List of top Mathematics Questions asked in CUET (UG)

For predicting the straight-line trend in the sales of washing machines (in thousands) on the basis of 8 consecutive years' data, the company calculates 4-year moving averages. If the sales of washing machines for respective years are \( a, b, c, d, e, f, g, \) and \( h \), then which of the following averages will be computed?
(A) \( \frac{a + b + c + d}{4} \)
(B) \( \frac{a + c + d + e}{4} \)
(C) \( \frac{c + d + f + h}{4} \)
(D) \( \frac{b + c + d + e}{4} \)
Choose the correct answer from the options given below:

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:

The correct solution of \(-22 < 8x - 6 \leq 26\) is the interval:

Vibhuti bought a car worth ₹10,25,000 and made a down payment of ₹4,00,000. The balance is to be paid in 3 years by equal monthly installments at an interest rate of 12% p.a. The EMI that Vibhuti has to pay for the car is:
(Use \( (1.01)^{-36} = 0.7 \))

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:

Match List-I with List-II.

List-I	List-II
(A) Confidence level	(I) Percentage of all possible samples that can be expected to include the true population parameter
(B) Significance level	(III) The probability of making a wrong decision when the null hypothesis is true
(C) Confidence interval	(II) Range that could be expected to contain the population parameter of interest
(D) Standard error	(IV) The standard deviation of the sampling distribution of a statistic

Choose the correct answer from the options given below:

If \( y = e^{{2}\log_e t} \) and \( x = \log_3(e^{t^2}) \), then \( \frac{dy}{dx} \) is equal to:

David can row a boat in still water at the rate of 5 km/hr. He rowed in a river downstream to meet his friend. After returning back, he observed that the duration of the upstream journey was three times that of the downstream journey. The speed of the stream was:

A furniture trader deals in tables and chairs. He has Rs. 75,000 to invest and a space to store at most 60 items. A table costs him Rs. 1,500 and a chair costs him Rs. 1,000. The trader earns a profit of Rs. 400 and Rs. 250 on a table and chair, respectively. Assuming that he can sell all the items that he can buy, which of the following is/are true for the above problem:

(A) Let the trader buy \( x \) tables and \( y \) chairs. Let \( Z \) denote the total profit. Thus, the mathematical formulation of the given problem is:

\[ Z = 400x + 250y, \]

subject to constraints:

\[ x + y \leq 60, \quad 3x + 2y \leq 150, \quad x \geq 0, \quad y \geq 0. \]

(B) The corner points of the feasible region are (0, 0), (50, 0), (30, 30), and (0, 60).

(C) Maximum profit is Rs. 19,500 when trader purchases 60 chairs only.

(D) Maximum profit is Rs. 20,000 when trader purchases 50 tables only.

Choose the correct answer from the options given below:

In a series of 4 trials, the probability of getting two successes is equal to the probability of getting three successes. The probability of getting at least one success is:

For the curve \( y(1 + x^2) = 2 - x \), if \(\frac{dy}{dx} = \frac{1}{A}\) at the point where the curve crosses the x-axis, then the value of \( A \) is:

A company produces 'x' units of geometry boxes in a day. If the raw material of one geometry box costs ₹2 more than the square of the number of boxes produced in a day, the cost of transportation is half the number of boxes produced in a day, and the cost incurred on storage is ₹150 per day. The marginal cost (in ₹) when 70 geometry boxes are produced in a day is:

If \( A = \begin{bmatrix} K & 4 \\ 4 & K \end{bmatrix} \) and \( |A^3| = 729 \), then the value of \( K^8 \) is:

Two pipes A and B can fill a tank in 32 minutes and 48 minutes respectively. If both the pipes are opened simultaneously, after how much time B should be turned off so that the tank is full in 20 minutes?