List of top Questions asked in CUET (UG)

Match the following financial terms with their most suitable meaning/synonym:

Choose the correct answer from the options given below :

Let $A$ be a matrix such that $A^2 = I$, where $I$ is an identity matrix. Then $(I + A)^4 - 8A$ is equal to:

An equilateral triangle of side \( 4\sqrt{3} \) cm formed out of a sheet is converted into a rectangle such that there is no loss of the area of the triangle. Then the least perimeter of the rectangle (in cm) will be:

A coin is tossed twice. Then Match List-I with List-II:

List-I	List-II (Adverbs)
(A) P(exactly 2 heads)	(I) \(\frac{1}{4}\)
(B) P(at least 1 head)	(II) \(1\)
(C) P(at most 2 heads)	(III) \(\frac{3}{4}\)
(D) P(exactly 1 head)	(IV) \(\frac{1}{2}\)

Choose the correct answer from the options given below :

If the solution of the differential equation \[ \frac{dy}{dx} = \frac{ax + 3}{2y + 5} \] represents a circle, then $a$ is equal to:

Match List-I with List-II:

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The area (in square units) enclosed between the curve $x^2 = 4y$ and the line $x = y$ is:

The area (in square units) bounded by the curve y = |x−2| between x = 0, y = 0, and x = 5 is:

Two charged particles, placed at a distance d apart in vacuum, exert a force F on each other. Now, each of the charges is doubled. To keep the force unchanged, the distance between the charges should be changed to_____
Fill in the blank with the correct answer from the options given below.

If \[ A = \begin{bmatrix} 2 & 4 \\ x & 2 \end{bmatrix} \] and $A$ is singular, then $x$ is equal to:

Let \( f : \mathbb{R} \to \mathbb{R} \) be defined as \( f(x) = 10 - x^2 \), then:

A particle moves along the curve \(6x = y^3 + 2\). The points on the curve at which the \(x\) coordinate is changing 8 times as fast as \(y\) coordinate are:

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

Relation \( R \) on the set \( A = \{1, 2, 3, \ldots, 13, 14\} \) defined as \( R = \{(x, y) : 3x - y = 0\} \) is:

The area (in square units) of the region bounded by curves \( y = x \) and \( y = x^3 \) is:

A pair of dice is rolled . If the two numbers appearing on them are different the probability that
Match List-I with List-II
 

LIST-I(EVENT)	LIST-II(PROBABILITY)
(A) The sum of the number is greater than 11	(i) 0
(B) The sum of the number is 4 or less	(ii) 1/15
(C) The sum of the number is 4	(iii) 2/15
(D) The sum of the number is 4	(iv) 3/15

Choose the correct answer from the option given below

The interval, in which the function \( f(x) = \frac{3}{x} + \frac{x}{3} \) is strictly decreasing, is:

The integral of the function \( \frac{1}{9 - 4x^2} \) is:

Let \( f(x) = x^3 - 6x^2 + 12x - 3 \), then at \( x = 2 \), \( f(x) \) has:

A random variable \( X \) has the following probability distribution:

X	0	1	2	otherwise
P(X)	k	2k	3k	0

Then: 
(A) \( k = \frac{1}{6} \) 
(B) \( P(X < 2) = \frac{1}{2} \) 
(C) \( E(X) = \frac{3}{4} \) 
(D) \( P(1 < X \leq 2) = \frac{5}{6} \) 
Choose the correct answer from the options given below:

Formaldehyde undergoes Cannizzaro reaction because
(A) It has alpha-hydrogen atom.
(B) It does not have alpha-hydrogen atom.
(C) It does not undergo self-oxidation and reduction on heating with concentrated alkali.
(D) It undergoes self-oxidation and reduction on heating with concentrated alkali.

If \( A = \begin{bmatrix} 5 & 1 \\ -2 & 0 \end{bmatrix} \) and \( B^T = \begin{bmatrix} 1 & 10 \\ -2 & -1 \end{bmatrix} \), then the matrix \( AB \) is:

A sample size of \(x\) is considered to be sufficient to hold the Central Limit Theorem (CLT). The value of \(x\) should be:

In a 600 m race, the ratio of the speeds of two participants A and B is 4:5. If A has a head start of 200 m, then the distance by which A wins is:

The cost of a machinery is ₹8,00,000. Its scrap value will be one-tenth of its original cost in 15 years. Using the linear method of depreciation, the book value of the machine at the end of the 10th year will be: