CUET 2026 Mathematics May 25 Shift 1 Question Paper- Download Answer Key and Solution PDF

CUET 2026 May 25 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 25 Shift 1 Mathematics Question Paper with Answer Key and Solution PDF from links provided below.

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CUET 2026 Mathematics May 25 Shift 1 Question Paper with Solution PDF

CUET May 25 Shift 1 Mathematics Question Paper 2026	Download PDF	Check Solutions

Question 1:

A bag contains 5 red and 3 blue balls. Two balls are drawn at random without replacement. The probability that both are red is:

(A) \( \frac{5}{14} \)
(B) \( \frac{10}{28} \)
(C) \( \frac{5}{28} \)
(D) \( \frac{15}{56} \)

Detailed Solution

Question 2:

A die is thrown twice. The probability of getting a sum equal to 8 is:

(A) \( \frac{1}{12} \)
(B) \( \frac{5}{36} \)
(C) \( \frac{1}{6} \)
(D) \( \frac{7}{36} \)

Detailed Solution

Question 3:

Evaluate: \(\int x \cdot e^x \, dx\)

(A) \( x e^x + C \)
(B) \( e^x(x - 1) + C \)
(C) \( e^x(x + 1) + C \)
(D) \( x^2 e^x + C \)

Detailed Solution

Question 4:

If \(y = \log(\sin x) + \log(\cos x)\), then \(\frac{dy}{dx}\) is:

(A) \( \cos x - \sin x \)
(B) \( \sin x - \cos x \)
(C) \( \cot x - \tan x \)
(D) \( -\sin x - \cos x \)

Detailed Solution

Question 5:

Evaluate: \(\int_0^{\pi/2} \sin x \, dx\)

(A) \( 0 \)
(B) \( 1 \)
(C) \( 2 \)
(D) \( \frac{\pi}{2} \)

Detailed Solution

Question 6:

If \(A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}\), then \(adj(A)\) is:

(A) \( \begin{bmatrix} 4 & -2 \\ -3 & 1 \end{bmatrix} \)
(B) \( \begin{bmatrix} 1 & -2 \\ -3 & 4 \end{bmatrix} \)
(C) \( \begin{bmatrix} 4 & 2 \\ 3 & 1 \end{bmatrix} \)
(D) \( \begin{bmatrix} -4 & 2 \\ 3 & -1 \end{bmatrix} \)

Detailed Solution

Question 7:

For any square matrix \(A\), \(A \cdot adj(A) =\)

(A) \( A \)
(B) \( |A| I \)
(C) \( I \)
(D) \( |A|^2 A \)

Detailed Solution

Question 8:

The feasible region of an LPP is always:

(A) Circle
(B) Triangle only
(C) Convex polygon
(D) Straight line

Detailed Solution

Question 9:

Find the maximum value of \(f(x) = -x^2 + 4x + 1\)

(A) \( 3 \)
(B) \( 4 \)
(C) \( 5 \)
(D) \( 6 \)

Detailed Solution

Question 10:

Evaluate: \(\int \frac{1}{1 + x^2} \, dx\)

(A) \( \sin^{-1}x + C \)
(B) \( \tan^{-1}x + C \)
(C) \( \log(1 + x^2) + C \)
(D) \( \sec^{-1}x + C \)

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 solution of the differential equation \[ (x-1)\frac{dx}{dy}+(y-2)=0, \] given that \(x=1\) when \(y=1\), represents a:

Parabola
Circle
Ellipse
Hyperbola

View Solution

2.
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

3.
The order of the differential equation \[ \left(\frac{d^5y}{dx^5}\right)^2 + \frac{dy}{dx} + y^2 = 0 \] is:

1
Not defined
5
2

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.
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

6.
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

CUET 2026 Mathematics May 25 Shift 1 Question Paper- Download Answer Key and Solution PDF

CUET 2026 Mathematics May 25 Shift 1 Question Paper with Solution PDF

CUET UG 2026 Exam Pattern

CUET UG 2026 Paper Analysis

CUET Questions

1.
The solution of the differential equation \[ (x-1)\frac{dx}{dy}+(y-2)=0, \] given that \(x=1\) when \(y=1\), represents a:

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

3.
The order of the differential equation \[ \left(\frac{d^5y}{dx^5}\right)^2 + \frac{dy}{dx} + y^2 = 0 \] is:

5.
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

6.
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:

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CUET 2026 Mathematics May 25 Shift 1 Question Paper with Solution PDF

CUET UG 2026 Exam Pattern

CUET UG 2026 Paper Analysis

CUET Questions

1. The solution of the differential equation \[ (x-1)\frac{dx}{dy}+(y-2)=0, \] given that \(x=1\) when \(y=1\), represents a:

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

3.The order of the differential equation \[ \left(\frac{d^5y}{dx^5}\right)^2 + \frac{dy}{dx} + y^2 = 0 \] is:

5.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

6.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:

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1.
The solution of the differential equation \[ (x-1)\frac{dx}{dy}+(y-2)=0, \] given that \(x=1\) when \(y=1\), represents a:

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

3.
The order of the differential equation \[ \left(\frac{d^5y}{dx^5}\right)^2 + \frac{dy}{dx} + y^2 = 0 \] is:

5.
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

6.
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: