List of top Mathematics Questions asked in CUET (UG)

The shortest distance (in units) between the lines \(\frac{1 - x}{1} = \frac{2y - 10}{2} = \frac{z + 1}{1}\) and  \(\frac{x - 3}{-1} = \frac{y - 5}{1} = \frac{z - 0}{1}\) is:

If the angle between a = \(2y^2 \hat{i} + 4y \hat{j} + \hat{k}\)  and  b = \(7\hat{i} - 2\hat{j} + y\hat{k}\)  is obtuse, then:

Optimize $Z = 3x + 9y$ subject to the constraints: \[ x + 3y \leq 60, \quad x + y \geq 10, \quad x \leq y, \quad x \geq 0, \quad y \geq 0. \]

The equation of a line passing through the origin and parallel to the line \[ \vec{r} = 3\hat{i} + 4\hat{j} - 5\hat{k} + t(2\hat{i} - \hat{j} + 7\hat{k}), \] where $t$ is a parameter, is:
  (A) $\frac{x}{2} = \frac{y}{-1} = \frac{z}{7}$  (B) $\vec{r} = m(12\hat{i} - 6\hat{j} + 42\hat{k});$ where $m$ is the parameter  (C) $\vec{r} = (12\hat{i} - 6\hat{j} + 42\hat{k}) + s(0\hat{i} - 0\hat{j} + 0\hat{k});$ where $s$ is the parameter  (D) $\frac{x - 3}{3} = \frac{y - 4}{-4} = \frac{z + 5}{0}$  (E) $\frac{x}{3} = \frac{y}{4} = \frac{z}{5}$
Choose the correct answer from the options given below:

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

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

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:  

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:

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

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:

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:

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:

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.

If \( e^y = x^x \), then which of the following is true?

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.

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

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

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.

For a square matrix } A_{n \times n}:
(A) \( |\text{adj } A| = |A|^{n-1} \) 
(B) \( |A| = |\text{adj } A|^{n-1} \) 
(C) \( A (\text{adj } A) = |A| \) 
(D) \( |A^{-1}| = \frac{1}{|A|} \) 
$\text{Choose the \textbf{correct} answer from the options given below:}$

The value of the integral \( \int_{\ln 2}^{\ln 3} \frac{e^{2x} - 1}{e^{2x} + 1} \, dx \) is: