List of top Questions asked in CUET (UG)

An even number is the determinant of \(\text{(A)} \ \begin{bmatrix} 1 & -1 \\ -1 & 5 \end{bmatrix} \quad \text{(B)} \ \begin{bmatrix} 13 & -1 \\ -1 & 15 \end{bmatrix} \quad \text{(C)} \ \begin{bmatrix} 16 & -1 \\ -11 & 15 \end{bmatrix} \quad \text{(D)} \ \begin{bmatrix} 6 & -12 \\ 11 & 15 \end{bmatrix}\)
Choose the \(\textbf{correct}\) answer from the options given below:  

Two pipes A and B together can fill a tank in 40 minutes. Pipe A is twice as fast as pipe B. Pipe A alone can fill the tank in:

A coin is tossed K times. If the probability of getting 3 heads is equal to the probability of getting 7 heads, then the probability of getting 8 tails is:

For I =\(\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix}\), if X and Y are square matrices of order 2 such that XY = X and Y X = Y , then (Y² + 2Y ) equals to:

A mixture contains apple juice and water in the ratio 10 : x. When 36 litres of the mixture and 9 litres of water are mixed, the ratio of apple juice and water becomes 5 : 4. The value of x is:

For an investment, if the nominal rate of interest is\(10\%\)compounded half-yearly, then the effective rate of interest is:

The following data is from a simple random sample: 15, 23, x, 37, 19, 32. If the point estimate of the population mean is 23, then the value of x is:

Which of the following are components of a time series?(A) Irregular component
(B) Cyclical component
(C) Chronological component
(D) Trend Component
Choose the correct answer from the options given below:

If\(\begin{bmatrix}5x+8 & 7 \\y+3 & 10x+12 \end{bmatrix} \)=\(\begin{bmatrix}2 & 3y+1 \\5 & 0 \end{bmatrix} \)then the value of 5x + 3y is equal to:

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.