List of top Mathematics Questions asked in CUET (UG)

If \( \begin{bmatrix} 1 & -4 \\ 3 & -2 \end{bmatrix} A = \begin{bmatrix} -16 & -6 \\ 7 & 2 \end{bmatrix} \), then the matrix A is:

Consider the following hypothesis test \( H_0: \mu = 18 \), \( H_a: \mu \neq 18 \). A sample of 81 provided a sample mean \( \bar{x} = 17 \) and a population standard deviation \( \sigma = 4.5 \). The value of test statistic and degree of freedom are:

The present value of a perpetuity of Rs.7500 payable at the end of each year, if money is worth 5% compounded annually is:

Which of the following are the methods of measuring trends of time series?
(A) Graphical method
(B) Method of least squares
(C) Method of cyclic component
(D) Moving averages method

In a game, A can give 20 points to B, A can give 32 points to C and B can give 15 points to C. How many points make the game?

Which of the following statements are correct for Maximize \( Z = 50x + 40y \) subject to \( 1000x + 1200y \le 7600 \), \( 3x + 2y \le 18 \), \( x, y \ge 0 \)?
(A) The LPP has a unique optimal solution at (4, 3) only.
(B) The feasible region is bounded.
(C) The maximum value is unique, but there are infinite optimal solutions.
(D) The feasible region is bounded with corner points (0,0), (6,0), (4,3) and (0,19/3).

The area bounded by curves \( y = -\frac{2}{3}x + 2 \), \( x = -1 \), \( x = 2 \) and the x-axis is:

A container contains 100 litres of apple juice. From this container, 10 litres of apple juice was taken out and replaced by water. This process was further repeated twice. How much apple juice is left in the container?

If A and B are non-singular square matrices of order n, match List-I with List-II:

The remainder, when \( 2^{100} \) is divided by 11, is:

If a girl takes twice as long to row a distance against the stream as to row the same distance in the direction of the stream, then the ratio of speed of the girl in still water to the speed of stream is:

The probability of a girl hitting a target is \( 1/2 \). How many times must she fire so that the probability of hitting the target at least once is more than \( 90% \)?

Mr. Sanjay borrowed Rs.10,00,000 from a bank to purchase a car on reducing balance payment for a period of 10 years. If bank charges interest at 9% per annum compounded monthly and EMI is Rs.12,658 to be paid by him. Then principal outstanding after payment of 12th EMI is: (Use \( (1.0075)^{12 = 1.0938 \))}

A firm anticipates an expenditure of Rs.5,000,000 for plant modernization at the end of 10 years from now, then the amount the company should deposit at the end of each year into a sinking fund earning interest 5% per annum is [use (1.05)¹⁰ = 1.629]:

If \( y = \frac{x^2}{1 + x^{b-a} + x^{c-a}} + \frac{x^2}{1 + x^{a-b} + x^{c-b}} + \frac{x^2}{1 + x^{a-c} + x^{b-c}} \), then \( \frac{dy}{dx} \) is:

A measurable characteristic of a sample is known as:

If a machine is correctly set up, it produces 80% acceptable items. If it is incorrectly set up, it produces only 30% acceptable items. From the past experience it was known that 90% of the setups are correctly done. If after a certain setup, the machine produces 2 acceptable items then the probability that the machine was correctly set up, is:

If \( A = \begin{bmatrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix} \) then \( A^2 - (2 \cos \alpha) A \) is equal to: (Where I is identity matrix of order 2)

The probability of drawing a one-rupee coin from a purse with two compartments, one of which contains 3 fifty paise coins and 2 one-rupee coins and other contains 2 fifty paise coins and 3 one-rupee coins, is

A line passes through (2, 1, 3) and (1, 2, -1), then
(A) Equation is \( \frac{x-2}{1} = \frac{y-1}{1} = \frac{z-3}{4} \)
(B) Equation is \( \frac{x+2}{-1} = \frac{y+1}{1} = \frac{z+3}{4} \)
(C) Equation is \( \vec{r} = 2\vec{i} + \vec{j} + 3\vec{k} + \lambda(\vec{i} - \vec{j} + 4\vec{k}) \)
(D) Equation is \( \frac{x-1}{1} = \frac{y-2}{-1} = \frac{z+1}{4} \)
Choose the correct answer:

The integral of \( \int_{-2}^{2} x^4 \, dx \) denominator \( (1+5x^2) \) is:

If A and B are two independent events and P(A) = 1/2, P(B) = 1/3, then Match List-I with List-II

The solution set of the inequation \( 2x + 3y > 12 \) is

Solution of \( \frac{x^2 - 4x + 7}{x^2 - 7x + 12} \le \frac{2}{3} \) is/are:
Choose the correct answer:

If \( A = \begin{bmatrix} 1 & 2 & -1 \\ -1 & 1 & 2 \\ 2 & -1 & 1 \end{bmatrix} \) then \( |adj(adj A)| \) is equal to