Inverse Trigonometric Functions

Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) = -1(2[x] + 1) is:

1. (- , )
2. (- , ) - \0\
3. (- , -1] [0, )
4. (- , -1] [1, )

If for some , ; , + =8 and 2 ( -1 )+cosec2 ( -1 )=36, then 2+ is

If > > >0, then the expression -1 \ + (1+ 2)( - ) \+ -1 \ + (1+ 2)( - ) \ + -1 \ + (1+ 2)( - ) \ is equal to :

1. 3
2. 2-( + + )
4. 0

If 2 x 3 4, then -1 ( 1213 x+ 513 x ) is equal to

1. x+ -1 512
2. x- -1 43
3. x+ -1 45
4. x- -1 512

Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of 16 ( ( -1x )2+ ( cosec-1x )2 ) is :

1. 24 2
2. 18 2
3. 22 2
4. 31 2

If the domain of the function f(x) = -1 ( x - 12x + 3 ) is R - ( , ), then 12 is equal to :

1. 40
2. 36
3. 24
4. 32

Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2 -1x + 3 -1x = 2 5, is .

For n N, if -13 + -14 + -15 + -1n = 4, then n is equal to .

Given that the inverse trigonometric function assumes principal values only. Let x, y be any two real numbers in [-1, 1] such that -1x - -1y = , - 2 . Then, the minimum value of x2 + y2 + 2xy is

1. 0
2. -1
3. 12
4. -12

For , , 0, if -1 + -1 + -1 = and ( + + )( - + )=3 , then equals

1. 3
2. 32
3. 1 2
4. 3-12 2