Trigonometric Functions

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 x + 2 x = 1, x (0, 2 ), then ( 12x + 12x) + 3( 10x + 10x + 8 x + 8 x) + ( 6 x + 6 x) is equal to:

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

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

Let A= \x (0, )- \ 2 \: (2/ )| x|+ (2/ )| x|=2 \ and B= \x 0: x( x-4)-3| x-2|+6=0 \. Then n(A ) is equal to :

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

The value of ( 70 ) ( 10 70 -1 ) is

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

Let the range of the function f(x)=6+16 x ( 3-x ) ( 3+x ) 3x 6x, x be [ , ]. Then the distance of the point ( , ) from the line 3x+4y+12=0 is :

1. 11
2. 10
3. 8
4. 9

The sum of all values of [0,2 ] satisfying 2 2 = 2 and 2 2 =3 is

2. 5 6
3. 2
4. 4

Let | (60 - ) (60 + ) | 18, [0, 2 ]. Then, the sum of all [0, 2 ], where 3 attains its maximum value, is :

1. 6
2. 9
3. 18
4. 15

Let the range of the function f(x) = 12 + 3x + 3x, x R be [a, b]. If and are respectively the A.M. and the G.M. of a and b, then is equal to

3. 2
4. 2

If x = - 35, where < x < 3 2, then 80 ( 2 x - x ) is equal to

1. 109
2. 108
3. 19
4. 18