Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 61

HARD

JEE Main/Advance

IMPORTANT

Earn 100

If $F (x) = \frac{sinπ [x]}{\{x\}},$ then $F (x)$ is: (where $\{.\}$ denotes fractional part function and $[.]$ denotes the greatest integer function and $s g n (x)$ is a signum function)

50% studentsanswered this correctly

Important Questions on Functions

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 62

Let

f : R \to R

and

g : R \to R

be two one-one and onto functions such that they are mirror images of each other about the line

y = a

. If

h (x) = f (x) + g (x),

then

h (x)

is

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 63

Which of following pairs of functions are identical.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 64

For the function

f (x) = \ln (\sin^{- 1} \log_{2} (x))

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 65

Which among the following functions defined from

[- 1, 1]

to

[- 1, 1],

are not bijective ?

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 66

Find number of all such functions

y = f (x)

which are one-one?

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 67

Find the number of all such functions

y = f (x)

which are onto

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-3>Q 1

Find the set of all solutions of the equation

2^{|y|} - |2^{y - 1} - 1| = 2^{y - 1} + 1 .

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-3>Q 4

Let $f (x) = x^{2}$ and $g (x) = \sin x$ for all $x \in R .$ Then the set of all $x$ satisfying $(f \circ g \circ g \circ f) (x) = (g \circ g \circ f) (x),$ where $(f \circ g) (x) = f (g (x)),$ is