Trigonometric Functions

Let = (1 - 2 ( 11 ) ) (1 - 2 ( 3 11 ) ) (1 - 2 ( 9 11 ) ) (1 - 2 ( 27 11 ) ) (1 - 2 ( 81 11 ) ). Then the value of 5 - 2 is .

Match each entry in List-I to the correct entry in List-II and choose the correct option.

1. (P) → (2), (Q) → (5), (R) → (3), (S) → (4)
2. (P) → (5), (Q) → (3), (R) → (2), (S) → (4)
3. (P) → (5), (Q) → (4), (R) → (1), (S) → (3)
4. (P) → (4), (Q) → (3), (R) → (2), (S) → (5)

The value of n is .

Let = 1 60 61 + 1 62 63 + + 1 118 119 . Then the value of ( cosec1 )2 is .

Let 2<x< be such that x= -5 11. Then ( 11x2 ) ( 6x- 6x )+ ( 11x2 ) ( 6x+ 6x ) is equal to

1. 11-12 3
2. 11+12 3
3. 11+13 2
4. 11-13 2

Let f: R R be a function defined by f(x)= cases x2 ( x2 ), & if x 0,\ 0, & if x=0. cases Then which of the following statements is TRUE?

1. f(x)=0 has infinitely many solutions in the interval [ 11010, ).
2. f(x)=0 has no solutions in the interval [ 1 , ).
3. The set of solutions of f(x)=0 in the interval (0, 11010 ) is finite.
4. f(x)=0 has more than 25 solutions in the interval ( 1 2, 1 ).