Trigonometric Functions

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

If the range of f( ) = 4 + 3 2 4 + 2 , R is [ , ], then the sum of the infinite G.P., whose first term is 64 and the common ratio is , is equal to .

If the value of 3 36 + 5 18 5 36 - 3 18 is a 5 - bc, where a, b, c are natural numbers and (a, c) = 1, then a + b + c is equal to :

1. 54
2. 52
3. 50
4. 40