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NDA Inverse Trigonometric Functions PYQs with Solutions

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

67 questionsMathematics2010–2026Answers + solutions

About Inverse Trigonometric Functions PYQs

Inverse Trigonometric Functions has 67 previous year questions in the Quantrex Academy NDA Mathematics bank. The 67 questions in this list come from NDA (67), spanning 2010 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Inverse Trigonometric Functions PYQs with Solutions

About Inverse Trigonometric Functions PYQs

Questions by year (this list)

Inverse Trigonometric Functions questions with solutions

Consider the following in respect of inverse circular functions : I. ^ -1 (-x)=- ^ -1 x II. ^ -1 (-x)= ^ -1 x III. ^ -1 (-x)=π- ^ -1 x IV. ^ -1 (-x)=π- ^ -1 x How many of the

What is [2 ^ -1 (1)/(2)-(π)/(4)] equal to ?

If ^ -1 k + ^ -1 (1)/(2) = (π)/(4) , then what is the value of k ?

What is the value of [(1)/(2) ^ -1 ( 2 3 )]?

Consider the following for the two (02) items that follow: Let y = ^ -1 (x - (4x^3)/(27)) . What is y equal to?

If k is a root of x^2 - 4x + 1 = 0 , then what is ^ -1 k + ^ -1 (1)/(k) equal to?

What is ^ -1 9 + cosec^ -1 ( 41 4 ) equal to?

What is ^2 ( ^ -1 2)+ ^2 (cosec^ -1 3) equal to?

If ^ -1 x= ^ -1 x , then which one of the following is correct?

What is 15+ ^2((π)/(4)-2 ^ -1 3) equal to?

If 4 ^ -1 x+ ^ -1 x=π , then what is ^ -1 x+4 ^ -1 x equal to?

What is ^ -1 ((a)/(b))- ^ -1 ((a-b)/(a+b))equal to?

What is 2 ((1)/(2) ^ -1 5 3 )equal to?

If ^ -1 p-cosec^ -1 q=0 , where p > 0, q > 0 ; then what is the value of ^ -2 + ^ -2 ?

What is 1+ ^2 ( ^ -1 ( 3 17 ))equal to?

What is ^ -1 (cosec^ -1 2) equal to?

If 3 ^ -1 x+ ^ -1 x=π , then what is x equal to?

If ^ -1 ((1)/(2))+ ^ -1 ((x)/(3))=(π)/(4) , where 0 < x < 6 , then what is x equal to?

What is the value of the following? [ ^ -1 (3)/(5)+ ^ -1 (3)/(2)]

What is the slope of the tangent of y= ^ -1 ( x) at x=-(π)/(4) ?

Let ^ -1 x+ ^ -1 y+ ^ -1 z=(3 π)/(2) for 0 ≤ x, y, z ≤ 1 . What is the value of x^ 1000 +y^ 1001 +z^ 1002 ?

The equation ^ -1 x- ^ -1 x=(π)/(6) has

^ -1 x+ ^ -1 x=(π)/(2) holds, when

What is the domain of the function f(x)= ^ -1 (x-2) ?

What is the value of ^ -1 (4)/(5)+ ^ -1 (5)/(4)-(π)/(2) ?

What is \ 2 ^ -1 ((1)/(3))\ equal to?

If ^ -1 (2 p)/(1+p^2)- ^ -1 (1-q^2)/(1+q^2)= ^ -1 (2 x)/(1-x^2) , then what is x equal to ?

Consider the following values of x : 1. 8 2. -4 3. (1)/(6) 4. -(1)/(4) Which of the above values of x is/are the solutions of the equation ^ -1 (2 x)+ ^ -1 (3 x)=(π)/(4)

Let the slope of the curve y= ^ -1 ( x) be θ : Then the value of θ in the interval (0, π) is

What is the principal value of ^ -1 ( (2 π)/(3)) ?

What is ^ -1 ((1)/(4))+ ^ -1 ((3)/(5))equal to?

The value of ^ -1 ((3)/(5))+ ^ -1 ((1)/(7))is equal to

The principal value of ^ -1 x lies in the interval

If y= ^ -1 ((2 x)/(1+x²)), then (d y)/(d x) is equal to

Let x, y, z be positive real numbers such that x, y, z are in GP and ^ -1 x, ^ -1 y and ^ -1 z are in AP. Then which one of the following is correct?

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

What is the value of (2 ^ -1 (0.8). ?

Consider the following statements: 1. ^ -1 x+ ^ -1 ((1)/(x))=π 2. There exist x, y ∈[-1,1] , where x ≠ y such that ^ -1 x+ ^ -1 y=(π)/(2) Which of the above statements is/are

Consider the following statements: 1. There exists θ ∈(-(π)/(2), (π)/(2)) for which ^ -1 ( θ) ≠ θ . 2. ^ -1 ((1)/(3))- ^ -1 ((1)/(5))= ^ -1 ( 2 2 ( 3 -1) 15 ) Which of the above

The value of (2 ^ -1 (1)/(5)-(π)/(4)) is

If y= ^ -1 [ 1+ x + 1- x 1+ x - 1- x ], where 0 < x < (π)/(2),then (d y)/(d x) is equal to

Consider the following : 1. ^ -1 (4)/(5)+ ^ -1 (3)/(5)=(π)/(2) 2. ^ -1 3 + ^ -1 1=- ^ -1 (2+ 3 ) which of the above is/are correct?

Consider x=4 ^ -1 ((1)/(5)), y= ^ -1 ((1)/(70)) and z= ^ -1 ((1)/(99))What is x equal to?

Consider x=4 ^ -1 ((1)/(5)), y= ^ -1 ((1)/(70)) and z= ^ -1 ((1)/(99))What is x-y+z equal to?

The equation ^ -1 (1+x)+ ^ -1 (1-x)=(π)/(2) is satisfied by

Consider x=4 ^ -1 ((1)/(5)), y= ^ -1 ((1)/(70)) and z= ^ -1 ((1)/(99))What is x-y equal to?

If x and y are positive and x y 1 , then what is ^ -1 x + ^ -1 y equal to?

What is ^ -1 (3)/(5)+ ^ -1 (4)/(5) equal to?

Consider the following statements: 1. ^ -1 1+ ^ -1 (0.5)=π / 2 2. ^ -1 (1 / 3)+ ^ -1 (1 / 3)=π / 2 Which of the above statements is/are correct?

What is ^ -1 (3 π)/(5) equal to?

What is ^ -1 ((1)/(2))+ ^ -1 ((1)/(3))equal to?

If ^ -1 ((2 a)/(1+a^2))+ ^ -1 ((2 b)/(1+b^2))=2 ^ -1 x , then x is equal to

What is [ ^ -1 ((3)/(4))+ ^ -1 ((4)/(5))]equal to?

If ^ -1 2, ^ -1 3 are two angles of a triangle, then what is the third angle?

What is the value of ^2 ^ -1 ((5)/(11))?

If ^ -1 1+ ^ -1 (4)/(5)= ^ -1 x , then what is x equal to?

What is the value of \ ^ -1 (4)/(5)+ ^ -1 (12)/(13)\ ?

What is the principal value of ^ -1 ( 2 3 )?

In a triangle A B C , if A= ^ -1 2 and B= ^ -1 3 , then C is equal to

Consider the following: 1. cosec^ -1 (- 2 3 )=-(π)/(3) 2. ^ -1 ( 2 3 )=(π)/(6) Which of the above is/are correct?

If ( ^ -1 (1)/(5)+ ^ -1 x)=1 then what is x equal to?

What is the value of ^ -1 (4)/(5)+2 ^ -1 (1)/(3) ?

What is the principal value of cosec^ -1 ( 2 ) ?

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

Statement I : y= ^ -1 (x^ -1 )+1 is an increasing function of x . Statement II : (d y)/(d x) is positive for all values of x . Which one of the following is correct in respect of

If ^ -1 (5)/(x)+ ^ -1 (12)/(x)=(π)/(2) , then what is the value of x ?

Statement I: If -1 ≤ x < 0 , then ( ^ -1 x)=- 1-x^2 ? Statement II : If -1 ≤ x < 0 , then ( ^ -1 x)= 1-x^2 Which one of the following is correct in respect of the above statements?

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Inverse Trigonometric Functions in other exams