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GATE CS Maxima and Minima, Mean Value Theorem, Integration questions

Practise Maxima and Minima, Mean Value Theorem, Integration questions for GATE CS. Explore official PYQs and original topic-wise quizzes, check answers and view available solutions. Free, no sign-in.

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Official PYQ2026Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMSQ · 1 mark
For a real number aa, let I(a)=∫−11(3x2−ax+1)dxI(a)=\int_{-1}^{1}\left(3 x^{2}-a x+1\right) d x. Which of the following statements is/are true?
Official PYQ2025Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
​​​​​The value of xx such that x>1x>1, satisfying the equation ∫1xtln⁡t dt=14\int_1^x t \ln t \: dt = \frac{1}{4} is
Official PYQ2024Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
​​​​​Let f(x)f(x) be a continuous function from R\mathbb{R} to R\mathbb{R} such that f(x)=1−f(2−x)f(x)=1-f(2-x) Which one of the following options is the CORRECT value of ∫02f(x)dx\int_{0}^{2} f(x) d x ?
Official PYQ2023Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMSQ · 1 mark
Let f(x)=x3+15x2−33x−36\qquad f(x)=x^{3}+15 x^{2}-33 x-36 be a real-valued function. Which of the following statements is/are TRUE?\text{TRUE}?
Official PYQ2020Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
Consider the functions e−xe^{-x} x2−sin⁡xx^{2}-\sin x x3+1\sqrt{x^{3}+1} Which of the above functions is/are increasing everywhere in [0,1][ 0,1]?
Official PYQ2018Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationNAT · 1 mark
The value of ∫0π/4xcos⁡(x2)dx\int^{\pi/4} _0 x \cos(x^2) dx correct to three decimal places (assuming that π=3.14\pi = 3.14) is ____
Official PYQ2015Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationNAT · 1 mark
Compute the value of: ∫1π2πcos⁡(1/x)x2dx\large \int \limits_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx
Official PYQ2015Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
Consider a function f(x)=1−∣x∣ on −1≤x≤1f(x) = 1- |x| \text{ on } -1 \leq x \leq 1. The value of xx at which the function attains a maximum, and the maximum value of the function are:
Official PYQ2015Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
If for non-zero x, af(x)+bf(1x)=1x−25x, \: af(x) + bf(\frac{1}{x}) = \frac{1}{x} - 25 where a≠b then ∫12f(x)dxa \neq b \text{ then } \int\limits_1^2 f(x)dx is
Official PYQ2014Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
The value of the integral given below is ∫0π x2 cos⁡x dx\int \limits_0^{\pi} \: x^2 \: \cos x\:dx
Official PYQ2014Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationNAT · 1 mark
If ∫02π∣x sin⁡x∣dx=kπ\int \limits_0^{2 \pi} |x \: \sin x| dx=k\pi, then the value of kk is equal to ______.
Official PYQ2012Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
Consider the function f(x)=sin⁡(x)f(x) = \sin(x) in the interval x=[π4,7π4]x =\left[\frac{\pi}{4},\frac{7\pi}{4}\right]. The number and location(s) of the local minima of this function are
Official PYQ2011Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
Given i=−1i = \sqrt{-1}, what will be the evaluation of the definite integral ∫0π/2cos⁡x+isin⁡xcos⁡x−isin⁡xdx\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx ?
Official PYQ2009Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
∫0π/4(1−tan⁡x)/(1+tan⁡x) dx\int^{\pi/4}_0 (1-\tan x)/(1+\tan x)\,dx
Official PYQ2008Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve 3x4−16x3+24x2+373x^4-16x^3+24x^2+37 is
Official PYQ2000Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
Let S=∑i=3100ilog⁡2iS = \sum_{i=3}^{100} i \log_{2} i, and T=∫2100xlog⁡2xdxT = \int_{2}^{100} x \log_{2}x dx. Which of the following statements is true?
Official PYQ1997Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
What is the maximum value of the function f(x)=2x2−2x+6f(x) = 2x^2 - 2x + 6 in the interval [0,2]\left[0,2 \right]?
Official PYQ1995Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationNAT · 1 mark
Find the minimum value of 3−4x+2x23-4x+2x^2.
Official PYQ1995Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
In the interval [0,π][0, \pi] the equation x=cos⁡xx=\cos x has
Official PYQ1993Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
The function f(x,y)=x2y−3xy+2y+xf\left(x,y\right) = x^2y - 3xy + 2y +x has