1=0 is

The Value of \(lim_{n\rightarrow \infty }\bigg[\frac{2}{1}\bigg(\frac{3}{2}\bigg)^2\bigg(\frac{4}{3}\bigg)^3.....\bigg(\frac{n+1}{n}\bigg)^n\bigg]^{\frac{1}{n}}is\)

If the solution of \(x\frac{dy}{dx}+y=x^3y^6\) is \(\frac{1}{y^\alpha x^\beta}=\frac{\gamma}{2x^2}+C\), then value of \(\alpha+\beta+\gamma\) is

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

The general solution of \((D^2+6D+9)y=\frac{e^{-3x}}{x^2}\), where \(D\equiv \frac{d}{dx}\) is
(given that c₁ and c₂ are arbitrary constants)