List of top Mathematics Questions asked in CUET (UG)

The least non-negative remainder when 3⁵¹ is divided by 7 is:

A multinational company creates a sinking fund by setting a sum of Rs. 12,000 annually for 10 years to pay off a bond issue of Rs. 72,000. If the fund accumulates at\(5\% \)per annum compound interest, then the surplus after paying for bond is

A random variable X has the following probability distribution:

X	-2	-1	0	1	2
P(X)	0.2	0.1	0.3	0.2	0.2

The variance of X will be:

The equation of the tangent to the curve x^5/2 + y^5/2 = 33 at the point(1, 4) is:

If A =\(\begin{bmatrix}2 & 4 \\4 & 3 \end{bmatrix} \), X =\(\begin{bmatrix}n \\1 \end{bmatrix}\),B =\(\begin{bmatrix}8 \\11 \end{bmatrix}\),and AX = B, then the value of n will be:

Three defective bulbs are mixed with 8 good ones. If three bulbs are drawn one by one with replacement, the probabilities of getting exactly 1 defective, more than 2 defective, no defective, and more than 1 defective respectively are:

If the lengths of the three sides of a trapezium other than the base are 10 cm each, then the maximum area of the trapezium is:

A company is selling a certain commodity ‘x’. The demand function for the commodity is linear. The company can sell 2000 units when the price is Rs. 8 per unit and it can sell 3000 units when the price is Rs. 4 per unit. The Marginal revenue at x = 5 is:

If the matrix\(\begin{bmatrix}0 & -1 & 3x\\1 & y & -5\\-6 & 5 & 0 \end{bmatrix} \)is skew-symmetric, then the value of 5x−y is:

The corner points of the feasible region for an L.P.P. are (0, 10), (5, 5), (5, 15), and (0, 30). If the objective function is Z = αx + βy, α, β > 0, the condition on α and β so that maximum of Z occurs at corner points (5, 5) and (0, 20) is:

A property dealer wishes to buy different houses given in the table below with some down payments and balance in EMI for 25 years. Bank charges 6% per annum compounded monthly.

For the given five values 12, 15, 18, 24, 36; the three-year moving averages are:

In a 700 m race, Amit reaches the finish point in 20 seconds and Rahul reaches in 25 seconds. Amit beats Rahul by a distance of:

A person wants to invest 75,000 in options A and B, which yield returns of 8% and 9% respectively. He plans to invest at least 15,000 in Plan A, 25,000 in Plan B, and keep Plan A ≤ Plan B. Formulate the LPP to maximize the return.

Ms. Sheela creates a fund of 100,000 to provide scholarships to needy children. The scholarship is provided at the beginning of each year, and the fund earns an interest of r% annually. If the scholarship amount is 8,000, find r.

Match List-I with List-II:

List-I	List-II
(A) Distribution of a sample leads to becoming a normal distribution	(I) Central Limit Theorem
(B) Some subset of the entire population	(II) Hypothesis
(C) Population mean	(III) Sample
(D) Some assumptions about the population	(IV) Parameter

Choose the correct answer from the options given below.

The probability of a shooter hitting a target is 3/4 How many minimum number of times must he fire so that the probability of hitting the target at least once is more than 90%?

If \( e^y = x^x \), then which of the following is true?

Arun's swimming speed in still water is 5 km/hr. He swims between two points in a river and returns to the starting point. He took 20 minutes more upstream than downstream. If the stream speed is 2 km/hr, the distance between the points is:

A flower vase costs 36,000. With an annual depreciation of 2,000, its cost will be 6,000 in how many years?

For which of the following purposes is CAGR (Compounded Annual Growth Rate) not used?

Match List-I with List-II:

List-I (Function)	List-II (Derivative w.r.t. x)
(A) \( \frac{5^x}{\ln 5} \)	(I) \(5^x (\ln 5)^2\)
(B) \(\ln 5\)	(II) \(5^x \ln 5\)
(C) \(5^x \ln 5\)	(III) \(5^x\)
(D) \(5^x\)	(IV) 0

Choose the correct answer from the options given below.

A random variable X has the following probability distribution:

X	1	2	3	4	5	6	7
P(X)	k	2k	2k	3k	k2	2k2	7k2 + k

Match the options of List-I to List-II:

List-I	List-II
(A) k	(I) 7/10
(B) P(X < 3)	(II) 53/100
(C) P(X ≥ 2)	(III) 1/10
(D) P(2 < X ≤ 7)	(IV) 3/10

Choose the correct answer from the options given below.

The probability of not getting 53 Tuesdays in a leap year is: