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Continuity and Differentiability — BITSAT Mathematics PYQs

18 previous year questions from Continuity and Differentiability with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

18 questionsMathematicsSolutions on every page
1

Let f be the function defined by f(x)= array cc x^2-1 x^2-2|x-1|-1 , & x 1 1 2 , & x=1 array .

BITSAT 2024 Solution View → 2

If f(x)= array cc x^2 ( x) (1+x) , & x 0 0, & x=0 array . , then at x=0, f(x) is

BITSAT 2024 Solution View → 3

f(x)= array cc 4 & - x - 5 x^2-1 & - 5 x 5 4 & 5 x array . If k is the number of points where f(x) is not differentiable then k-2=

BITSAT 2024 Solution View → 4

Let f be the function defined by f(x)= array ll x²-1 x²-2|x-1|-1 , & x 1 1 / 2, & x=1 array .

BITSAT 2020 Solution View → 5

Let f x = x p sin 1 x , x ≠ 0 0 , x = 0 then f x is continuous but not differentiable at x = 0 , if

BITSAT 2018 Solution View → 6

If f x = e x , x ≤ 0 1 - x , x > 0 , then

BITSAT 2017 Solution View → 7

The value of f ( 0 ) , so that the function f x = 2 x - sin - 1 x 2 x + tan - 1 x is continuous at each point in its domain, is

BITSAT 2017 Solution View → 8

Consider the greatest integer function, defined by f ( x ) = [ x ] , 0 ≤ x < 2 . Then

BITSAT 2017 Solution View → 9

The number of points at which the function f ( x )= 1 | x | is discontinuous is:

BITSAT 2016 Solution View → 10

If f(x)= array cl x x (1+x² ) & , x 0 0 & , x=0 array . then f(x) is

BITSAT 2016 Solution View → 11

If a function f(x) is given by f(x)= x 1+x + x (x+1)(2 x+1) + x (2 x+1)(3 x+1) + , , then at x=0, f(x)

BITSAT 2015 Solution View → 12

Let f: R R be a function such that f(x+y)=f(x)+f(y), x, y R If f ( x ) is differentiable at x =0 , then which one of the following is incorrect?

BITSAT 2015 Solution View → 13

Let f(x)= array c (x-1) 1 x-1 if x 1 0 if x=1 array . Then which one of the following is true?

BITSAT 2014 Solution View → 14

Let f ( x )= array l 1- ³ x 3 ² x , x 2 array . If f(x) is continuous at x= 2 ,(p, q)=

BITSAT 2014 Solution View → 15

If the function f(x)= cases A x-B, & x 1 3 x & , 1<x<2 B x²-A, & x 2 cases is continuous at x=2 and 4, then the values of a and b are

BITSAT 2012 Solution View → 16

The function ( f ( x )=( x -1) | n x | ) is at ( x =1 )

BITSAT 2011 Solution View → 17

The value of ( | array ccc 1 & 2 & 3 -4 & 3 & 6 2 & -7 & 9 array | ) is

BITSAT 2010 Solution View → 18

Let (f(x)= (e^x-1 )^2 ( x a ) (1+ x 4 ) ) for (x 0 ), and (f(0)=12 ). If ( f ) is continuous at (x=0 ), then the value of (a ) is equal to

BITSAT 2010 Solution View →
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