CUET 2026 Mathematics May 29 Shift 2 Question Paper- Download Answer Key and Solution PDF

CUET 2026 May 29 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 29 Shift 2 Mathematics Question Paper with Answer Key and Solution PDF from links provided below.

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CUET 2026 Mathematics May 29 Shift 2 Question Paper with Solution PDF

CUET May 25 Shift 2 Mathematics Question Paper 2026	Download PDF	Check Solutions

Question 1:

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 2:

Consider a \(3 \times 3\) matrix \(A\). If

\[ \operatorname{adj}(A)= \begin{pmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{pmatrix} \]

find \(\det(A)\).

(A) \(8\)
(B) \(4\)
(C) \(2\sqrt2\)
(D) \(2\)

Detailed Solution

Question 3:

Find the shortest distance between the lines \[ \vec r= \hat i+2\hat j+\hat k+\lambda(\hat i-\hat j+\hat k) \]
and \[ \vec r= 2\hat i-\hat j-\hat k+\mu(2\hat i+\hat j+2\hat k) \]

(A) \(3/\sqrt2\)
(B) \(9/\sqrt{54}\)
(C) \(\sqrt6\)
(D) \(0\)

Detailed Solution

Question 4:

Maximize \[ Z=3x+4y \]
subject to \[ x+y\le10,\qquad x,y\ge0 \]

(A) \((10,0)\)
(B) \((0,10)\)
(C) \((5,5)\)
(D) \((0,0)\)

Detailed Solution

Question 5:

Probability that the second ball is red, given the first was blue
(3 red and 5 blue balls, without replacement).

(A) \(3/7\)
(B) \(3/8\)
(C) \(2/7\)
(D) \(5/14\)

Detailed Solution

Question 6:

Find the local maximum of \[ f(x)=x^3-3x+2 \]

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

Detailed Solution

Question 7:

Find the domain of \[ f(x)=\sin^{-1}(2x-1) \]

(A) \([0,1]\)
(B) \([-1,1]\)
(C) \([0,\infty)\)
(D) \([-0.5,0.5]\)

Detailed Solution

Question 8:

Is \[ f(x)=|x-2| \]
differentiable at \(x=2\)?

(A) Yes
(B) No
(C) Only for \(x>2\)
(D) Only for \(x<2\)

Detailed Solution

Question 9:

Find the adjoint of

\[ A= \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \]

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

Detailed Solution

Detailed Solution

Concept:

For a \(2 \times 2\) matrix: \[ A= \begin{pmatrix} a & b \\ c & d \end{pmatrix} \] the adjoint is: \[ \operatorname{adj}(A)= \begin{pmatrix} d & -b \\ -c & a \end{pmatrix} \]
Step 1: Identify matrix entries

Given: \[ A= \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \]
Hence: \[ a=1,\quad b=2,\quad c=3,\quad d=4 \]
Step 2: Apply adjoint formula

Swap diagonal elements: \[ 1 \leftrightarrow 4 \]
Change signs of off-diagonal elements: \[ 2 \to -2 \] \[ 3 \to -3 \]
Thus: \[ \operatorname{adj}(A)= \begin{pmatrix} 4 & -2 \\ -3 & 1 \end{pmatrix} \]
Final Answer: \[ \boxed{ \begin{pmatrix} 4 & -2 \\ -3 & 1 \end{pmatrix} } \]

Question 10:

Find the derivative of \[ f(x)=e^{x^2} \]

(A) \(e^{x^2}\)
(B) \(2xe^{x^2}\)
(C) \(x^2e^{x^2-1}\)
(D) \(e^{2x}\)

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

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.
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

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.
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

6.
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

CUET 2026 Mathematics May 29 Shift 2 Question Paper- Download Answer Key and Solution PDF

CUET 2026 Mathematics May 29 Shift 2 Question Paper with Solution PDF

CUET UG 2026 Exam Pattern

CUET UG 2026 Paper Analysis

CUET Questions

1.
If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), 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 \( -\log 1.667 = 0.2219 \); \( \log 1.089 = 0.0370 \)]

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

6.
The order of the differential equation \[ \left(\frac{d^5y}{dx^5}\right)^2 + \frac{dy}{dx} + y^2 = 0 \] is:

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CUET 2026 Mathematics May 29 Shift 2 Question Paper with Solution PDF

CUET UG 2026 Exam Pattern

CUET UG 2026 Paper Analysis

CUET Questions

1.If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), 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 \( -\log 1.667 = 0.2219 \); \( \log 1.089 = 0.0370 \)]

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

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

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1.
If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), 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 \( -\log 1.667 = 0.2219 \); \( \log 1.089 = 0.0370 \)]

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

6.
The order of the differential equation \[ \left(\frac{d^5y}{dx^5}\right)^2 + \frac{dy}{dx} + y^2 = 0 \] is: