CUET 2026 Mathematics May 14 Shift 2 Question Paper- Download Answer Key and Solution PDF

If \( f(x) = x^5 - 5x^3 + 5x^2 - 1 \), then the number of critical points of \( f(x) \) is:

• (a) 1
• (b) 2
• (c) 3
• (d) 4

The integral \( \int \frac{2+x^4}{1+x^2} dx \) is equal to

• (a) \(\frac{1}{3}x^3 + 3 \tan^{-1}x - x + C\)
• (b) \(\frac{1}{3}x^3 + 3 \tan^{-1}x + x + C\)
• (c) \(\frac{1}{3}x^3 - 3 \tan^{-1}x - x + C\)
• (d) \(\frac{1}{3}x^3 - 3 \tan^{-1}x + x + C\)

The value of the integral \( I = \int_{-3}^3 (x^3 - x) dx \) is

• (a) 0
• (b) 3/2
• (c) 1/2
• (d) x

The integral \( \int e^x \left(\tan^{-1}x + \frac{1}{1+x^2}\right) dx \) is equal to

• (a) \( e^x (\tan^{-1}x + 2) + C \)
• (b) \( \tan^{-1}x + C \)
• (c) \( e^x \tan^{-1}x + C \)
• (d) \( e^x \cot^{-1}x + C \)

The value of \( \int_0^2 |x - 2| dx = \)

• (a) 1
• (b) 2
• (c) 3
• (d) 3/2

If \( X + Y = \begin{pmatrix} 5 & 3
0 & 7 \end{pmatrix} \) and \( X - Y = \begin{pmatrix} 7 & 1
2 & 3 \end{pmatrix} \). Then X and Y are

• (A) \( X = \begin{pmatrix} 6 & 2
  1 & 5 \end{pmatrix} and Y = \begin{pmatrix} -1 & 1
  -1 & 2 \end{pmatrix} \)
• (B) \( X = \begin{pmatrix} 0 & 5
  1 & 4 \end{pmatrix} and Y = \begin{pmatrix} -1 & -1
  -1 & 2 \end{pmatrix} \)
• (C) \( X = \begin{pmatrix} 6 & 2
  1 & 5 \end{pmatrix} and Y = \begin{pmatrix} -1 & -1
  -1 & 2 \end{pmatrix} \)
• (D) \( X = \begin{pmatrix} 1 & 4
  5 & 0 \end{pmatrix} and Y = \begin{pmatrix} 0 & 2
  1 & 1 \end{pmatrix} \)

A certain type of fish has a 4/5 probability of surviving in a pond, while another fish has a 2/5 probability of survival. What is the probability that exactly one of them survives?

• (a) 2/5
• (b) 9/16
• (c) 14/25
• (d) 16/25

A card is picked at random from a pack of 52 playing cards. Given that the picked card is a king, the probability of this card to be a card of spade is:

• (a) 1/3
• (b) 4/13
• (c) 1/4
• (d) 1/2

If \(\vec{a}\) and \(\vec{b}\) are unit vectors, then the angle between \(\vec{a}\) and \(\vec{b}\) for \( \sqrt{3}\vec{a} - \vec{b} \) to be a unit vector is given by :

• (a) \(\pi/6\)
• (b) \(\pi/4\)
• (c) \(\pi/3\)
• (d) \(2\pi/3\)

Consider the function \( f(x) = -2x^3 - 9x^2 - 12x + 5 \). Then, which of the following is/are correct?

(a) \( f(x) \) decreasing in \((0, \infty)\) and increasing in \((-\infty, 0)\)

(b) \( f(x) \) increasing in \((-\infty, 1) \cup (2, \infty)\) and decreasing in \((1, 2)\)

(c) \( f(x) \) increasing in \((0, \infty)\) and decreasing in \((-\infty, 0)\)

(d) \( f(x) \) is increasing in \((-2, -1)\) and decreasing in \((-\infty, -2) \cup (-1, \infty)\)