List of top Mathematics Questions asked in CUET (PG)

If \(A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix} \)and I = unit matrix, then the value of \(A^2-4A\) is:

Aman travels from P to Q at a speed of 40 km/hour and returns to P by increasing his speed by 50%. What is his average speed for the entire journey?

Values of \(K\) for which the quadratic equation \(2x^2 - Kx + K=0\) has equal roots are:

A, B, C and D entered into a partnership. 'A' contributed one-third of the capital, 'B' contributed one-fourth, 'C' contributed one-fifth and 'D' contributed the rest. All four of them agreed to share profit in the ratio of their capital. What is the share of 'D' when total profit is ₹6000?

Cost price of 100 copies of a book is equal to the selling price of 60 copies of the same book. The gain or loss percentage is:

Which property is true for convolution integral?
A.$ h_1(t)*h_2(t)=h_2(t)*h_1(t) $
B. $[h_1(t)+h_2(t)]* h_3(t) = h_1(t)* h_3 (t) +h_2 (t) * h_3(t)$
C. $[h_!(t)+h_2(t)]*h_3(t) = h_1(t)h_3(t)+h_2(t)h_3(t) $
D. $h_1(t)*h_2(t)=h_2(t)h_1(t) $
Choose the correct answer from the options given below.

Consider the following three equations:
2x+3y+5z=9,        7x+3y-2z=8,           2x+3y+λz=μ 
A. For λ ≠5, system will have a unique solution. 
B. For λ=5, μ ≠ 9, system will have infinite solution. 
C. If λ=5 and μ=9, system will have infinite solution. 
D. For μ = 9, system will have no solution.
E. For λ = 5, system will have no solution. 
Choose the correct answer from the options given below.

Given below are two statements
Statement-I :   \(f(x)=\begin{cases} \frac{3x-2}x \quad &\text{for  0≤x≤1}\\          \frac{sin(x-1)}{x-1} \quad &\text{for} \,\, x>1 \\      \end{cases}\)
Function is continuous at x=1
Statement-II: \(f(x)=\begin{cases} \frac{xe^\frac{1}x}{1+e^{\frac1{x}}} \quad &\ ; x\neq 0\\          0\quad &\text{; } \,\, x=0 \\      \end{cases}\)
Function is continuous at origin. 
In the light of the above statements, choose the correct answer from the options given below.

If $V_1$ and $V_2$ are the 3-dimensional subspaces of the 4-dimensional vector space, then the smallest possible dimension of $V_1 ∩ V_2$ is

Laplace transform and Z-transform are related by

$ \begin{vmatrix} 1+a & 1 & 1 & 1 \\ 1 & 1+b & 1 & 1 \\ 1 & 1 & 1+c & 1 \\ 1 & 1 & 1 & 1=d  \end{vmatrix} $ is equal to

A cone of height at 24 cm and base radius 6 cm is made of modelling clay. A child reshapes it in the form of a sphere. The radius of the sphere is:

Let F: [0,π ]→R be defined as f(x) = sinx, then maximum value of f(x) exists at

The mean deviation from the mean of the AP: a,a+d, a+2d,..., a+2nd, is

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): cos(x²), is a periodic function.
Reasons (R): If f(x) is periodic function with periods T and if a,b ∈ R such that a>0 then (ax+b) is periodic with period T/a.
In the light of the above Statements, choose the correct answer from the options given below:

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): Sum of n terms of series 1²+3²+5²+... to n terms is \(\frac{n}{3}(4n^2-1)\).
Reasons (R): Sum of the squares of first a natural numbers 1², 2², 3²,....,n² is \(\frac{n(n+1)(2n+1)}6\).
In the light of the above Statements, choose the correct answer from the options given below:

Given below are two statements:
Statement I: The sum of the series 2{7^-1+3^-17^-3 +5^-1.7^-5 +....} is log_e(\(\frac{4}{3}\)).
Statement II: The value of e always lies between 2 and 3.
In the light of the above Statements, choose the most appropriate answer from the options given below :

Given below are two statements:
Statement I: For n ≥1, we have \(\frac{1}{1·2}+\frac{1}{2·3}+\frac{1}{3·4}+.....+\frac{1}{n(n+1)}=\frac{n^2}{n+1}\)
Statement II: (1+x)ⁿ ≥ (1+nx) for all natural number n, where x > -1.
In the light of the above Statements, choose the most appropriate answer from the options given below :

Match List-I and List-II

LIST I		LIST II
A.	\(\lim\limits_{x\rightarrow0}(1+sinx)^{2\cot x}\)	I.	e-1/6
B.	\(\lim\limits_{x\rightarrow0}e^x-(1+x)/x^2\)	II.	e
C.	\(\lim\limits_{x\rightarrow0}(\frac{sinx}{x})^{1/x^2}\)	III.	e2
D.	\(\lim\limits_{x\rightarrow\infty}(\frac{x+2}{x+1})^{x+3}\)	IV.	½

Choose the correct answer from the options given below:

Which of the following is not correct?
(A) If A, B are two matrices such that AB = A and BA=B, then A and B are idempotent.
(B) Every skew - symmetric matrix of odd order is invertible.
(C) If A is a non-singular matrix, then A^-1 is skew-symmetric.
(D) The adjoint of a diagonal matrix is a diagonal matrix.
Choose the correct answer from the options given below :

Which of the following assertions are correct?
(A) Adding 7 to each entry in a list adds 7 to the mean of the list.
(B) Adding 7 to each entry in a list adds 7 to the standard deviation of the list.
(C) Doubling each entry in a list doubles the mean of the list.
(D) Doubling each entry in a list leaves the standard deviation of the list unchanged.
Choose the most appropriate answer from the options given below :

Let f(w,x,y,z) = ∑(0, 4, 5, 7, 8, 9, 13, 15). Which of the following expressions are NOT equivalent to f?
(A) x'y'z'+w'xy'+wy'z +xz
(B) w'y'z'+wx'y'+xz
(C) w'x'y'z'+wx'y'+xyz + xy'z
(D) x'y'z'+x'y'+w'y
(E) x'y'z'+wx'y'+w'y
Choose the correct answer from the options given below:

Consider the following statements:
(A) If P ={m,n} and Q={n, m}, then P×Q = {(m,n), (n,m)}.
(B) If A and B are the non-empty sets, then A×B is a non empty set of ordered pairs (x, y) such that x ∈ A and y ∈ B.
(C) If A = {1, 2}, B={3,4}, then A × (B∩Φ)=Φ.
Choose the most appropriate answer from the options given below :

For the given Truth Table is true:

A	B	C	Y
0	1	1	?

(A) Y is 1 for A XOR B AND C
(B) Y is 1 for A NOR B NAND C
(C) Y is 0 for A AND B AND C
Choose the most appropriate answer from the options given below :

Given below are two statements:
Statement I: The locus of the middle points of chords of the circle x²+ y² = a² which are parallel to the line y=mx is x-my = 0.
Statement II: The two tangents drawn from (4, 2) to x² + y² = 10 are perpendicular.
In the light of the above Statements, choose the most appropriate answer from the options given below :