List of top Mathematics Questions asked in CUET (PG)

With the help of suitable transform of the independent variable, the differential equation
\(x\frac{d^2y}{dx^2}+\frac{2dy}{dx}=6x+\frac{1}{x}\) reduces to the form:
If \(f(z)=\frac{1}{z^2-3z+2}\)is expanded in the region |z|<1, then
The order of the permutation\(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\   2 & 4 & 6 & 5 & 1 & 3 \end{pmatrix}\)is
The given series \(\frac{x}{1.3}+\frac{x^2}{2.4}+\frac{x^3}{3.5}+......,(x\gt0)\)is convergent in the interval
The order of the given permutation \(\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6& 7&8&9 \\2 &4& 6 &1 &7&3& 8&9 &5  \end{pmatrix}\) 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?
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:
Which of the following are generators of the multiplicative group {(1,2,3,4,5,6), x7} where x7 denotes multiplication moduls 7?
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?
The point (-1, 2, 7, 6) lies in which of the following half spaces corresponding to hyperplane 2x1+3x2+4x3+5x4 = 6
In a group G, if a5 = e, aba-1 = b2 for a, b ∈ G then o(b) is equal to:
If W is a subspace of R3, where W = {(a, b, c): a+b+c = 0}, then dim W is equal to
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 volume generated by the revolution of the cardiod r = a(1-cosθ) about x-axis is
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 f(x) satisfies the conditions of Rolle's theorem in [1, 2] and f(x) is continuous in [1, 2], then \(\int_1^2f'(x)dx\) is equal to
The Value of \(lim_{n\rightarrow \infty }\bigg[\frac{2}{1}\bigg(\frac{3}{2}\bigg)^2\bigg(\frac{4}{3}\bigg)^3.....\bigg(\frac{n+1}{n}\bigg)^n\bigg]^{\frac{1}{n}}is\)
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
Let \(F: R^4 → R^3\) be the linear mapping defined by:
F(x,y,z,t)=(x-y+z+t, 2x-2y+3z+4t, 3x-3y+4z+5t), then nullity (F) equals
Given below are two statements
Statement I: Every cyclic group is abelian
Statement II: (Z,+) is a cyclic group with 1 and -1 as the only generators
In the light of the above statements, choose the most appropriate answer from the options given below
The average of 5 consecutive odd positive integers is 9. Then sum of smallest and greatest number is
The orthogonal trajectories of the family of curves y = \(ax^3\) is