Quantrex Academy Quantrex AcademyPYQs with solutions · JEE · NEET · NDA

Home · JEE Main & Advanced · Mathematics · Continuity and Differentiability

Continuity and Differentiability — JEE Main & Advanced Mathematics PYQs

576 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.

576 questionsMathematicsSolutions on every page
1

Let R denote the set of all real numbers. Let f : R R be an arbitrary function and let g : R R be the function defined by g(x) = x f(x) , for all x R . Then which of the following

JEE Advanced 2026 Solution View → 2

Consider the function f : (- 2 , 2 ) (- , ) defined by f(x) = (|x| + |x - 1|) x + [x x] , where [x x] is the greatest integer less than or equal to x x . Let be the total number of

JEE Advanced 2026 Solution View → 3

For a real number , let [ ] denote the greatest integer less than or equal to . For a finite set S , let |S| denote the number of elements in the set S . Consider the functions f :

JEE Advanced 2026 Solution View → 4

For the function f(x) = e^ |x| - |x| , x R , consider the following statements: Statement I: f is differentiable for all x R . Statement II: f is increasing in (- , - 2 ) . In the

JEE Main 2026 Solution View → 5

Let f(x) = cases 1 3 , & x /2 b(1- x) ( -2x)^2 , & x > /2 cases . If f is continuous at x= /2 , then the value of ₀^ 3b-6 |x^2+2x-3| ,dx is:

JEE Main 2026 Solution View → 6

Let f(x) = cases x^3 + 8 ; & x Then the number of points, where the function g f is discontinuous, is __________.

JEE Main 2026 Solution View → 7

Let f(x)= cases e^ x-1 , & x<0 x^2-5x+6, & x 0 cases and g(x)=f(|x|)+|f(x)| . If the number of points where g is not continuous and is not differentiable are and respectively, then

JEE Main 2026 Solution View → 8

The number of points, at which the function f(x) = 6x, 2 + 3x^2 + |x - 1| | |x^2 - 1 4 | | , x (- , ) , is not differentiable, is _____.

JEE Main 2026 Solution View → 9

The number of points in the interval [2, 4] , at which the function f(x) = [x^2 - x - 1 2 ] , where [ ] denotes the greatest integer function, is discontinuous, is _______.

JEE Main 2026 Solution View → 10

Let f(x)= _ 0 ( x-x^ ( 2 ) (x-1) 1+x^ ( 2 ) (x-1) ), x R . Consider the following two statements : (I) f(x) is discontinous at x=1 . (II) f(x) is continous at x=-1 . Then,

JEE Main 2026 Solution View → 11

Let [t] denote the greatest integer less than or equal to t . If the function f(x)= array cl b² ( 2 [ 2 ( x+ x) x ] ), & x 0 a &, x=0 array . is continuous at x=0 , then a²+b² is e

JEE Main 2026 Solution View → 12

If the function f(x)= e^ x (e^ x-x -1 )+ _ e ( x+ x)-x x-x is continuous at x=0 , then the value of f(0) is equal to

JEE Main 2026 Solution View → 13

Let , R be such that the function f(x)= cases 2 (x²-2 )+2 x &, x be differentiable at all x R . Then 34( + ) is equal to

JEE Main 2026 Solution View → 14

If f(x)= array cc a|x|+x²-2( |x|)( |x|) x &, x 0 b &, x=0 array . is continuous at x=0 , then a+b is equal to

JEE Main 2026 Solution View → 15

Let f(x)= cases a x²+2 a x+3 4 x²+4 x-3 &, x - 3 2 , 1 2 ~b &, x=- 3 2 , 1 2 cases be continuous at x=- 3 2 . If f f(x)= 7 5 , then x is equal to:

JEE Main 2026 Solution View → 16

Let [ ] denote the greatest integer function, and let f(x)= 2 x, x² . Let S = x (-2,2) . : the function g (x)=|x| [x² ] is discontinuous at .x . Then _ x S f(x) equals

JEE Main 2026 Solution View → 17

The number of points of discontinuity of the function f( x )= [ x ^2 2 ]-[ x ], x [0,4] , where [ ] denotes the greatest integer function is ________

JEE Main 2025 Solution View → 18

Let m and n be the number of points at which the function f( x )= x , x ^3, x ^5, ., x ²¹ , x R , is not differentiable and not continuous, respectively. Then m + n is equal to ___

JEE Main 2025 Solution View → 19

Let f( x )= cases (1+ ax )^ 1 / x & , x 0 1+ b & , x =0 ( x +4)^ 1 / 2 -2 ( x + c )^ 1 / 3 -2 & , cases be continuous at x=0 . Then e^a b c is equal to

JEE Main 2025 Solution View → 20

Let the function f(x)= (x^2+1 ) |x^2-a x+2 |+ |x| be not differentiable at the two points x= =2 and x= . Then the distance of the point ( , ) from the line 12 x+5 y+10=0 is equal t

JEE Main 2025 Solution View → 21

Let f (x)= array lc 3 x, & x 0 1+x+[x], x+2[x] , & 0 x 2 5, & x 2, array . where [.] denotes greatest integer function. If and are the number of points, where f is not continuous a

JEE Main 2025 Solution View → 22

Let [x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function f(x)=[x]+|x-2|,-2 x 3 , is not continuous and not differ

JEE Main 2025 Solution View → 23

If the function f(x)= array l 2 x (k₁+1 ) x+ (k₂-1 ) x , x 0 4, x=0 2 x _e ( 2+k₁ x 2+k₂ x ), x 0 array . is continuous at x =0 , then k ₁^2+ k ₂^2 is equal to

JEE Main 2025 Solution View → 24

Let f(x) be a real differentiable function such that f(0)=1 and f(x+y)=f(x) f^ (y)+f^ (x) f(y) for all x, y R . Then _ n =1 ¹⁰⁰ _ e f( n ) is equal to :

JEE Main 2025 Solution View → 25

Let the function, f(x)= cases -3 a x^2-2, & x 1 a^2+b x, & x 1 cases be differentiable for all x R , where a 1, b R . If the area of the region enclosed by y=f(x) and the line y=-2

JEE Main 2025 Solution View → 26

Let f:(0, ) R be a function given by f(x)= ( array cc ( 8 7 )^ 8 x 7 x , & 0 where a , b Z . If f is continuous at x= 2 , then a ^2+ b ^2 is equal to

JEE Main 2024 Solution View → 27

For a , b >0 , let f(x)= array cc (( a +1) x)+ b x x , & x 0 array . be a continous function at x=0 . Then b a is equal to :

JEE Main 2024 Solution View → 28

Let [ t ] denote the greatest integer less than or equal to t . Let f:[0, ) R be a function defined by f(x)= [ x 2 +3 ]-[ x ] . Let S be the set of all points in the interval [0,8]

JEE Main 2024 Solution View → 29

Let f:[-1,2] R be given by f(x)=2 x^2+x+ [x^2 ]-[x] , where [t] denotes the greatest integer less than or equal to t . The number of points, where f is not continuous, is :

JEE Main 2024 Solution View → 30

If the function f(x)= 3 x+ x- 3 x x^3 , x R , is continuous at x=0 , then f(0) is equal to :

JEE Main 2024 Solution View → 31

If the function f(x)= cases 72^x-9^x-8^x+1 2 - 1+ x , & x 0 a _e 2 _e 3 & , x=0 cases is continuous at x=0 , then the value of a^2 is equal to

JEE Main 2024 Solution View → 32

Let f: R R be a function given by f(x)= array ll 1- 2 x x^2 , & x 0 array . where , R . If f is continuous at x=0 , then ^2+ ^2 is equal to :

JEE Main 2024 Solution View → 33

Let f x = 2 x 2 + 5 x - 3 , x ∈ R . If m and n denote the number of points where f is not continuous and not differentiable respectively, then m + n is equal to:

JEE Main 2024 Solution View → 34

Let f : R → R be defined as f x = a − b cos 2 x x 2 ; x < 0 x 2 + c x + 2 ; 0 ≤ x ≤ 1 2 x + 1 ; x > 1 If f is continuous everywhere in R and m is the number of points where f is NO

JEE Main 2024 Solution View → 35

Consider the function f : 0 , ∞ → R defined by f x = e − log e x . If m and n be respectively the number of points at which f is not continuous and f is not differentiable, then m

JEE Main 2024 Solution View → 36

Let g x be a linear function and f x = g x , x ≤ 0 1 + x 2 + x 1 x , x > 0 , is continuous at x = 0 . If f ' 1 = f − 1 , then the value of g 3 is

JEE Main 2024 Solution View → 37

Let a and b be real constants such that the function f defined by f x = x 2 + 3 x + a , x ≤ 1 b x + 2 , x > 1 be differentiable on R . Then, the value of ∫ - 2 2 f x d x equals

JEE Main 2024 Solution View → 38

Let f : R - 0 → R be a function satisfying f x y = f ( x ) f ( y ) for all x , y , f ( y ) ≠ 0 . If f ' ( 1 ) = 2024 , then

JEE Main 2024 Solution View → 39

If the function f x = 1 | x | , | x | ≥ 2 a x 2 + 2 b , | x | < 2 is differentiable on R , then 48 ( a + b ) is equal to _______.

JEE Main 2024 Solution View → 40

Let f x = lim r → x 2 r 2 ( f ( r ) ) 2 - f ( x ) f ( r ) r 2 - x 2 - r 3 e f ( r ) r be differentiable in ( - ∞ , 0 ) ∪ ( 0 , ∞ ) and f ( 1 ) = 1 . Then the value of a e , such th

JEE Main 2024 Solution View → 41

Consider the function f : ( 0 , 2 ) → R defined by f ( x ) = x 2 + 2 x and the function g ( x ) defined by g x = min f ( t ) , 0 < t ≤ x and 0 < x ≤ 1 3 2 + x , 1 < x < 2 . Then

JEE Main 2024 Solution View → 42

Consider the function f x = a 7 x - 12 - x 2 b x 2 - 7 x + 12 , x < 3 2 sin ( x - 3 ) x - [ x ] , x > 3 b , x = 3 ,where [ x ] denotes the greatest integer less than or equal to x

JEE Main 2024 Solution View → 43

Let f : 0 , 1 &#8594; &#8477; be the function defined as f x = 4 x x - 1 4 2 x - 1 2 , where [ x ] denotes the greatest integer less than or equal to x . Then which of the followin

JEE Advanced 2023 Solution View → 44

Let x denote the greatest integer function and f x = max 1 + x + x , 2 + x , x + 2 x , 0 &#8804; x &#8804; 2 , where f is not continuous and n be the number of points in 0 , 2 , wh

JEE Main 2023 Solution View → 45

Let x be the greatest integer &#8804; x . Then the number of points in the interval ( &#8211; 2 , 1 ) where the function f x = x + x - x is discontinuous, is _____.

JEE Main 2023 Solution View → 46

Let f and g be two functions defined by f x = x + 1 , x &#60; 0 x - 1 , x &#8805; 0 and g x = x + 1 , x &#60; 0 1 , x &#8805; 0 .Then g o f x is

JEE Main 2023 Solution View → 47

Let f x = x 2 - x + - x + x , where x &#8712; &#8477; and t denotes the greatest integer less than or equal to t . Then, f is

JEE Main 2023 Solution View → 48

Let f : - 2 , 2 &#8594; &#8477; be defined by f x = x x , - 2 &#60; x &#60; 0 x - 1 x , 0 &#8804; x &#60; 2 where x denotes the greatest integer function. If m and n respectively a

JEE Main 2023 Solution View → 49

Let k and m be positive real numbers such that the function f x = 3 x 2 + k x + 1 , 0 &#60; x &#60; 1 m x 2 + k 2 , x &#8805; 1 is differentiable for all x &#62; 0 . Then 8 f &#39;

JEE Main 2023 Solution View → 50

Let a &#8712; &#8484; and t be the greatest integer &#8804; t , then the number of points, where the function f x = a + 13 &#160; sin x , &#160; x &#8712; 0 , &#960; is not differe

JEE Main 2023 Solution View → 51

Let f and g be twice differentiable functions on R such that f &#34; x = g &#34; x + 6 x f &#39; 1 = 4 g &#39; 1 - 3 = 9 f 2 = 3 g 2 = 12 Then which of the following is NOT true ?

JEE Main 2023 Solution View → 52

Suppose f is a function satisfying f ( x + y ) = f ( x ) + f ( y ) for all x , y &#8712; &#8469; and f ( 1 ) = 1 5 . If &#8721; n = 1 m f ( n ) n ( n + 1 ) ( n + 2 ) = 1 12 then m

JEE Main 2023 Solution View → 53

If the function f x = 1 + | cos x | &#955; | cos x | , 0 &#60; x &#60; &#960; 2 &#956; , x = &#960; 2 e cot 6 x cot 4 x , &#960; 2 &#60; x &#60; &#960; is continuous at x = &#960;

JEE Main 2023 Solution View → 54

Let f x = x 2 sin 1 x ; x &#8800; 0 0 ; x = 0 , then at x = 0

JEE Main 2023 Solution View → 55

Let the function f x = log e 1 + 5 x - log e 1 + &#945; x x if x &#8800; 0 10 if x = 0 be continuous at x = 0 . Then &#945; is equal to

JEE Main 2022 Solution View → 56

If t denotes the greatest integer &#8804; t , then number of points, at which the function f x = 4 2 x + 3 + 9 x + 1 2 - 12 x + 20 is not differentiable in the open interval - 20 ,

JEE Main 2022 Solution View → 57

The number of points, where the function f : R &#8594; R , f x = x - 1 cos x - 2 sin x - 1 + x - 3 x 2 - 5 x + 4 , is NOT differentiable, is

JEE Main 2022 Solution View → 58

The function f : R &#8594; R defined by f x = lim n &#8594; &#8734; cos 2 &#960; x - x 2 n sin x - 1 1 + x 2 n + 1 - x 2 n is continuous for all x in

JEE Main 2022 Solution View → 59

If for p &#8800; q &#8800; 0 , then function f x = p 729 + x 7 - 3 729 + q x 3 - 9 is continuous at x = 0 , then

JEE Main 2022 Solution View → 60

Let f x = 2 + x - x - 1 + x + 1 , x &#8712; R . Consider S 1 : f &#39; - 3 2 + f &#39; - 1 2 + f &#39; 1 2 + f &#39; 3 2 = 2 S 2 : &#8747; - 2 2 f x d x = 12 Then,

JEE Main 2022 Solution View → 61

Let a function f : &#8477; &#8594; &#8477; be defined as: f x = &#8747; 0 x 5 - t - 3 d t , x &#62; 4 x 2 + b x , x &#8804; 4 where b &#8712; &#8477; . If f is continuous at x = 4

JEE Main 2022 Solution View → 62

If the function f x = log e 1 - x + x 2 + log e 1 + x + x 2 s e c x - cos x , x &#8712; - &#960; 2 , &#960; 2 - 0 k , x = 0 is continuous at x = 0 , then k is equal to:

JEE Main 2022 Solution View → 63

If f x = x + a , x &#8804; 0 x - 4 , x &#62; 0 and g x = x + 1 , x &#60; 0 x - 4 2 + b , x &#8805; 0 are continuous on R , then g o f 2 + f o g - 2 is equal to:

JEE Main 2022 Solution View → 64

Let f x = 4 x 2 - 8 x + 5 , if &#160; 8 x 2 - 6 x + 1 &#8805; 0 4 x 2 - 8 x + 5 , if &#160; 8 x 2 - 6 x + 1 &#60; 0 , where &#945; denotes the greatest integer less than or equal t

JEE Main 2022 Solution View → 65

Let f : R &#8594; R be a function defined by : f x = max t &#8804; x t 3 - 3 t ; x &#8804; 2 x 2 + 2 x - 6 ; 2 &#60; x &#60; 3 x - 3 + 9 ; 3 &#8804; x &#8804; 5 2 x + 1 ; x &#62; 5

JEE Main 2022 Solution View → 66

Let f , g : R &#8594; R be functions defined by f x = x , x &#60; 0 1 - x , x &#8805; 0 and g x = e x - x , x &#60; 0 x - 1 2 - 1 , x &#8805; 0 where x denote the greatest integer

JEE Main 2022 Solution View → 67

Let f : &#8477; &#8594; &#8477; be defined as f x = e x , x &#60; 0 a e x + x - 1 , 0 &#8804; x &#60; 1 b + sin &#960; x , 1 &#8804; x &#60; 2 e - x - c , x &#8805; 2 where a , b ,

JEE Main 2022 Solution View → 68

Let f x = min 1 , 1 + x sin x , 0 &#8804; x &#8804; 2 &#960; . If m is the number of points, where f is not differentiable and n is the number of points, where f is not continuous,

JEE Main 2022 Solution View → 69

f , g : R &#8594; R be two real valued function defined as f x = - x + 3 , x &#60; 0 e x , x &#8805; 0 and g x = x 2 + k 1 x , x &#60; 0 4 x + k 2 , x &#8805; 0 , where k 1 and k 2

JEE Main 2022 Solution View → 70

Let f x = 2 x 2 + 1 and g x = 2 x - 3 , x &#60; 0 2 x + 3 , x &#8805; 0 , where t is the greatest integer &#8804; t . Then, in the open interval - 1 , 1 , the number of points wher

JEE Main 2022 Solution View → 71

Let f x = sin x - x x - x , x &#8712; - 2 , - 1 max 2 x , 3 x , x &#60; 1 1 , otherwise where t denotes greatest integer &#8804; t . If m is the number of points where f is not con

JEE Main 2022 Solution View → 72

The number of points where the function f x = 2 x 2 - 3 x - 7 if x &#10877; - 1 4 x 2 - 1 if - 1 &#60; x &#60; 1 x + 1 + x - 2 if x &#10878; 1 , where t denotes the greatest intege

JEE Main 2022 Solution View → 73

Let [ t ] denote the greatest integer &#8804; t . The number of points where the function f ( x ) = [ x ] x 2 - 1 + sin &#960; [ x ] + 3 - [ x + 1 ] , x &#8712; ( - 2 , 2 ) is not

JEE Main 2021 Solution View → 74

The function f x = x 2 - 2 x - 3 &#183; e 9 x 2 - 12 x + 4 is not differentiable at exactly :

JEE Main 2021 Solution View → 75

If the function f x = 1 x log e 1 + x a 1 - x b , x &#60; 0 k , x = 0 cos 2 x - sin 2 x - 1 x 2 + 1 - 1 , x &#62; 0 is continuous at x = 0 , then 1 a + 1 b + 4 k is equal to :

JEE Main 2021 Solution View → 76

Let [ t ] denote the greatest integer less than or equal to t . Let f ( x ) = x - [ x ] , g ( x ) = 1 - x + [ x ] , and h ( x ) = min f ( x ) , g ( x ) , x &#8712; [ - 2 , 2 ] . Th

JEE Main 2021 Solution View → 77

Let a , b &#8712; R , b &#8800; 0 . Defined a function, f x = a sin &#960; 2 ( x &#8722; 1 ) , &#8197;&#8197;&#8197;&#8197; for x &#8804; 0 tan 2 x &#8722; sin 2 x b x 3 , &#8197;&

JEE Main 2021 Solution View → 78

Let f : 0 , &#8734; &#8594; 0 , 3 be a function defined by f x = max sin t : 0 &#8804; t &#8804; &#960; , x &#8712; 0 , &#960; 2 + cos x , x &#62; &#960; . Then which of the follow

JEE Main 2021 Solution View → 79

Let f : - &#960; 4 , &#960; 4 &#8594; R be defined as, f x = 1 + sin x 3 a sin x , - &#960; 4 &#60; x &#60; 0 b , x = 0 e cot 4 x / cot 2 x , 0 &#60; x &#60; &#960; 4 If f is conti

JEE Main 2021 Solution View → 80

Let f : 0 , 3 &#8594; R be defined by f x = min x - x , 1 + x - x where x is the greatest integer less than or equal to x . Let P denote the set containing all x &#8712; 0 , 3 wher

JEE Main 2021 Solution View → 81

If f x = &#8747; 0 x 5 + 1 - t d t , x &#62; 2 5 x + 1 , x &#8804; 2 , then

JEE Main 2021 Solution View → 82

Consider the function f x = P x sin x - 2 , x &#8800; 2 , and f x = 7 , x = 2 where P x is a polynomial such that P &#34; x is always a constant and P 3 = 9 . If f x is continuous

JEE Main 2021 Solution View → 83

Let f : R &#8594; R be defined as f x = &#955; x 2 - 5 x + 6 &#956; 5 x - x 2 - 6 x &#60; 2 e tan ( x - 2 ) x - [ x ] x &#62; 2 &#956; x = 2 where x is the greatest integer less th

JEE Main 2021 Solution View → 84

Let f : [ 0 , &#8734; ) &#8594; [ 0 , &#8734; ) be defined as f x = &#8747; 0 x y d y where [ x ] is the greatest integer less than or equal to x . Which of the following is true?

JEE Main 2021 Solution View → 85

Let f : R &#8594; R be defined as f x = x 3 ( 1 - cos 2 x ) 2 log e 1 + 2 x e - 2 x 1 - x e - x 2 , x &#8800; 0 &#945; , x = 0 If f is continuous at x = 0 , then &#945; is equal to

JEE Main 2021 Solution View → 86

Let f : R &#8594; R be a function defined as f x = 3 1 - | x | 2 if | x | &#8804; 2 0 if | x | &#62; 2 . Let g : R &#8594; R be given by g ( x ) = f ( x + 2 ) - f ( x - 2 ) . If n

JEE Main 2021 Solution View → 87

Let a function g : 0 , 4 &#8594; R be defined as g x = max t 3 - 6 t 2 + 9 t - 3 0 &#8804; t &#8804; x , 0 &#8804; x &#8804; 3 4 - x , 3 &#60; x &#8804; 4 then the number of points

JEE Main 2021 Solution View → 88

Let a function f : R &#8594; R be defined as, f x = sin x &#8722; e x if x &#8804; 0 a + - x if 0 &#60; x &#60; 1 2 x &#8722; b if x &#8805; 1 Where x is the greatest integer less

JEE Main 2021 Solution View → 89

Let f : R &#8594; R be a function defined as f x = sin ( a + 1 ) x + sin 2 x 2 x , if x &#60; 0 b , if x = 0 x + b x 3 - x b x 5 / 2 , if x &#62; 0 If f is continuous at x = 0 , th

JEE Main 2021 Solution View → 90

Let f : R &#8594; R satisfy the equation f ( x + y ) = f ( x ) &#183; f ( y ) for all x , y &#8712; R and f ( x ) &#8800; 0 for any x &#8712; R . If the function f is differentiabl

JEE Main 2021 Solution View → 91

If f x = 1 | x | ; | x | &#8805; 1 a x 2 + b ; | x | &#60; 1 is differentiable at every point of the domain, then the values of a and b are respectively:

JEE Main 2021 Solution View → 92

If the function f x = cos ( sin x ) - cos x x 4 is continuous at each point in its domain and f 0 = 1 k , then k is _________.

JEE Main 2021 Solution View → 93

Let &#945; &#8712; R be such that the function f x = cos - 1 1 - x 2 sin - 1 1 - x x - x 3 , x &#8800; 0 &#945; , x = 0 is continuous at x = 0 , where x = x - x , x is the greatest

JEE Main 2021 Solution View → 94

Let f : R &#8594; R and g : R &#8594; R be defined as f x = x + a , x &#60; 0 | x - 1 | , x &#8805; 0 and g x = x + 1 , x &#60; 0 ( x - 1 ) 2 + b , x &#8805; 0 , where a , b are no

JEE Main 2021 Solution View → 95

Let the functions f : R &#8594; R and g : R &#8594; R be defined as : f x = x + 2 , x &#60; 0 x 2 , x &#8805; 0 and g x = x 3 , x &#60; 1 3 x - 2 , x &#8805; 1 Then, the number of

JEE Main 2021 Solution View → 96

Let f : R &#8594; R be defined as f x = 2 sin - &#960; x 2 , if x &#60; - 1 a x 2 + x + b , if - 1 &#8804; x &#8804; 1 sin &#960; x , if x &#62; 1 If f x is continuous on R , then

JEE Main 2021 Solution View → 97

Let f be any function defined on R and let it satisfy the condition: f x - f y &#8804; x - y 2 , &#8704; x , y &#8712; R . If f 0 = 1 , then :

JEE Main 2021 Solution View → 98

A function f is defined on [ - 3 , 3 ] as f x = min | x | , 2 - x 2 , - 2 &#8804; x &#8804; 2 [ | x | ] , 2 &#60; | x | &#8804; 3 where [ x ] denotes the greatest integer &#8804; x

JEE Main 2021 Solution View → 99

The number of points, at which the function f x = 2 x + 1 - 3 x + 2 + x 2 + x - 2 , x &#8712; R is not differentiable, is

JEE Main 2021 Solution View → 100

If f : R &#8594; R is a function defined by f x = x - 1 cos 2 x - 1 2 &#960; , where &#183; denotes the greatest integer function, then f is:

JEE Main 2021 Solution View → 101

Let the functions f : - 1 , 1 &#8594; &#8477; and g : - 1 , 1 &#8594; - 1 , 1 be defined by f x = 2 x - 1 + 2 x + 1 &#38; g x = x - x , where x denotes the greatest integer less th

JEE Advanced 2020 Solution View → 102

Let f : &#8477; &#8594; &#8477; and g : &#8477; &#8594; &#8477; be functions satisfying f x + y = f x + f y + f x f y and f x = x g x for all x , y &#8712; &#8477; . If lim x &#859

JEE Advanced 2020 Solution View → 103

Let the function f : R &#8594; R be defined by f x = x 3 &#8722; x 2 + x &#8722; 1 sin x and let g : R &#8594; R be an arbitrary function. Let f g : R &#8594; R be the product func

JEE Advanced 2020 Solution View → 104

Let f : R &#8594; R be a function defined by f x = max x , x 2 .Let S denote the set of all points in R ,where f is not differentiable.Then :

JEE Main 2020 Solution View → 105

Let f : R &#8594; R be defined as f x = x 5 sin 1 x + 5 x 2 , x &#60; 0 0 , x = 0 x 5 cos 1 x + &#955; x 2 , x &#62; 0 . The value of &#955; for which f &#34; ( 0 ) exists, is___.

JEE Main 2020 Solution View → 106

If the function f x = k 1 ( x - &#960; ) 2 - 1 , x &#8804; &#960; k 2 cos x , x &#62; &#960; is twice differentiable, then the ordered pair k 1 , k 2 is equal to:

JEE Main 2020 Solution View → 107

Let f ( x ) = x &#183; x 2 , for - 10 &#60; x &#60; 10 , where t denotes the greatest integer function. Then the number of points of discontinuity of f x is equal to

JEE Main 2020 Solution View → 108

The function f x = &#960; 4 + tan - 1 x , x &#8804; 1 1 2 x - 1 , x &#62; 1 is :

JEE Main 2020 Solution View → 109

Let f : ( 0 , &#8734; ) &#8594; ( 0 , &#8734; ) be a differentiable function such that f ( 1 ) = e and lim t &#8594; x t 2 f 2 ( x ) - x 2 f 2 ( t ) t - x = 0 . If f ( x ) = 1 , th

JEE Main 2020 Solution View → 110

If a function f x defined by f x = a e x + b e &#8722; x , &#8722; 1 &#8804; x &#60; 1 c x 2 , 1 &#8804; x &#8804; 3 a x 2 + 2 c x , 3 &#60; x &#8804; 4 be continuous for some a ,

JEE Main 2020 Solution View → 111

Let t denote the greatest integer &#8804; t and lim x &#8594; 0 &#8289; x 4 x = A . Then the function, f x = x 2 sin &#8289; &#960; x is discontinuous, when x is equal to:

JEE Main 2020 Solution View → 112

If f x = s i n a + 2 x + s i n x x ; x &#60; 0 b ; x = 0 x + 3 x 2 1 / 3 - x 1 / 3 x 1 / 3 ; x &#62; 0 is continuous at x = 0 , then a + 2 b is equal to:

JEE Main 2020 Solution View → 113

Let S , be the set of all functions f : 0 , 1 &#8594; R , which are continuous on 0 , 1 , and differentiable on 0 , 1 . Then for every f in S , there exists c &#8712; 0 , 1 , depen

JEE Main 2020 Solution View → 114

If the function f defined on - 1 3 , 1 / 3 by f x = 1 x l o g e 1 + 3 x 1 - 2 x , when x &#8800; 0 k , when x = 0 , is continuous, then k is equal to.

JEE Main 2020 Solution View → 115

Let S be the set of points where the function , f x = | 2 - | x - 3 | , x &#8712; R , is not differentiable. Then &#8721; x &#8712; S f f x is equal to

JEE Main 2020 Solution View → 116

The number of discontinuity of the greatest integer function f x = x , x ∈ - 7 2 , 100 is equal to

NTA Abhyas JEE Main 2020 Solution View → 117

In ( 0 , 2 π ) , the total number of points where f x = m a x . sin ⁡ x , cos ⁡ x , 1 – cos ⁡ x is not differentiable, are equal to

NTA Abhyas JEE Main 2020 Solution View → 118

The value of f 0 so that the function f x = 1 - cos 1 - cos x x 4 is continuous everywhere is k , then value of 10 k is

NTA Abhyas JEE Main 2020 Solution View → 119

The function f x = 1 - sin x + cos x 1 + sin x + cos x is not defined at x = &#960; . The value of f ( &#960; ) , so that f ( x ) is continuous at x = &#960; , is

NTA Abhyas JEE Main 2020 Solution View → 120

If f x = 4 + a x − 4 − a x x , − 1 ≤ x < 0 3 x + 2 x − 8 , 0 ≤ x ≤ 1 is continuous in [ − 1 , 1 ], then the value of a is

NTA Abhyas JEE Main 2020 Solution View →
Practice all Continuity and Differentiability questions in the app →