Trigonometric Functions · Question 14

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

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

1. 4 - 10
2. -1
3. 4 + 10
4. 1

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

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

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 .

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

1. 2
2. 6
3. 8
4. 4

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

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

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

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