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Inverse Trigonometric Functions · Question 1

JEE Main 2026 (Online) 8th April Evening ShiftMCQHard📈 Topic in 19% papers+4−1
1

Let =3 -1 ( 611 ) and =3 -1 ( 49 ), where inverse trigonometric functions take only the principal values. Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

  1. Both Statement I and Statement II are true
  2. Both Statement I and Statement II are false
  3. Statement I is true but Statement II is false
  4. Statement I is false but Statement II is true

Answer

(1) Both Statement I and Statement II are true

Solution

Let = -1 611, = -1 49; both lie in (0, 2 ), so =3 , =3

= 8511, = 659

= 3 = (4 2 -3 )= 8511 ( 340121-3 )=- 23 851331<0

Statement II is true

= (3-4 2 )= 611 219121>0

= (4 2 -3 )= 49 ( 6481-3 )=- 716729<0

= (3-4 2 )= 659 (3- 26081 )=- 17 65729<0

( + )= - =(-)(-)-(+)(-)>0

Statement I is true

Answer: (1)

JEE Main 2026 (Online) 8th April Evening Shift

Keep practising — Inverse Trigonometric Functions

2

Let 0< <1, = 13 and -1(1- )+ -1(1- )= 4. Then 6( + ) is equal to :

  1. 6
  2. 7
  3. 8
  4. 9
JEE Main 2026 (Online) 6th April Morning Shift
3

If ( -1 (x 2 ) )= ( -1 1-x2 ), x (0, 1), then the value of x is :

  1. 12
  2. 13
  3. 23
  4. 58
JEE Main 2026 (Online) 6th April Evening Shift
4

If 4+ p=111 -1 ( 2p-11+22p-1 )= , then is equal to .

JEE Main 2026 (Online) 5th April Morning Shift
5

Let [ ] denote the greatest integer function. If the domain of the function f(x)= -1 ( 4x+2[x]3 ) is [ , ], then 12( + ) is equal to :

  1. 6
  2. 8
  3. 9
  4. 4
JEE Main 2026 (Online) 4th April Morning Shift
6

If k = ( 4 + 12 -1 ( 23 ) ) + ( 12 -1 ( 23 ) ), then the number of solutions of the equation -1(kx - 1) = -1x - -1x is .

JEE Main 2026 (Online) 28th January Morning Shift
7

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

  1. 3356
  2. - 3356
  3. - 1663
  4. 1663
JEE Main 2026 (Online) 28th January Evening Shift
8

If the domain of the function f(x) = -1 ( 1x2 - 2x - 2 ) is (- , ] [ , ] [ , ), then + + + is equal to

  1. 4
  2. 2
  3. 5
  4. 3
JEE Main 2026 (Online) 24th January Evening Shift
9

The number of solutions of -1 4x + -1 6x = 6, where - 12 6 < x < 12 6, is equal to :

  1. 2
  2. 0
  3. 3
  4. 1
JEE Main 2026 (Online) 22nd January Morning Shift
10

If the domain of the function f(x) = -1 ( 2x - 511 - 3x ) + -1(2x2 - 3x + 1) is the interval [ , ], then + 2 is equal to :

  1. 5
  2. 2
  3. 3
  4. 1
JEE Main 2026 (Online) 21st January Morning Shift
11

Let the maximum value of ( -1x )2 + ( -1x )2 for x [- 32, 1 2 ] be mn 2, where (m, n) = 1. Then m + n is equal to .

JEE Main 2026 (Online) 21st January Evening Shift

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