Trigonometric Functions

Let S= \ (-2 , 2 ) : +1= 3 \. Then S is equal to :

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

Let A, B, where A, B (- 2, 2 ), be the roots of the quadratic equation x2-2x-5=0. Then 20 2 ( A+B2 ) is equal to :

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

The sum of all the integral values of p such that the equation 3 2 x+12 x-3=p, x R, has at least one solution, is:

1. -54
2. -60
3. -75
4. -84

If S= \ [- , ] : . . 5 2= 7 7 2 \, then n(S) is equal to .

If A= 3 9 + 9 27 + 27 81 and B= 81 - 3 , then BA is equal to .

If ( 18 ) ( 5 18 ) ( 7 18 )=K, then the value of ( 10K 3 ) is :

1. 3+12 2
2. 3-1 2
3. 32
4. 12

Let S=\x [- , ] : x( x+ x)=a, a Z\. Then n(S) is equal to :

1. 3
2. 6
3. 7
4. 9

Let P=\ [0, 4 ] : 2 1\ and S=\a Z : 2( 8 - 8 ) 2 =a2, P\. Then n(S) is:

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

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

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

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

If [-2 , 2 ], then the number of solutions of 2 2 2 + (2 - 6) - 3 = 0, is equal to:

1. 8
2. 6
3. 10
4. 12

If [- 7 6, 4 3 ], then the number of solutions of 3 cosec2 - 2( 3 - 1) cosec - 4 = 0, is equal to :

1. 7
2. 10
3. 6
4. 8

If r=113 \ 1 ( 4 + (r - 1) 6 ) ( 4 + r 6 ) \ = a 3 + b, a, b Z, then a2 + b2 is equal to :

1. 10
2. 4
3. 8
4. 2