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Trigonometric Functions · Question 13

JEE Main 2026 (Online) 24th January Evening ShiftNumericalHard📈 Topic in 32% papers+4
1

The number of elements in the set \x [0, 180 ] : (x + 100 ) = (x + 50 ) x (x - 50 )\ is .

Answer

4

Solution

(x + 100 ) x = (x + 50 ) (x - 50 )

(x + 100 ) x (x + 100 ) x = (x + 50 ) (x - 50 ) (x + 50 ) (x - 50 ) = 100 - 2x 100 + 2x

Componendo–dividendo:

(2x + 100 ) 100 = 2 100 -2 2x

2 (2x + 100 ) 2x = -2 100 100

(4x + 100 ) + 100 = - 200

(4x + 100 ) = -( 100 + 200 ) = -2 150 50 = - 40

4x + 100 = 360 k - 40 or 4x + 100 = 360 k + 220

x = 90 k - 35 or x = 90 k + 30

In [0, 180 ]: x = 30 , 55 , 120 , 145

none of these makes x, (x 50 ) or (x + 100 ) undefined or zero, all four are valid.

Number of elements = 4

Answer: 4

JEE Main 2026 (Online) 24th January Evening Shift

Keep practising — Trigonometric Functions

2

Number of solutions of 3 2 + 8 + 3 3 = 0, [-3 , 2 ] is :

  1. 5
  2. 4
  3. 3
  4. 0
JEE Main 2026 (Online) 23rd January Morning Shift
3

Let α and β respectively be the maximum and the minimum values of the function f( ) = 4 ( 4 ( 7 2 - ) + 4(11 + ) ) - 2 ( 6 ( 3 2 - ) + 6(9 - ) ), R. Then α + 2β is equal to :

  1. 6
  2. 5
  3. 4
  4. 3
JEE Main 2026 (Online) 23rd January Morning Shift
4

The least value of ( 2 - 6 + 3 2 + 2 ) is

  1. 4 - 10
  2. -1
  3. 4 + 10
  4. 1
JEE Main 2026 (Online) 23rd January Evening Shift
5

Let 2 < < and = - 12 2. Then the value of ( 15 2 )( 8 + 8 ) + ( 15 2 )( 8 - 8 ) is equal to :

  1. 2 - 1 3
  2. 2 3
  3. 1 - 2 3
  4. - 2 3
JEE Main 2026 (Online) 23rd January Evening Shift
6

If 2 48 - 2 12 2 24 - 2 6 = + 52, where , N, then + is equal to

JEE Main 2026 (Online) 22nd January Morning Shift
7

Let ( + ) = - 110 and ( - ) = 38, where 0 < < 3 and 0 < < 4. If 2 = 3(1 - r 5) 11(s + 5), r, s N, then r + s is equal to .

JEE Main 2026 (Online) 22nd January Evening Shift
8

The value of cosec 10 - 3 10 is equal to :

  1. 2
  2. 6
  3. 8
  4. 4
JEE Main 2026 (Online) 21st January Morning Shift
9

If for [- 3, 0 ], the points (x, y) = (3 ( + 3 ), 2 ( + 6 ) ) lie on xy + x + y + = 0, then 2 + 2 + 2 is equal to :

  1. 75
  2. 96
  3. 80
  4. 72
JEE Main 2025 (Online) 7th April Morning Shift
10

The number of solutions of the equation 2 2 + 5 2 = 2 3 5 2 in [- 2, 2 ] is :

  1. 5
  2. 7
  3. 6
  4. 9
JEE Main 2025 (Online) 7th April Evening Shift
11

If 10 4 + 15 4 = 6, then the value of 27 cosec6 + 8 6 16 8 is

  1. 25
  2. 35
  3. 15
  4. 34
JEE Main 2025 (Online) 4th April Morning Shift

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