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JEE Inverse Trigonometric Functions PYQs with Solutions

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

266 questionsMathematics2002–2026Answers + solutions

About Inverse Trigonometric Functions PYQs

Inverse Trigonometric Functions has 266 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (91), NTA Abhyas JEE Main (71), 99 Percentile Qs Bank for JEE Main (40) and 2 other sources, 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: 13
  • 2025: 10
  • 2024: 9
  • 2023: 10
  • 2022: 14
  • 2021: 15
  • 2020: 74
  • 2019: 8
  • 2018: 1
  • 2017: 2
  • 2015: 3
  • 2014: 4

Inverse Trigonometric Functions questions with solutions

1

Considering only the principal values of the inverse trigonometric functions, the value of ^ -1 ( (-11)) + 10 (2 ^ -1 ( 1 2 )) + 10 (2 ^ -1 (2)) is

JEE Advanced 2026 Solution View → 2

Let α = 3 ^ -1 ((6)/(11)) and β = 3 ^ -1 ((4)/(9)) , where inverse trigonometric functions take only the principal values. Given below are two statements: Statement I: (α+β) > 0 .

JEE Main 2026 Solution View → 3

If ( ^ -1 (x 2 )) = ( ^ -1 1-x^2 ) , x ∈ (0,1) , then the value of x is :

JEE Main 2026 Solution View → 4

Let [·] denote the greatest integer function. If the domain of the function f(x) = ^ -1 ((x+[x])/(3)) is [α, β) , then α^2 + β^2 is equal to:

JEE Main 2026 Solution View → 5

Let 0 < α < 1 , β = (1)/(3α) and ^ -1 (1-α) + ^ -1 (1-β) = (π)/(4) . Then 6(α + β) is equal to:

JEE Main 2026 Solution View → 6

If (π)/(4) + ∑_ p=1 ^ 11 ^ -1 ( 2^ p-1 1 + 2^ 2p-1 ) = α , then α is equal to __________.

JEE Main 2026 Solution View → 7

If y = ^ -1 ((3 x - 4 x)/(4 x + 3 x)) + 2 ^ -1 ( x 1+ 1-x^2 ) , then (dy)/(dx) at x = 3 2 is equal to:

JEE Main 2026 Solution View → 8

Considering the principal values of inverse trigonometric functions, the value of the expression (2 ^ -1 ( 2 13 )-2 ^ -1 ( 3 10 )) is equal to :

JEE Main 2026 Solution View → 9

If k= ((π)/(4)+(1)/(2) ^ -1 ((2)/(3)))+ ((1)/(2) ^ -1 ((2)/(3))) , then the number of solutions of the equation ^ -1 (k x-1)= ^ -1 x- ^ -1 x is \_\_\_\_

JEE Main 2026 Solution View → 10

If the domain of the function f(x)= ^ -1 ( 1 x^ 2 -2 x-2 ) , is (-∞, α] ∪[β, γ] ∪[δ, ∞) , then α+β+γ+δ is equal to

JEE Main 2026 Solution View → 11

The number of solutions of ^ -1 4x + ^ -1 6x = (π)/(6) , where - 1 2 6 < x < 1 2 6 , is equal to

JEE Main 2026 Solution View → 12

Let the maximum value of ( ^ -1 x)^ 2 +( ^ -1 x)^ 2 for x ∈[- 3 2 , 1 2 ] be m n π^ 2 , where gcd(m, n)=1 . Then m+n is equal to \_\_\_\_ .

JEE Main 2026 Solution View → 13

If the domain of the function f(x)= ^ -1 ((2 x-5)/(11-3 x))+ ^ -1 (2 x^ 2 -3 x+1) is the interval [α, β] , then α+2 β is equal to :

JEE Main 2026 Solution View → 14

The total number of real solutions of the equation θ= ^ -1 (2 θ)-(1)/(2) ^ -1 ((6 θ)/(9+ ^2 θ)) is (Here, the inverse trigonometric functions ^ -1 x and ^ -1 x assume values in

JEE Advanced 2025 Solution View → 15

The value of ^ -1 ( 1+ ^2(2) -1 (2) )- ^ -1 ( 1+ ^2((1)/(2)) +1 ((1)/(2)) ) is equal to

JEE Main 2025 Solution View → 16

The sum of the infinite series ^ -1 ((7)/(4))+ ^ -1 ((19)/(4))+ ^ -1 ((39)/(4))+ ^ -1 ((67)/(4))+… . is :-

JEE Main 2025 Solution View → 17

Considering the principal values of the inverse trigonometric functions, ^ -1 ( 3 2 x+(1)/(2) 1-x^2 ),-(1)/(2) x 1 2 , is equal to

JEE Main 2025 Solution View → 18

If y= ((π)/(3)+ ^ -1 (x)/(2)) , then (x-y)^2+3 y^2 is equal to _____.

JEE Main 2025 Solution View → 19

Let \(S=\ x: ^ -1 x=π+ ^ -1 x+ ^ -1 (2 x+1)\ \). Then \(∑_ x ∈ ~S (2 x-1)^2\) is equal to ______.

JEE Main 2025 Solution View → 20

( ^ -1 (3)/(5)+ ^ -1 (5)/(13)+ ^ -1 (33)/(65)) is equal to:

JEE Main 2025 Solution View → 21

If α β γ 0 , then the expression ^ -1 \ β+((1+β^2))/((α-β))\ + ^ -1 \ γ+((1+γ^2))/((β-γ))\ + ^ -1 \ α+((1+α^2))/((γ-α))\ is equal to :

JEE Main 2025 Solution View → 22

If for some α, β ; α ≤ β, α+β-8 and ^2( ^ -1 α)+cosec^2( ^ -1 β)-36 , then α^2+β is_______.

JEE Main 2025 Solution View → 23

Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of 16(( ^ -1 x)^2+(cosec^ -1 x)^2) is :

JEE Main 2025 Solution View → 24

Considering only the principal values of the inverse trigonometric functions, the value of ( ^ -1 ((3)/(5))-2 ^ -1 ( 2 5 )) is

JEE Advanced 2024 Solution View → 25

The integral ∫_ 1 / 4 ^ 3 / 4 (2 ^ -1 (1-x)/(1+x) ) d x is equal to

JEE Main 2024 Solution View → 26

Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2 ^ -1 x+3 ^ -1 x=(2 π)/(5) , is _______

JEE Main 2024 Solution View → 27

For n ∈ N , if ^ -1 3+ ^ -1 4+ ^ -1 5+ ^ -1 n=(π)/(4) , then n is equal to_____

JEE Main 2024 Solution View → 28

Given that the inverse trigonometric function assumes principal values only. Let x , y be any two real numbers in [-1,1] such that ^ -1 x- ^ -1 y=α, (-π)/(2) ≤ α ≤ π . Then, the

JEE Main 2024 Solution View → 29

If a = ^ - 1 (sin(5)) and b = ^ - 1 (cos(5)) , then a ^ 2 + b ^ 2 is equal to

JEE Main 2024 Solution View → 30

For α, β, γ ≠ 0 . If ^ - 1 α + ^ - 1 β + ^ - 1 γ = π and (α + β + γ)(α - γ + β) = 3αβ , then γ equal to

JEE Main 2024 Solution View → 31

Let x = (m)/(n) ( m, n are co-prime natural numbers) be a solution of the equation cos(2 ^ - 1 x) = (1)/(9) and let α, β ( α > β ) be the roots of the equation m x ^ 2 - nx - m +

JEE Main 2024 Solution View → 32

Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying ^ - 1 ( x ) + ^ - 1 ( 2x ) = (π)/(4) is :

JEE Main 2024 Solution View → 33

For x ∈ ( - 1, 1 ] , the number of solutions of the equation ^ - 1 x = 2 ^ - 1 x is equal to

JEE Main 2023 Solution View → 34

If S = \ x ∈ ℝ: ^ - 1 ( x + 1 x ^ 2 + 2x + 2 ) - ^ - 1 ( x x ^ 2 + 1 ) = (π)/(4)\ then ∑ _ x ∈ S (sin(( x ^ 2 + x + 5)(π)/(2)) - cos(( x ^ 2 + x + 5)π)) is equal to _________ .

JEE Main 2023 Solution View → 35

Let S = \ x ∈ R: 0 < x < 1and2 ^ - 1 ((1 - x)/(1 + x)) = ^ - 1 ( 1 - x ^ 2 1 + x ^ 2 )\ . If n ( S ) denotes the number of elements in S then :

JEE Main 2023 Solution View → 36

Let S be the set of all solutions of the equation ^ - 1 (2x) - 2 ^ - 1 ( 1 - x ^ 2 ) = π, x ∈ [- (1)/(2), (1)/(2)] . Then ∑ _ x ∈ S 2 ^ - 1 ( x ^ 2 - 1) is equal to

JEE Main 2023 Solution View → 37

Let (a, b) ⊂ (0, 2π) be the largest interval for which ^ - 1 (sinθ) - ^ - 1 (sinθ) > 0, θ ∈ (0, 2π) , holds . If α x ^ 2 + + ^ - 1 ( x ^ 2 - 6x + 10) + ^ - 1 ( x ^ 2 - 6x + 10) =

JEE Main 2023 Solution View → 38

If ^ - 1 (α)/(17) + ^ - 1 (4)/(5) - ^ - 1 (77)/(36) = 0, 0 < α < 13 , then ^ - 1 (sinα) + ^ - 1 (cosα) is equal to

JEE Main 2023 Solution View → 39

Let y = f(x) represent a parabola with focus (- (1)/(2), 0) and directrix y = - (1)/(2) . Then S = \ x ∈ ℝ: ^ - 1 ( f(x) + ^ - 1 ( f(x) + 1 )) = (π)/(2)\ :

JEE Main 2023 Solution View → 40

Let a _ 1 = 1, a _ 2 , a _ 3 , a _ 4 , … . . be consecutive natural numbers. Then ^ - 1 ( 1 1 + a _ 1 a _ 2 ) + ^ - 1 ( 1 1 + a _ 2 a _ 3 ) + … . . + ^ - 1 ( 1 1 + a _ 2021 a _

JEE Main 2023 Solution View → 41

If the sum of all the solutions of ^ - 1 ( 2x 1 - x ^ 2 ) + cot ^ - 1 ( 1 - x ^ 2 2x ) = (π)/(3) , - 1 < x < 1, x ≠ 0 , is α - 4 3 , then α is equal to _____ .

JEE Main 2023 Solution View → 42

^ - 1 ( 1 + 3 3 + 3 ) + sec ^ - 1 8 + 4 3 6 + 3 3 =

JEE Main 2023 Solution View → 43

Considering only the principal values of the inverse trigonometric functions, the value of (3)/(2) ^ - 1 2 2 + π ^ 2 + (1)/(4) ^ - 1 2 2 π 2 + π ^ 2 + ^ - 1 2 π is _______. (If

JEE Advanced 2022 Solution View → 44

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation ^ - 1 (x) - 2 ^ - 1 (x) = ^ - 1 (2x) is equal to

JEE Main 2022 Solution View → 45

For k ∈ ℝ , let the solutions of the equation cos( ^ - 1 (xcot( ^ - 1 (cos( ^ - 1 x))))) = k, 0 < |x| < 1 2 be α and β , where the inverse trigonometric functions take only

JEE Main 2022 Solution View → 46

If 0 < x < 1 2 and ^ - 1 x α = ^ - 1 x β , then a value of sin((2πα)/(α + β)) is

JEE Main 2022 Solution View → 47

tan (2 ^ - 1 ( 1)/(5) + ^ - 1 ( 5)/(2) +2 ^ - 1 ( 1)/(8)) & is equal to:

JEE Main 2022 Solution View → 48

Let x = sin(2 ^ - 1 α) and y = sin((1)/(2) ^ - 1 (4)/(3)) . If S = \ α ∈ ℝ: y ^ 2 = 1 - x\ , then ∑ _ α ∈ S 16 α ^ 3 is equal to _______.

JEE Main 2022 Solution View → 49

50tan(3 ^ - 1 ((1)/(2)) + 2 ^ - 1 ( 1 5 )) + 4 2 tan((1)/(2) ^ - 1 (2 2 )) is equal to ______.

JEE Main 2022 Solution View → 50

The value of _ n → ∞ 6tan\ ∑ _ r = 1 ^ n ^ - 1 ( 1 r ^ 2 + 3r + 3 )\ is equal to

JEE Main 2022 Solution View → 51

The value of cot( ∑ _ n = 1 ^ 50 ^ - 1 ( 1 1 + n + n ^ 2 )) is

JEE Main 2022 Solution View → 52

^ - 1 (sin(2π)/(3)) + ^ - 1 (cos(7π)/(6)) + ^ - 1 (tan(3π)/(4)) is equal to

JEE Main 2022 Solution View → 53

If the inverse trigonometric functions take principal values, then ^ - 1 ((3)/(10)cos( ^ - 1 ((4)/(3))) + (2)/(5)sin( ^ - 1 ((4)/(3)))) is equal to

JEE Main 2022 Solution View → 54

The value of ^ - 1 [(cos((15π)/(4)) - 1)/(sin((π)/(4)))] is equal to

JEE Main 2022 Solution View → 55

Let x × y = x ^ 2 + y ^ 3 and (x × 1) × 1 = x ×(1 × 1). Then a value of 2 ^ - 1 ( x ^ 4 + x ^ 2 - 2 x ^ 4 + x ^ 2 + 2 ) is

JEE Main 2022 Solution View → 56

The set of all values of k for which ( ^ - 1 x) ^ 3 + ( cot ^ - 1 x) ^ 3 = k π ^ 3 , x ∈ R , is the interval

JEE Main 2022 Solution View → 57

For any positive integer n , let S _ n : ( 0, ∞ ) → R be defined by S _ n (x) = ∑ _ k = 1 ^ n cot ^ - 1 ( 1 + k ( k + 1 ) x ^ 2 x ) where for any x ∈ R, cot ^ - 1 ( x ) ∈ ( 0, π )

JEE Advanced 2021 Solution View → 58

^ - 1 ( cos ( - 5 ) ) + ^ - 1 ( sin ( 6 ) ) - ^ - 1 ( tan ( 12 ) ) is equal to : (The inverse trigonometric functions take the principal values)

JEE Main 2021 Solution View → 59

If ( ^ - 1 x) ^ 2 - ( ^ - 1 x) ^ 2 = a; 0 < x < 1, a ≠ 0, then the value of 2 x ^ 2 - 1 is

JEE Main 2021 Solution View → 60

If ∑ _ r = 1 ^ 50 ^ - 1 1 2 r ^ 2 = p, then the value of tanp is :

JEE Main 2021 Solution View → 61

The value of tan(2 ^ - 1 ((3)/(5)) + ^ - 1 ((5)/(13))) is equal to:

JEE Main 2021 Solution View → 62

The number of real roots of the equation ^ - 1 x(x + 1) + ^ - 1 x ^ 2 + x + 1 = (π)/(4) is:

JEE Main 2021 Solution View → 63

The number of solutions of the equation ^ - 1 [ x ^ 2 + (1)/(3)] + ^ - 1 [ x ^ 2 - (2)/(3)] = x ^ 2 for x ∈ [ - 1, 1 ] , and [ x ] denotes the greatest integer less than or equal

JEE Main 2021 Solution View → 64

If cot ^ - 1 ( α ) = cot ^ - 1 2 + cot ^ - 1 8 + cot ^ - 1 18 + cot ^ - 1 32 + … . upto 100 terms, then α is:

JEE Main 2021 Solution View → 65

The sum of possible values of x for ^ - 1 (x + 1) + cot ^ - 1 ((1)/(x - 1)) = ^ - 1 ((8)/(31)) is:

JEE Main 2021 Solution View → 66

Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy ^ - 1 ((3x)/(5)) + ^ - 1 ((4x)/(5)) = ^ - 1 x is

JEE Main 2021 Solution View → 67

Let S _ k = ∑ _ r = 1 ^ k ^ - 1 ( 6 ^ r 2 ^ 2r + 1 + 3 ^ 2r + 1 ), then _ k → ∞ S _ k is equal to :

JEE Main 2021 Solution View → 68

If ^ - 1 x a = ^ - 1 x b = ^ - 1 y c ; 0 < x < 1, then the value of cos(( )/(a + b)) is:

JEE Main 2021 Solution View → 69

cosec [2 cot ^ - 1 (5) + ^ - 1 ((4)/(5))] is equal to:

JEE Main 2021 Solution View → 70

A possible value of tan((1)/(4) ^ - 1 63 8 ) is:

JEE Main 2021 Solution View → 71

_ n → ∞ tan\ ∑ _ r = 1 ^ n ^ - 1 ( 1 1 + r + r ^ 2 )\ is equal to_______.

JEE Main 2021 Solution View → 72

If S is the sum of the first 10 terms of the series, ^ - 1 ((1)/(3)) + ^ - 1 ((1)/(7)) + ^ - 1 ((1)/(13)) + ^ - 1 ((1)/(21)) + … … then tan ( S ) is equal to :

JEE Main 2020 Solution View → 73

2π - ( ^ - 1 (4)/(5) + ^ - 1 (5)/(13) + ^ - 1 (16)/(65)) is equal to :

JEE Main 2020 Solution View → 74

If y = ∑ _ k = 1 ^ 6 k ^ - 1 \ (3)/(5)coskx - (4)/(5)sinkx\ then (dy)/(dx) at x = 0 is

JEE Main 2020 Solution View → 75

If ^ -1 ⁡ (1)/(3) + ^ -1 ⁡ (2)/(3) = ^ -1 ⁡ x , then the value of x is

NTA Abhyas JEE Main 2020 Solution View → 76

If x takes all permissible negative values, then ^ -1 ⁡ x is equal to

NTA Abhyas JEE Main 2020 Solution View → 77

In a , if ∠ A = ∠ B = (1)/(2) ( ^ - 1 ( 6 + 1 2 3 ) + ^ - 1 ( 1 3 )) and length of the side opposite to ∠ C is c = 6 ⋅ 3 (1)/(4) , then the area of is

NTA Abhyas JEE Main 2020 Solution View → 78

If α = ^ -1 ⁡ 3 2 + ^ -1 ⁡ (1)/(3) and β = ^ -1 ⁡ 3 2 + ^ -1 ⁡ (1)/(3) , then

NTA Abhyas JEE Main 2020 Solution View → 79

The complete solution set of the inequality ^ -1 ⁡ ( cos4 ) > 3x^ 2 - 4x is

NTA Abhyas JEE Main 2020 Solution View → 80

The value of sin ⁡ ( ^ -1 ⁡ x) is

NTA Abhyas JEE Main 2020 Solution View → 81

Solution set of [ ^ -1 ⁡ x ] > [ ^ -1 ⁡ x ] , where [.] denotes the greatest integer function, is

NTA Abhyas JEE Main 2020 Solution View → 82

The relation ^ -1 ⁡ ((1 + x)/(1 - x)) = (π)/(4) + ^ -1 ⁡ x holds true for all

NTA Abhyas JEE Main 2020 Solution View → 83

The domain set of the function f( x ) = ^ -1 x - ^ -1 x + ^ -1 ( 2 - x ) is

NTA Abhyas JEE Main 2020 Solution View → 84

Let x + (1)/(x) = 2, y + (1)/(y) = - 2 and ^ - 1 x + ^ - 1 y = mπ ,&#160; then the value of m is

NTA Abhyas JEE Main 2020 Solution View → 85

The value of the expression ^ -1 (1)/(2) + ^ -1 and (9)/(2) + ^ -1 and (2 5)/(2) + ^ -1 and (4 9)/(2) + ....... upto n terms is

NTA Abhyas JEE Main 2020 Solution View → 86

The value of a for which ax^ 2 + ^ -1 ⁡ (x^ 2 - 2x + 2) + ^ -1 ⁡ (x^ 2 - 2x + 2) = 0 has a real solution, is

NTA Abhyas JEE Main 2020 Solution View → 87

The real solutions of the equation ^ -1 x (x + 1) + ^ -1 and x^ 2 + x + 1 = π 2 and are

NTA Abhyas JEE Main 2020 Solution View → 88

If x, y, z are in arithmetic progression and ^ -1 ⁡ x, ^ -1 ⁡ y and ^ -1 ⁡ z are also in arithmetic progression, then

NTA Abhyas JEE Main 2020 Solution View → 89

Let S _ 1 is the complete solution set of the inequality cos^ - 1 (x) > cos^ - 1 (x^ 2 ) and S _ 2 is the complete solution set of the inequality (cot^ - 1 x) ^ 2 - 5cot^ - 1 x +

NTA Abhyas JEE Main 2020 Solution View → 90

Consider the function f (x) = cos^ - 1 ( [ 2 ^ x ]) +sin^ - 1 ([ 2 ^ x ] -1), then (where [.] represents the greatest integer part function)

NTA Abhyas JEE Main 2020 Solution View → 91

If ( ^ -1 ⁡ x) ^ 2 - 7( ^ -1 ⁡ x) + 10 > 0 , then the range of x will be

NTA Abhyas JEE Main 2020 Solution View → 92

The range of the function f(x) = sin^ - 1 ( x^ 2 1 + x^ 2 ), x ∈ ℝ is

NTA Abhyas JEE Main 2020 Solution View → 93

The value(s) of x satisfying the equation ^ -1 ⁡ (1 - x) - 2 ^ -1 ⁡ x = (π)/(2) & is/are

NTA Abhyas JEE Main 2020 Solution View → 94

If x satisfies the inequality (tan^ - 1 x) ^ 2 + 3(tan^ - 1 x) - 4 > 0 , then the complete set of values of x is

NTA Abhyas JEE Main 2020 Solution View → 95

The value of x for which sin ⁡ ( ^ -1 ⁡ (1 + x)) = cos ⁡ ( ^ -1 ⁡ x ) is

NTA Abhyas JEE Main 2020 Solution View → 96

The area bounded by the curve y = |cos^ - 1 (sin ⁡ x)| + |(π)/(2) - cos^ - 1 (cos ⁡ x)| and the& x -axis, where (π)/(2) ≤ x ≤ π , is equal to

NTA Abhyas JEE Main 2020 Solution View → 97

If a _ 1 , a _ 2 , a _ 3 are in arithmetic progression and d is the common difference, then ^ -1 ⁡ ( d 1 + a _ 1 a _ 2 ) + ^ -1 ⁡ ( d 1 + a _ 2 a _ 3 ) =

NTA Abhyas JEE Main 2020 Solution View → 98

If f(x) = tan^ - 1 x^ 2 + 4x + sin^ - 1 x^ 2 + 4x + 1 , then

NTA Abhyas JEE Main 2020 Solution View → 99

If the value of the expression tan ⁡ ((1)/(2) ^ - 1 ⁡ 2 5 ) is in the form of a + b where a, b ∈ Z, then the value of (a + b)/(b) is

NTA Abhyas JEE Main 2020 Solution View → 100

Let f(x) = sin^ - 1 \ x 1 - x - x (1 - x^ 2 ) \ , ∀ 0 ≤ x ≤ 1 , then f (x) is

NTA Abhyas JEE Main 2020 Solution View → 101

If f(x) = co s ^ - 1 (x(3)/(2) - 1 - x - x ^ 2 + x ^ 3 ), ∀ 0 ≤ x ≤ 1 , then the minimum value of f(x) is

NTA Abhyas JEE Main 2020 Solution View → 102

If f(x) = ta n ^ - 1 ( 2 ^ x 1 + 2 ^ 2x + 1 ), then ∑ _ r = 0 ^ 9 f(r) is

NTA Abhyas JEE Main 2020 Solution View → 103

If cot^ - 1 ((n)/(2π)) > (2π)/(3) , then the maximum value of the integer n is

NTA Abhyas JEE Main 2020 Solution View → 104

The maximum value of x that satisfies the equation si n ^ - 1 ( 2 15 |x| ) = co s ^ - 1 ((14)/(|x|)) is

NTA Abhyas JEE Main 2020 Solution View → 105

If x = sin (2tan^ - 1 3) and& y = sin ((1)/(2) tan ^ - 1 (4)/(3)),then

NTA Abhyas JEE Main 2020 Solution View → 106

For x ∈ (0, (π)/(2)), if cos^ - 1 ((7)/(2)(1 + cos ⁡ 2x) + (sin^ 2 x - 48cos^ 2 x) sin ⁡ x)= x - ^ -1 (kcos ⁡ x), then the value of k is equal to

NTA Abhyas JEE Main 2020 Solution View → 107

The value of tan^ - 1 [ 1 - sin ⁡ x + 1 + sin ⁡ x 1 - sin ⁡ x - 1 + sin ⁡ x ] (∀ x ∈ [0, (π)/(2)]) is equal to

NTA Abhyas JEE Main 2020 Solution View → 108

The number of roots of the equation sin^ - 1 x - cos^ - 1 x = sin^ - 1 (5x - 3) is/are

NTA Abhyas JEE Main 2020 Solution View → 109

If si n ^ - 1 ((5)/(x)) + si n ^ - 1 ((12)/(x)) = si n ^ - 1 ((2)/(x)) + co s ^ - 1 ((2)/(x)) , then the value of x is equal to

NTA Abhyas JEE Main 2020 Solution View → 110

The range of the function f (x) = sin^ - 1 [x^ 2 - (1)/(3)] - cos^ - 1 [x^ 2 + (2)/(3)] is (where, [x] represents the greatest integer value of x )

NTA Abhyas JEE Main 2020 Solution View → 111

The minimum value of x which satisfies the inequality si n ^ - 1 x ≥ co s ^ - 1 x is λ , then the value of 2λ is (use 2 = 1.41 )

NTA Abhyas JEE Main 2020 Solution View → 112

If tan^ - 1 (1)/(2x + 1) + tan^ - 1 (1)/(4x + 1) = cot^ - 1 ( x^ 2 2 ), then the number of all possible values of x is/are

NTA Abhyas JEE Main 2020 Solution View → 113

The number of solutions of the equation sin^ - 1 x = (sin ⁡ x) ^ - 1 is/are

NTA Abhyas JEE Main 2020 Solution View → 114

If cos^ - 1 |sin ⁡ x| ≥ sin^ - 1 | sin ⁡ x| , then the number of integral values of x in the interval x ∈ [0,3π]are

NTA Abhyas JEE Main 2020 Solution View → 115

The minimum value of x which satisfies the inequality (si n ^ - 1 x) ^ 2 ≥ (co s ^ - 1 x) ^ 2 is

NTA Abhyas JEE Main 2020 Solution View → 116

If 3 ta n ^ - 1 ( 1 2 + 3 ) - ta n ^ - 1 (1)/(3) = ta n ^ - 1 (1)/(x), then the value of x is equal to

NTA Abhyas JEE Main 2020 Solution View → 117

If y = tan^ - 1 1 1 + x + x^ 2 + tan^ - 1 1 x^ 2 + 3x + 3 + tan^ - 1 1 x^ 2 + 5x + 7 +.... + upto 2n terms (∀ x ≥ 0) , then y (0) is

NTA Abhyas JEE Main 2020 Solution View → 118

If [sin^ - 1 x] ^ 2 - 2 [sin^ - 1 x] + 1 ≤ 0 (where, [.] represents the greatest integral part of x ), then

NTA Abhyas JEE Main 2020 Solution View → 119

If f(x) = ta n ^ - 1 ( ln( e ^ 2 / x ^ 3 ) ln( e ^ 2 x ^ 3 ) ) + ta n ^ - 1 ( ln( e ^ 2 x ^ 3 ) ln(e / x ^ 6 ) )(∀ x ≥ e) , then the incorrect statement is

NTA Abhyas JEE Main 2020 Solution View → 120

If the range of f (x) = tan^ - 1 x + 2sin^ - 1 x + cos^ - 1 x is [a, b] , then

NTA Abhyas JEE Main 2020 Solution View → 121

If ^ - 1 ⁡ (x - x ^ 2 2 + x ^ 3 4 - …) + ^ - 1 ⁡ ( x ^ 2 - x ^ 4 2 + x ^ 6 4 - …) = (π)/(2) for 0 < |x| < 2 , then x is equal to

NTA Abhyas JEE Main 2020 Solution View → 122

If ^ - 1 ⁡ (x)/(π) ≤ (π)/(6), then the maximum value of 3 x is (Use π = 3 . 14 )

NTA Abhyas JEE Main 2020 Solution View → 123

The value of sin\ cot ^ - 1 [cos( cot ^ - 1 ((1)/(x)))]\ is equal to (x > 0)

NTA Abhyas JEE Main 2020 Solution View → 124

If θ = cot^ - 1 α, φ = cot^ - 1 β and αβ = - 1 (α > β), then the value of θ - equal to

NTA Abhyas JEE Main 2020 Solution View → 125

If x = sin ⁡ (2 tan ^ - 1 ⁡ 2 3 ) and y = sin ⁡ ((1)/(2) tan ^ - 1 ⁡ (12)/(5)), then

NTA Abhyas JEE Main 2020 Solution View → 126

If the maximum value of x which satisfies the inequality ^ - 1 ⁡ (sin ⁡ x) ≥ ^ - 1 ⁡ (sin ⁡ x) for x ∈ ((π)/(2), 2π) is λ , then (2λ)/(3) is equal to (take π = 3 .14 )

NTA Abhyas JEE Main 2020 Solution View → 127

The domain of the function f(x) = 4 ^ -1 ⁡ ((1 - |x|)/(2)) is

NTA Abhyas JEE Main 2020 Solution View → 128

The domain of the function f(x) = 2 sin ^ - 1 ⁡ \ _ 2 ⁡ ((1)/(2) x ^ 2 )\ is

NTA Abhyas JEE Main 2020 Solution View → 129

The range of the function y = 2 sin ^ - 1 ⁡ [ x ^ 2 + (1)/(2)] + cos ^ - 1 ⁡ [ x ^ 2 - (1)/(2)] is (where, [·] denotes the greatest integer function)

NTA Abhyas JEE Main 2020 Solution View → 130

If the trigonometric equation ^ -1 ⁡ x = 2 ^ -1 ⁡ a has a solution, then the complete set of values of a is

NTA Abhyas JEE Main 2020 Solution View → 131

If ^ -1 ⁡ (x - x^ 2 2 + x^ 3 4 -. … …) + ^ -1 ⁡ (x^ 2 - x^ 4 2 + x^ 6 4 -. … …) = (π)/(2) for 0 < |x| < 2 , then x & is equal to

NTA Abhyas JEE Main 2020 Solution View → 132

The number of real solutions of ^ -1 ⁡ x(x + 4) + ^ -1 ⁡ x^ 2 + 4x + 1 = (π)/(2) is equal to

NTA Abhyas JEE Main 2020 Solution View → 133

The value of 2 ^ -1 ⁡ (2)/(3) - 2 ^ -1 ⁡ 6 + 1 2 3 is equal to

NTA Abhyas JEE Main 2020 Solution View → 134

If sin ^ - 1 ⁡ ( 2a 1 + a^ 2 ) + sin ^ - 1 ⁡ ( 2b 1 + b^ 2 ) = 2 cot ^ - 1 ⁡ ((1)/(x)), then xis equal to [ ∀ a, b ∈ (0, 1)]

NTA Abhyas JEE Main 2020 Solution View → 135

If x ∈ (0, 1), then the value of 2 ^ -1 ⁡ ( 1 - x^ 2 2x ) +2 ^ -1 ⁡ ( 1 - x^ 2 1 + x^ 2 ) is equal to

NTA Abhyas JEE Main 2020 Solution View → 136

Consider the following two statements P and Q. P: ^ -1 ⁡ (cos ⁡ (4π)/(3)) = (4π)/(3) Q: ^ 2 ⁡ ( ^ -1 ⁡ (1)/(2)) + cosec ^ 2 ( ^ -1 ⁡ (1)/(3)) = 15 Then, which of the following is

NTA Abhyas JEE Main 2020 Solution View → 137

The value of ^ -1 ⁡ sin ⁡ 17 + ^ -1 ⁡ cos ⁡ 10 is equal to

NTA Abhyas JEE Main 2020 Solution View → 138

Consider the function f(x) = ^ -1 ⁡ ( [ 3 ^ x ]) + ^ -1 ⁡ ([ 3 ^ x ] - 1) , then (where, [⋅] represents the greatest integer part of x )

NTA Abhyas JEE Main 2020 Solution View → 139

If the function f: R → A defined as f (x) = ^ -1 ⁡ ( 2x^ 3 1 + x^ 6 ) is a surjective function, then the setA is equal to

NTA Abhyas JEE Main 2020 Solution View → 140

The value of 2 ^ -1 ⁡ (4)/(5) + 2 ^ -1 ⁡ (5)/(13) + 2 ^ -1 ⁡ (16)/(65) is equal to

NTA Abhyas JEE Main 2020 Solution View → 141

If sin ⁡ ( cot ^ - 1 ⁡ (1 - x)) = cos ⁡ ( tan ^ - 1 ⁡ (- x)) , then x is

NTA Abhyas JEE Main 2020 Solution View → 142

The value of cos ⁡ ( ^ -1 ⁡ (3)/(4)) + cos ⁡ ( ^ -1 ⁡ x) is equal to

NTA Abhyas JEE Main 2020 Solution View → 143

The value of ^ -1 ⁡ (cos ⁡ ^ -1 ⁡ x) + ^ -1 ⁡ (sin ⁡ ^ -1 ⁡ x) is equal to

NTA Abhyas JEE Main 2020 Solution View → 144

The natural domain of the function f(x) = ^ -1 ⁡ (2x) + (π)/(3) is

NTA Abhyas JEE Main 2020 Solution View → 145

The number of integers for which the equation ^ -1 ⁡ x + ^ -1 ⁡ x + ^ -1 ⁡ x = n has real solution(s) is

NTA Abhyas JEE Main 2020 Solution View → 146

The value of ^ - 1 ⁡ ((12)/(13)) - ^ - 1 ⁡ ((3)/(5)) is equal to:

JEE Main 2019 Solution View → 147

If ^ - 1 x - ^ – 1 (y)/(2) = α, where - 1 ≤ x ≤ 1, - 2 ≤ y ≤ 2, x ≤ (y)/(2), then for all x, y, 4 x ^ 2 - 4xycosα + y ^ 2 is equal to :

JEE Main 2019 Solution View → 148

If α = ^ - 1 ((3)/(5)) , β = ^ - 1 ((1)/(3)) , where 0 < α, β < (π)/(2), then α - β is equal to

JEE Main 2019 Solution View → 149

Considering only the principal values of inverse functions, the set A = \ x ≥ 0: ^ - 1 (2x) + ^ - 1 (3x) = (π)/(4)\

JEE Main 2019 Solution View → 150

All x satisfying the inequality ( ^ -1 x)^ 2 -7( ^ -1 x)+10> 0 , lie in the interval :

JEE Main 2019 Solution View → 151

The value of cot ⁡ ( ∑ _ n = 1 ^ 19 cot ^ - 1 ⁡ (1 + ∑ _ p = 1 ^ n 2p)) is:

JEE Main 2019 Solution View → 152

If x = ^ - 1 (sin ⁡ 10) and y = ^ - 1 (cos ⁡ 10), then y - x is equal to:

JEE Main 2019 Solution View → 153

If ^ - 1 ((2)/(3x)) + ^ - 1 ((3)/(4x)) = (π)/(2)(x > (3)/(4)), then x is equal to :

JEE Main 2019 Solution View → 154

For any positive integer n , define f _ n : (0, ∞) → R as f _ n (x) = ∑ _ i = 1 ^ n ^ - 1 ((1)/(1 + (x + j)(x + j - 1))) for all x ∈ (0, ∞) . ( Here, the inverse trigonometric

JEE Advanced 2018 Solution View → 155

A value of x satisfying the equation sin ⁡ [ cot ^ - 1 ⁡ (1 + x)] = cos ⁡ [ ^ - 1 ⁡ x], is:

JEE Main 2017 Solution View → 156

The value of ^ - 1 ⁡ [ 1 + x ^ 2 + 1 - x ^ 2 1 + x ^ 2 - 1 - x ^ 2 ], |x| < (1)/(2), x ≠ 0, is equal to:

JEE Main 2017 Solution View → 157

If α = 3 ^ - 1 ⁡ ((6)/(11))andβ = 3 ^ - 1 ⁡ ((4)/(9)), where the inverse trigonometric functions take only the principal values, then the correct options(s) is(are)

JEE Advanced 2015 Solution View → 158

If f(x) = 2 ^ - 1 x + ^ - 1 ( 2x 1 + x ^ 2 ), x > 1 , then f(5) is equal to

JEE Main 2015 Solution View → 159

Let ^ - 1 y = ^ - 1 x + ^ - 1 ( 2x 1 - x ^ 2 ), where |x| < 1 3 ,Then a value of y is

JEE Main 2015 Solution View → 160

Match the following. List &ndash; I List &ndash; II (A) Let y(x) = cos ⁡ (3 ^ - 1 ⁡ x), xϵ[- 1, 1], x ≠ ± 3 2 . Then (1)/(y(x))\ ( x ^ 2 - 1) d ^ 2 y(x) d x ^ 2 + x(dy(x))/(dx)\

JEE Advanced 2014 Solution View → 161

Let f: [0, 4π] → [0, π] be defined by f(x) = ^ - 1 ⁡ (cos ⁡ x) . The number of points x ∈ [0, 4π] satisfying the equation f(x) = (10 - x)/(10) is_________

JEE Advanced 2014 Solution View → 162

The principal value of ^ - 1 (cot(43π)/(4)) is

JEE Main 2014 Solution View → 163

Statement I: The equation ( ^ -1 x)^3+ ( ^ -1 x)^3-a π^3=0 has a solution for all a ≥ (1)/(32) . Statement II: For any x ∈ R , ^ -1 x+ ^ -1 x=(π)/(2) and 0 ≤( ^ -1 x-(π)/(4))^2 ≤

JEE Main 2014 Solution View → 164

Match List I with List II and select the correct answer using the code given below the lists : List - I List - II A. ( 1 y ^ 2 ( ( ^ - 1 y) + y sin ( ^ - 1 y) cot ( ^ - 1 y) + ( ^

JEE Advanced 2013 Solution View → 165

The value of cot( Σ _ n = 1 ^ 23 cot ^ - 1 (1 + Σ _ k = 1 ^ n 2k)) is

JEE Advanced 2013 Solution View → 166

Let S=\ ( array ll a_ 11 & a_ 12 a_ 21 & a_ 22 array ): a_ i j ∈\ 0,1,2\ , a_ 11 =a_ 22 \ Then the number of non-singular matrices in the set S is :

JEE Main 2013 Solution View → 167

S= ^ -1 ((1)/(n^2+n+1))+ ^ -1 ((1)/(n^2+3 n+3))+… + ^ -1 ((1)/(1+(n+19)(n+20))) , then S is equal to :

JEE Main 2013 Solution View → 168

A value of ^ -1 ( ( ^ -1 ( (2)/(3) ))) is

JEE Main 2012 Solution View → 169

Let f(θ)= [ ^ -1 ( θ 2 θ )] , where -(π)/(4) < θ < (π)/(4) . Then, the value of (d)/(d( θ))(f(θ)) is

JEE Advanced 2011 Solution View → 170

If 0 < x < 1 , then 1+x^2 [\ x ( ^ -1 x)+ ( ^ -1 x)\ ^2-1]^ (1)/(2) is equal to

JEE Advanced 2008 Solution View → 171

The value of (cosec^ -1 (5)/(3)+ ^ -1 (2)/(3)) is

JEE Main 2008 Solution View → 172

Let (x, y) be such that ^ -1 (a x)+ ^ -1 (y)+ ^ -1 (b x y)=(π)/(2) . Match the statements in Column I with the values in Column II.

JEE Advanced 2007 Solution View → 173

If ^ -1 ((x)/(5))+cosec^ -1 ((5)/(4))=(π)/(2) then a value of x is

JEE Main 2007 Solution View → 174

If ^ -1 x- ^ -1 (y)/(2)=α , then 4 x^2-4 x y α+y^2 is equal to

JEE Main 2005 Solution View → 175

The trigonometric equation ^ -1 x=2 ^ -1 a has a solution for

JEE Main 2003 Solution View → 176

^ -1 ( α )= ^ -1 ( α )=x , then x=

JEE Main 2002 Solution View → 177

If& ^ - 1 x + ^ - 1 y = (2π)/(3) ~and~ ^ - 1 x - ^ - 1 y = (π)/(3) .Then, ( x, y ) is equal to

99 Percentile Qs Bank for JEE Main Solution View → 178

If ^ - 1 x + ^ - 1 y + ^ - 1 z = π, then the value of~ k ~in the expression~ x^ 4 + y^ 4 + z^ 4 + 4x^ 2 y^ 2 z^ 2 = k[x^ 2 y^ 2 + y^ 2 z^ 2 + z^ 2 x^ 2 ], & is:

99 Percentile Qs Bank for JEE Main Solution View → 179

If ^ -1 x- ^ -1 (y)/(3)=α , where -1 ≤ x ≤ 1 , -3 ≤ y ≤ 3, x ≤ (y)/(3) , then for all x, y , 9 x^2-6 x y α+y^2 is equal to

99 Percentile Qs Bank for JEE Main Solution View → 180

^ - 1 ⁡ \ (1)/(2)x^ 2 + 1 - x^ 2 1 - x^ 2 4 \ = ^ - 1 ⁡ (x)/(2) - ^ - 1 ⁡ x holds for

99 Percentile Qs Bank for JEE Main Solution View → 181

If ^ - 1 (tan(&#960;)/(4)) - ^ - 1 (3)/(x) = (&#960;)/(6) , then x & is a root of the equation

99 Percentile Qs Bank for JEE Main Solution View → 182

Given 0 ≤ x ≤ (1)/(2) , then the value of ( ^ -1 \ left( x 2 + 1-x^2 2 )- ^ -1 x) is

99 Percentile Qs Bank for JEE Main Solution View → 183

Let f (x) = cosec ^ - 1 [1 + ^ 2 x], ~where~ [·]denotes the greatest integer function. Then f (x) equals;

99 Percentile Qs Bank for JEE Main Solution View → 184

If& f(x) = ^ - 1 (cosec( ^ - 1 x)) + ^ - 1 (sec( ^ - 1 x)), ~then~ f ( x ) & takes:

99 Percentile Qs Bank for JEE Main Solution View → 185

The value of sin ⁡ ( ^ - 1 ⁡ x) is

99 Percentile Qs Bank for JEE Main Solution View → 186

If the value of the expression tan ⁡ ((1)/(2) ^ - 1 ⁡ 2 5 ) is in the form of a + b where a, b ∈ Z, then the value of (a + b)/(b) is K, Find 10K.

99 Percentile Qs Bank for JEE Main Solution View → 187

If [sin^ - 1 x] ^ 2 - 2 [ sin^ - 1 x] + 1 ≤ 0 (where, [.] represents the greatest integral part of x ), then

99 Percentile Qs Bank for JEE Main Solution View → 188

If y= ^ -1 ( x+ x), then (d y)/(d x)=

99 Percentile Qs Bank for JEE Main Solution View → 189

If ^ -1 ((1-x)/(1+x))-(1)/(2) ^ -1 x=0 , for x>0 , then x=

99 Percentile Qs Bank for JEE Main Solution View → 190

With usual notations in Δ ABC , if C=90^ ^ ^ ∘ , then ^ -1 ((a)/(b+c))+ ^ -1 ((b)/(c+a))=

99 Percentile Qs Bank for JEE Main Solution View → 191

If x=cosec ( ^ -1 ( ( ^ -1 ( ( ^ -1 a))))) , a ∈[ 0,1]

99 Percentile Qs Bank for JEE Main Solution View → 192

The natural domain of the function& f(x) = ^ - 1 ⁡ (2x) + (π)/(3) is

99 Percentile Qs Bank for JEE Main Solution View → 193

If ^ -1 p + ^ -1 1-p + ^ -1 1-q =(3 π)/(4) , then q

99 Percentile Qs Bank for JEE Main Solution View → 194

If ∑_ r=1 ^ 50 ^ -1 (1)/(2 r^2)=p then p is

99 Percentile Qs Bank for JEE Main Solution View → 195

[ ( ^ -1 (3)/(4))]^ 2 +[ ( ^ -1 (4)/(3))]^ 2 =

99 Percentile Qs Bank for JEE Main Solution View → 196

If ^ -1 a+ ^ -1 b+ ^ -1 c=π , then which of the following is true?

99 Percentile Qs Bank for JEE Main Solution View → 197

If ^ -1 x+ ^ -1 (1-x)= ^ -1 x , then x ∈ to

99 Percentile Qs Bank for JEE Main Solution View → 198

What is the value of ^ -1 (12)/(13)+ ^ -1 (4)/(5)+ ^ -1 (63)/(16) is equal to

99 Percentile Qs Bank for JEE Main Solution View → 199

If ^ -1 ((3)/(x))+ ^ -1 ((4)/(x))=(π)/(2) , then x is equal to

99 Percentile Qs Bank for JEE Main Solution View → 200

(1+ (x)/(2))/(1- (x)/(2)) is equal to

99 Percentile Qs Bank for JEE Main 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)

Inverse Trigonometric Functions in other exams

NDA Inverse Trigonometric Functions (67)BITSAT Inverse Trigonometric Functions (18)