List of top Mathematics Questions asked in CUET (UG)

If \(e^y = \log x\), then which of the following is true?
The slope of the normal to the curve y = \(2x^2\) at x = 1 is:
The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = \(0.007x^3 - 0.003x^2 + 15x + 400\). The marginal cost when 10 items are produced is:
If \(\int \frac{(1 + x \log x)}{xe^{-x}} dx = e^x f(x) + C\), where C is constant of integration, then f(x) is
Two runners, Ajay and Vijay complete a 600 m race in 38 seconds and 48 seconds respectively. By how many meters will Ajay defeat Vijay?

Match List-I with List-II

List-I (Matrix)List-II (Inverse of the Matrix)
(A) \(\begin{bmatrix} 1 & 7 \\ 4 & -2 \end{bmatrix}\)(I) \(\begin{bmatrix} \tfrac{2}{15} & \tfrac{1}{10} \\[6pt] -\tfrac{1}{15} & \tfrac{1}{5} \end{bmatrix}\)
(B) \(\begin{bmatrix} 6 & -3 \\ 2 & 4 \end{bmatrix}\)(II) \(\begin{bmatrix} \tfrac{1}{5} & -\tfrac{2}{15} \\[6pt] -\tfrac{1}{10} & \tfrac{7}{30} \end{bmatrix}\)
(C) \(\begin{bmatrix} 5 & 2 \\ -5 & 4 \end{bmatrix}\)(III) \(\begin{bmatrix} \tfrac{1}{15} & \tfrac{7}{30} \\[6pt] \tfrac{2}{15} & -\tfrac{1}{30} \end{bmatrix}\)
(D) \(\begin{bmatrix} 7 & 4 \\ 3 & 6 \end{bmatrix}\)(IV) \(\begin{bmatrix} \tfrac{2}{15} & -\tfrac{1}{15} \\[6pt] \tfrac{1}{6} & \tfrac{1}{6} \end{bmatrix}\)
The least non-negative remainder when \(3^{128}\) is divided by 7 is:
A tub contains 60 litres of milk. From this tub, 6 litres of milk was taken out and replaced with water. This whole process was repeated further two more times. How much milk is there in the tub now?
If X = 11 and Y = 3, then X mod Y = (X + aY) mod Y holds
A person can row a boat in still water at the rate of 5 km/hr. It takes him 4 times as long to row upstream of a river as to row downstream to cover same distance in the same river. The speed of flow of the stream is
Which of the following inequalities holds true?
(A) \(\sqrt{5} + \sqrt{3}>\sqrt{6} + \sqrt{2}\)
(B) If \(a>b\) and \(c<0\), then \(\frac{a}{c}<\frac{b}{c}\)
(C) \(\frac{1}{x^2}>\frac{1}{x}>1\), if \(0<x<1\)
(D) If a and b are positive integers and \(\frac{a-b}{6.25} = \frac{4}{2.5}\) then \(b>a\)
Choose the correct answer from the options given below:
Which of the following statements is incorrect?
If \(A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}\), \(X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}\), \(B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}\) and \(AX = B\), then the value of the \(\alpha\) is
Let A be a non-singular matrix of order 3 and \(|A| = 15\), then \(|\text{adj } A|\) is equal to
A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than 9, given that the black die resulted in a 5 is

Let A and B be two events such that: \[ P(A) = 0.8, \quad P(B) = 0.5, \quad P(B|A) = 0.4 \]

Match List-I with List-II:

List-IList-II
(A) \(P(A \cap B)\)(I) 0.2
(B) \(P(A|B)\)(II) 0.32
(C) \(P(A \cup B)\)(III) 0.64
(D) \(P(A')\)(IV) 0.98
If P, Q and R are three singular matrices given by \(P = \begin{bmatrix} 2 & 3a \\ 4 & 3 \end{bmatrix}\), \(Q = \begin{bmatrix} b & 5 \\ 2a & 6 \end{bmatrix}\) and \(R = \begin{bmatrix} a^2 + b^2 - c & 1-c \\ c+1 & c \end{bmatrix}\), then the value of \((2a + 6b + 17c)\) is
The corner points of the feasible region of the LPP: Minimize \( Z = -50x + 20y \) subject to \( 2x - y \geq -5 \), \( 3x + y \geq 3 \), \( 2x - 3y \leq 12 \), and \( x, y \geq 0 \) are:
The shortest distance between the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$ and $\frac{x-2}{4} = \frac{y-4}{6} = \frac{z-5}{8}$ is equal to

Consider the line \[ \vec{r} = (\hat{i} - 2\hat{j} + 4\hat{k}) + \lambda(-\hat{i} + 2\hat{j} - 4\hat{k}) \]

Match List-I with List-II:

List-IList-II
(A) A point on the given line(I) \(\left(-\tfrac{1}{\sqrt{21}}, \tfrac{2}{\sqrt{21}}, -\tfrac{4}{\sqrt{21}}\right)\)
(B) Direction ratios of the line(II) (4, -2, -2)
(C) Direction cosines of the line(III) (1, -2, 4)
(D) Direction ratios of a line perpendicular to given line(IV) (-1, 2, -4)
Which one of the following set of constraints does the given shaded region represent?
If A and B are any two events such that P(B) = P(A and B), then which of the following is correct
If the points A, B, C with position vectors $20\hat{i} + \lambda\hat{j}$, $5\hat{i} - \hat{j}$ and $10\hat{i} - 13\hat{j}$ respectively are collinear, then the value of $\lambda$ is
If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ and $|\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7$, then the angle between $\vec{a}$ and $\vec{b}$ is
If a line makes angles $\alpha, \beta, \gamma$ with the positive directions of x-axis, y-axis and z-axis respectively, then $\sin^2\alpha + \sin^2\beta + \sin^2\gamma$ is equal to