CUET PG PYQs for Double and triple integrals with Solutions: Practice CUET PG Previous Year Questions

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Double and triple integrals is an important topic in the Mathematics 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 Double and triple integrals with explanations for effective preparation. Practice of CUET PG Mathematics PYQs including Double and triple integrals questions regularly will improve accuracy, speed, and confidence in the CUET PG 2026 exam.

CUET PG PYQs for Double and triple integrals with Solutions

1.
The value of double integal $\int\limits_0^∞\int\limits_0^xe^{-xy} ydydx$ is equal to:
- $\sqrt π$
- $2\sqrt π$
- $\frac{1}{2}\sqrt π$
- $\frac{1}{4}\sqrt π$
View Solution
2.
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The integral $\int \int \int (x^2+y^2+z^2)dxdydz$ taken over the volume enclosed by the sphere x²+ y²+z² = 1 is $\frac{4\pi}{5}$
Reason R: $\int^{1}_{0}\int^{1}_{0}x\ dxdy=\frac{1}{2}$
In the light of the above statements, choose the most appropriate answer from the options given below:
- 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
3.
If $f(x)=\begin{cases}\frac{\log_{e}(1+\frac{x}{a})-\log_{e}(1-\frac{x}{b})}{x}& if~x\ne0\\k& if~x=0\end{cases}$ is continuous at $x=0$, then value of $k$ is:
- 0
- 1
- $\frac{1}{a}+\frac{1}{b}$
- $\frac{1}{a}-\frac{1}{b}$
View Solution
4.
The value of integral $\int_{0}^{1}\int_{x}^{1}\frac{1}{1+y^{2}}\cdot dydx$ is equal to
- $1-\ln(2)$
- $\frac{1}{2}\ln(2)$
- $\frac{\pi}{4}$
- $\frac{\pi}{2}-\ln 2$
View Solution
5.
Double integral $\int\limits_0^2\int\limits_0^{\sqrt{2x-x^2}}\frac{xdydx}{\sqrt{x^2+y^2}}$ equals:
- $\frac{2}{3}$
- $\frac{4}{3}$
- $\frac{1}{3}$
- $\frac{8}{3}$
View Solution
6.
Integral $\int_{0}^{2}\int_{y^{2}}^{y+2} dxdy$ equals
- $\int_{0}^{1}\int_{0}^{\sqrt{x}}dydx+\int_{1}^{2}\int_{x=2}^{\sqrt{x}}dy~dx$
- $\int_{0}^{2}\int_{0}^{\sqrt{x}}dydx+\int_{2}^{4}\int_{x=2}^{x}dydx$
- $\int_{0}^{2}\int_{0}^{\sqrt{x}}dydx+\int_{2}^{4}\int_{x-2}^{\sqrt{x}}dy~dx$
- $\int_{0}^{2}\int_{0}^{\sqrt{x}}dydx+\int_{2}^{4}\int_{0}^{4\sqrt{x}}dydx$
View Solution
7.
The value of $∫_0^{\frac{π}{2}}∫_0^{соs \theta} r\text{ }sin\theta\text{ }dr\text{ }d\theta$ is
- 0
- $\frac{1}{6}$
- $\frac{4}{3}$
- $\pi$
View Solution
8.
If $\int \int\limits_{R} \int xyz\ dxdydz=\frac{m}{n}$ where, m,n, are coprime and R:0≤x≤1,1≤ y ≤2, 2 ≤ z ≤3 , then m.n is equal to:
- 135
- 90
- 150
- 120
View Solution
9.
The integral $\int\limits_0^1\int\limits_0^x(x^2+ y^2) dy dx$ is:
- $\frac{1}{6}$
- $\frac{1}{2}$
- $\frac{1}{3}$
- 1
View Solution
10.
Given below are two statements
Statement I: If $x=\frac{1}{3}(2u + v)$ and $y =\frac{1}{3}(u − v)$, then $dxdy=\frac{-1}{3}\ dudv$
Statement II: Area in Polar Co-ordinater $\int\limits^{\theta_1}_{\theta_1} \int\limits^{r_2}_{r_1} rd\theta dr$
In the light of the above statements, choose the correct answer from the options given below:
- Both Statement I and Statement II are true
- Both Statement I and Statement II are false
- Statement I is true but statement II is false
- Statement I is false but statement II is true
View Solution
11.
The area of region in the first quadrant that is bounded by $y=\sqrt{x}$, $y=2-x$ and x-axis is
- $\frac{5}{6}$
- $\frac{2}{3}$
- 1
- $\frac{7}{6}$
View Solution
12.
Given below are two statements
Statement I: In cylindrical co-ordinates, $Volume = \int \int\limits_{V} \int rdrdødz $
Statement II: In spherical polar Co-ordinates, $Volume = \int \int\limits_{V} \int r^2\ \cos\theta\ drd\theta d\phi$
In the light of the above statements, choose the correct answer from the options given below :
- Both Statement I and Statement II are true
- Both Statement I and Statement II are false
- Statement I is true but statement II is false
- Statement I is false but statement II is true
View Solution

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CUET PG PYQs for Double and triple integrals with Solutions: Practice CUET PG Previous Year Questions

CUET PG PYQs for Double and triple integrals with Solutions

1.
The value of double integal \(\int\limits_0^∞\int\limits_0^xe^{-xy} ydydx\) is equal to:

3.
If $f(x)=\begin{cases}\frac{\log_{e}(1+\frac{x}{a})-\log_{e}(1-\frac{x}{b})}{x}& if~x\ne0\\k& if~x=0\end{cases}$ is continuous at $x=0$, then value of $k$ is:

4.
The value of integral $\int_{0}^{1}\int_{x}^{1}\frac{1}{1+y^{2}}\cdot dydx$ is equal to

5.
Double integral \(\int\limits_0^2\int\limits_0^{\sqrt{2x-x^2}}\frac{xdydx}{\sqrt{x^2+y^2}}\) equals:

6.
Integral $\int_{0}^{2}\int_{y^{2}}^{y+2} dxdy$ equals

7.
The value of \(∫_0^{\frac{π}{2}}∫_0^{соs \theta} r\text{ }sin\theta\text{ }dr\text{ }d\theta\) is

8.
If \(\int \int\limits_{R} \int xyz\ dxdydz=\frac{m}{n}\) where, m,n, are coprime and R:0≤x≤1,1≤ y ≤2, 2 ≤ z ≤3 , then m.n is equal to:

9.
The integral \(\int\limits_0^1\int\limits_0^x(x^2+ y^2) dy dx\) is:

11.
The area of region in the first quadrant that is bounded by $y=\sqrt{x}$, $y=2-x$ and x-axis is

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CUET PG PYQs for Double and triple integrals with Solutions

1.The value of double integal \(\int\limits_0^∞\int\limits_0^xe^{-xy} ydydx\) is equal to:

3.If $f(x)=\begin{cases}\frac{\log_{e}(1+\frac{x}{a})-\log_{e}(1-\frac{x}{b})}{x}& if~x\ne0\\k& if~x=0\end{cases}$ is continuous at $x=0$, then value of $k$ is:

4.The value of integral $\int_{0}^{1}\int_{x}^{1}\frac{1}{1+y^{2}}\cdot dydx$ is equal to

5.Double integral \(\int\limits_0^2\int\limits_0^{\sqrt{2x-x^2}}\frac{xdydx}{\sqrt{x^2+y^2}}\) equals:

6.Integral $\int_{0}^{2}\int_{y^{2}}^{y+2} dxdy$ equals

7.The value of \(∫_0^{\frac{π}{2}}∫_0^{соs \theta} r\text{ }sin\theta\text{ }dr\text{ }d\theta\) is

8.If \(\int \int\limits_{R} \int xyz\ dxdydz=\frac{m}{n}\) where, m,n, are coprime and R:0≤x≤1,1≤ y ≤2, 2 ≤ z ≤3 , then m.n is equal to:

9.The integral \(\int\limits_0^1\int\limits_0^x(x^2+ y^2) dy dx\) is:

11.The area of region in the first quadrant that is bounded by $y=\sqrt{x}$, $y=2-x$ and x-axis is

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1.
The value of double integal \(\int\limits_0^∞\int\limits_0^xe^{-xy} ydydx\) is equal to:

3.
If $f(x)=\begin{cases}\frac{\log_{e}(1+\frac{x}{a})-\log_{e}(1-\frac{x}{b})}{x}& if~x\ne0\\k& if~x=0\end{cases}$ is continuous at $x=0$, then value of $k$ is:

4.
The value of integral $\int_{0}^{1}\int_{x}^{1}\frac{1}{1+y^{2}}\cdot dydx$ is equal to

5.
Double integral \(\int\limits_0^2\int\limits_0^{\sqrt{2x-x^2}}\frac{xdydx}{\sqrt{x^2+y^2}}\) equals:

6.
Integral $\int_{0}^{2}\int_{y^{2}}^{y+2} dxdy$ equals

7.
The value of \(∫_0^{\frac{π}{2}}∫_0^{соs \theta} r\text{ }sin\theta\text{ }dr\text{ }d\theta\) is

8.
If \(\int \int\limits_{R} \int xyz\ dxdydz=\frac{m}{n}\) where, m,n, are coprime and R:0≤x≤1,1≤ y ≤2, 2 ≤ z ≤3 , then m.n is equal to:

9.
The integral \(\int\limits_0^1\int\limits_0^x(x^2+ y^2) dy dx\) is:

11.
The area of region in the first quadrant that is bounded by $y=\sqrt{x}$, $y=2-x$ and x-axis is