Test: Theorems of Integral Calculus- 1


20 Questions MCQ Test Engineering Mathematics | Test: Theorems of Integral Calculus- 1


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Attempt Test: Theorems of Integral Calculus- 1 | 20 questions in 60 minutes | Mock test for GATE preparation | Free important questions MCQ to study Engineering Mathematics for GATE Exam | Download free PDF with solutions
QUESTION: 1

As x is increased from – ∞ to ∞ , the function 

Solution:

QUESTION: 2

Solution:

QUESTION: 3

Solution:

Given  

Square both side, we get

QUESTION: 4

Solution:

 

QUESTION: 5

Solution:

cos x and sin x are finite whatever x may be  

QUESTION: 6

Solution:

QUESTION: 7

Which of the following functions is not differentiable in the domain [-1,1]? 

Solution:

QUESTION: 8

If f(x) =    then limx-►3 f(x) will be  

Solution:

QUESTION: 9

Solution:

= 1/12

QUESTION: 10

What should be the value of λ such that the function defined below is continuous at x = π/2? 

Solution:

By the given condition 

From (1), λ = 1 

QUESTION: 11

The value of the function  

Solution:

QUESTION: 12

Consider the function f(x) = |x|3, where x is real. Then the function f(x) at x = 0 is

Solution:

QUESTION: 13

The expression e–ln x for x > 0 is equal to  

Solution:

QUESTION: 14

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? 

Solution:

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. 

QUESTION: 15

What is the value of 

Solution:

QUESTION: 16

The integral    is given by

Solution:

QUESTION: 17

Which one of the following function is strictly bounded?   

Solution:

For a strictly bounded function f(x), limit should be finite 

QUESTION: 18

Solution:

QUESTION: 19

Which of the following integrals is unbounded? 

Solution:

QUESTION: 20

What is the value of the definite integral, 

Solution:

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