`int_0^(sqrt(2)) [x^2] dx` is equal to (A) `2-sqrt(2)` (B) `2+sqrt(2)` (C) `sqrt(2)-1` (D) `sqrt(2)-2`

1/(sqrt(9)-\ sqrt(8)) is equal to: (a) 3+2sqrt(2) (b) 1/(3+2sqrt(2)) (c) 3-2sqrt(2) (d) 3/2-\ sqrt(2)

A solution of sin^-1 (1) -sin^-1 (sqrt(3)/x^2)- pi/6 =0 is (A) x=-sqrt(2) (B) x=sqrt(2) (C) x=2 (D) x= 1/sqrt(2)

int_(0)^(2) sqrt(2-x)dx .

1+(sqrt(2))/(2-sqrt(2)) is equal to

min[(x_1-x_2)^2+(5+sqrt(1-x_1^2)-sqrt(4x_2))^2],AAx_1,x_2 in R , is (a) 4sqrt(5)-1 (b) 3-2sqrt(2) (c) sqrt(5)+1 (d) sqrt(5)-1

The value of the integral int_0^(3/2) [x^2]dx , where [] denotes the greatest integer function, is (A) 2+sqrt(2) (B) 2-sqrt(2) (C) 4+2sqrt(2) (D) 4-2sqrt(2)

int1/(1+sqrt(x))"dx" is equal to 2sqrt(x)+2ln|1+sqrt(x)|+c b. 2sqrt(x)-2ln|1+sqrt(x)|+c c. 2sqrt(x)-2ln|1-sqrt(x)|+c d. 2sqrt(x)-ln|1+sqrt(x)|+c

If cos (sin^(-1)(2/sqrt(5)) + cos^(-1)x) = 0, then x is equal to A) 1/sqrt(5) B) (-2/sqrt(5)) C) (2/sqrt(5)) D) 1

d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a) 1/2sqrt(1+s e cx) (b) sqrt(1+secx) (c) -1/2sqrt(1+secx) (d) -sqrt(1+secx)

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)