CUET PG PYQs for Mathematics with Solutions: Practice CUET PG Previous Year Questions

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Mathematics is an important topic in the Geophysics section in CUET PG exam. Practising this topic will increase your score overall and make your conceptual grip on CUET PG exam stronger.

This article gives you a full set of CUET PG PYQs for Mathematics with explanations for effective preparation. Practice of CUET PG Geophysics PYQs including Mathematics questions regularly will improve accuracy, speed, and confidence in the CUET PG 2026 exam.

CUET PG PYQs for Mathematics with Solutions

1.
\[ (1+i\sqrt{3})^{10}+(1-i\sqrt{3})^{10} \] equals to:
- \(1024\)
- \(-1024\)
- \(-624\)
- \(624\)
View Solution
2.
The strength of a linear association between two quantitative variables can be measured by the:
- Regression coefficient
- Correlation coefficient
- Standard deviation
- Coefficient of variance
View Solution
3.
Consider the following statements related to a matrix:
A. Inverse of a matrix is unique if it exists.
B. A matrix \(A\) is non-singular if \(|A|=0\).
C. Matrix \[ A=\begin{pmatrix} \cos x & \sin x -\sin x & \cos x \end{pmatrix} \] is orthogonal.
D. Matrix \[ A=\begin{pmatrix} 0 & -2 & -8 2 & 0 & -4 8 & -4 & 0 \end{pmatrix} \] is skew symmetri
C.
- A, B, C Only
- A, C, D Only
- A, C Only
- A, D Only
View Solution
4.
The linear differential equation \[ a_0\frac{d^ny}{dx^n}+a_1\frac{d^{n-1}y}{dx^{n-1}}+\cdots+a_ny=F(x) \] is non-homogeneous if:
- \(F(x)=0\)
- \(F(x)\neq 0\)
- Degree is greater than order
- Order is greater than degree
View Solution

5.
Principal Values of Logarithmic Functions
Case Complex Number Principal Value
A \(\log(-2)\) \(\log 2 + i\pi\)
B \(\log(5i)\) \(\log 5 + \dfrac{i\pi}{2}\)
C \(\log(\sqrt{3}-i)\) \(\log 2 - \dfrac{i\pi}{6}\)
D \(\log(2-3i)\) \(\dfrac{1}{2}\log 13 - i\tan^{-1}\left(\dfrac{3}{2}\right)\)

Case	Complex Number	Principal Value
A	\(\log(-2)\)	\(\log 2 + i\pi\)
B	\(\log(5i)\)	\(\log 5 + \dfrac{i\pi}{2}\)
C	\(\log(\sqrt{3}-i)\)	\(\log 2 - \dfrac{i\pi}{6}\)
D	\(\log(2-3i)\)	\(\dfrac{1}{2}\log 13 - i\tan^{-1}\left(\dfrac{3}{2}\right)\)

A, B
B, C
B, D
A, D

View Solution

6.
Match List-I with List-II
List-I Function List-II \(n^{\text{th}}\) Derivative Form
A \(e^{ax}\) IV \(a^n e^{ax}\)
B \(\log(ax+b)\) III \(\dfrac{(-1)^{n-1}(n-1)!a^n}{(ax+b)^n}\)
C \(\cos(ax+b)\) II \(a^n\cos\left(ax+b+\dfrac{n\pi}{2}\right)\)
D \(e^{ax}\cos(bx+c)\) I \(r^n e^{ax}\cos(bx+c+n\theta)\),
where \(r=\sqrt{a^2+b^2}\), \(\theta=\tan^{-1}\left(\dfrac{b}{a}\right)\)

List-I	Function	List-II	\(n^{\text{th}}\) Derivative Form
A	\(e^{ax}\)	IV	\(a^n e^{ax}\)
B	\(\log(ax+b)\)	III	\(\dfrac{(-1)^{n-1}(n-1)!a^n}{(ax+b)^n}\)
C	\(\cos(ax+b)\)	II	\(a^n\cos\left(ax+b+\dfrac{n\pi}{2}\right)\)
D	\(e^{ax}\cos(bx+c)\)	I	\(r^n e^{ax}\cos(bx+c+n\theta)\), where \(r=\sqrt{a^2+b^2}\), \(\theta=\tan^{-1}\left(\dfrac{b}{a}\right)\)

A-IV, B-III, C-II, D-I
A-III, B-I, C-IV, D-II
A-II, B-I, C-III, D-IV
A-III, B-IV, C-II, D-I

View Solution

7.
Assertion (A) and Reason (R)
Assertion (A):
If a polynomial \(f(x)\) is divisible by \((x-a)^m\), but not divisible by \((x-a)^{m+1}\), then \(a\) is called a root of multiplicity \(m\) of the equation \(f(x)=0\).
Reason (R):
\(x=-1\) is the root of multiplicity \(3\) of the equation \[ x^4+x^3-3x^2-5x-2=0. \]
- Both (A) and (R) are correct and (R) is the correct explanation of (A)
- Both (A) and (R) are correct but (R) is not the correct explanation of (A)
- (A) is correct but (R) is not correct
- (A) is not correct but (R) is correct
View Solution
8.
The function of two variables is maximum if:
A. \(rt-s^2>0\),
B. \(r<0\),
C. \(rt-s^2<0\),
D. \(r>0\), E. \(rt-s^2=0,\ r<0\).
- A, B
- B, C
- C, D
- A, B, E
View Solution
9.
Assertion (A) and Reason (R)
Assertion (A):
\[ (\cos\theta+i\sin\theta)^{p/q} \] has \(q\) and only \(q\) different roots, where \(q\) is a positive integer.
Reason (R):
\[ (-1)^{1/3} \] has three different roots.
- Both (A) and (R) are correct and (R) is the correct explanation of (A)
- Both (A) and (R) are correct but (R) is not the correct explanation of (A)
- (A) is correct but (R) is not correct
- (A) is not correct but (R) is correct
View Solution
10.
Match List-I with List-II for the hyperbola
\[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \]
List-I Element List-II Corresponding Value / Equation
A Coordinate of centre II \((0,0)\)
B One coordinate of vertex I \((a,0)\)
C Equation of transverse axis III \(y=0\)
D Equation of conjugate axis IV \(x=0\)
- A-I, B-II, C-III, D-IV
- A-I, B-II, C-IV, D-III
- A-II, B-I, C-III, D-IV
- A-II, B-I, C-IV, D-III
View Solution
11.
If the roots of the equation \[ x^3+3px^2+3qx+r=0 \] are in geometric progression, then:
- \(p^3r+q^3=0\)
- \(p^3r-q^3=0\)
- \(p^3+rq^2=0\)
- \(p^3-rq^2=0\)
View Solution
12.
Two forces of magnitude \(8\ \text{N}\) and \(6\ \text{N}\) act at a point making an angle of \(90^\circ\) between them. The magnitude of resultant force is:
- \(10\ \text{N}\)
- \(2\ \text{N}\)
- \(13\ \text{N}\)
- \(9\ \text{N}\)
View Solution

List-I	Element	List-II	Corresponding Value / Equation
A	Coordinate of centre	II	\((0,0)\)
B	One coordinate of vertex	I	\((a,0)\)
C	Equation of transverse axis	III	\(y=0\)
D	Equation of conjugate axis	IV	\(x=0\)

13.
Match List-I with List-II
List-I Matrix Type List-II Property
A Orthogonal matrix I Product of matrix and its transpose equals identity matrix
B Skew-Hermitian matrix IV Diagonal elements are either zero or pure imaginary
C Real skew symmetric matrix II Diagonal elements are zero
D Hermitian matrix III Diagonal elements are real

List-I	Matrix Type	List-II	Property
A	Orthogonal matrix	I	Product of matrix and its transpose equals identity matrix
B	Skew-Hermitian matrix	IV	Diagonal elements are either zero or pure imaginary
C	Real skew symmetric matrix	II	Diagonal elements are zero
D	Hermitian matrix	III	Diagonal elements are real

A-II, B-I, C-III, D-IV
A-II, B-III, C-I, D-IV
A-III, B-I, C-II, D-IV
A-I, B-IV, C-II, D-III

View Solution

14.
Given below are two statements:
Assertion (A): If a curve cut every member of a given family of curves at right angle, it is called orthogonal trajectory.
Reason (R): For the orthogonal trajectory of a differential equation, the derivative \(\dfrac{dy}{dx}\) is replaced by \(-\dfrac{dx}{dy}\).
- Both (A) and (R) are correct and (R) is the correct explanation of (A)
- Both (A) and (R) are correct but (R) is not the correct explanation of (A)
- (A) is correct but (R) is not correct
- (A) is not correct but (R) is correct
View Solution

15.
Match List-I with List-II
List-I \(F(x)\) List-II Particular Integral Rule
A \(F(x)=e^{ax}\) III \(\dfrac{e^{ax}}{f(a)}, \quad f(a)\neq 0\)
B \(F(x)=\sin ax\) II \(\dfrac{\sin ax}{f(-a^2)}\)
C \(F(x)=xe^{ax}\) I \(\left(\dfrac{x}{f(a)}-\dfrac{f'(a)}{[f(a)]^2}\right)e^{ax}, \quad f(a)\neq 0\)
D \(F(x)=\cos ax\) IV \(D^2\) is replaced by \(-a^2\) in \(f(D)\)

List-I	\(F(x)\)	List-II	Particular Integral Rule
A	\(F(x)=e^{ax}\)	III	\(\dfrac{e^{ax}}{f(a)}, \quad f(a)\neq 0\)
B	\(F(x)=\sin ax\)	II	\(\dfrac{\sin ax}{f(-a^2)}\)
C	\(F(x)=xe^{ax}\)	I	\(\left(\dfrac{x}{f(a)}-\dfrac{f'(a)}{[f(a)]^2}\right)e^{ax}, \quad f(a)\neq 0\)
D	\(F(x)=\cos ax\)	IV	\(D^2\) is replaced by \(-a^2\) in \(f(D)\)

A-I, B-II, C-III, D-IV
A-III, B-IV, C-I, D-II
A-III, B-II, C-I, D-IV
A-I, B-IV, C-III, D-II

View Solution

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CUET PG PYQs for Mathematics with Solutions: Practice CUET PG Previous Year Questions

CUET PG PYQs for Mathematics with Solutions

1.
\[ (1+i\sqrt{3})^{10}+(1-i\sqrt{3})^{10} \] equals to:

2.
The strength of a linear association between two quantitative variables can be measured by the:

4.
The linear differential equation \[ a_0\frac{d^ny}{dx^n}+a_1\frac{d^{n-1}y}{dx^{n-1}}+\cdots+a_ny=F(x) \] is non-homogeneous if:

5.
Principal Values of Logarithmic Functions
Case Complex Number Principal Value
A \(\log(-2)\) \(\log 2 + i\pi\)
B \(\log(5i)\) \(\log 5 + \dfrac{i\pi}{2}\)
C \(\log(\sqrt{3}-i)\) \(\log 2 - \dfrac{i\pi}{6}\)
D \(\log(2-3i)\) \(\dfrac{1}{2}\log 13 - i\tan^{-1}\left(\dfrac{3}{2}\right)\)

8.
The function of two variables is maximum if:
A. \(rt-s^2>0\),
B. \(r<0\),
C. \(rt-s^2<0\),
D. \(r>0\), E. \(rt-s^2=0,\ r<0\).

9.
Assertion (A) and Reason (R)
Assertion (A):
\[ (\cos\theta+i\sin\theta)^{p/q} \] has \(q\) and only \(q\) different roots, where \(q\) is a positive integer.
Reason (R):
\[ (-1)^{1/3} \] has three different roots.

10.
Match List-I with List-II for the hyperbola
\[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \]
List-I Element List-II Corresponding Value / Equation
A Coordinate of centre II \((0,0)\)
B One coordinate of vertex I \((a,0)\)
C Equation of transverse axis III \(y=0\)
D Equation of conjugate axis IV \(x=0\)

11.
If the roots of the equation \[ x^3+3px^2+3qx+r=0 \] are in geometric progression, then:

12.
Two forces of magnitude \(8\ \text{N}\) and \(6\ \text{N}\) act at a point making an angle of \(90^\circ\) between them. The magnitude of resultant force is:

14.
Given below are two statements:
Assertion (A): If a curve cut every member of a given family of curves at right angle, it is called orthogonal trajectory.
Reason (R): For the orthogonal trajectory of a differential equation, the derivative \(\dfrac{dy}{dx}\) is replaced by \(-\dfrac{dx}{dy}\).

Comments

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CUET PG PYQs for Mathematics with Solutions

1.\[ (1+i\sqrt{3})^{10}+(1-i\sqrt{3})^{10} \] equals to:

2.The strength of a linear association between two quantitative variables can be measured by the:

4.The linear differential equation \[ a_0\frac{d^ny}{dx^n}+a_1\frac{d^{n-1}y}{dx^{n-1}}+\cdots+a_ny=F(x) \] is non-homogeneous if:

5.Principal Values of Logarithmic FunctionsCaseComplex NumberPrincipal ValueA\(\log(-2)\)\(\log 2 + i\pi\)B\(\log(5i)\)\(\log 5 + \dfrac{i\pi}{2}\)C\(\log(\sqrt{3}-i)\)\(\log 2 - \dfrac{i\pi}{6}\)D\(\log(2-3i)\)\(\dfrac{1}{2}\log 13 - i\tan^{-1}\left(\dfrac{3}{2}\right)\)

8.The function of two variables is maximum if: A. \(rt-s^2>0\), B. \(r<0\), C. \(rt-s^2<0\), D. \(r>0\), E. \(rt-s^2=0,\ r<0\).

9.Assertion (A) and Reason (R)Assertion (A):\[ (\cos\theta+i\sin\theta)^{p/q} \] has \(q\) and only \(q\) different roots, where \(q\) is a positive integer.Reason (R):\[ (-1)^{1/3} \] has three different roots.

10.Match List-I with List-II for the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \]List-IElementList-IICorresponding Value / EquationACoordinate of centreII\((0,0)\)BOne coordinate of vertexI\((a,0)\)CEquation of transverse axisIII\(y=0\)DEquation of conjugate axisIV\(x=0\)

11.If the roots of the equation \[ x^3+3px^2+3qx+r=0 \] are in geometric progression, then:

12.Two forces of magnitude \(8\ \text{N}\) and \(6\ \text{N}\) act at a point making an angle of \(90^\circ\) between them. The magnitude of resultant force is:

14.Given below are two statements: Assertion (A): If a curve cut every member of a given family of curves at right angle, it is called orthogonal trajectory. Reason (R): For the orthogonal trajectory of a differential equation, the derivative \(\dfrac{dy}{dx}\) is replaced by \(-\dfrac{dx}{dy}\).

Comments

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1.
\[ (1+i\sqrt{3})^{10}+(1-i\sqrt{3})^{10} \] equals to:

2.
The strength of a linear association between two quantitative variables can be measured by the:

4.
The linear differential equation \[ a_0\frac{d^ny}{dx^n}+a_1\frac{d^{n-1}y}{dx^{n-1}}+\cdots+a_ny=F(x) \] is non-homogeneous if:

5.
Principal Values of Logarithmic Functions
Case Complex Number Principal Value
A \(\log(-2)\) \(\log 2 + i\pi\)
B \(\log(5i)\) \(\log 5 + \dfrac{i\pi}{2}\)
C \(\log(\sqrt{3}-i)\) \(\log 2 - \dfrac{i\pi}{6}\)
D \(\log(2-3i)\) \(\dfrac{1}{2}\log 13 - i\tan^{-1}\left(\dfrac{3}{2}\right)\)

8.
The function of two variables is maximum if:
A. \(rt-s^2>0\),
B. \(r<0\),
C. \(rt-s^2<0\),
D. \(r>0\), E. \(rt-s^2=0,\ r<0\).

9.
Assertion (A) and Reason (R)
Assertion (A):
\[ (\cos\theta+i\sin\theta)^{p/q} \] has \(q\) and only \(q\) different roots, where \(q\) is a positive integer.
Reason (R):
\[ (-1)^{1/3} \] has three different roots.

10.
Match List-I with List-II for the hyperbola
\[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \]
List-I Element List-II Corresponding Value / Equation
A Coordinate of centre II \((0,0)\)
B One coordinate of vertex I \((a,0)\)
C Equation of transverse axis III \(y=0\)
D Equation of conjugate axis IV \(x=0\)

11.
If the roots of the equation \[ x^3+3px^2+3qx+r=0 \] are in geometric progression, then:

12.
Two forces of magnitude \(8\ \text{N}\) and \(6\ \text{N}\) act at a point making an angle of \(90^\circ\) between them. The magnitude of resultant force is:

14.
Given below are two statements:
Assertion (A): If a curve cut every member of a given family of curves at right angle, it is called orthogonal trajectory.
Reason (R): For the orthogonal trajectory of a differential equation, the derivative \(\dfrac{dy}{dx}\) is replaced by \(-\dfrac{dx}{dy}\).