List of top Questions asked in CUET (PG)- 2023

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?
Which of the following are generators of the multiplicative group {(1,2,3,4,5,6), x7} where x7 denotes multiplication moduls 7?
In a group G, if a5 = e, aba-1 = b2 for a, b ∈ G then o(b) is equal to:
Which one of the following statements is wrong.
Which one of the following is wrong?
If W is a subspace of R3, where W = {(a, b, c): a+b+c = 0}, then dim W is equal to
Which of the following is incorrect?
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
Given below are two statements
Statement I: Let G a finite group and H a subgroup of G. Then, the order of H is a divisor of the order of G. That is, |H| divides |G|
Statement II: Let a be an element in a finite group G. Then, O(a) divides |G|
In the light of the above statements, choose the most appropriate answer from the options given below
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
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
The function f(z) defined by \(f(z)= \begin{cases}     \frac{Re(z)}{z}       & z\neq0\\     0  & z=0   \end{cases}\)then which one of the following is true?
Which one of the following is not correct?
A rectangular box open at the top is to have volume of 32 cubic feets. The minimum outer surface area of the box is
If 2.5x=0.05 y, then find the value of \((\frac{y-x}{y+x}).\)
If f: R2→R2 is a function defined as \(f(x,y) =   \begin{cases}   \frac{x}{\sqrt{x^2+y^2}},      & x\neq0,y\neq0\\     2,  & x=0,y=0   \end{cases}\)then, which of the following is correct?
The extreme points of the set \({(x, y); |x|≤2,|y|≤2}\) are
If \(f(z)=\frac{1}{z^2-3z+2}\)is expanded in the region |z|<1, then
The given series \(\frac{x}{1.3}+\frac{x^2}{2.4}+\frac{x^3}{3.5}+......,(x\gt0)\)is convergent in the interval
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
A single 6-sided dice is rolled, then the probability of getting an odd number is
Match List I with List II
LIST I LIST II
A.A square matrix A is said to be symmetric if I.A=A'
B.A square matrix A is said to be skew symmetric ifII.A= -A'
C.If A is any square matrix thenIII.A+A' is a symmetric matrix
D.If A is any square matrix thenIV.A-A' is a skew symmetric matrix
Choose the correct answer from the options given below:
Given below are two statements
Statement I: Draw back in Lagrange's method of undetermined multipliers is that nature of stationary point cannot be determined
Statement II: \(\displaystyle\sum_{n=1}^{∞} (-1)^{n-1}\frac{1}{n\sqrt n}\)convergent
In the light of the above statements, choose the correct answer from the options given below
If \(\int\int_R(x + y) dydx = A\), where R is the region bounded by x = 0, x = 2, y = x, y = x+2, then \(\frac{A}{12}\) is equal to: