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Mechanical Engineering  >  GATE Mechanical (ME) 2024 Mock Test Series  >  Test: Theorems of Integral Calculus- 1 Download as PDF

Test: Theorems of Integral Calculus- 1 - Mechanical Engineering


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20 Questions MCQ Test GATE Mechanical (ME) 2024 Mock Test Series - Test: Theorems of Integral Calculus- 1

Test: Theorems of Integral Calculus- 1 for Mechanical Engineering 2023 is part of GATE Mechanical (ME) 2024 Mock Test Series preparation. The Test: Theorems of Integral Calculus- 1 questions and answers have been prepared according to the Mechanical Engineering exam syllabus.The Test: Theorems of Integral Calculus- 1 MCQs are made for Mechanical Engineering 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Theorems of Integral Calculus- 1 below.
Solutions of Test: Theorems of Integral Calculus- 1 questions in English are available as part of our GATE Mechanical (ME) 2024 Mock Test Series for Mechanical Engineering & Test: Theorems of Integral Calculus- 1 solutions in Hindi for GATE Mechanical (ME) 2024 Mock Test Series course. Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free. Attempt Test: Theorems of Integral Calculus- 1 | 20 questions in 60 minutes | Mock test for Mechanical Engineering preparation | Free important questions MCQ to study GATE Mechanical (ME) 2024 Mock Test Series for Mechanical Engineering Exam | Download free PDF with solutions
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Test: Theorems of Integral Calculus- 1 - Question 1
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As x is increased from – ∞ to ∞ , the function 

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Test: Theorems of Integral Calculus- 1 - Question 2
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Test: Theorems of Integral Calculus- 1 - Question 3
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Given  

Square both side, we get

Test: Theorems of Integral Calculus- 1 - Question 4
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Test: Theorems of Integral Calculus- 1 - Question 5
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cos x and sin x are finite whatever x may be  

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Test: Theorems of Integral Calculus- 1 - Question 7
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Which of the following functions is not differentiable in the domain [-1,1]? 
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Test: Theorems of Integral Calculus- 1 - Question 8
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If f(x) =    then limx-►3 f(x) will be  
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Test: Theorems of Integral Calculus- 1 - Question 9
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= 1/12

Test: Theorems of Integral Calculus- 1 - Question 10
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What should be the value of λ such that the function defined below is continuous at x = π/2? 
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By the given condition 

From (1), λ = 1 

Test: Theorems of Integral Calculus- 1 - Question 11
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The value of the function  

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Test: Theorems of Integral Calculus- 1 - Question 12
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Consider the function f(x) = |x|3, where x is real. Then the function f(x) at x = 0 is
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Test: Theorems of Integral Calculus- 1 - Question 13
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The expression e–ln x for x > 0 is equal to  
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Test: Theorems of Integral Calculus- 1 - Question 14
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Consider the following two statements about the function f(x) = |x|  

P: f(x) is continuous for all real values of x

 Q: f(x) is differentiable for all real values of x  

Which of the f oll owi ng is TRU E? 
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The graph of f(x) is  

f(x) is continuous for all real values of x   Lim |x| = Lim |x| = 0 

as can be seen from graph of |x|. 

and  Lim f(x) = +1 as can be seen from graph of |x| 

 x → 0+ 

Left deriva tive ≠ Rig ht derivative 

So |x| is continuous but not differentiable at x = 0. 

Test: Theorems of Integral Calculus- 1 - Question 15
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What is the value of 

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Test: Theorems of Integral Calculus- 1 - Question 16
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The integral    is given by
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Test: Theorems of Integral Calculus- 1 - Question 17
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Which one of the following function is strictly bounded?   
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For a strictly bounded function f(x), limit should be finite 

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Test: Theorems of Integral Calculus- 1 - Question 19
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Which of the following integrals is unbounded? 
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Test: Theorems of Integral Calculus- 1 - Question 20
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What is the value of the definite integral, 

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