CUET 2026 Mathematics May 29 Shift 1 Question Paper- Download Answer Key and Solution PDF

CUET 2026 May 29 Shift 1 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 29 Shift 1 Mathematics Question Paper with Answer Key and Solution PDF from links provided below.

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CUET 2026 Mathematics May 29 Shift 1 Question Paper with Solution PDF

CUET May 29 Shift 1 Mathematics Question Paper 2026	Download PDF	Check Solutions

Question 1:

Let \(A\) be a \(3 \times 3\) matrix such that \(A^2 = I\). If \(\det(A) = -1\) and the sum of eigenvalues is \(1\), find the set of eigenvalues of \(A\).

(A) \( 1, 1, 1 \)
(B) \( 1, 1, -1 \)
(C) \( -1, -1, 1 \)
(D) \( -1, -1, -1 \)

Detailed Solution

Question 2:

Analyze the function \( f(x) = |x-1| + |x-2| + |x-3| \). Determine the points where the derivative \( f'(x) \) is undefined.

(A) \( x = 1, 3 \)
(B) \( x = 1, 2, 3 \)
(C) \( x = 1.5, 2.5 \)
(D) \( x = 0 \)

Detailed Solution

Question 3:

Identify the order and degree of the differential equation: \[ \left(\frac{d^3y}{dx^3}\right)^2 + 4\left(\frac{dy}{dx}\right)^4 + y = \sin(x) \]

(A) \( Order 3, Degree 4 \)
(B) \( Order 3, Degree 2 \)
(C) \( Order 4, Degree 3 \)
(D) \( Order 1, Degree 4 \)

Detailed Solution

Question 4:

For the linear differential equation \[ \frac{dy}{dx} + \frac{2}{x}y = x^2 \]
calculate the integrating factor (I.F.).

(A) \( x \)
(B) \( x^2 \)
(C) \( x^3 \)
(D) \( \ln(x) \)

Detailed Solution

Question 5:

Maximize \( Z = 5x + 3y \) subject to \( x + y \le 6 \) and \( x, y \ge 0 \). Where does the maximum value occur?

(A) \( (0,0) \)
(B) \( (0,6) \)
(C) \( (6,0) \)
(D) \( (3,3) \)

Detailed Solution

Question 6:

A bag has 4 red and 6 black balls. Two balls are drawn without replacement. What is the probability that the second is red given the first was black?

(A) \( 4/10 \)
(B) \( 4/9 \)
(C) \( 6/9 \)
(D) \( 2/9 \)

Detailed Solution

Question 7:

Find the domain of the function \( f(x)=\sin^{-1}(3x-1) \).

(A) \( [-1,1] \)
(B) \( [0,\frac{2}{3}] \)
(C) \( [-\frac13,\frac13] \)
(D) \( [\frac13,1] \)

Detailed Solution

Question 8:

For vectors \( \vec{a}=3\hat{i}-\hat{j}+2\hat{k} \) and \( \vec{b}=\hat{i}+2\hat{j}-\hat{k} \), find the scalar projection of \( \vec{a} \) onto \( \vec{b} \).

(A) \( -\frac1{\sqrt6} \)
(B) \( \frac1{\sqrt6} \)
(C) \( -\frac16 \)
(D) \( \frac16 \)

Detailed Solution

Question 9:

Let \( R \) be a relation on \( \{1,2,3\} \) defined by \[ R=\{(1,1),(2,2),(3,3),(1,2)\} \]
Identify the properties satisfied by \(R\).

(A) Symmetric only
(B) Reflexive and Transitive
(C) Equivalence relation
(D) None of these

Detailed Solution

Question 10:

Find the local maximum point of the function \[ f(x)=-x^3+3x+1 \]

(A) \( x=1 \)
(B) \( x=-1 \)
(C) \( x=0 \)
(D) \( x=\sqrt3 \)

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.
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

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.
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

4.
For the function \[ f(x)=ax+\frac{b}{x}, \qquad a>0,\; b>0, \] which of the following statements are correct?

(A) Function \(f(x)\) is increasing on \[ \left(\sqrt{\frac{b}{a}},\,\infty\right) \]

(B) Function \(f(x)\) is increasing on \[ (-\infty,\infty) \]

(C) Function \(f(x)\) is decreasing on \[ \left(-\sqrt{\frac{b}{a}},\,\sqrt{\frac{b}{a}}\right) \]

(D) Function \(f(x)\) is increasing on \[ \left(-\infty,\,-\sqrt{\frac{b}{a}}\right) \]

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

View Solution

5.
A simple random sample consists of five observations: 4, 5, 9, 10 & 12. What is the point estimate of population standard deviation?

View Solution

6.
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

CUET 2026 Mathematics May 29 Shift 1 Question Paper- Download Answer Key and Solution PDF

CUET 2026 Mathematics May 29 Shift 1 Question Paper with Solution PDF

CUET UG 2026 Exam Pattern

CUET UG 2026 Paper Analysis

CUET Questions

1.
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

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 \( -\log 1.667 = 0.2219 \); \( \log 1.089 = 0.0370 \)]

3.
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) \( P(B \mid A) = \frac{17}{36} \)

5.
A simple random sample consists of five observations: 4, 5, 9, 10 & 12. What is the point estimate of population standard deviation?

6.
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?

Comments

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CUET 2026 Mathematics May 29 Shift 1 Question Paper with Solution PDF

CUET UG 2026 Exam Pattern

CUET UG 2026 Paper Analysis

CUET Questions

1.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

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 \( -\log 1.667 = 0.2219 \); \( \log 1.089 = 0.0370 \)]

3.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) \( P(B \mid A) = \frac{17}{36} \)

5.A simple random sample consists of five observations: 4, 5, 9, 10 & 12. What is the point estimate of population standard deviation?

6.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?

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
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

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 \( -\log 1.667 = 0.2219 \); \( \log 1.089 = 0.0370 \)]

3.
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) \( P(B \mid A) = \frac{17}{36} \)

5.
A simple random sample consists of five observations: 4, 5, 9, 10 & 12. What is the point estimate of population standard deviation?

6.
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?