List of top Mathematics Questions asked in CUET (UG)

Match List-I with List-II:

List-I	List-II
(A) 4î − 2ĵ − 4k̂	(I) A vector perpendicular to both î + 2ĵ + k̂ and 2î + 2ĵ + 3k̂
(B) 4î − 4ĵ + 2k̂	(II) Direction ratios are −2, 1, 2
(C) 2î − 4ĵ + 4k̂	(III) Angle with the vector î − 2ĵ − k̂ is cos⁻¹(1/√6)
(D) 4î − ĵ − 2k̂	(IV) Dot product with −2î + ĵ + 3k̂ is 10

Choose the correct answer from the options given below:

The interval, in which the function $ f(x) = \frac{3}{x} + \frac{x}{3} $ is strictly decreasing, is:

Two events $X$ and $Y$ are such that $P(X) = \frac{1}{3}$, $P(Y) = n$, and the probability of occurrence of at least one event is 0.8. If the events are independent, then the value of $n$ is:

Match List-I with List-II.
\[ \begin{array}{|c|c|} \hline \textbf{List-I (Function)} & \textbf{List-II (Interval in which function is increasing)} \\ \hline \frac{x}{\log_e x} & (-\infty, -2) \cup (2, \infty) \\ \hline \frac{x}{2} + \frac{2}{x}, x \neq 0 & \left(-\frac{\pi}{4}, \frac{\pi}{4}\right) \\ \hline x^x, x > 0 & \left(\frac{1}{e}, \infty\right) \\ \hline \sin x - \cos x & (e, \infty) \\ \hline \end{array} \]
Choose the correct answer from the options given below:

The area of the parallelogram, whose adjacent sides are given by the vectors $\vec{a} = 2\hat{i} - \hat{j} + 5\hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} + 2\hat{k}$, is:

The ratio in which a grocer must mix two varieties of tea worth ₹60 per kg and ₹65 per kg so that by selling the mixture at ₹68.20 per kg, he may gain 10% is:

The integrating factor of the differential equation \[ (y \log_e y) \frac{dx}{dy} + x = 2 \log_e y \] is:

For the following probability distribution:

X	3	4	5
P(X)	0.5	0.2	0.3

The mean, variance, and standard deviation respectively are:

The minimum value of $x^2 + \frac{1}{x}$ 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:

The particular solution of the differential equation $(y - x^2) dy = (1 - x^3) dx$ with $y(0) = 1$, is:

A random variable $ X $ has the following probability distribution:

X	0	1	2	otherwise
P(X)	k	2k	3k	0

Then:
(A) $ k = \frac{1}{6} $
(B) $ P(X < 2) = \frac{1}{2} $
(C) $ E(X) = \frac{3}{4} $
(D) $ P(1 < X \leq 2) = \frac{5}{6} $
Choose the correct answer from the options given below:

If $ (\cos x)^y = (\sin y)^x $ then $ \frac{dy}{dx} $ is:

Let $ A $ and $ B $ be two independent events such that $ P(A) = \frac{3}{5} $ and $ P(B) = \frac{4}{9} $.

List-I (Sentences)	List-II (Adverbs)
(A) $ P(A \cap B) $	(I) $\frac{2}{5}$
(B) $ P(A \| B) $	(II)$ \frac{4}{15}$
(C) $ P(A' \| B) $	(III) $\frac{3}{5}$
(D) $ P(A' \cap B') $	(IV) $\frac{2}{9}$

Choose the correct answer from the options given below :

Let $ f(x) = x^3 - 6x^2 + 12x - 3 $, then at $ x = 2 $, $ f(x) $ has:

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:

The angle between the lines $\vec{r} = 3\hat{i} - 2\hat{j} + 1\hat{k} + \mu (4\hat{i} + 6\hat{j} + 12\hat{k})$ and $\vec{r} = 7\hat{i} - 3\hat{j} + 9\hat{k} + \lambda (5\hat{i} + 8\hat{j} - 4\hat{k})$ is:

A delay in production for some days in a factory due to an electric fault is:

Subject to constraints: 2x + 4y ≤ 8, 3x + y ≤ 6, x + y ≤ 4, x, y ≥ 0; The maximum value of Z = 3x + 15y is:

The integral of the function $ \frac{1}{9 - 4x^2} $ is:

If $ x = at^4 $ and $ y = 2at^2 $, then $ \frac{d^2y}{dx^2} $ is equal to:

A pair of dice is rolled . If the two numbers appearing on them are different the probability that
Match List-I with List-II

LIST-I(EVENT)	LIST-II(PROBABILITY)
(A) The sum of the number is greater than 11	(i) 0
(B) The sum of the number is 4 or less	(ii) 1/15
(C) The sum of the number is 4	(iii) 2/15
(D) The sum of the number is 4	(iv) 3/15

Choose the correct answer from the option given below

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 the solution of the differential equation \[ \frac{dy}{dx} = \frac{ax + 3}{2y + 5} \] represents a circle, then $a$ is equal to:

The function f(x) = |x| + |1 − x| is:

List-I (Sentences)	List-II (Adverbs)
(A) \( P(A \cap B) \)	(I) \(\frac{2}{5}\)
(B) \( P(A \| B) \)	(II)\( \frac{4}{15}\)
(C) \( P(A' \| B) \)	(III) \(\frac{3}{5}\)
(D) \( P(A' \cap B') \)	(IV) \(\frac{2}{9}\)