Trigonometric Functions · Question 8

If (A - B) A + 2 C 2 A = 1, A, B, C (0, 2 ), then

1. A, C, B are in A.P.
2. A, C, B are in G.P.
3. A, B, C are in G.P.
4. A, B, C are in A.P.

The sum of all the elements in the range of f(x) = Sgn( x) + Sgn( x) + Sgn( x) + Sgn( x), x n 2, n Z, where Sgn(t) = cases 1, & if t > 0 \ -1, & if t < 0 cases is :

1. 4
2. 0
3. 2
4. -2

The value of 3 cosec 20 - 20 20 40 60 80 is equal to

1. 32
2. 64
3. 12
4. 16

If x = 512 for some x ( , 3 2 ), then 7x ( 13x2 + 13x2 ) + 7x ( 13x2 - 13x2 ) is equal to

1. 5 13
2. 6 26
3. 4 26
4. 1 13

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

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

1. 5
2. 4
3. 3
4. 0

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