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

If \(y=log[\frac{x^2}{e^2}]\) then value of \(\frac{d^2y}{dx^2}\) is:

A metallic sphere of radius 8 cm is melted to form a cone with radius same as that of sphere. What is the height of the cone (in cm) ?

Let \(tan^{-1}y=tan^{-1}x+tan^{-1}(\frac{2x}{1-x^2})\). Then y is:

In an A.P., the product of the first term and the second term is 120 and the product of the second term and the third term is 168. Find the tenth term of the A.P. when common difference \(d>0\)

The Matrix \(M = \begin{bmatrix}        0 & 1 & -1           \\[0.3em]        -1  & 0           &1 \\[0.3em]       1          & -1 & 0     \end{bmatrix}\)is
(A) Symmetric matrix 
(B) Square matrix 
(C) Diagonal matrix
(D) Skew-symmetric matrix
(E) Scalar matrix
Choose the correct answer from the options given below:

The value of \(K\),If \(\begin{bmatrix}    1 & K & 3          \\[0.3em]        3 & K   & -2 \\[0.3em]  2  & 3 & -1      \end{bmatrix}=33\),is :

If A and B are symmetric matrices, then which statements are correct?
(A) \((A-B)' = B' - A'\)
(B) \((AB+BA)\) is symmetric matrix
(C) \((AB)'= B'A'\)
(D)\( A'B' = B'A'\)
(E)\( (AB-BA) \)is skew symmetric matrix
Choose the correct answer from the options given below:

The number of phone calls (in thousands) are made by a telephone company for five weeks as given below:

Week	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)
No. of Telephone calls	\(110\)	\(130\)	\(93\)	\(104\)	\(211\)

Taking a period of moving averages as 3 weeks, the graph of moving averages can be depicted directly as :

A piece of paper is folded and a cut is made as shown below. How it will appear when opened?

The sum of order and degree of the differential equation\[\frac{\{1+(\frac{dy}{dx})^2\}^\frac{5}{2}}{\frac{d^2y}{dx^2}}=p\]is:

A loan of ₹200000 at the interest rate of 6% p.a. compounded monthly is to be amortized by equal payments at the end of each month for 5 years. The monthly payment is:
[Given (1.005)^-60 = 0.74137220]

The points of non differentiability of \(f(x) = |x-2| + |x - 3|\)
A. 1
B. 2
C. 3
D. 4
E. 5
Choose the correct answer from the options given below:

The area of the shaded portion

is:

Let a pair of dice be thrown and the random variable X be the sum of numbers on the two dice. Then.
Match List I with List II.

List I	List II
A. P (X = 2)	I. \(\frac{4}{36}\)
B. P (X = 4)	II. \(\frac{5}{36}\)
C. P (X - 5)	III. \(\frac{1}{36}\)
D. P (X - 6)	IV. \(\frac{3}{36}\)

Choose the correct answer from the options given below:

For the LPP, Min \(Z= 5x + 7y\) subject to \(x≥0, y≥0; 2x+y≥8, x+2y≥ 10,\) the basic feasible solutions are:

The price per unit of a commodity produced by a company is given by P = 92 - 2x², where x is the quantity demanded. The marginal revenue of producing 3 units of such a commodity shall be :

The differential equation whose solution is Ax²+By²=1 where A and B are arbitrary constant is of:
(A) first order and first degree
(B) second order and first degree
(C) second order and second degree
(D) second order
Choose the correct answer from the options given below:

The radius of a spherical ball is increasing at the rate of 1 m/sec. At the radius equal to 3m, the volume of the ball is increasing at the rate given by:

Simplify \(\sqrt{54-\sqrt{20+\sqrt{32-\sqrt{49}}}}\)

The inverse of the function f: R→R given by f(x) = 2x +7 is:

If \(|A|=3\)  and \(A^{-1}=\begin{bmatrix}        3 &-1 \\[0.3em]        \frac{-5}{3} & \frac{2}{3}    \\[0.3em]     \end{bmatrix}\) then adj \(A\) is 

If, \(f(x) = \begin{bmatrix}0 & x-a & x-b \\[0.3em]x+a&o & x-c \\[0.3em]x+b & x+c & 0\\[0.3em] \end{bmatrix}\), then \(f(0)\) is:

Domain of function \(f(x) = cos^{-1}\sqrt {2x-1}\) is

The area of the region bounded by the curve \(y=\sqrt{3x+10}\), x-axis and between the lines x = -3 and x = 2 is equal to :

What is emprical relationship between mean, median and mode ?
A. Mean - mode = 3(Mean - Median)
B. Mode = Mean - Median
C. Mode = 3 Median - 2 Mean
D. Median - Mode = 3 (Mean - Median)
E. Mode = 2 Mean + 3 Median
Choose the correct answer from the options given below