CUET 2026 Mathematics May 22 Shift 2 Question Paper- Download Answer Key and Solution PDF

CUET 2026 May 22 Shift 2 Mathematics Question Paper is available for download here. NTA is conducting the CUET 2026 exam from 11th May to 31st May.

CUET 2026 Mathematics exam consists of 50 questions for 250 marks to be attempted in 60 minutes.
As per the marking scheme, 5 marks are awarded for each correct answer, and 1 mark is deducted for incorrect answer.

Candidates can download CUET 2026 May 22 Shift 2 Mathematics Question Paper with Answer Key and Solution PDF from links provided below.

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CUET 2026 Mathematics May 22 Shift 2 Question Paper with Solution PDF

CUET May 22 Shift 2 Mathematics Question Paper 2026	Download PDF	Check Solutions

Question 1:

If \( A \) is a non-singular square matrix of order \( 3 \times 3 \) such that its determinant is \( |A| = 5 \), find the absolute value of the determinant of its adjoint matrix, represented as \( |adj(A)| \).

(A) \( 5 \)
(B) \( 125 \)
(C) \( 25 \)
(D) \( 15 \)

Detailed Solution

Question 2:

Determine the exact expression for the Integrating Factor (I.F.) of the following first-order linear differential equation: \( \frac{dy}{dx} - y\tan x = e^x \)

(A) \( \sec x \)
(B) \( \cos x \)
(C) \( \sin x \)
(D) \( e^{-\tan x} \)

Detailed Solution

Question 3:

Find the open interval across which the cubic polynomial function \( f(x) = 2x^3 - 3x^2 - 36x + 7 \) is classified as strictly decreasing.

(A) \( (-2, 3) \)
(B) \( (-\infty, -2) \cup (3, \infty) \)
(C) \( (-3, 2) \)
(D) \( (0, \infty) \)

Detailed Solution

Question 4:

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

(A) \( \sqrt{2} \)
(B) \( \frac{\sqrt{293}}{7} \)
(C) \( 0 \)
(D) \( \frac{5}{7} \)

Detailed Solution

Question 5:

Find the maximum value of the linear objective optimization function \[ Z = 4x + y \]
evaluated over a feasible region bounded by the corner vertices: \[ (0,0), \ (3,0), \ (2,3), \ and \ (0,4). \]

(A) \( 12 \)
(B) \( 4 \)
(C) \( 11 \)
(D) \( 16 \)

Detailed Solution

Question 6:

If \( A \) is a square matrix of order 3 such that its determinant is \( |A| = 3 \), calculate the value of the scalar matrix determinant represented by \( |2A| \).

(A) \( 6 \)
(B) \( 24 \)
(C) \( 12 \)
(D) \( 18 \)

Detailed Solution

Question 7:

An unbiased coin is tossed twice. Let event \( A \) represent getting a head on the first toss, and event \( B \) represent getting a head on the second toss. Determine the mathematical relationship between events \( A \) and \( B \).

(A) Dependent Events
(B) Independent Events
(C) Mutually Exclusive Events
(D) Equivalence Events

Detailed Solution

Question 8:

Find the equation of the normal to the curve \( y = x^2 - x \) at the coordinate point position \( (1, 0) \).

(A) \( x + y - 1 = 0 \)
(B) \( x - y - 1 = 0 \)
(C) \( x + y + 1 = 0 \)
(D) \( 2x + y - 2 = 0 \)

Detailed Solution

Question 9:

Evaluate the value of the following definite integral using standard calculus integrations: \( \int_{0}^{1} x e^x \, dx \)

(A) \( e \)
(B) \( 1 \)
(C) \( e - 1 \)
(D) \( 0 \)

Detailed Solution

Question 10:

Find the total number of distinct binary relations that can be defined over a set \( A \) containing exactly 3 elements.

(A) \( 9 \)
(B) \( 64 \)
(C) \( 512 \)
(D) \( 27 \)

Detailed Solution

CUET UG 2026 Exam Pattern

Parameter	Details
Exam Name	Common University Entrance Test (CUET UG) 2026
Conducting Body	National Testing Agency (NTA)
Exam Mode	Computer-Based Test (CBT)
Exam Duration	60 minutes per test
Total Sections	3 (Languages, Domain Subjects, General Test)
Question Type	Multiple Choice Questions (MCQs)
Questions per Test	50 questions (all compulsory)
Marking Scheme	+5 for correct, -1 for incorrect
Maximum Marks	250 marks per test
Maximum Subject Choices	5 subjects in total
Syllabus Base	Class 12 NCERT (mainly for Domain Subjects)

CUET UG 2026 Paper Analysis

CUET Questions

1.
The function \[ f(x)=\sum_{k=1}^{7}(x-k)^2 \] has a minimum value at \(x=a\). Then, \(a\) is equal to:

View Solution

2.
A person invested Rs.15,000 in a mutual fund; it became Rs.25,000. If CAGR is 8.88%, then the number of years \( n \) is: [Use \( -\log 1.667 = 0.2219 \); \( \log 1.089 = 0.0370 \)]

View Solution

3.
A function \[ f(x)=12x^{4/3}-6x^{1/3}, \qquad x\in[-1,1] \] is given. Then, which of the following are TRUE?

(A) \(f(x)\) has a critical point at \(x=\dfrac{1}{8}\)
(B) Absolute maximum value of \(f(x)\) is \(18\)
(C) Absolute maximum value of \(f(x)\) is \(6\)
(D) Absolute minimum value of \(f(x)\) is \(-\dfrac{9}{4}\)

(A), (C) and (D) only
(A) and (B) only
(A), (B) and (D) only
(C) and (D) only

View Solution

4.
A pump can fill a tank in 2 hours. Because of a leak, it took \( 2 \frac{1}{3} \) hours (or 7/3 hours) to fill the tank. In how many hours can the leak drain all the water?

14 hours
7/3 hours
3/7 hours
7 hours

View Solution

5.
If \( P(A) = \frac{3}{5} \), \( P(\overline{B}) = \frac{4}{7} \), and \( P(A \cup B) = \frac{2}{3} \), which of the following are correct?

(A) \( P(A \cap B) = \frac{17}{105} \)
(B) \( P(A \mid B) = \frac{17}{45} \)
(C) A and B are independent events
(D) \( P(B \mid A) = \frac{17}{36} \)

(A), (B) and (D) only
(B) and (C) only
(A) and (D) only
(A) and (B) only

View Solution

6.
If \[ f(x)= \begin{cases} \dfrac{x-2}{|x-2|}+a, & x<2, \\[6pt] a+b, & x=2, \\[6pt] \dfrac{x-2}{|x-2|}+b, & x>2, \end{cases} \] is continuous at \(x=2\), then

\( a = 1, b = 1 \)
\( a = 1, b = -1 \)
\( a = -1, b = 1 \)
\( a = -1, b = -1 \)

View Solution

CUET 2026 Mathematics May 22 Shift 2 Question Paper- Download Answer Key and Solution PDF

CUET 2026 Mathematics May 22 Shift 2 Question Paper with Solution PDF

CUET UG 2026 Exam Pattern

CUET UG 2026 Paper Analysis

CUET Questions

1.
The function \[ f(x)=\sum_{k=1}^{7}(x-k)^2 \] has a minimum value at \(x=a\). Then, \(a\) is equal to:

2.
A person invested Rs.15,000 in a mutual fund; it became Rs.25,000. If CAGR is 8.88%, then the number of years \( n \) is: [Use \( -\log 1.667 = 0.2219 \); \( \log 1.089 = 0.0370 \)]

4.
A pump can fill a tank in 2 hours. Because of a leak, it took \( 2 \frac{1}{3} \) hours (or 7/3 hours) to fill the tank. In how many hours can the leak drain all the water?

5.
If \( P(A) = \frac{3}{5} \), \( P(\overline{B}) = \frac{4}{7} \), and \( P(A \cup B) = \frac{2}{3} \), which of the following are correct?

(A) \( P(A \cap B) = \frac{17}{105} \)
(B) \( P(A \mid B) = \frac{17}{45} \)
(C) A and B are independent events
(D) \( P(B \mid A) = \frac{17}{36} \)

6.
If \[ f(x)= \begin{cases} \dfrac{x-2}{|x-2|}+a, & x<2, \\[6pt] a+b, & x=2, \\[6pt] \dfrac{x-2}{|x-2|}+b, & x>2, \end{cases} \] is continuous at \(x=2\), then

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CUET 2026 Mathematics May 22 Shift 2 Question Paper with Solution PDF

CUET UG 2026 Exam Pattern

CUET UG 2026 Paper Analysis

CUET Questions

1. The function \[ f(x)=\sum_{k=1}^{7}(x-k)^2 \] has a minimum value at \(x=a\). Then, \(a\) is equal to:

2.A person invested Rs.15,000 in a mutual fund; it became Rs.25,000. If CAGR is 8.88%, then the number of years \( n \) is: [Use \( -\log 1.667 = 0.2219 \); \( \log 1.089 = 0.0370 \)]

4.A pump can fill a tank in 2 hours. Because of a leak, it took \( 2 \frac{1}{3} \) hours (or 7/3 hours) to fill the tank. In how many hours can the leak drain all the water?

5.If \( P(A) = \frac{3}{5} \), \( P(\overline{B}) = \frac{4}{7} \), and \( P(A \cup B) = \frac{2}{3} \), which of the following are correct? (A) \( P(A \cap B) = \frac{17}{105} \) (B) \( P(A \mid B) = \frac{17}{45} \) (C) A and B are independent events (D) \( P(B \mid A) = \frac{17}{36} \)

6.If \[ f(x)= \begin{cases} \dfrac{x-2}{|x-2|}+a, & x<2, \\[6pt] a+b, & x=2, \\[6pt] \dfrac{x-2}{|x-2|}+b, & x>2, \end{cases} \] is continuous at \(x=2\), then

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1.
The function \[ f(x)=\sum_{k=1}^{7}(x-k)^2 \] has a minimum value at \(x=a\). Then, \(a\) is equal to:

2.
A person invested Rs.15,000 in a mutual fund; it became Rs.25,000. If CAGR is 8.88%, then the number of years \( n \) is: [Use \( -\log 1.667 = 0.2219 \); \( \log 1.089 = 0.0370 \)]

4.
A pump can fill a tank in 2 hours. Because of a leak, it took \( 2 \frac{1}{3} \) hours (or 7/3 hours) to fill the tank. In how many hours can the leak drain all the water?

5.
If \( P(A) = \frac{3}{5} \), \( P(\overline{B}) = \frac{4}{7} \), and \( P(A \cup B) = \frac{2}{3} \), which of the following are correct?

(A) \( P(A \cap B) = \frac{17}{105} \)
(B) \( P(A \mid B) = \frac{17}{45} \)
(C) A and B are independent events
(D) \( P(B \mid A) = \frac{17}{36} \)

6.
If \[ f(x)= \begin{cases} \dfrac{x-2}{|x-2|}+a, & x<2, \\[6pt] a+b, & x=2, \\[6pt] \dfrac{x-2}{|x-2|}+b, & x>2, \end{cases} \] is continuous at \(x=2\), then