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

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
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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:

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 

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 value of \(\lambda\), for which the projection of \(\vec{a} = \lambda \hat{i} + \hat{j} +4 \hat{k}\) on \(\vec{b} =2\hat{i} +6 \hat{j} +3\hat{k}\) is 4 units

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
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A 180 m long train crosses a man standing on the platform in 6 seconds. What is the speed of the train?

If each side of a cube is x, then the angle between the diagonals of the cube 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:

The value of the determinant \(\begin{vmatrix}acosθ&bsinθ&0 \\-bsinθ&acosθ&0\\ 0&0&c\end{vmatrix}\) is:

By selling on book for 250, loss percentage is 10%. What is the cost price?

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. \(\frac{3}{36}\)

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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 :

A's month salary was ₹40000 and he used to save ₹10000 per month. His salary increased by 25% and expenditure increased by 15%. By what percent his savings increased ?

Consider the following hypothesis test:
\(Η_0: μ ≤ 20\)
\(Η_1 : μ > 20\)
A sample of 81 produced a sample mean of 20.55. The population standard deviation is 3. The value of the test statistic is:

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

Which of the following speeds is maximum?

Two years ago, population of a city was \(16,52,600 \)which increased by \( 10\%\) in the first year and by \(15\%\) in the second year. Find the present population of the city.

Find the area of an equilateral triangle each of whose sides measures 4 cm :

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

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

Let A and B be symmetric matrices of same order, then which of the following statement is true?

Match List I with List II

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If y = \(10^{10^x}\), then \(\frac{dy}{dx}\) is :

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: