CUET 2026 Mathematics May 21 Shift 1 Question Paper- Download Answer Key and Solution PDF

CUET 2026 May 21 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 21 Shift 1 Mathematics Question Paper with Answer Key and Solution PDF from links provided below.

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CUET 2026 Mathematics May 21 Shift 1 Question Paper with Solution PDF

CUET May 21 Shift 1 Mathematics Question Paper 2026	Download PDF	Check Solutions

Question 1:

If the function \( f(x) \) defined below is continuous at \( x = 2 \), find the value of the constant \( k \): \[ f(x) = \begin{cases} kx^2 & if x \le 2
3x - 2 & if x > 2 \end{cases} \]

(A) \( 1 \)
(B) \( 2 \)
(C) \( 4 \)
(D) \( 0 \)

Detailed Solution

Question 2:

Find the slope of the normal to the curve \( y = 2x^2 + 3\sin x \) at the coordinate point where \( x = 0 \).

(A) \( -\frac{1}{3} \)
(B) \( 3 \)
(C) \( -3 \)
(D) \( \frac{1}{3} \)

Detailed Solution

Question 3:

The total area of a parallelogram constructed with adjacent vector sides given by \( \vec{a} = \hat{i} - \hat{j} + 3\hat{k} \) and \( \vec{b} = 2\hat{i} - 7\hat{j} + \hat{k} \) is equal to:

(A) \( 15\sqrt{2} \)
(B) \( 15 \)
(C) \( \sqrt{35} \)
(D) \( 0 \)

Detailed Solution

Question 4:

A random variable \( X \) has the following probability distribution table:

\( X \)	0	1	2
\( P(X) \)	\( k \)	\( 2k \)	\( 3k \)

Find the exact value of the unknown parameter \( k \).

(A) \( \frac{1}{6} \)
(B) \( \frac{1}{3} \)
(C) \( 1 \)
(D) \( \frac{1}{5} \)

Detailed Solution

Question 5:

If two vectors \( \vec{a} = 2\hat{i} + \lambda\hat{j} + \hat{k} \) and \( \vec{b} = 4\hat{i} - 2\hat{j} - 2\hat{k} \) are perpendicular to each other, determine the value of the scalar constant \( \lambda \).

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

Detailed Solution

Question 6:

Evaluate the principal value of the inverse trigonometric expression: \( \sin^{-1}\left(\sin\frac{2\pi}{3}\right) \)

(A) \( \frac{\pi}{3} \)
(B) \( \frac{2\pi}{3} \)
(C) \( -\frac{\pi}{3} \)
(D) \( \frac{\pi}{6} \)

Detailed Solution

Question 7:

If a square matrix \( A \) satisfies the condition \( A^T = -A \), then the matrix \( A \) is classified as a:

(A) Skew-symmetric matrix
(B) Symmetric matrix
(C) Identity matrix
(D) Orthogonal matrix

Detailed Solution

Question 8:

Find the interval where the function \( f(x) = x^2 - 4x + 6 \) is strictly decreasing.

(A) \( (-\infty, 2) \)
(B) \( (2, \infty) \)
(C) \( (-\infty, 4) \)
(D) \( [-2, 2] \)

Detailed Solution

Question 9:

Simplify the following expression using inverse trigonometric properties: \( \tan\left(\sin^{-1}x + \cos^{-1}x\right) \) where \( |x| \le 1 \).

(A) Not defined (\( \infty \))
(B) \( 1 \)
(C) \( 0 \)
(D) \( \frac{\pi}{2} \)

Detailed Solution

Question 10:

Calculate the mean (expected value) of a random variable \( X \) given its probability distribution setup below:

\( X \)	1	2	3
\( P(X) \)	0.2	0.5	0.3

(A) \( 2.1 \)
(B) \( 2.0 \)
(C) \( 1.0 \)
(D) \( 3.0 \)

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.
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

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.
Water is leaking from the bottom of a conical funnel at the rate of \(0.15\pi\) cm³/s. If the radius of the base is 10 cm and the height is 20 cm, then the rate at which the water level is dropping when it is 5 cm from the top is:

\( 1/375 \) cm/s
3.75 cm/s
\( 1/375 \) cm/s
2.75 cm/s

View Solution

4.
Simplify the inverse trigonometric expression to find its principal value: \[ \tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{3}\right) \]

\( \frac{\pi}{2} \)
\( \tan^{-1}\left(\frac{2}{5}\right) \)
\( \frac{\pi}{3} \)
\( \frac{\pi}{4} \)

View Solution

5.
If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), then:

\( A^{-1}=\frac{1}{11}A \)
\( A^{-1}=\frac{1}{19}A \)
\( A^{-1}=-\frac{1}{19}A \)
\( A^{-1}=\frac{1}{7}A \)

View Solution

6.
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

CUET 2026 Mathematics May 21 Shift 1 Question Paper- Download Answer Key and Solution PDF

CUET 2026 Mathematics May 21 Shift 1 Question Paper with Solution PDF

CUET UG 2026 Exam Pattern

CUET UG 2026 Paper Analysis

CUET Questions

1.
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?

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.
Water is leaking from the bottom of a conical funnel at the rate of \(0.15\pi\) cm³/s. If the radius of the base is 10 cm and the height is 20 cm, then the rate at which the water level is dropping when it is 5 cm from the top is:

4.
Simplify the inverse trigonometric expression to find its principal value: \[ \tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{3}\right) \]

5.
If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), then:

6.
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) \( P(B \mid A) = \frac{17}{36} \)

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CUET 2026 Mathematics May 21 Shift 1 Question Paper with Solution PDF

CUET UG 2026 Exam Pattern

CUET UG 2026 Paper Analysis

CUET Questions

1.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?

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.Water is leaking from the bottom of a conical funnel at the rate of \(0.15\pi\) cm3/s. If the radius of the base is 10 cm and the height is 20 cm, then the rate at which the water level is dropping when it is 5 cm from the top is:

4.Simplify the inverse trigonometric expression to find its principal value: \[ \tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{3}\right) \]

5.If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), then:

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

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1.
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?

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.
Water is leaking from the bottom of a conical funnel at the rate of \(0.15\pi\) cm³/s. If the radius of the base is 10 cm and the height is 20 cm, then the rate at which the water level is dropping when it is 5 cm from the top is:

4.
Simplify the inverse trigonometric expression to find its principal value: \[ \tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{3}\right) \]

5.
If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), then:

6.
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) \( P(B \mid A) = \frac{17}{36} \)