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JEE Limits PYQs with Solutions

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

497 questionsMathematics2002–2026Answers + solutions

About Limits PYQs

Limits has 497 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (145), NTA Abhyas JEE Main (44) and JEE Advanced (31), 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: 9
  • 2025: 15
  • 2024: 26
  • 2023: 11
  • 2022: 16
  • 2021: 19
  • 2020: 55
  • 2019: 15
  • 2018: 4
  • 2017: 3
  • 2016: 8
  • 2015: 4

Limits questions with solutions

1

Let _ x → 2 (( (x-2))(rx^2 + (p-2)x - 2p))/((x-2)^2) = 5 for some r, p ∈ ℝ . If the set of all possible values of q , such that the roots of the equation rx^2 - px + q = 0 lie in

JEE Main 2026 Solution View → 2

The value of _ x → 0 ((x^2 ^2 x)/(x^2 - ^2 x)) is:

JEE Main 2026 Solution View → 3

Let f(x) = _ y → 0 ((1 - (xy)) (xy))/(y^3) . Then the number of solutions of the equation f(x) = x , x ∈ R is :

JEE Main 2026 Solution View → 4

The product of all possible values of α , for which _ x → 0 ((1 - (α x) ((α+1)x) ((α+2)x))/( ^2((α+1)x))) = 2 , is:

JEE Main 2026 Solution View → 5

If _ x → 2 (x^3 - 5x^2 + ax + b) ( x-1 - 1) _e(x-1) = m , then a + b + m is equal to :

JEE Main 2026 Solution View → 6

The value of _ x arrow 0 _ e ( (e x) · (e^ 2 x) · … · (e^ 10 x)) e^ 2 -e^ 2 x is equal to

JEE Main 2026 Solution View → 7

If _ x arrow 0 e^ (a-1) x +2 ~b x+(c-2) e^ -x x x- _ e (1+x) =2 , then a^ 2 +b^ 2 +c^ 2 is equal to :

JEE Main 2026 Solution View → 8

Let [·] denote the greatest integer function and f(x)= _ n arrow ∞ 1 n^ 3 ∑_ k=1 ^ n [ k^ 2 3^ x ] . Then 12 ∑_ j=1 ^ ∞ f(j) is equal to \_\_\_\_ .

JEE Main 2026 Solution View → 9

Let f: R arrow(0, ∞) be a twice differentiable function such that f(3)=18, f^ (3)=0 and f^ (3)=4 . Then _ x arrow 1 ( _ e ((f(2+x))/(f(3)))^ 18 (x-1)^ 2 ) is equal to :

JEE Main 2026 Solution View → 10

Let α and β be the real numbers such that _ x arrow 0 (1)/(x^3)((α)/(2) ∫_0^x (1)/(1-t^2) d t+β x x)=2 . Then the value of α+β is _______

JEE Advanced 2025 Solution View → 11

Let x_0 be the real number such that e^ x_0 +x_0=0 . For a given real number α , define g(x)=(3 x e^x+3 x-α e^x-α x)/(3(e^x+1)) for all real numbers x . Then which one of the

JEE Advanced 2025 Solution View → 12

Given below are two statements : Statement I : _ x arrow 0 ( ^ -1 x+ _e (1+x)/(1-x) -2 x x^5 )=(2)/(5) Statement II : _ x arrow 1 (x^ 2 1-x )= 1 e^2 In the light of the above

JEE Main 2025 Solution View → 13

If the function f(x)=( ( x)- ( x))/( x- x) is continuous at x=0 , then f(0) is equal to ________

JEE Main 2025 Solution View → 14

_ x arrow 0^ + (5(x)^ (1)/(3) ) _e(1+3 x^2) ( ^ -1 3 x )^2(e^ 5(x)^ (4)/(3) -1) is equal to

JEE Main 2025 Solution View → 15

If _ x arrow 1^ + ((x-1)(6+λ (x-1))+μ (1-x))/((x-1)^3)=-1 , where λ, μ ∈ ℝ , then λ+μ is equal to

JEE Main 2025 Solution View → 16

If Lim_ x arrow 0 (( x)/(x))^ (1)/(x^2) =p , then 96 _e p is equal to ______

JEE Main 2025 Solution View → 17

If _ x arrow 0 ( (2 x)+a (4 x)-b)/(x^4) is finite, then (a+b) is equal to :

JEE Main 2025 Solution View → 18

For α, β, γ, ∈ R , if _ x arrow 0 x^2 α x+(γ-1) e^ x^2 2 x-β x =3 , then β+γ-α is equal to:

JEE Main 2025 Solution View → 19

If _ t arrow 0 (∫_0^1(3 x+5)^ t d x)^ (1)/(t) = α 5 e ((8)/(5))^ (2)/(3) , then α is equal to ________

JEE Main 2025 Solution View → 20

Let [t] be the greatest integer less than or equal to t. Then the least value of \( p ∈ N \) for which \( _ x arrow 0^ + ( x ([(1)/(x)]+[(2)/(x)]+…+[ p x ])- x^2

JEE Main 2025 Solution View → 21

Let f(x)= _ n arrow ∞ ∑_ r=0 ^ n ( (x / 2^ r+1 )+ ^3(x / 2^ r+1 ) 1- ^2(x / 2^ r+1 ) ) . Then _ x arrow 0 e^x-e^ f(x) (x-f(x)) is equal to

JEE Main 2025 Solution View → 22

_ x arrow 0 cosec x( 2 ^2 x+3 x - ^2 x+ x+4 ) is:

JEE Main 2025 Solution View → 23

_ x arrow ∞ (2 x^2-3 x+5)(3 x-1)^ (x)/(2) (3 x^2+5 x+4) (3 x+2)^x is equal to :

JEE Main 2025 Solution View → 24

If _ x arrow ∞ (( e 1-e )( 1 e -(x)/(1+x)))^x=α , then the value of _ e α 1+ _ e α equals :

JEE Main 2025 Solution View → 25

Let k ∈ ℝ . If _ x arrow 0^+ ( ( k x)+ x+x)^ (2)/(x) =e^6 , then the value of k is

JEE Advanced 2024 Solution View → 26

Let S be the set of all (α, β) ∈ ℝ × ℝ such that _ x arrow ∞ (x^2)( _e x)^α ((1)/(x^2)) x^ α β ( _e(1+x))^β =0 . Then which of the following is (are) correct?

JEE Advanced 2024 Solution View → 27

Let the function f:[1, ∞) arrow ℝ be defined by f(t)=\ array cc (-1)^ n+1 2, & if t=2 n-1, n ∈ ℕ , ((2 n+1-t))/(2) f(2 n-1)+ ((t-(2 n-1)))/(2) f(2 n+1), & if 2 n-1 < t < 2 n+1, n

JEE Advanced 2024 Solution View → 28

Let f(x) be a continuously differentiable function on the interval (0, ∞) such that f(1)=2 and t arrow x t^ 10 f(x)-x^ 10 f(t) t^9-x^9 =1 for each x>0 . Then, for all x>0, f(x) is

JEE Advanced 2024 Solution View → 29

_ x arrow (π)/(2) ( ∫_ x^3 ^ (π / 2)^3 ( (2 t^ 1 / 3 )+ (t^ 1 / 3 )) d t (x-(π)/(2))^2 ) is equal to

JEE Main 2024 Solution View → 30

_ x arrow 0 e-(1+2 x)^ (1)/(2 x) x is equal to

JEE Main 2024 Solution View → 31

Let _ n arrow ∞ ( n n^4+1 - 2 n (n^2+1) n^4+1 + n n^4+16 - 8 n (n^2+4) n^4+16 . .+…+ n n^4+n^4 - 2 n · n^2 (n^2+n^2) n^4+n^4 ) be (π)/(k) , using only the principal values of the

JEE Main 2024 Solution View → 32

If α= _ x arrow 0^ + ( e^ x -e^ x x - x ) and β= _ x arrow 0 (1+ x)^ (1)/(2) x are the roots of the quadratic equation a x^2+b x- e =0 , then 12 _ e (a+b) is equal to__________

JEE Main 2024 Solution View → 33

The value of _ x arrow 0 2 ( 1- x 2 x [3] 3 x … … [10] 10 x x^2 )is

JEE Main 2024 Solution View → 34

_ n arrow ∞ ((1^2-1)(n-1)+(2^2-2)(n-2)+⋯+((n-1)^2-(n-1)) · 1)/((1^3+2^3+⋯ ⋯+n^3)-(1^2+2^2+⋯ ⋯+n^2)) is equal to :

JEE Main 2024 Solution View → 35

Let f:(-∞, ∞)-\ 0\ arrow ℝ be a differentiable function such that f^ (1)= _ a arrow ∞ a^2 f((1)/(a)) . Then _ a arrow ∞ (a(a+1))/(2) ^ -1 ((1)/(a))+a^2-2 _e a is equal to

JEE Main 2024 Solution View → 36

Let a>0 be a root of the equation 2 x^2+x-2=0 . If _ x arrow 1 a 16(1- (2+x-2 x^2)) (1-a x)^2 =α+β 17 , where α, β ∈ Z , then α+β is equal to_______

JEE Main 2024 Solution View → 37

Let f be a differentiable function in the interval (0, ∞) such that f(1)=1 and _ t arrow x (t^2 f(x)-x^2 f(t))/(t-x)=1 for each x>0 . Then 2 f(2)+3 f(3) is equal to _______

JEE Main 2024 Solution View → 38

Let f(x)=∫_0^x(t+ (1-e^ )) d t, x ∈ ℝ . Then, _ x arrow 0 (f(x))/(x^3) is equal to

JEE Main 2024 Solution View → 39

If _ x arrow 1 (5 x+1)^ 1 / 3 -(x+5)^ 1 / 3 (2 x+3)^ 1 / 2 -(x+4)^ 1 / 2 = m 5 n(2 n)^ 2 / 3 , where gcd(m, n)=1 , then 8 ~m+12 n is equal to______

JEE Main 2024 Solution View → 40

Let f(x) = \ array ll x - 1, x is even , 2x, x is odd , array x ∈ N . If for some a ∈ N, f(f(f(a))) = 21 , then _ x → a ^ - \ |x| ^ 3 a - [(x)/(a)]\ , where [t] denotes the

JEE Main 2024 Solution View → 41

Let \ x\ denote the fractional part of x and f(x) = ^ - 1 (1 - \ x\ ^ 2 ) ^ - 1 (1 - \ x\ ) \ x\ - \ x\ ^ 3 , x ≠ 0 . If LandR respectively denotes the left hand limit and the

JEE Main 2024 Solution View → 42

Let f:ℝ→ (0, ∞) be strictly increasing function such that _ x → ∞ (f(7x))/(f(x)) = 1 . Then, the value of _ x → ∞ [(f(5x))/(f(x)) - 1] is equal to

JEE Main 2024 Solution View → 43

If _ x → 0 a x ^ 2 e ^ x - b _ e (1 + x) + cx e ^ - x x ^ 2 sinx = 1 , then 16( a ^ 2 + b ^ 2 + c ^ 2 ) is equal to ______.

JEE Main 2024 Solution View → 44

_ x → 0 e ^ 2|sinx| - 2|sinx| - 1 x ^ 2

JEE Main 2024 Solution View → 45

Let a be the sum of all coefficients in the expansion of ( 1 – 2x + 2 x ^ 2 ) ^ 2023 ( 3 - 4 x ^ 2 + 2 x ^ 3 ) ^ 2024 and b = _ x → 0 ( ∫ _ 0 ^ x log(1 + t) t ^ 2024 + 1 dt x ^ 2

JEE Main 2024 Solution View → 46

Let f: [- (π)/(2), (π)/(2)] → R be a differentiable function such that f(0) = (1)/(2) , If _ x → 0 x ∫ _ 0 ^ x f ( t ) dt e ^ x ^ 2 - 1 = α , then 8 α ^ 2 is equal to :

JEE Main 2024 Solution View → 47

Let the slope of the line 45x + 5y + 3 = 0 be 27 r _ 1 + 9 r _ 2 2 for some r _ 1 , r _ 2 ∈ R . Then _ x → 3 ( ∫ _ 3 ^ x 8 t ^ 2 3 r _ 2 x 2 - r _ 2 x ^ 2 - r _ 1 x ^ 3 - 3x dt)

JEE Main 2024 Solution View → 48

_ x → (π)/(2) ((1)/( ( x - (π)/(2))2) ∫ _ x3 ^ ((π)/(2))3 cos ((1)/(t3)) dt) is equal to

JEE Main 2024 Solution View → 49

If _ x → 0 3 + + + _ e ( 1 - x ) 3 ^ 2 x = (1)/(3) , then 2α - β is equal to :

JEE Main 2024 Solution View → 50

If a = _ x → 0 1 + 1 + x ^ 4 - 2 x ^ 4 and b = _ x → 0 ^ 2 x 2 - 1 + cosx , then the value of a b ^ 3 is :

JEE Main 2024 Solution View → 51

Let f: (0, 1) → ℝ be the function defined as f(x) = n if x ∈ [ (1)/(n + 1), (1)/(n) ) where n ∈ ℕ . Let g: (0, 1) → ℝ be a function such that ∫ _ x ^ 2 ^ x (1 - t)/(t) dt < g(x) <

JEE Advanced 2023 Solution View → 52

If _ x → 0 e ^ ax - cos ( bx ) - cx e ^ - cx 2 1 - cos ( 2x ) = 17 , then 5 a ^ 2 + b ^ 2 is equal to

JEE Main 2023 Solution View → 53

If α > β > 0 are the roots of the equation a x ^ 2 + bx + 1 = 0 , and _ x → (1)/(α) ( 1 - cos( x ^ 2 + bx + a) 2 ( 1 - ) ^ 2 )(1)/(2) = (1)/(k)((1)/(β) - (1)/(α)) , then k is

JEE Main 2023 Solution View → 54

_ x → 0 (( 1 - ^ 2 ( 3x ) ^ 3 ( 4x ) )( ^ 3 ( 4x ) ( _ e (2x + 1)) ^ 5 )) is equal to

JEE Main 2023 Solution View → 55

_ n → ∞ \ (2(1)/(2) - 2(1)/(3))(2(1)/(2) - 2(1)/(5)) . . . . (2(1)/(2) - 2(1)/(2n + 1))\ is equal to

JEE Main 2023 Solution View → 56

_ x → ∞ ( 3x + 1 + 3x - 1 ) ^ 6 + ( 3x + 1 - 3x - 1 ) ^ 6 (x + x ^ 2 - 1 ) ^ 6 + (x - x ^ 2 - 1 ) ^ 6 x ^ 3

JEE Main 2023 Solution View → 57

Let f, g and h be the real valued functions defined on ℝ as f(x) = \ cases (x)/(|x|), & x ≠ 0 1, & x = 0 cases , g(x) = \ cases (sin(x + 1))/((x + 1)), & x ≠ - 1 1, & x = - 1

JEE Main 2023 Solution View → 58

Let x = 2 be a root of the equation x ^ 2 + px + q = 0 and f(x) = \ cases 1 - cos( x ^ 2 - 4px + q ^ 2 + 8q + 16) (x - 2p) ^ 4 , & x ≠ 2p 0, & x = 2p cases ). Then _ x → 2 p ^ +

JEE Main 2023 Solution View → 59

The value of _ n → ∞ 1 + 2 - 3 + 4 + 5 - 6 + … + ( 3n - 2 ) + ( 3n - 1 ) - 3n 2 n ^ 4 + 4n + 3 - n ^ 4 + 5n + 4 is

JEE Main 2023 Solution View → 60

The set of values of a for which _ x → a ([x - 5] - [2x + 2]) = 0 , where, [ζ] denotes the greatest integer less than or equal to ζ is equal to

JEE Main 2023 Solution View → 61

_ t → 0 (1 1 ^ 2 t + 2 1 ^ 2 t + 3 1 ^ 2 t . . . . . . n 1 ^ 2 t ) ^ ^ 2 t is equal to

JEE Main 2023 Solution View → 62

If β = _ x → 0 e ^ x ^ 3 - (1 - x ^ 3 )(1)/(3) + ((1 - x ^ 2 )(1)/(2) - 1)sinx x ^ 2 x , then the value of 6β is

JEE Advanced 2022 Solution View → 63

Let α be a positive real number. Let f: ℝ → ℝ and g: (α, ∞) → ℝ be the functions defined by f(x) = sin(( )/(12)) and g(x) = 2 _ e ( x - α ) _ e ( e ^ x - e ^ α ) . Then the value

JEE Advanced 2022 Solution View → 64

If _ x → 0 α e ^ x + β e ^ - x + x ^ 2 x = (2)/(3) , where α, β, γ ∈ R , then which of the following is NOT correct?

JEE Main 2022 Solution View → 65

_ x → 0 ( (x + 2cosx) ^ 3 + 2 (x + 2cosx) ^ 2 + 3sin(x + 2cosx) (x + 2) ^ 3 + 2 (x + 2) ^ 2 + 3sin(x + 2) )(100)/(x) is equal to

JEE Main 2022 Solution View → 66

Let f: ℝ → ℝ be a function defined as f(x) = asin((π[x])/(2)) + [2 - x], a ∈ ℝ , where [t] is the greatest integer less than or equal to t . If _ x → - 1 f (x) exists, then the

JEE Main 2022 Solution View → 67

Let β = _ x → 0 - ( e ^ 3x - 1) ( e ^ 3x - 1) for some α ∈ ℝ . Then the value of α + β is:

JEE Main 2022 Solution View → 68

_ x → (π)/(4) 8 2 - (cosx + sinx) ^ 7 2 - 2 sin2x is equal to

JEE Main 2022 Solution View → 69

If _ n → ∞ ( n ^ 2 - n - 1 + nα + β) = 0 then 8(α + β) is equal to

JEE Main 2022 Solution View → 70

The value of _ x → 1 ( x ^ 2 - 1) ^ 2 ( ) x ^ 4 - 2 x ^ 3 + 2x - 1 is equal to:

JEE Main 2022 Solution View → 71

If _ x → 1 ( sin(3 x ^ 2 - 4x + 1) - x ^ 2 + 1 2 x ^ 3 - 7 x ^ 2 + ax + b ) = - 2 , then the value of (a - b) is equal to

JEE Main 2022 Solution View → 72

Let [t] denote the greatest integer ≤ t and \ t\ denote the fractional part of t . Then integral value of α for which the left hand limit of the function f(x) = [1 + x] + α ^ 2[x]

JEE Main 2022 Solution View → 73

Let a be an integer such that _ x → 7 (18 - [1 - x])/([x - 3a]) exists, where [t] is greatest integer ≤ t . Then a is equal to

JEE Main 2022 Solution View → 74

_ x → 0 cos ( sinx ) - cosx x ^ 4 is equal to

JEE Main 2022 Solution View → 75

_ x → 1 2 sin( ^ - 1 x) - x 1 - tan( ^ - 1 x) is equal to

JEE Main 2022 Solution View → 76

_ x → (π)/(2) ( ^ 2 x((2 ^ 2 x + 3sinx + 4)(1)/(2) - ( ^ 2 x + 6sinx + 2)(1)/(2))) is equal to

JEE Main 2022 Solution View → 77

Let f(x) be a polynomial function such that f(x) + f ^ ' (x) + f ^ ' ' (x) = x ^ 5 + 64 . Then, the value of _ x → 1 (f(x))/(x - 1) is equal to

JEE Main 2022 Solution View → 78

Let f ( x ) = x ^ 6 + 2 x ^ 4 + x ^ 3 + 2x + 3, x ∈ R . Then the natural number n for which _ x → 1 x ^ n f ( 1 ) - f ( x ) x - 1 = 44 is _____ .

JEE Main 2021 Solution View → 79

If α = _ x → π / 4 ^ 3 x - tanx cos(x + (π)/(4)) and β = _ x → 0 (cosx) ^ cotx are the roots of the equation, a x ^ 2 + bx - 4 = 0, then the ordered pair (a, b) is :

JEE Main 2021 Solution View → 80

_ x → 0 ^ 2 (π ^ 4 x) x ^ 4 is equal to :

JEE Main 2021 Solution View → 81

If _ x → ∞ ( x ^ 2 - x + 1 - ax) = b , then the ordered pair ( a, b ) is:

JEE Main 2021 Solution View → 82

If α, β are the distinct roots of x ^ 2 + bx + c = 0, then _ x → β e ^ 2( x ^ 2 + bx + c) - 1 - 2( x ^ 2 + bx + c) ( x - β ) ^ 2 is equal to

JEE Main 2021 Solution View → 83

_ x → 2 ( ∑ _ n = 1 ^ 9 x n ( n + 1 ) x ^ 2 + 2 ( 2n + 1 ) x + 4 ) is equal to :

JEE Main 2021 Solution View → 84

The value of _ x → 0 ((x)/(1 - sinx8 - 1 + sinx8)) is equal to :

JEE Main 2021 Solution View → 85

Let f: R → R be a function such that f(2) = 4 and f ^ ' (2) = 1 . Then, the value of _ x → 2 x ^ 2 f(2) - 4f(x) x - 2 is equal to:

JEE Main 2021 Solution View → 86

If _ x → 0 [ e ^ x - β _ e ( 1 + x ) + γ x ^ 2 e ^ - x x ^ 2 x ] = 10, α, β, γ ∈ R , then the value of α + β + γ is __________.

JEE Main 2021 Solution View → 87

If the value of _ x → 0 (2 - cosx cos2x ) ^ ( x + 2 x ^ 2 ) is equal to e ^ a , then a is equal to_____.

JEE Main 2021 Solution View → 88

If _ x → 0 ^ - 1 x - ^ - 1 x 3 x ^ 3 is equal to L, then the value of ( 6L + 1 ) is

JEE Main 2021 Solution View → 89

The value of _ n → ∞ [r] + [2r] + . . . + [nr] n ^ 2 , where r is non-zero real number and [r] denotes the greatest integer less than or equal to r, is equal to :

JEE Main 2021 Solution View → 90

The value of the limit _ θ → 0 tan(π ^ 2 θ) sin(2π ^ 2 θ) is equal to :

JEE Main 2021 Solution View → 91

The value of _ x → 0 ^ + ^ - 1 (x - [ x ] ^ 2 ) · ^ - 1 (x - [ x ] ^ 2 ) x - x ^ 3 , where [x] denotes the greatest integer ≤ x is:

JEE Main 2021 Solution View → 92

If _ x → 0 a e ^ x - bcosx + c e ^ - x xsinx = 2 , then a + b + c is equal to ________.

JEE Main 2021 Solution View → 93

Let f(x) be a differentiable function at x = a with f ^ ' (a) = 2 and f(a) = 4 . Then _ x → a (xf(a) - af(x))/(x - a) equals:

JEE Main 2021 Solution View → 94

The value of _ h → 0 \ 3 sin((π)/(6) + h) - cos((π)/(6) + h) 3 h( 3 cosh - sinh) \ is :

JEE Main 2021 Solution View → 95

If _ x → 0 ax - ( e ^ 4x - 1) ax( e ^ 4x - 1) exists and is equal to b , then the value of a - 2b is ___ .

JEE Main 2021 Solution View → 96

_ n → ∞ (1 + 1 + (1)/(2) + … … + (1)/(n) n ^ 2 ) ^ n is equal to

JEE Main 2021 Solution View → 97

The value of the limit _ x → (π)/(2) 4 2 (sin3x + sinx) (2sin2xsin(3x)/(2) + cos(5x)/(2)) - ( 2 + 2 cos2x + cos(3x)/(2)) is _________

JEE Advanced 2020 Solution View → 98

Let e denote the base of the natural logarithm. The value of the real number a for which the right-hand limit _ x → 0 ^ + (1 - x)(1)/(χ) - e ^ - 1 x ^ a is equal to a non-zero

JEE Advanced 2020 Solution View → 99

_ x → 0 x( e ^ ( 1 + x ^ 2 + x ^ 4 - 1) / x - 1) 1 + x ^ 2 + x ^ 4 - 1

JEE Main 2020 Solution View → 100

If α is the positive root of the equation, p(x) = x ^ 2 - x - 2 = 0 , then _ x → α ^ + 1 - cosp(x) x + α - 4 is equal to

JEE Main 2020 Solution View → 101

_ x → a (a + 2x\ right)(1)/(3) -(3x\ right)(1)/(3) (3a + x\ right)(1)/(3) -(4x\ right) dfrac 1 3 (a ≠ 0) & is equal to:

JEE Main 2020 Solution View → 102

Let [t] denote the greatest integer ≤ t . If λεR - \ 0, 1\ , _ x → 0 |(1 - x + |x|)/(λ - x + [x])| = L , then L is equal to

JEE Main 2020 Solution View → 103

If _ x → 0 \ 1 x ^ 8 (1 - cos x ^ 2 2 - cos x ^ 2 4 + cos x ^ 2 2 cos x ^ 2 4 )\ = 2 ^ - k then the value of k is

JEE Main 2020 Solution View → 104

_ x → 0 (tan((π)/(4) + x)) ^ 1 / x is equal to

JEE Main 2020 Solution View → 105

If _ x → 1 x + x ^ 2 + x ^ 3 + . . . + x ^ n - n x - 1 = 820, (n ∈ N) then the value of n is equal to....

JEE Main 2020 Solution View → 106

_ x → 0 ( 3 x ^ 2 + 2 7 x ^ 2 + 2 ) 1 x ^ 2 is equal to

JEE Main 2020 Solution View → 107

_ x → 2 3 ^ x + 3 ^ 3 - x - 12 3 ^ - (x)/(2) - 3 ^ 1 - x is equal to

JEE Main 2020 Solution View → 108

If f(x) is a polynomial satisfying f(x)f((1)/(x)) = f(x) + f((1)/(x)) and f(2) > 1, then _ x → 1 f (x) is

NTA Abhyas JEE Main 2020 Solution View → 109

If _ x → 0 ⁡ ^ - 1 ⁡ x - ^ - 1 ⁡ x x ^ 3 equals L , then the value of ( 4L + 1 ) is

NTA Abhyas JEE Main 2020 Solution View → 110

_ x → 2 3 ^ x + 3 ^ 3 - x - 12 3 ^ - (x)/(2) - 3 ^ 1 - x is equal to

NTA Abhyas JEE Main 2020 Solution View → 111

& If p,q,r,s > 0, then _ x → ∞ ( p(1)/(x) + q(1)/(x) + r(1)/(x) + s(1)/(x) 4 )^ 3 x is equal to

NTA Abhyas JEE Main 2020 Solution View → 112

The value of _ x → 0 x^ 6000 - (sin x)6000 x^ 2 (sin x)6000 & is

NTA Abhyas JEE Main 2020 Solution View → 113

The value of _ x → ∞ ⁡ ((3x - 4)/(3x + 2)) ^ (x + 1)/(3) is equal to

NTA Abhyas JEE Main 2020 Solution View → 114

If f(x) = \ cases g(x) – 1 x – 1 ; & x ≠ 1 1; & x = 1 cases ) and g^ &#39; (1) = 2, g (1) = 1 , then _ x → 1 ⁡ f (x) is equal to

NTA Abhyas JEE Main 2020 Solution View → 115

The value of _ x → 0 ( 1 + x + x^ 2 ) + ( 1 - x + x^ 2 ) secx - cosx & is equal to

NTA Abhyas JEE Main 2020 Solution View → 116

_ x → 0 ⁡ (1 + x) x^ 2 + (x - 1)/(x) =

NTA Abhyas JEE Main 2020 Solution View → 117

_ x → (π)/(2) [1 - tan((x)/(2))][1 - sinx] [1 + tan((x)/(2))] [π - 2x] ^ 3 is equal to

NTA Abhyas JEE Main 2020 Solution View → 118

If _ x → 0 ( ( a - n ) nx - tan x)sinnx x2 = 0, where n is a non zero real number, then a is equal to

NTA Abhyas JEE Main 2020 Solution View → 119

The value of _ x → ∞ ⁡ 2 (x) ^ 1 / 2 + 3 (x) ^ 1 / 3 + 4 (x) ^ 1 / 4 +..... + (x) ^ 1 / n (2x - 3) ^ 1 / 2 + (2x - 3) ^ 1 / 3 +.... + (2x - 3) ^ 1 / n is

NTA Abhyas JEE Main 2020 Solution View → 120

The value of _ x → 0 1 + sin x - cos x + (1 - x) x · ^ 2 x & is

NTA Abhyas JEE Main 2020 Solution View → 121

The value of _ n → ∞ ⁡ 3.2 ^ n + 1 - 4.5 ^ n + 1 5.2 ^ n + 7.5 ^ n is equal to

NTA Abhyas JEE Main 2020 Solution View → 122

The value of _ x → π tan ⁡ (π ^ 2 ⁡ x ) ^ 2 ⁡ x is equal to

NTA Abhyas JEE Main 2020 Solution View → 123

The value of _ x → 0 ^ - 2 ^ (1)/(x) + 2 ^ (3)/(x) 3( 2 ^ (1)/(x) ) + 5( 2 ^ (3)/(x) ) is

NTA Abhyas JEE Main 2020 Solution View → 124

The value of _ x → 0 ( (sin ⁡ 5x + cos ⁡ 5x))/(tan ⁡ 3x) is equal to

NTA Abhyas JEE Main 2020 Solution View → 125

The value of _ x → 0 (sin ⁡ x)/(3)[(5)/(x)]is equal to (where, [.] represents the greatest integer function)

NTA Abhyas JEE Main 2020 Solution View → 126

The value of _ x → 0 tan^ 2 3x 5 - 4 + secx & is equal to

NTA Abhyas JEE Main 2020 Solution View → 127

The value of _ x → 1 ^ - π - 4tan^ - 1 x 1 - x is equal to

NTA Abhyas JEE Main 2020 Solution View → 128

The value of _ x → ∞ (ln ⁡ x) ^ 2 2 + 3x^ 2 is equal to

NTA Abhyas JEE Main 2020 Solution View → 129

The value of _ x → 0 xcot(4x) tan^ 2 (3x)cot^ 2 (6x) is equal to

NTA Abhyas JEE Main 2020 Solution View → 130

The value of _ x → 0 e^ - (x2)/(2) - cos ⁡ x x^ 3 tan ⁡ x is equal to

NTA Abhyas JEE Main 2020 Solution View → 131

The value of _ x → 1 ^ + ∫ _ 1 ^ x |t - 1|dt sin ⁡ ( x - 1 ) is equal to

NTA Abhyas JEE Main 2020 Solution View → 132

If _ x → 0 ( 1 + px + qx^ 2 ) ^ cosecx = e^ 5 , then

NTA Abhyas JEE Main 2020 Solution View → 133

The value of _ x → 0 (1 - 2 x) (3 + x) x 4 x & is equal to&

NTA Abhyas JEE Main 2020 Solution View → 134

If _ x → 0 (sin ⁡ 2x - asin ⁡ x)/(x3) exists finitely, then the value of a is

NTA Abhyas JEE Main 2020 Solution View → 135

The value of _ x → 0 ⁡ 1 x ^ 18 (1 - cos ⁡ ( x ^ 3 3 ) - cos ⁡ ( x ^ 6 6 ) + cos ⁡ ( x ^ 3 3 ) ⋅ cos ⁡ ( x ^ 6 6 )) is λ ^ 2 , then the value of 900λ is equal to (here, λ > 0 )

NTA Abhyas JEE Main 2020 Solution View → 136

If _ x → ∞ a e ^ x + bcosx + c + dx xsi n ^ 2 x = 3 , then the value of 272 abd c ^ 3 is equal to

NTA Abhyas JEE Main 2020 Solution View → 137

The value of _ x → 0 ^ - 4(2 + (3)/(x)) + 5 ( 2 ^ (1)/(x) ) 2(1 + (6)/(x)) + 6 ( 2 ^ (1)/(x) ) is equal to

NTA Abhyas JEE Main 2020 Solution View → 138

The value of _ x → 0 sec ⁡ x - (sec ⁡ x) ^ secx 1 - sec ⁡ x + ln ⁡ (sec ⁡ x) is equal to

NTA Abhyas JEE Main 2020 Solution View → 139

The value of _ n → ∞ ( cos ⁡ xcos dfrac x 2 cos(x)/(4) . . . cos x 2 ^ n ) is equal to

NTA Abhyas JEE Main 2020 Solution View → 140

The value of _ x → (π)/(4) ⁡ (sin ⁡ 2x) ^ ^ 2 ⁡ 2x is equal to

NTA Abhyas JEE Main 2020 Solution View → 141

If _ x → 0 x(1 + acos ⁡ x) - bsin ⁡ x x ^ 3 = 1 , then the value of ab is equal to

NTA Abhyas JEE Main 2020 Solution View → 142

If L = _ x → (π)/(4) (1 - tanx)(1 - sin2x) (1 + tanx) (π - 4x) ^ 3 , then the value of 40L is equal to

NTA Abhyas JEE Main 2020 Solution View → 143

The value of _ x → 0 1 - cos^ 3 (sin ⁡ x) sin ⁡ xsin(sin ⁡ x)cos(sin ⁡ x) is equal to

NTA Abhyas JEE Main 2020 Solution View → 144

The value of _ x → 1 xtan\ x\ x - 1 ~is equal to (where \ x\ denotes the fractional part of x )

NTA Abhyas JEE Main 2020 Solution View → 145

The value of _ x → 0 (sec ⁡ x + tan ⁡ x) ^ (1)/(x) is equal to

NTA Abhyas JEE Main 2020 Solution View → 146

The value of _ x → (π)/(3) 2 - 3 sin ⁡ x - cos ⁡ x (3x - π) ^ 2 is equal to the reciprocal of the number

NTA Abhyas JEE Main 2020 Solution View → 147

The value of _ n → ∞ [x] + [ 2 ^ 2 x] + [ 3 ^ 2 x] +..... + [n^ 2 x] 1 ^ 2 + 2 ^ 2 + 3 ^ 2 +.... + n^ 2 is equal to (where [x] represents the greatest integer part of x )

NTA Abhyas JEE Main 2020 Solution View → 148

The value of _ x → ∞ e ^ x + 1 log( x ^ 3 e ^ - x + 1) si n ^ 3 (2x) is equal to (Use e = 2.7 )

NTA Abhyas JEE Main 2020 Solution View → 149

The value of _ x → 0 ln ⁡ (1 + 2x + 4x^ 2 ) + ln ⁡ (1 - 2x + 4x^ 2 ) sec ⁡ x - cos ⁡ x & is equal to

NTA Abhyas JEE Main 2020 Solution View → 150

The value of _ x → π sin(2 ^ 2 x) tan( ^ 2 x) is equal to

NTA Abhyas JEE Main 2020 Solution View → 151

The value of _ x → - ∞ x^ 2 tan((1)/(x)) 4x^ 2 - x + 1 is equal to

NTA Abhyas JEE Main 2020 Solution View → 152

Let F: R → R be a function. We say that f has: PROPERTY 1 if _ h → 0 ⁡ f(h) - f(0) |h| exists and is finite, and PROPERTY 2 if _ h → 0 ⁡ f(h) - f(0) h ^ 2 exists and is finite.

JEE Advanced 2019 Solution View → 153

For a ∈ R, |a| > 1, let _ n → ∞ ⁡ ( 1 + 23 + … + n3 n ^ 7 / 3 ( 1 (an + 1) ^ 2 + 1 (an + 2) ^ 2 + … + 1 (an + n) ^ 2 ) ) = 54 . Then the possible value(s) of a is/are:

JEE Advanced 2019 Solution View → 154

_ x → 0 x + 2sinx x ^ 2 + 2sinx + 1 - ^ 2 x - x + 1 is

JEE Main 2019 Solution View → 155

If _ x → 1 x ^ 2 - ax + b x - 1 = 5, then a + b is equal to:

JEE Main 2019 Solution View → 156

If _ x → 1 x ^ 4 - 1 x - 1 = _ x → k x ^ 3 - k ^ 3 x ^ 2 - k ^ 2 , then k is

JEE Main 2019 Solution View → 157

If f(x) = [x] - [(x)/(4)], x ∈ R, where [x] denotes the greatest integer function, then:

JEE Main 2019 Solution View → 158

Let f: R → R be a differentiable function satisfying f ^ ' (3) + f ^ ' (2) = 0 . Then _ x → 0 ((1 + f(3 + x) - f(3))/(1 + f(2 - x) - f(2))) ^ (1)/(x) is equal to

JEE Main 2019 Solution View → 159

_ x → 0 ^ 2 x 2 - 1 + cosx equals

JEE Main 2019 Solution View → 160

_ x → 1 ^ - π - 2 ^ - 1 x 1 - x is equal to

JEE Main 2019 Solution View → 161

_ x → (π)/(4) co t ^ 3 x - tanx cos(x + (π)/(4)) is

JEE Main 2019 Solution View → 162

_ x arrow 0 x (4 x) ^ 2 x ^ 2 (2 x) is equal to:

JEE Main 2019 Solution View → 163

Let [x] denote the greatest integer less than or equal to X . Then : _ x arrow 0 (π ^ 2 x)+(|x|- (x[x]))^ 2 x^ 2

JEE Main 2019 Solution View → 164

For each t ∈ R, let [t] be the greatest integer less than or equal to t . Then, _ x → 1 ^ + ((1 - |x| + sin|1 - x|)sin([1 - x](π)/(2)))/(|1 - x|[1 - x])

JEE Main 2019 Solution View → 165

For each x ∈ R , let [x] be the greatest integer less than or equal to x . Then _ x → 0 ^ - (x([x] + |x|)sin ⁡ [x])/(|x|) is equal to

JEE Main 2019 Solution View → 166

The value of _ y → 0 1 + 1 + y ^ 4 - 2 y ^ 4

JEE Main 2019 Solution View → 167

For each positive integer n , let y _ n = (1)/(n) ( ( n + 1 )( n + 2 )...( n + n ) )(1)/(n) . If _ n → ∞ ⁡ y _ n = L, then the value of [L] (where [x] is the greatest integer less

JEE Advanced 2018 Solution View → 168

_ x → 0 (( 27 + x )(1)/(3) - 3)/(9 - ( 27 + x )(2)/(3)) equals

JEE Main 2018 Solution View → 169

_ x arrow 0 (x 2 x-2 x x)/((1- 2 x)^2) equals.

JEE Main 2018 Solution View → 170

For each t ∈ R, let [t] be the greatest integer less than or equal to t . Then _ x → 0 ^ + x([(1)/(x)] + [(2)/(x)] + … + [(15)/(x)])

JEE Main 2018 Solution View → 171

Let f(x) = (1 - x ( 1 + |1 - x| ))/(| 1 - x |)cos ⁡ ((1)/(1 - x))forx ≠ 1, then

JEE Advanced 2017 Solution View → 172

_ x → 3 ⁡ 3x - 3 2x - 4 - 2 is equal to

JEE Main 2017 Solution View → 173

_ x → (π)/(2) cotx - cosx (π - 2x) ^ 3 equals

JEE Main 2017 Solution View → 174

Let f(x) = _ n → ∞ ⁡ ( n ^ n (x + n)(x + (n)/(2)) … . . (x + (n)/(n)) n ! ( x ^ 2 + n ^ 2 )( x ^ 2 + n ^ 2 4 ) … . . ( x ^ 2 + n ^ 2 n ^ 2 ) ) ^ (x)/(n) , for all x > 0 . Then

JEE Advanced 2016 Solution View → 175

Let f: ℝ → (0, ∞) and g: ℝ → ℝ be twice differentiable functions such that f ^ ″ and g ^ ″ are continuous functions on ℝ . Suppose f ^ ′ ( 2 ) = g( 2 ) = 0, f ^ ″ ( 2 ) ≠ 0 and g

JEE Advanced 2016 Solution View → 176

Let α, β ∈ R be such that _ x → 0 ⁡ x ^ 2 sin ⁡ ( ) - sin ⁡ x = 1 . Then 6(α + β) equals

JEE Advanced 2016 Solution View → 177

_ x → 0 ⁡ (1 - cos ⁡ 2x) ^ 2 2xtan ⁡ x - xtan ⁡ 2x is

JEE Main 2016 Solution View → 178

If f(x) is a differentiable function in the interval (0, ∞) such that f(1) = 1 and _ t → x ⁡ t ^ 2 f(x) - x ^ 2 f(t) t - x = 1, for each x > 0, then f((3)/(2)) is equal to

JEE Main 2016 Solution View → 179

If _ x → ∞ ⁡ (1 + (a)/(x) - 4 x ^ 2 ) ^ 2x = e ^ 3 , then a is equal to

JEE Main 2016 Solution View → 180

_ n → ∞ ( (n + 1)(n + 2) … . 3n n ^ 2n )(1)/(n) is equal to

JEE Main 2016 Solution View → 181

Let P = _ x → 0 ^ + (1 + ^ 2 x )(1)/(2x) , then logP is equal to

JEE Main 2016 Solution View → 182

Let f: ℝ → ℝ be a continuous odd function, which vanishes exactly at one point and f(1) = (1)/(2) . Suppose that F(x) = ∫ _ - 1 ^ x f ( t )dt for all x ∈ [- 1, 2] and G(x) = ∫ _

JEE Advanced 2015 Solution View → 183

Let m and n be two positive integers greater than 1. If _ α → 0 ⁡ ( e ^ cos ⁡ ( α ^ n ) - e α ^ m ) = - ((e)/(2)) then the value of (m)/(n) is

JEE Advanced 2015 Solution View → 184

_ x → 0 ⁡ e ^ x ^ 2 - cos ⁡ x ^ 2 ⁡ x is equal to

JEE Main 2015 Solution View → 185

_ x → 0 ((1 - cos 2x)(3 + cos x))/(x tan 4x) =

JEE Main 2015 Solution View → 186

The largest value of the non - negative integer a for which _ x → 1 ⁡ \ (- ax + sin ⁡ (x - 1) + a)/(x + sin ⁡ (x - 1) - 1)\ ^ 1 - x 1 - x = (1)/(4) is _________

JEE Advanced 2014 Solution View → 187

If _ x arrow 2 (x-2\ x^2+k+2 x-2 k\ . x^2-4 x+4 =5 , then k is equal to:

JEE Main 2014 Solution View → 188

If f(x) is continuous and f((9)/(2)) = (2)/(9), then _ x → 0 f( 1 - cos3x x ^ 2 ) equals to

JEE Main 2014 Solution View → 189

_ x → 0 sin( π cos ^ 2 x) x ^ 2 is equal to

JEE Main 2014 Solution View → 190

The value of _ x arrow 0 (1)/(x)[ ^ -1 ((x+1)/(2 x+1))-(π)/(4)] is :

JEE Main 2013 Solution View → 191

The value of _ x → 0 ((1 - cos2x)(3 + cosx))/(xtan4x) is equal to

JEE Main 2013 Solution View → 192

Let α(a) and β(a) be the roots of the equation ( [3] 1+a -1) x^ 2 +( 1+a -1) x+( [6] 1+a -1)=0 where a >-1 . Then _ a arrow 0^ + α(a) and _ x arrow 0^ + β(a) are

JEE Advanced 2012 Solution View → 193

If _ x arrow ∞ ( x^ 2 +x+1 x+1 -a x-b)=4 , then

JEE Advanced 2012 Solution View → 194

_ x arrow 0 ( (π ^2 x))/(x^2) equals

JEE Main 2012 Solution View → 195

If f(x)=3 x^ 10 -7 x^8+5 x^6-21 x^3+3 x^2-7 , then _ α arrow 0 (f(1-α)-f(1))/(α^3+3 α) is

JEE Main 2012 Solution View → 196

_ x arrow 0 ((x- x)/(x)) ((1)/(x))

JEE Main 2012 Solution View → 197

If _ x arrow 0 [1+x (1+b^2)]^ 1 / x =2 b ^2 θ b>0 and θ ∈(-π, π] , then the value of θ is

JEE Advanced 2011 Solution View → 198

_ x arrow 2 ( 1- \ 2 (x-2)\ x-2 )

JEE Main 2011 Solution View → 199

The value of _ x arrow 0 (1)/(x^3) ∫_0^x (t (1+t))/(t^4+4) d t is

JEE Advanced 2010 Solution View → 200

Let f: R arrow R be a positive increasing function with _ x arrow ∞ (f(3 x))/(f(x))=1 . Then _ x arrow ∞ (f(2 x))/(f(x))=

JEE Main 2010 Solution View →
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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

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