Trigonometric Functions

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

In a triangle ABC, BC = 7, AC = 8, AB = N and = 23. If 49 (3C) + 42 = mn, where (m, n) = 1, then m + n is equal to .

Suppose [0, 4 ] is a solution of 4 - 3 = 1. Then is equal to :

1. 6 - 6(3 6 - 2)
2. 4(3 6 + 2)
3. 6 + 6(3 6 + 2)
4. 4(3 6 - 2)

The number of solutions of 2 x + (2 + 2x - x2 ) x - 3(x - 1)2 = 0, where - x , is .

If = 1 x(x2+x+1), = x x2+x+1 and = (x-3+x-2+x-1 )1/2, 0<A, B, C< 2, then A+B is equal to :

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

The number of solutions of the equation 4 2 x-4 3 x+9-4 x=0 ; x [-2 , 2 ] is :

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

The number of solutions, of the equation e x-2e- x=2, is :

1. 0
2. 1
3. 2
4. more than 2

If 2 3 x+ 2x x+4 x-4=0 has exactly 3 solutions in the interval [0, n 2 ], n N, then the roots of the equation x2+nx+(n-3)=0 belong to :

1. (0, )
2. Z
3. (- 172, 172 )
4. (- , 0)

For , (0, /2), let 3 ( + )=2 ( - ) and a real number k be such that =k . Then, the value of k is equal to

1. 5
2. -2/3
3. -5
4. 2/3

If ,- 2< < 2 is the solution of 4 +5 =1, then the value of is

1. 10- 1012
2. 10-106
3. 10-1012
4. 10- 106

The sum of the solutions x R of the equation 3 2x+ 3 2x 6 x- 6 x=x3-x2+6 is

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

Let the set of all a such that the equation 2x+a x=2a-7 has a solution be [p, q] and r= 9 - 27 - 1 63 + 81 , then pqr is equal to .

If 2 2 -5 =1 has exactly 7 solutions in the interval [0, n 2 ], for the least value of n , then k=1n k2k is equal to:

1. 1214 (215-15 )
2. 1- 15213
3. 1215 (214-14 )
4. 1213 (214-15 )