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JEE Continuity and Differentiability PYQs with Solutions

576 previous year questions from Continuity and Differentiability (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

576 questionsMathematics2002–2026Answers + solutions

About Continuity and Differentiability PYQs

Continuity and Differentiability has 576 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (154), NTA Abhyas JEE Main (44) and JEE Advanced (22), spanning 2002 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 16
  • 2025: 9
  • 2024: 17
  • 2023: 12
  • 2022: 18
  • 2021: 28
  • 2020: 59
  • 2019: 14
  • 2018: 6
  • 2017: 2
  • 2016: 5
  • 2015: 3

Continuity and Differentiability questions with solutions

1

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

JEE Advanced 2026 Solution View → 2

Consider the function f : (-(π)/(2), (π)/(2)) arrow (-∞, ∞) 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 α be

JEE Advanced 2026 Solution View → 3

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

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 (-π, -(π)/(2))

JEE Main 2026 Solution View → 5

Let f(x) = cases (1)/(3), & x ≤ π/2 (b(1- x))/((π-2x)^2), & x > π/2 cases . If f is continuous at x=π/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 α and β

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 ∈ (-π, π) , 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)= _ θ arrow 0 ( π x-x^ ((2)/(θ)) (x-1) 1+x^ ((2)/(θ)) (x-1) ), x ∈ R . Consider the following two statements : (I) f(x) is discontinous at x=1 . (II) f(x) is continous at

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 b^ 2 ((π)/(2)[(π)/(2)( x+ x) x]), & x 0 a &, x=0 array . is continuous at x=0 , then

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

JEE Main 2026 Solution View → 14

If f(x)=\ array cc a|x|+x^ 2 -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 x^ 2 +2 a x+3 4 x^ 2 +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, x^ 2 \ . Let S = \ x ∈(-2,2). : the function g (x)=|x| [x^ 2 ] is discontinuous at .x\ . Then ∑_ x ∈ S f(x)

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=α=2 and x=β . Then the distance of the point (α, β) from the line 12 x+5 y+10=0 is equal to

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 α and β are the number of points, where f is not

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

JEE Main 2025 Solution View → 23

If the function f(x)=\ array l (2)/(x)\ (k_1+1) x+ (k_2-1) x\ , x 0 4, x=0 (2)/(x) _e((2+k_1 x)/(2+k_2 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

JEE Main 2025 Solution View → 26

Let f:(0, π) arrow 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=(π)/(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, ∞) arrow R be a function defined by f(x)=[(x)/(2)+3]-[ x ] . Let S be the set of all points in the interval

JEE Main 2024 Solution View → 29

Let f:[-1,2] arrow 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+α x-β 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 arrow R be a function given by f(x)=\ array ll (1- 2 x)/(x^2), & x 0 array . where α, β ∈ R . If f is continuous at x=0 , then α^2+β^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) = \ array ll a - bcos2x x ^ 2 ; x < 0 x ^ 2 + cx + 2; 0 ≤ x ≤ 1 2x + 1; x > 1 array ) If f is continuous everywhere in R and m is the number of

JEE Main 2024 Solution View → 35

Consider the function f: (0, ∞) → R defined by f(x) = e ^ - | _ e x| . If m and n be respectively the number of points at which f is not continuous and f is not differentiable

JEE Main 2024 Solution View → 36

Let g(x) be a linear function and f(x) = \ cases g(x), & x ≤ 0 ((1 + x)/(2 + x))(1)/(x), & x > 0 cases ), 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) = \ cases x ^ 2 + 3x + a, & x ≤ 1 bx + 2, & x > 1 cases ) be differentiable on R . Then, the value of ∫ _

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) = \ cases (1)/(| x |), & | x | ≥ 2 a x ^ 2 + 2b, & | x | < 2 cases ) is differentiable on R , then 48 ( a + b ) is equal to _______.

JEE Main 2024 Solution View → 40

Let f(x) = _ 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

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) = \ cases min f ( t ) , & 0 < t ≤ xand0 < x ≤ 1 (3)/(2) + x

JEE Main 2024 Solution View → 42

Consider the function f(x) = \ cases a(7x - 12 - x ^ 2 ) b| x ^ 2 - 7x + 12| & , x < 3 2(sin ( x - 3 ))/(x - [ x ]) & , x > 3 b & , x = 3 cases ),where [ x ] denotes the greatest

JEE Main 2024 Solution View → 43

Let f: (0, 1) → ℝ be the function defined as f(x) = [4x] (x - (1)/(4)) ^ 2 (x - (1)/(2)) , where [ x ] denotes the greatest integer less than or equal to x . Then which of the

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 ≤ x ≤ 2 , where f is not continuous and n be the number of points in (0, 2) , where

JEE Main 2023 Solution View → 45

Let [x] be the greatest integer ≤ x . Then the number of points in the interval ( – 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) = \ array ll x + 1, x < 0 |x - 1| , x ≥ 0 array and g(x) = \ array ll x + 1, x < 0 1, x ≥ 0 array .Then (gof) (x) is

JEE Main 2023 Solution View → 47

Let f(x) = [ x ^ 2 - x] + |- x + [x]| , where x ∈ ℝ 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) → ℝ be defined by f(x) = \ cases x[x] & , & - 2 < x < 0 (x - 1)[x] & , & 0 ≤ x < 2 cases ) where [x] denotes the greatest integer function. If m and n respectively

JEE Main 2023 Solution View → 49

Let k and m be positive real numbers such that the function f(x) = \ cases 3 x ^ 2 + k x + 1 , & 0 0 . Then 8 f ^ ' ( 8 ) f ^ ' ((1)/(8)) is equal to

JEE Main 2023 Solution View → 50

Let a ∈ ℤ and [t] be the greatest integer ≤ t , then the number of points, where the function f(x) = [a + 13sinx], x ∈ (0, π) is not differentiable, is ____________

JEE Main 2023 Solution View → 51

Let f and g be twice differentiable functions on R such that f ^ " (x) = g ^ " (x) + 6x f ^ ' (1) = 4 g ^ ' (1) - 3 = 9 f(2) = 3g(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 ∈ ℕ and f ( 1 ) = (1)/(5) . If ∑ _ n = 1 ^ m (f ( n ))/(n ( n + 1 ) ( n + 2 )) = (1)/(12) then m is

JEE Main 2023 Solution View → 53

If the function f(x) = \ cases (1 + | cosx |)(λ)/(| cosx |), & 0

JEE Main 2023 Solution View → 54

Let f(x) = \ array ll x ^ 2 sin((1)/(x)); x ≠ 0 0; x = 0 array ), then at x = 0

JEE Main 2023 Solution View → 55

Let the function f(x) = \ cases _ e (1 + 5x) - _ e (1 + ) x & ifx ≠ 0 10 & ifx = 0 cases ) be continuous at x = 0 . Then α is equal to

JEE Main 2022 Solution View → 56

If [t] denotes the greatest integer ≤ t , then number of points, at which the function f(x) = 4|2x + 3| + 9[x + (1)/(2)] - 12[x + 20] is not differentiable in the open interval (

JEE Main 2022 Solution View → 57

The number of points, where the function f: R → R, f(x) = |x - 1|cos|x - 2|sin|x - 1| + (x - 3)| x ^ 2 - 5x + 4| , is NOT differentiable, is

JEE Main 2022 Solution View → 58

The function f: R → R defined by f(x) = _ n → ∞ cos(2 ) - x ^ 2n sin(x - 1) 1 + x ^ 2n + 1 - x ^ 2n is continuous for all x in

JEE Main 2022 Solution View → 59

If for p ≠ q ≠ 0 , then function f(x) = (p(729 + x)7 - 3)/(729 + qx3 - 9) is continuous at x = 0 , then

JEE Main 2022 Solution View → 60

Let f(x) = 2 + |x| - |x - 1| + |x + 1|, x ∈ R . Consider (S1): f ^ ' (- (3)/(2)) + f ^ ' (- (1)/(2)) + f ^ ' ((1)/(2)) + f ^ ' ((3)/(2)) = 2 (S2): ∫ _ - 2 ^ 2 f(x)dx = 12 Then,

JEE Main 2022 Solution View → 61

Let a function f: ℝ → ℝ be defined as: f(x) = \ cases ∫ _ 0 ^ x (5 - |t - 3|)dt, & x > 4 x ^ 2 + bx, & x ≤ 4 cases ) where b ∈ ℝ . If f is continuous at x = 4 , then which of the

JEE Main 2022 Solution View → 62

If the function f(x) = \ cases _ e (1 - x + x ^ 2 ) + _ e (1 + x + x ^ 2 ) secx - cosx , & x ∈ ((- π)/(2), (π)/(2)) - \ 0\ k & , x = 0 cases ) is continuous at x = 0 , then k is

JEE Main 2022 Solution View → 63

If f(x) = \ cases x + a, & x ≤ 0 |x - 4|, & x > 0 cases ) and g(x) = \ cases x + 1, & x < 0 (x - 4) ^ 2 + b, & x ≥ 0 cases ) are continuous on R , then (gof)(2) + (fog)(- 2) is

JEE Main 2022 Solution View → 64

Let f(x) = \ cases |4 x ^ 2 - 8x + 5|, & if8 x ^ 2 - 6x + 1 ≥ 0 [4 x ^ 2 - 8x + 5], & if8 x ^ 2 - 6x + 1 < 0 cases ), where [α] denotes the greatest integer less than or equal to

JEE Main 2022 Solution View → 65

Let f: R → R be a function defined by : f(x) = \ cases max _ t ≤ x \ t ^ 3 - 3t\ ; & x ≤ 2 x ^ 2 + 2x - 6; & 2 5 cases ) Where [t] is the greatest integer less than or equal to t

JEE Main 2022 Solution View → 66

Let f, g: R → R be functions defined by f(x) = \ cases [x] & , x g(x) = \ cases e ^ x - x, & x where [x] denote the greatest integer less than or equal to x . Then, the function

JEE Main 2022 Solution View → 67

Let f: ℝ → ℝ be defined as f(x) = [ cases [ e ^ x ], & x where a, b, c ∈ ℝ and [t] denotes greatest integer less than or equal to t . Then, which of the following statements is

JEE Main 2022 Solution View → 68

Let f(x) = min\ 1, 1 + xsinx\ , 0 ≤ x ≤ 2π . If m is the number of points, where f is not differentiable and n is the number of points, where f is not continuous, then the ordered

JEE Main 2022 Solution View → 69

f, g: R → R be two real valued function defined as f(x) = \ cases - |x + 3| & , & x < 0 e ^ x & , & x ≥ 0 cases ) and g(x) = \ cases x ^ 2 + k _ 1 x & , & x < 0 4x + k _ 2 & , & x

JEE Main 2022 Solution View → 70

Let f(x) = [2 x ^ 2 + 1] and g(x) = \ cases 2x - 3, & x < 0 2x + 3, & x ≥ 0 cases ), where [t] is the greatest integer ≤ t . Then, in the open interval (- 1, 1) , the number of

JEE Main 2022 Solution View → 71

Let f(x) = \ cases (sin(x - [x]))/(x - [x]), & x ∈ (- 2, - 1) max(2x, 3[|x|]), & |x| where [t] denotes greatest integer ≤ t . If m is the number of points where f is not

JEE Main 2022 Solution View → 72

The number of points where the function f(x) = \ cases |2 x ^ 2 - 3x - 7| & ifx ⩽ - 1 [4 x ^ 2 - 1] & if - 1 < x < 1 |x + 1| + |x - 2| & ifx ⩾ 1 cases ), where [t] denotes the

JEE Main 2022 Solution View → 73

Let [ t ] denote the greatest integer ≤ t . The number of points where the function f ( x ) = [ x ] | x ^ 2 - 1| + sin((π)/([ x ] + 3)) - [ x + 1 ] , x ∈ ( - 2, 2 ) is not

JEE Main 2021 Solution View → 74

The function f(x) = | x ^ 2 - 2x - 3| · e ^ 9 x ^ 2 - 12x + 4 is not differentiable at exactly :

JEE Main 2021 Solution View → 75

If the function f(x) = \ array ll (1)/(x) _ e ((1 + (x)/(a))/(1 - (x)/(b))), x 0 array ) 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 ∈ [ - 2, 2 ] . Then h

JEE Main 2021 Solution View → 77

Let a, b ∈ R, b ≠ 0 . Defined a function, f(x) = \ array ll asin(π)/(2) ( x - 1 ) ,forx ≤ 0 tan2x - sin2x b x ^ 3 , forx > 0 array ) If f is continuous at x = 0 , then 10 - ab is

JEE Main 2021 Solution View → 78

Let f: [0, ∞) → [0, 3] be a function defined by f(x) = \ array ll max\ sint: 0 ≤ t ≤ π\ , x ∈ [0, π] 2 + cosx, x > π array ). Then which of the following is true ?

JEE Main 2021 Solution View → 79

Let f: (- (π)/(4), (π)/(4)) → R be defined as, f(x) = \ cases (1 + |sinx|)(3a)/(|sinx|) & , - (π)/(4) If f is continuous at x = 0 then the value of 6a + b ^ 2 is equal to:

JEE Main 2021 Solution View → 80

Let f: [0, 3] → 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 ∈ [0, 3] where

JEE Main 2021 Solution View → 81

If f(x) = \ cases ∫ _ 0 ^ x (5 + |1 - t|)dt, & x > 2 5x + 1, & x ≤ 2 cases , then

JEE Main 2021 Solution View → 82

Consider the function f(x) = (P(x))/(sin(x - 2)), x ≠ 2 , and f(x) = 7, x = 2 where P(x) is a polynomial such that P ^ " (x) is always a constant and P(3) = 9 . If f(x) is

JEE Main 2021 Solution View → 83

Let f: R → R be defined as f(x) = \ cases λ| x ^ 2 - 5x + 6| μ(5x - x ^ 2 - 6) & x 2 μ & x = 2 cases ) where [x] is the greatest integer less than or equal to x . If f is

JEE Main 2021 Solution View → 84

Let f: [ 0, ∞ ) → [ 0, ∞ ) be defined as f(x) = ∫ _ 0 ^ x [y]dy 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 → R be defined as f(x) = \ cases x ^ 3 ( 1 - cos2x ) ^ 2 _ e ( 1 + 2x e ^ - 2x (1 - x e ^ - x ) ^ 2 ) & , x ≠ 0 α & , x = 0 cases ) If f is continuous at x = 0, then α is

JEE Main 2021 Solution View → 86

Let f: R → R be a function defined as f(x) = \ cases 3(1 - (| x |)/(2)) & if & | x | ≤ 2 0 & if & | x | > 2 cases . Let g: R → R be given by g ( x ) = f ( x + 2 ) - f ( x - 2 ) .

JEE Main 2021 Solution View → 87

Let a function g: [0, 4] → R be defined as g(x) = \ cases max\ t ^ 3 - 6 t ^ 2 + 9t - 3\ _ 0 ≤ t ≤ x , & 0 ≤ x ≤ 3 4 - x, & 3 then the number of points in the interval (0, 4)

JEE Main 2021 Solution View → 88

Let a function f: R → R be defined as, f(x) = \ cases sinx - e ^ x & ifx ≤ 0 a + [- x] & if0 Where [x] is the greatest integer less than or equal to x . If f is continuous on R

JEE Main 2021 Solution View → 89

Let f: R → R be a function defined as f(x) = \ cases (sin ( a + 1 ) x + sin2x)/(2x) & , if x 0 cases ) If f is continuous at x = 0 , then the value of a + b is equal to :

JEE Main 2021 Solution View → 90

Let f: R → R satisfy the equation f ( x + y ) = f ( x ) · f ( y ) for all x, y ∈ R and f ( x ) ≠ 0 for any x ∈ R . If the function f is differentiable at x = 0 and f ^ ' ( 0 ) = 3

JEE Main 2021 Solution View → 91

If f(x) = \ cases (1)/(| x |) & ; & | x | ≥ 1 a x ^ 2 + b & ; & | x | < 1 cases ) 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 ( sinx ) - cosx 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 α ∈ R be such that the function f(x) = \ cases ^ - 1 (1 - \ x\ ^ 2 ) ^ - 1 (1 - \ x\ ) \ x\ - \ x\ ^ 3 , & x ≠ 0 α, & x = 0 cases ) is continuous at x = 0, where \ x\ = x

JEE Main 2021 Solution View → 94

Let f: R → R and g: R → R be defined as f(x) = \ cases x + a, & x

JEE Main 2021 Solution View → 95

Let the functions f: R → R and g: R → R be defined as : f(x) = \ cases x + 2, & x Then, the number of points in R where (fog)(x) is NOT differentiable is equal to :

JEE Main 2021 Solution View → 96

Let f: R be defined as f(x) = \ cases 2sin(- ( )/(2)), & ifx 1 cases ) If f(x) is continuous on R , then a + b equals :

JEE Main 2021 Solution View → 97

Let f be any function defined on R and let it satisfy the condition: |f(x) - f(y)| ≤ | (x - y) ^ 2 |, ∀ (x, y) ∈ R . If f(0) = 1, then :

JEE Main 2021 Solution View → 98

A function f is defined on [ - 3, 3 ] as f(x) = \ array ll min \ | x | , 2 - x ^ 2 \ , - 2 ≤ x ≤ 2 [ | x | ] , 2 where [ x ] denotes the greatest integer ≤ x . The number of

JEE Main 2021 Solution View → 99

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

JEE Main 2021 Solution View → 100

If f: R → R is a function defined by f(x) = [x - 1]cos((2x - 1)/(2))π, where [·] denotes the greatest integer function, then f is:

JEE Main 2021 Solution View → 101

Let the functions f: (- 1, 1) → ℝ and g: (- 1, 1) → (- 1, 1) be defined by f(x) = |2x - 1| + |2x + 1| and g(x) = x - [x] , where [x] denotes the greatest integer less than or

JEE Advanced 2020 Solution View → 102

Let f: ℝ → ℝ and g: ℝ → ℝ be functions satisfying f(x + y) = f(x) + f(y) + f(x)f(y)andf(x) = xg(x) for all x, y ∈ ℝ . If _ x → 0 g(x) = 1, then which of the following statements

JEE Advanced 2020 Solution View → 103

Let the function f: R → R be defined by f(x) = x ^ 3 - x ^ 2 + (x - 1)sinx and let g: R → R be an arbitrary function. Let fg: R → R be the product function defined by (fg)(x) =

JEE Advanced 2020 Solution View → 104

Let f: R → 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 → R be defined as f(x) = \ cases x ^ 5 sin((1)/(x)) + 5 x ^ 2 & , & x 0 cases ). The value of λ for which f ^ " ( 0 ) exists, is___.

JEE Main 2020 Solution View → 106

If the function f(x) = \ cases k _ 1 ( x - π ) ^ 2 - 1, & x ≤ π k _ 2 cosx, & x > π cases ) is twice differentiable, then the ordered pair ( k _ 1 , k _ 2 ) is equal to:

JEE Main 2020 Solution View → 107

Let f ( x ) = x · [(x)/(2)], for - 10 < x < 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) = \ cases (π)/(4) + ^ - 1 x, & |x| ≤ 1 (1)/(2)(|x| - 1), & |x| > 1 cases ) is :

JEE Main 2020 Solution View → 109

Let f: ( 0, ∞ ) → ( 0, ∞ ) be a differentiable function such that f ( 1 ) = e and _ t → x t ^ 2 f ^ 2 ( x ) - x ^ 2 f ^ 2 ( t ) t - x = 0 . If f ( x ) = 1 , then x is equal to:

JEE Main 2020 Solution View → 110

If a function f(x) defined by f(x) = \ cases a e ^ x + b e ^ - x , & - 1 ≤ x

JEE Main 2020 Solution View → 111

Let [t] denote the greatest integer ≤ t and _ x → 0 ⁡ x[(4)/(x)] = A . Then the function, f(x) = [ x ^ 2 ]sin ⁡ ( ) is discontinuous, when x is equal to:

JEE Main 2020 Solution View → 112

If f(x) = \ cases (sin(a + 2)x + sinx)/(x) & ; x 0 cases ) is continuous at x = 0 , then a + 2b is equal to:

JEE Main 2020 Solution View → 113

Let S , be the set of all functions f: [0, 1] → R , which are continuous on [0, 1] , and differentiable on (0, 1) . Then for every f in S , there exists c ∈ (0, 1), depending on f

JEE Main 2020 Solution View → 114

If the function f defined on (- (1)/(3), 1 / 3) by f(x) = \ cases (1)/(x) _ e ((1 + 3x)/(1 - 2x)), & whenx ≠ 0 k & , whenx = 0 cases ), 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 ∈ R, is not differentiable. Then ∑ _ x ∈ 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, 2π ) , the total number of points where f(x) = max. \ 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 - (1 - x) x^ 4 is continuous everywhere is k, then value of 10k is&

NTA Abhyas JEE Main 2020 Solution View → 119

The function f(x) = (1 - sinx + cosx)/(1 + sinx + cosx) is not defined at x = π . The value of f ( π ) , so that f ( x ) is continuous at x = π , is

NTA Abhyas JEE Main 2020 Solution View → 120

If f(x) = \ cases 4 + ax - 4 - ax x , & - 1 ≤ x < 0 (3x + 2)/(x - 8) , & 0 ≤ x ≤ 1 cases ) is continuous in [ - 1, 1 ], then the value of a is

NTA Abhyas JEE Main 2020 Solution View → 121

Given f ( x ) = array ll x ^ 2 e ^ 2 ( x - 1 ) , 0 ≤ x ≤ 1 . asgn ( x + 1 ) cos ( 2x - 2 ) + b x ^ 2 , 1 < x ≤ 2 array If f( x ) is differentiable at x = 1, then the value of | a

NTA Abhyas JEE Main 2020 Solution View → 122

For x ∈ ℝ, f (x) = | log ⁡ 2 - sin ⁡ x| and g(x) = f (f (x)) , then

NTA Abhyas JEE Main 2020 Solution View → 123

Let f, g and h are differentiable functions. If f(0) = 1; g(0) = 2; h(0) = 3 and the derivatives of their pair wise products at x = 0 are (fg) '(0) = 6;(gh) '(0) = 4 and (hf) '

NTA Abhyas JEE Main 2020 Solution View → 124

If f(x) = \ cases x^ p cos ⁡ ((1)/(x)), & x ≠ 0 0, & x = 0 cases ) is differentiable at x = 0 , then

NTA Abhyas JEE Main 2020 Solution View → 125

The function f (x) =\ x\ (π [x]),where [.] denotes the greatest integer function and . is the fractional part function, is discontinuous at

NTA Abhyas JEE Main 2020 Solution View → 126

On differentiating ^ -1 [ 1 + x^ 2 - 1 x ] with respect to x , the result would be

NTA Abhyas JEE Main 2020 Solution View → 127

Let f: (- 1, 1) → R be a function defined by f(x) = max ⁡ \ - |x|, - 1 - x^ 2 \ . If K be the set of all points at which f is not differentiable, then K has exactly

NTA Abhyas JEE Main 2020 Solution View → 128

If f(x) = max ⁡ \ (x)/(n), |sin ⁡ |\ , n ∈ ℕ has maximum points of non-differentiability for x ∈ (0,4) , then n cannot be

NTA Abhyas JEE Main 2020 Solution View → 129

The value of f (0) , such that f (x) = 1 x^ 2 (1 - cos( x)) can be made continuous at x = 0, is&

NTA Abhyas JEE Main 2020 Solution View → 130

The number of points at which the function f(x) = |x - 0.5| + |x - 1| + tan ⁡ x is not differentiable in the interval (0,2) is/are

NTA Abhyas JEE Main 2020 Solution View → 131

If f(x) = \ cases - 2sinx & π ≤ x ≤ (3π)/(2) pcosx + q & (3π)/(2) < x < 2π cosx - 2 & 2π ≤ x ≤ (5π)/(2) rsinx & (5π)/(2) < x ≤ 3π cases ) is continuous in [π, 3π] , then the

NTA Abhyas JEE Main 2020 Solution View → 132

If f(x) = \ array ll λ 2x + 3 , 0 ≤ x ≤ 3 + 12,3 < x ≤ 9 array is differentiable at x = 3 , then the value of λ + μ is equal to

NTA Abhyas JEE Main 2020 Solution View → 133

If f(x) = \ cases (sin2x)/(cx) + x 4( x + a ^ 2 - a) & ; x ≠ 0, (a < 0, c ≠ 0) b & ; x = 0, (b ≠ 0) cases ) and f(x) is continuous at x = 0 , then the value of bc is equal to

NTA Abhyas JEE Main 2020 Solution View → 134

If f(x) = \ cases 1 + 5 + x - a (x - 4) & 0 ≤ x then value of (1)/(ab) is equal to

NTA Abhyas JEE Main 2020 Solution View → 135

If f(x) = \ cases px + q & : & x ≤ 2 x ^ 2 - 5x + 6 & : & 2 then |p| + |q| + |(1)/(a)| + |(1)/(b)| is equal to

NTA Abhyas JEE Main 2020 Solution View → 136

Let f(x) = \ cases a & ; x = (π)/(2) 2x - π 9 + 2x - π - b & ; x > (π)/(2) cases ). If f(x) is continuous at x = (π)/(2) , then the value of a ^ 2 5b is

NTA Abhyas JEE Main 2020 Solution View → 137

If f(x) = \ cases (1 + |sinx|)(p)/(|sin ⁡ x|) & : & - (π)/(6) < x < 0 q & : & x = 0 e ^ tan ⁡ 3x . cot ⁡ 5x & : & 0 < x < (π)/(6) cases ) is continuous at x = 0 , then the value

NTA Abhyas JEE Main 2020 Solution View → 138

Let f(x) = 10 - |x - 5|, x ∈ ℝ , then the set of all values of x at which f (f (x)) is not differentiable is

NTA Abhyas JEE Main 2020 Solution View → 139

If f(x) = \ cases a + bcosx + csinx x ^ 2 & ; & x > 0 9 & ; & x ≤ 0 cases ) is continuous at x = 0 , then the value of (|a| + |b|)/(5) is

NTA Abhyas JEE Main 2020 Solution View → 140

If f(x) = [x] ^ \ x\ + \ x\ ^ [x] + sin ⁡ ( ), where [·] and · represent the greatest integer function and the fractional part function respectively, then f^ ' ((7)/(2))is equal to

NTA Abhyas JEE Main 2020 Solution View → 141

Consider the function f(x) = max\ |sin ⁡ x|, |cos ⁡ x|\ , ∀ x ∈ [0,3π] . If λ is the number of points at which f(x) is non-differentiable, then the value of λ ^ 3 5 is

NTA Abhyas JEE Main 2020 Solution View → 142

If f(x) = \ cases x 4 + x - a & x > 0 c & x = 0 (4e(2)/(x) + 3e(1)/(x))/(e(2)/(x) + be(1)/(x)) & x < 0 cases ) is continuous at x = 0 for some constants a, b and c , then the

NTA Abhyas JEE Main 2020 Solution View → 143

If f(x) = \ cases 2x^ 2 + 3 & ; & x > 3 ax^ 2 + bx + 1 & ; & x ≤ 3 cases ) is differentiable everywhere, then a b^ 2 is equal to

NTA Abhyas JEE Main 2020 Solution View → 144

The function f(x) = max\ (1 - x), (1 + x), 2\ ∀ x ∈ ℝ is

NTA Abhyas JEE Main 2020 Solution View → 145

Consider the function f (x) = (x^ 3 - x)| x^ 2 - 6x + 5|, ∀ x ∈ ℝ , then f(x) is

NTA Abhyas JEE Main 2020 Solution View → 146

Consider the function f(x) = (sin ⁡ 2x)tan^ 2 2x, x ≠ (π)/(4) . The value of f( (π)/(4) ) such that f is continuous at x = (π)/(4) is

NTA Abhyas JEE Main 2020 Solution View → 147

If f (x) = min \ 9 - x^ 2 , 1 + x^ 2 \ , ∀ x ∈ [-3,3], then the number of point(s) wheref (x) is non-differentiable is/are

NTA Abhyas JEE Main 2020 Solution View → 148

If f(x) = \ array ll ( 2 ^ x - 1) ^ 2 tan ⁡ 3x xsi n ^ 2 x λ array array ll : : array array ll 0 < x < (π)/(6) x = 0 array is continuous at x = 0 , then the value of 10 3λ ln2 is

NTA Abhyas JEE Main 2020 Solution View → 149

Consider the function f(x) = \ cases sin (x - 4). ^ -1 ((1)/(x - 4)) & x ≠ 4 0 & x = 4 cases ,) then

NTA Abhyas JEE Main 2020 Solution View → 150

If f(x) = \ cases x^ p + 1 (1)/(x) & :x ≠ 0 0 & :x = 0 cases ,) then at x = 0 the function f (x) is

NTA Abhyas JEE Main 2020 Solution View → 151

Let f(x) = \ cases (1)/(x2) & : |x| ≥ 1 ^ 2 + β& : |x| < 1 cases .) If f (x) is continuous and differentiable at any point, then

NTA Abhyas JEE Main 2020 Solution View → 152

Consider the function f(x) = min\ |x^ 2 - 9|, | x^ 2 - 1|\ , then the number of points where f(x) is non-differentiable is/are

NTA Abhyas JEE Main 2020 Solution View → 153

The value of f (0) such that the function f(x) = (1 + 2x3 - 1 + x4)/(x) is continuous at x = 0, is

NTA Abhyas JEE Main 2020 Solution View → 154

If f(x) = \ cases e ^ (1 + (1)/(x)) - a e(1)/(x) + 1 & : & x ≠ 0 b & : & x = 0 cases ) (where a and b are arbitrary constants) is continuous at x = 0 , then the value of a ^ 2 is

NTA Abhyas JEE Main 2020 Solution View → 155

If f(x) = \ cases e^ [x] + |x| - 1 [x] + |x| & : x ≠ 0 - 1 & : x = 0 cases ) (where [.] denotes the greatest integer function), then

NTA Abhyas JEE Main 2020 Solution View → 156

The function f(x) = _ n → ∞ (x - 2) ^ 2n - 1 (x - 2) ^ 2n + 1 (∀ n ∈ ℕ) is discontinuous at&

NTA Abhyas JEE Main 2020 Solution View → 157

If f(x) = \ cases a + cos^ - 1 (x + b) & : & x ≥ 1 - x & : & x < 1 cases ) is differentiable at x = 1 , then the value of b - a is equal to

NTA Abhyas JEE Main 2020 Solution View → 158

Let f(x) = \ cases ( 1 - cosx (2π - x) ^ 2 )( ^ 2 x log(1 + 4 π ^ 2 - 4 + x ^ 2 ) ) & : & x ≠ 2π λ & : & x = 2π cases ) is continuous at x = 2π , then the value of λ is equal to

NTA Abhyas JEE Main 2020 Solution View → 159

If f(x) = \ cases e^ 2x^ 2 + x & : x > 0 ax + b & : x ≤ 0 cases ) is differentiable at x = 0, then

NTA Abhyas JEE Main 2020 Solution View → 160

Let f: R → R be differentiable at c ∈ R and f(c) = 0 . If g(x) = |f(x)| , then at x = c, g is:

JEE Main 2019 Solution View → 161

If f(x) = \ cases (sin ( p + 1 ) x + sinx)/(x) & , & x 0 cases ) is continuous at x = 0 , then the ordered pair ( p, q ) is equal to:

JEE Main 2019 Solution View → 162

If the function f(x) = \ array ll a|π - x| + 1, x ≤ 5 b|x - π| + 3, x > 5 array ) is continuous at x = 5, then the value of a - b is:

JEE Main 2019 Solution View → 163

Let f(x) = 15 – |x – 10|; x ∈ R . Then the set of all values of x , at which the function g(x) = f ( f(x) ) is not differentiable, is:

JEE Main 2019 Solution View → 164

If the function f defined on ((π)/(6), (π)/(3)) by f(x) = \ array ll 2 cosx - 1 cotx - 1 , x ≠ (π)/(4) k, x = (π)/(4) array ) is continuous, then k is equal to

JEE Main 2019 Solution View → 165

Let ∑ _ k = 1 ^ 10 f(a + k) = 16( 2 ^ 10 - 1), where the function f satisfies f(x + y) = f(x)f(y) for all natural numbers x, y and f(1) = 2 . Then the natural number 'a' is:

JEE Main 2019 Solution View → 166

Let f: [- 1,3] → R be defined as f(x) = \ array ll |x| + [x] , x + |x| , x + [x] , array array ll - 1 ≤ x Where [t] denotes the greatest integer less than or equal tot . Then, f

JEE Main 2019 Solution View → 167

Let S be the set of all points in (- π, π) at which the function, f(x) = min\ sinx, cosx\ is not differentiable. Then S is a subset of which of the following?

JEE Main 2019 Solution View → 168

Let K be the set of all real values of x where the function f(x)= |x|-|x|+2(x-π) |x| is not differentiable. Then the set K is equal to :

JEE Main 2019 Solution View → 169

Let f(x)=\ array cl -1, & -2 ≤ x < 0 x^ 2 -1, & 0 ≤ x ≤ 2 array . and g(x)=|η(x)|+f(x ) . Then, in the interval (-2,2), g is:

JEE Main 2019 Solution View → 170

Let f: (- 1, 1) → R be a function defined by f(x) = max\ - |x|, - 1 - x ^ 2 \ . If K be the set of all points at which f is not differentiable, then K has exactly

JEE Main 2019 Solution View → 171

Let f(x) = \ cases max(|x|, x ^ 2 ), & |x| ≤ 2 8 - 2|x|, & 2 < |x| ≤ 4 cases .) Let S be the set of points in the interval (- 4, 4) at which f is not differentiable. Then S

JEE Main 2019 Solution View → 172

Let f be a differentiable function from R to R such that |f(x) - f(y)| ≤ 2 |x - y| ^ 3 / 2 , for all x, y ∈ R. If f(0) = 1 then ∫ _ 0 ^ 1 f ^ 2 (x)dx is equal to

JEE Main 2019 Solution View → 173

Let f: R → R be a function defined as f(x) = \ array ll 5, ifx ≤ 1 a + bx, if1 Then f is:

JEE Main 2019 Solution View → 174

Let f _ 1 : ℝ → ℝ, f _ 2 (- (π)/(2), (π)/(2)) → ℝ, f _ 3 : (- 1, e ^ (π)/(2) - 2) → ℝ and f _ 4 : ℝ → ℝ be functions defined by (i) f _ 1 (x) = sin ⁡ ( 1 - e ^ - x ^ 2 ) (ii) f _

JEE Advanced 2018 Solution View → 175

If the function f defined as f(x) = (1)/(x) - k - 1 e ^ 2x - 1 , x ≠ 0 is continuous at x = 0 , then ordered pair (k, f(0)) is equal to

JEE Main 2018 Solution View → 176

Let f(x)=\ array cc (x-1)^ (1)/(2-x) , & x>1, x ≠ 2 k, & x=2 array . The value of k for which f is continuous at x=2 is

JEE Main 2018 Solution View → 177

Let S=\ (λ, μ) ∈ R × R: f(t)=(|λ| e^t-μ) · (2|t|). , t ∈ R , is a differentiable function \ . Then S is a subest of?

JEE Main 2018 Solution View → 178

Let S = (λ, μ) ∈ R × R: f(t) = (|λ| e ^ |t| - μ)sin ⁡ (2|t|), t ∈ R is a differential function . Then, S is a subset of :

JEE Main 2018 Solution View → 179

Let S = \ t ∈ R: f(x) = |x - π| ⋅ ( e ^ |x| - 1)sin|x|is not differentiable att\ . Then, the set S is equal to:

JEE Main 2018 Solution View → 180

Let [x] be the greatest integer less than or equals to x . Then, at which of the following point(s) the function f(x) = xcos ⁡ (π(x + [x])) is discontinuous?

JEE Advanced 2017 Solution View → 181

The value of k which the function f(x) = \ cases ((4)/(5))(tan ⁡ 4x)/(tan ⁡ 5x), & 0 < x < (π)/(2) k + (2)/(5), & x = (π)/(2) cases ) is continuous at x = (π)/(2), is

JEE Main 2017 Solution View → 182

Let a, b ∈ ℝ and f: ℝ → ℝ be defined by f(x) = acos ⁡ (| x ^ 3 - x|) + b|x|sin ⁡ (| x ^ 3 + x|) . Then f is -

JEE Advanced 2016 Solution View → 183

Let f: [- (1)/(2), 2] → ℝ and g: [- (1)/(2), 2] → ℝ be functions defined by f(x) = [ x ^ 2 - 3] and g (x) = |x|f(x) + |4x - 7| f (x) , where [y] denotes the greatest integer less

JEE Advanced 2016 Solution View → 184

Let a, b ∈ R, (a ≠ 0) . If the function f , defined as f(x) = \ array ll 2 x ^ 2 a , 0 ≤ x < 1 a, 1 ≤ x < 2 2 b ^ 2 - 4b x ^ 3 , 2 ≤ x < 8 array ,is continuous in the interval [0

JEE Main 2016 Solution View → 185

If the function f(x) = \ cases - x, & x < 1 a + ^ - 1 ⁡ (x + b), & 1 ≤ x ≤ 2 cases ) is differentiable at x = 1 , then (a)/(b) is equal to

JEE Main 2016 Solution View → 186

For x ∈ R, f(x) = |log ⁡ 2 - sin ⁡ x| and g(x) = f(f(x)) , then

JEE Main 2016 Solution View → 187

Let g: ℝ → ℝ be a differentiable function with g(0) = 0, g ^ ′ (0) = 0 and g ^ ′ (1) ≠ 0 . Let f(x) = \ cases (x)/(| x |)g(x), & x ≠ 0 0, & x = 0 cases ) and h(x) = e ^ | x | for

JEE Advanced 2015 Solution View → 188

Let k be a non - zero real number. If f(x) = \ array ll ( e ^ x - 1 ) ^ 2 sin((x)/(k))log(1 + (x)/(4)) , x ≠ 0 array cases 12, & x = 0 cases ) is a continuous function at x = 0

JEE Main 2015 Solution View → 189

If the function g (x) = cases k x + 1 , & 0 ≤ x ≤ 3 mx + 2, & 3 < x ≤ 5 cases is differentiable, then the value of k + m is

JEE Main 2015 Solution View → 190

Let f: [a, b] → [1, ∞) be a continuous function and let g: R → R be defined as g(x) = \ cases 0 & if & x b cases ) . Then

JEE Advanced 2014 Solution View → 191

Let f: R → R and g: R → R be respectively given by f(x) = |x| + 1 and g(x) = x ^ 2 + 1 . Define h: R → R by h(x) = \ cases max ⁡ \ f(x), g(x)\ & if & x ≤ 0 min ⁡ \ f(x), g(x)\ &

JEE Advanced 2014 Solution View → 192

If the function f(x) = \ cases 2 + cos x - 1 (π - x) ^ 2 , & x ≠ π k, & x = π cases ) is continuous at x = π , then k equals

JEE Main 2014 Solution View → 193

Let f: R → R be a function such that |f(x)| ≤ x ^ 2 , for all x ∈ R . Then, at x = 0, f is

JEE Main 2014 Solution View → 194

Let f, g: R arrow R be two functions defined by f(x)= cases x ((1)/(x)) & , x ≠ 0 0, & , x=0 cases and g(x)=x f(x) Statement I: f is a continuous function at x=0 . Statement II: g

JEE Main 2014 Solution View → 195

Let f(x)=x|x|, g(x)= x and h(x)=(g ∘ f)(x) . Then

JEE Main 2014 Solution View → 196

Consider the function : f(x)=[x]+|1-x|,-1 ≤ x ≤ 3 where [x] is the greatest integer function. Statement 1: f is not continuous at x=0,1,2 and 3 Statement 2:f(x)= = array cc -x, &

JEE Main 2013 Solution View → 197

Let f be a composite function of x defined by f(u)=(1)/(u^2+u-2), u(x)=(1)/(x-1) . Then the number of points x where f is discontinuous is :

JEE Main 2013 Solution View → 198

Let f(x)=-1+|x-2| , and g(x)=1-|x| ; then the set of all points where f_ o g is discontinuous is :

JEE Main 2013 Solution View → 199

For every integer n , let a_ n and b_ n be real numbers. Let function f: I R arrow I R be given by f(x)=\ array lll a_ n + π x, & for & x ∈[2 n, 2 n+1] b_ n + π x, & for & x ∈(2

JEE Advanced 2012 Solution View → 200

Let ∫(x)=\ array r x^ 2 | (π)/(x)|, x ≠ 0 0, x=0 array , x ∈ R. then ∫ is

JEE Advanced 2012 Solution View →
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Continuity and Differentiability in other exams

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