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Trigonometric Functions · Question 15

JEE Main 2026 (Online) 23rd January Morning ShiftMCQMedium📈 Topic in 13% papers+4−1
1

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

Answer

(2) 5

Solution

( 7 2 - ) = - , (11 + ) = -

( 3 2 - ) = - , (9 - ) =

f( ) = 4 ( 4 + 4 ) - 2 ( 6 + 6 )

4 + 4 = 1 - 2 2 2 and 6 + 6 = 1 - 3 2 2

f( ) = 4 - 8 2 2 - 2 + 6 2 2

= 2 - 2 2 2 = 2 - 12 2 2

0 2 2 1 = 2, = 32

+ 2 = 2 + 3 = 5

Answer: (2)

JEE Main 2026 (Online) 23rd January Morning Shift

Keep practising — Trigonometric Functions

2

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
3

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
4

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

JEE Main 2026 (Online) 22nd January Morning Shift
5

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
6

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
7

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
8

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
9

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
10

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

  1. 4
  2. 5
  3. 3
  4. 6
JEE Main 2025 (Online) 3rd April Morning Shift
11

The number of solutions of the equation (4 - 3) x - 2 3 2 x = - 41 + 3, x [-2 , 5 2 ] is

  1. 4
  2. 3
  3. 6
  4. 5
JEE Main 2025 (Online) 3rd April Evening Shift

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