CUET 2026 Mathematics May 21 Shift 2 Question Paper- Download Answer Key and Solution PDF

Find the shortest distance between the two skew lines whose vector equations are given by: \[ \vec{r} = (\hat{i} + 2\hat{j} + 3\hat{k}) + \lambda(\hat{i} - 3
hat{j} + 2\hat{k}) \] \[ \vec{r} = (4\hat{i} + 5\hat{j} + 6\hat{k}) + \mu(2\hat{i} + 3\hat{j} + \hat{k}) \]

• (A) \( \frac{3}{\sqrt{19}} \)
• (B) \( 0 \)
• (C) \( 9 \)
• (D) \( \sqrt{151} \)

Evaluate the definite integral using standard definite integral properties: \[ \int_{0}^{\frac{\pi}{2}} \frac{\sin^5 x}{\sin^5 x + \cos^5 x} \, dx \]

• (A) \( \frac{\pi}{4} \)
• (B) \( \frac{\pi}{2} \)
• (C) \( \pi \)
• (D) \( 0 \)

If \( A \) is a skew-symmetric matrix of order \( 5 \times 5 \), what is the value of its determinant \( |A| \)?

• (A) \( 0 \)
• (B) \( 1 \)
• (C) \( -1 \)
• (D) \( 5 \)

Two independent events \( A \) and \( B \) have individual probabilities of occurring given by \( P(A) = 0.4 \) and \( P(B) = 0.5 \). Find the probability that at least one of these two events occurs.

• (A) \( 0.70 \)
• (B) \( 0.90 \)
• (C) \( 0.20 \)
• (D) \( 0.30 \)

Find the general solution of the following homogeneous differential equation: \[ \frac{dy}{dx} = \frac{x^2 + y^2}{xy} \]

• (A) \( y^2 = 2x^2\ln|x| + Cx^2 \)
• (B) \( y = x\ln|x| + C \)
• (C) \( y^2 = x^2 + C \)
• (D) \( y = e^x + Cx \)

Find the angle \( \theta \) between the line \( \frac{x-1}{1} = \frac{y+2}{-2} = \frac{z-3}{2} \) and the plane \( 2x - y + 2z = 7 \).

• (A) \( \sin^{-1}\left(\frac{8}{9}\right) \)
• (B) \( \cos^{-1}\left(\frac{8}{9}\right) \)
• (C) \( \frac{\pi}{2} \)
• (D) \( \sin^{-1}\left(\frac{2}{3}\right) \)

Let a relation \( R \) be defined on the set of all natural numbers \( \mathbb{N} \) by the rule: \( (a, b) \in R \) if and only if \( a + b \) is an even number. This relation \( R \) is classified as an:

• (A) Equivalence Relation
• (B) Symmetric but not Transitive Relation
• (C) Reflexive but not Symmetric Relation
• (D) Anti-symmetric Relation

Find the total area of the bounded region enclosed between the parabola curve \( y^2 = 8x \) and its vertical latus rectum boundary line.

• (A) \( \frac{32}{3} square units \)
• (B) \( \frac{16}{3} square units \)
• (C) \( 8 square units \)
• (D) \( \frac{64}{3} square units \)

If the direction vectors of two straight lines are given by \( \vec{m} = \hat{i} + \hat{j} + 0\hat{k} \) and \( \vec{n} = \hat{i} + 0\hat{j} + \hat{k} \), calculate the value of \( \cos\phi \) representing the acute angle between them.

• (A) \( \frac{1}{2} \)
• (B) \( \frac{\sqrt{3}}{2} \)
• (C) \( 0 \)
• (D) \( 1 \)

A pair of standard unbiased six-sided dice are rolled simultaneously. Given that the sum of the numbers showing is exactly 6, what is the conditional probability that one of the dice shows the number 2?

• (A) \( \frac{2}{5} \)
• (B) \( \frac{1}{5} \)
• (C) \( \frac{1}{6} \)
• (D) \( \frac{2}{36} \)