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Inverse Trigonometric Functions

JEE Main 2026 (Online) 21st January Morning ShiftMCQEasy📈 Topic in 9% papers+4−1
Ques. 1JEE Main 2026, 21 January (Morning Shift)

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

Answer

(3) 3

Solution

For -1(2x2 - 3x + 1) we need -1 2x2 - 3x + 1 1.

Right part: 2x2 - 3x 0 x(2x - 3) 0 0 x 32

Left part: 2x2 - 3x + 2 0, which is true for all real x (discriminant 9 - 16 < 0).

For -1 ( 2x - 511 - 3x ) we need -1 2x - 511 - 3x 1. For 0 x 32, 11 - 3x > 0, so

-(11 - 3x) 2x - 5 11 - 3x

x 6 and x 165, both true for every x [0, 32 ].

Hence the domain is [0, 32 ], so = 0 and = 32.

+ 2 = 0 + 3 = 3

Answer: (3)

Keep practising — Inverse Trigonometric Functions

Ques. 2JEE Main 2026, 21 January (Evening Shift)

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 .

Ques. 3JEE Main 2025, 8 April (Evening Shift)

The value of -1 ( 1+ 2(2)-1 (2) ) - -1 ( 1+ 2 ( 12 )+1 ( 12 ) ) is equal to

  1. - 32
  2. + 52
  3. - 54
  4. + 32
Ques. 4JEE Main 2025, 4 April (Morning Shift)

Considering the principal values of the inverse trigonometric functions, -1 ( 32x + 12 1 - x2 ), - 12 < x < 1 2, is equal to

  1. -5 6 - -1x
  2. 5 6 - -1x
  3. 6 + -1x
  4. 4 + -1x
Ques. 5JEE Main 2025, 4 April (Evening Shift)

The sum of the infinite series -1 ( 74 )+ -1 ( 194 )+ -1 ( 394 )+ -1 ( 674 )+ is :

  1. 2+ -1 ( 12 )
  2. 2- -1 ( 12 )
  3. 2- -1 ( 12 )
  4. 2+ -1 ( 12 )
Ques. 6JEE Main 2025, 2 April (Evening Shift)

If y = ( 3 + -1 x2 ), then (x - y)2 + 3y2 is equal to .

Ques. 7JEE Main 2025, 29 January (Morning Shift)

Let S = \x : -1x = + -1x + -1(2x + 1) \. Then x S(2x - 1)2 is equal to .

Ques. 8JEE Main 2025, 28 January (Morning Shift)

( -1 35 + -1 513 + -1 3365 ) is equal to:

  1. 3365
  2. 1
  3. 3265
  4. 0
Ques. 9JEE Main 2025, 28 January (Evening Shift)

Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) = -1(2[x] + 1) is:

  1. (- , )
  2. (- , ) - \0\
  3. (- , -1] [0, )
  4. (- , -1] [1, )
Ques. 10JEE Main 2025, 24 January (Morning Shift)

If for some , ; , + =8 and 2 ( -1 )+cosec2 ( -1 )=36, then 2+ is

Ques. 11JEE Main 2025, 24 January (Evening Shift)

If > > >0, then the expression -1 \ + (1+ 2)( - ) \+ -1 \ + (1+ 2)( - ) \ + -1 \ + (1+ 2)( - ) \ is equal to :

  1. 3
  2. 2-( + + )
  4. 0

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