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QUESTION: 1

If , where a >1 and [.] denotes the greatest integer function, then the value of a^{2} 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

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QUESTION: 4

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

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QUESTION: 5

is equal to

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QUESTION: 6

If f is continuous function and then the value of is

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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

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QUESTION: 9

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

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QUESTION: 10

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

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QUESTION: 11

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QUESTION: 12

Let and then f ( 4 ) equals

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QUESTION: 13

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QUESTION: 14

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QUESTION: 15

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QUESTION: 16

If the value of then the value of k is

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QUESTION: 17

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QUESTION: 18

if then

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QUESTION: 19

If and then

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QUESTION: 20

where [.] denote greatest integer function, is equal to

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QUESTION: 21

,where denotes greatest integer function is given by

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QUESTION: 22

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QUESTION: 23

Let then

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QUESTION: 24

If [.] denotes G.I.F,

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QUESTION: 25

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

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QUESTION: 26

A function f is defined by

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QUESTION: 27

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QUESTION: 28

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QUESTION: 29

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

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QUESTION: 30

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