List of top Mathematics Questions asked in CUET (UG)

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.

An objective function $Z = ax + by$ is maximum at points $(8, 2)$ and $(4, 6)$. If $a \geq 0$ and $b \geq 0$ and $ab = 25$, then the maximum value of the function is:

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.

If \( A \), \( B \), and \( C \) are three singular matrices given by \[ A = \begin{bmatrix} 1 & 4 \\ 3 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 3b & 5 \\ a & 2 \end{bmatrix}, \quad \text{and} \quad C = \begin{bmatrix} a + b + c & c + 1 \\ a + c & c \end{bmatrix}, \] then the value of \( abc \) is:

If \((\vec{a} - \vec{b}) \cdot (\vec{a} + \vec{b}) = 27\) and \(|\vec{a}| = 2|\vec{b}|\), then \(|\vec{b}|\) is:

The angle between two lines whose direction ratios are proportional to \(1, 1, -2\) and \((\sqrt{3} - 1), (-\sqrt{3} - 1), -4\) is:

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

Let \( R \) be the relation over the set \( A \) of all straight lines in a plane such that \( l_1 \, R \, l_2 \iff l_1 \) is parallel to \( l_2 \). Then \( R \) is:

Which one of the following represents the correct feasible region determined by the following constraints of an LPP?
\[ x + y \geq 10, \quad 2x + 2y \leq 25, \quad x \geq 0, \quad y \geq 0 \]

Which of the following cannot be the direction ratios of the straight line \(\frac{x - 3}{2} = \frac{2 - y}{3} = \frac{z + 4}{-1}\)?

There are two bags. Bag-1 has 4 white and 6 black balls, and Bag-2 has 5 white and 5 black balls. A die is rolled, and if it shows a multiple of 3, a ball is drawn from Bag-1; otherwise, from Bag-2. If the ball drawn is not black, the probability it was not drawn from Bag-2 is:

For the differential equation \((x \log x) \, dy = (\log x - y) \, dx\):
(A) Degree of the given differential equation is 1.
(B) It is a homogeneous differential equation.
(C) Solution is \(2y \log x + A = (\log x)^2\), where \(A\) is an arbitrary constant.
(D) Solution is \(2y \log x + A = \llog(\ln x)\), where \(A\) is an arbitrary constant.