A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 10 - Sets, Relations and Functions>EXERCISE>Q 13

EASY

JEE Main Paper 2A- B.Arch

IMPORTANT

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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

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Important Questions on Sets, Relations and Functions

EASY

JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 10 - Sets, Relations and Functions>EXERCISE>Q 14

If

f (x) = \frac{1}{\sqrt{| x - 1 | - [x]}},

where

[]

denotes the greatest integer function, then the domain of

f (x)

is

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JEE Main Paper 2A- B.Arch

IMPORTANT

A Complete Self Study Guide B. Arch (Bachelor of Architecture) Entrance Examination Mathematics>Chapter 10 - Sets, Relations and Functions>EXERCISE>Q 15

Statement I : The functions

f (x) = x^{2} - x + 1, x \geq \frac{1}{2}

and

g (x) = \frac{1}{2} + \sqrt{(x - \frac{3}{4})},

then the number of solutions of the equation

f (x) - g (x)

is two.
Statement II :

f (x)

and

g (x)

are inverse of each other.