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Inverse Trigonometric Functions — NDA Mathematics PYQs

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

Inverse Trigonometric Functions — NDA Mathematics PYQs

Consider the following in respect of inverse circular functions : I. ⁻¹(-x)=- ⁻¹x II. ⁻¹(-x)= ⁻¹x III. ⁻¹(-x)= - ⁻¹x IV. ⁻¹(-x)= - ⁻¹x How many of the above are correct ?

What is [2 ⁻¹ 1 2 - 4 ] equal to ?

If ⁻¹k + ⁻¹ 1 2 = 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 ⁻¹k + ⁻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 ( 4 -2 ⁻¹ 3 ) equal to?

If 4 ⁻¹ x+ ⁻¹ x= , 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 p ⁻²+ q ⁻² ?

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

What is ⁻¹ ( cosec ⁻¹ 2 ) equal to?

If 3 ⁻¹ x+ ⁻¹ x= , then what is x equal to?

If ⁻¹ ( 1 2 )+ ⁻¹ ( x 3 )= 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=- 4 ?

Let ⁻¹ x+ ⁻¹ y+ ⁻¹ z= 3 2 for 0 x, y, z 1 . What is the value of x¹⁰⁰⁰+y¹⁰⁰¹+z¹⁰⁰² ?

The equation ⁻¹ x- ⁻¹ x= 6 has

⁻¹ x+ ⁻¹ x= 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 - 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)= 4

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

What is the principal value of ⁻¹ ( 2 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+x^2 ) , 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 )= 2. There exist x, y [-1,1] , where x y such that ⁻¹ x+ ⁻¹ y= 2 Which of the above statements is/are correct?

Consider the following statements: 1. There exists (- 2 , 2 ) for which ⁻¹( ) . 2. ⁻¹ ( 1 3 )- ⁻¹ ( 1 5 )= ⁻¹ ( 2 2 ( 3 -1) 15 ) Which of the above statements is/are correct?

The value of (2 ⁻¹ 1 5 - 4 ) is

If y= ⁻¹ [ 1+ x + 1- x 1+ x - 1- x ] , where 0 x 2 , then d y d x is equal to

Consider the following : 1. ⁻¹ 4 5 + ⁻¹ 3 5 = 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)= 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)= / 2 2. ⁻¹(1 / 3)+ ⁻¹(1 / 3)= / 2 Which of the above statements is/are correct?

What is ⁻¹ 3 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 )=- 3 2. ⁻¹ ( 2 3 )= 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 the above

If ⁻¹ 5 x + ⁻¹ 12 x = 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?