Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 3 - Relations and Functions>Target Exercises>Q 49

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

$f (x) = \frac{\cos x}{[\frac{2 x}{π}] + \frac{1}{2}}$ , where $x$ is not an integral multiple of $π$ and $[]$ denotes the greatest integer function, is

50% studentsanswered this correctly

Important Questions on Relations and Functions

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 3 - Relations and Functions>Target Exercises>Q 50

If

f

is an even function defined on the interval

[- 5, 5]

, then the real values of

x

satisfying the equation

f (x) = f (\frac{x + 1}{x + 2})

, are

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 3 - Relations and Functions>Target Exercises>Q 51

The function

f (x) = \sec [\log (x + \sqrt{1 + x^{2}})]

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 3 - Relations and Functions>Target Exercises>Q 52

Which of the following functions is odd?

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 3 - Relations and Functions>Target Exercises>Q 53

Let the function

f (x) = 3 x^{2} - 4 x + 8 \log (1 + |x|)

be defined on the interval

[0, 1]

. The even extension of

f (x)

to the interval

[- 1, 1]

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 3 - Relations and Functions>Target Exercises>Q 54

If

[x]

and

\{x\}

represent the integral and fractional parts of

x

respectively, then the value of

\sum_{r = 1}^{2000} \frac{\{x + r\}}{2000}

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 3 - Relations and Functions>Target Exercises>Q 55

If

f (x) = \sqrt[n]{x^{m}}, n \in N

, is an even function, then

m

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 3 - Relations and Functions>Target Exercises>Q 56

The period of the function

f (x) = \sqrt{\tan x}

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 3 - Relations and Functions>Target Exercises>Q 57

The period of the function

f (x) = \cos (\frac{8 x + 5}{4 π})

is