Skills in Mathematics Play with Graphs for JEE Main & Advanced>Chapter 1 - Introduction of Graphs>EXERCISE>Q 5

MEDIUM

JEE Main

IMPORTANT

Earn 100

Construct the graph for $f (x) = [[x] - x]$ , where $[\cdot]$ denotes greatest integer function.

Important Questions on Introduction of Graphs

HARD

JEE Main

IMPORTANT

Skills in Mathematics Play with Graphs for JEE Main & Advanced>Chapter 1 - Introduction of Graphs>EXERCISE>Q 6

If

0 < α < 1

, then show

\frac{\tan^{- 1} (α)}{α} > \frac{π}{4}

.

HARD

JEE Main

IMPORTANT

Skills in Mathematics Play with Graphs for JEE Main & Advanced>Chapter 1 - Introduction of Graphs>EXERCISE>Q 7

Find the number of solutions for

\cos^{- 1} (\cos x) = [x]

, where

[\cdot]

denotes the greatest integer function.

MEDIUM

JEE Main

IMPORTANT

Skills in Mathematics Play with Graphs for JEE Main & Advanced>Chapter 1 - Introduction of Graphs>EXERCISE>Q 8

Find the number of solutions for $[[x] - x] = \sin x$ , where $[\cdot]$ denotes the greatest integer function.

HARD

JEE Main

IMPORTANT

Skills in Mathematics Play with Graphs for JEE Main & Advanced>Chapter 1 - Introduction of Graphs>EXERCISE>Q 9

Find the values of

x

graphically, which satisfy

|\frac{x^{2}}{x - 1}| \leq 1

.

HARD

JEE Main

IMPORTANT

Skills in Mathematics Play with Graphs for JEE Main & Advanced>Chapter 1 - Introduction of Graphs>EXERCISE>Q 10

Find the number of value(s) of

x

for which

x^{3} - [x] = 3

, where

[\cdot]

denotes the greatest integer function.