# Test: Definite Integral (Competition Level) - 2

## 30 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Definite Integral (Competition Level) - 2

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QUESTION: 1

### If , where a >1 and [.] denotes the greatest integer function, then the value of a2 is

Solution:  QUESTION: 2

### Number of positive continuous functions f (x ) defined in [0,1] for which  is

Solution:

Multiplying these integrals by 4, -4,1 and adding we get Hence, there does not exist any function satisfying these conditions.

QUESTION: 3

### For and has the  value equal to

Solution:  QUESTION: 4

If and where [.] denotes the greatest integer function,  then the value of equals to

Solution:   QUESTION: 5 is equal to

Solution:  QUESTION: 6

If f is continuous function and then the value  of is

Solution:  QUESTION: 7

Let a >0 and f (x ) is monotonic increasing such that f ( 0) = 0 and f ( a ) = b, then is equal to

Solution:  QUESTION: 8

If f ( x ) = x+ sin x, then the value of is equal to

Solution:  QUESTION: 9

If f ( x ) = sin x+ cos x and , then the value  of is   equal to

Solution:   QUESTION: 10

Let and g ( x ) = f ( x - 1) + f ( x + 1) for all x ÎR , then the  of value is

Solution:    QUESTION: 11 Solution:  QUESTION: 12

Let and  then f ( 4 ) equals

Solution:  QUESTION: 13 Solution:
QUESTION: 14 Solution:
QUESTION: 15 Solution:
QUESTION: 16

If the value of then the value of k is

Solution: QUESTION: 17 Solution: QUESTION: 18

if then

Solution:
QUESTION: 19

If and then

Solution:
QUESTION: 20 where [.] denote greatest integer function, is equal to

Solution:   QUESTION: 21 ,where denotes greatest integer function is given by

Solution: QUESTION: 22 Solution:
QUESTION: 23

Let then

Solution:
QUESTION: 24

If [.] denotes G.I.F, Solution:  QUESTION: 25

The value of constant a >0 such that where denotes G.I.F is ___

Solution:  QUESTION: 26

A function f is defined by Solution: QUESTION: 27 Solution:
QUESTION: 28 Solution:
QUESTION: 29

If Then in the interval  (0,4); f(x)=0 has

Solution:  QUESTION: 30 Solution: