Trigonometric Functions

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 )