JEE Advance Previous Year Questions (2018 - 2023): Inverse Trigonometric Functions | Mathematics (Maths) for JEE Main & Advanced PDF Download

JEE Advance PYQ 2023

Q1: Let , for x ∈ R. Then the number of real solutions of the equation  in the set  is equal to:         [JEE Advanced 2023 Paper 1]
Ans: 3

Number of solution = 3.

Q2: For any , let  and . Then the sum of all the solutions of the equation, is equal to :   [JEE Advanced 2023 Paper 2]
(a) 2√3 - 3
(b) 3 - 2√3
(c) 4√3 - 6
(d) 6 - 4√3
Ans: (c)
Concept :

Solution : Given, 0<|y|<3
⇒ y ∈ (−3, 3)− {0}
9 − y² is always positive when y ∈ (−3, 3)− {0}
And 6y is positive when y ∈ (0, 3)
And 6y is negative when y ∈ (−3, 0)
∴ In overall, 6y / 9 − y² > 0 when y ∈ (0, 3)
And 6y / 9 − y² < 0 when y∈(−3, 0)
Case - 1 :
When -3 < y < 0

as,

Case-2 : When 0 < y < 3

∴ Sum of solutions =

JEE Advance PYQ 2022

Q1: Considering only the principal values of the inverse trigonometric functions, the value of is            [JEE Advanced 2022 Paper 1]
Ans: 

Let,

We know,

= 2.36

 

JEE Advance PYQ 2019

Q1: The value of  in the interval  equals _________                    [JEE Advanced 2019 Paper 2]
Ans:

So,

= sec⁻¹ (1) = 0 

Q2: For non-negative integers n, let

Assuming cos⁻¹ x takes values in [0, π], which of the following options is/are correct?
(a) If α = tan(cos⁻¹ f(6)), then α² + 2α −1 = 0
(b)
(c) sin(7 cos⁻¹ f(5)) = 0
(d)      [JEE Advanced 2019 Paper 2]
Ans: (a), (b) & (c)
It is given, that for non-negative integers 'n', 

Now,
Now,  and Now,

Hence, options (a), (b) and (c) are correct.

JEE Advance PYQ 2018

Q1: The number of real solutions of the equation
  lying in the interval  is ____________. (Here, the inverse trigonometric functions sin⁻¹ x and cos⁻¹ x assume values in [−π/2, π/2] and [0, π], respectively.)         [JEE Advanced 2018 Paper 1]
Ans: 2
We have,

 using sum of infinite terms of GP

∴ x³ + 2x² + 5x - 2 has only one real roots
Therefore, total number of real solution is 2.

Q2: In a ΔPQR = 30^∘ and the sides PQ and QR have lengths 10√3 and 10, respectively. Then, which of the following statement(s) is(are) TRUE?
(a) ∠QPR = 45∘
(b) The area of the ΔPQR is 25√3 and ∠QRP = 120∘
(c) The radius of the incircle of the ΔPQR is 10√3 − 15
(d) The area of the circumcircle of the ΔPQR is 100π                [JEE Advanced 2018 Paper 1]
Ans: (b), (c) & (d)
We have,
In ΔPQR

By cosine rule

⇒ PR = 10
Since, PR = QR = 10

Radius of incircle of

and radius of circumcircle

∴ Area of circumcircle of

Hence, option (b), (c) and (d) are correct answer.