Inverse Trigonometric Functions

Considering the principal values of the inverse trigonometric functions, -1 ( 32x + 12 1 - x2 ), - 12 < x < 1 2, is equal to

1. -5 6 - -1x
2. 5 6 - -1x
3. 6 + -1x
4. 4 + -1x

The sum of the infinite series -1 ( 74 )+ -1 ( 194 )+ -1 ( 394 )+ -1 ( 674 )+ is :

1. 2+ -1 ( 12 )
2. 2- -1 ( 12 )
3. 2- -1 ( 12 )
4. 2+ -1 ( 12 )

If y = ( 3 + -1 x2 ), then (x - y)2 + 3y2 is equal to .

Let S = \x : -1x = + -1x + -1(2x + 1) \. Then x S(2x - 1)2 is equal to .

( -1 35 + -1 513 + -1 3365 ) is equal to:

1. 3365
2. 1
3. 3265
4. 0

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