If `x=(sqrt(3)+sqrt(2))^(6)` ,then the largest integer not exceeding `x` is (A) `729` (B) `971`(c) `969`(D) `970`

If [f((sqrt(3))/2)] is [.] denotes the greatest integer function) 4 (b) 5 (c) 6 (d) -7

If x=\ ^3sqrt(2+sqrt(3)) , then x^3+1/(x^3)= (a) 2 (b) 4 (c) 8 (d) 9

If x=(sqrt(3)-\ sqrt(2))/(sqrt(3)+sqrt(2)) and y=(sqrt(3)+\ sqrt(2))/(sqrt(3)-\ sqrt(2)) , then x^2+\ x y+y^2= (a) 101 (b) 99 (c) 98 (d) 102

If x=2/(3+sqrt(7)) , then (x-3)^2= (a)1 (b) 3 (c) 6 (d) 7

int_0^oo[3/(x^2+1)]dx, where [.] denotes the greatest integer function, is equal to (A) sqrt2 (B) sqrt2+1 (C) 3/sqrt2 (D) infinite

If y=sqrt(x)+1/(sqrt(x)) , then (dy)/(dx) \ at \ x=1 is a. 1 b. 1/2 c. 1/(sqrt(2)) d. 0

If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/((sqrt(a-x)+sqrt(x-b)) ,then (dy)/(dx) wherever it is defined is (a) (x+(a+b))/(sqrt((a-x)(x-b))) (b) (2x-a-b)/(2sqrt(a-x)sqrt(x-b)) (c) -((a+b))/(2sqrt((a-x)(x-b))) (d) (2x+(a+b))/(2sqrt((a-x)(x-b)))

If int(x+1)/(x^2+x+3)dx=a ln|x^2+x+3|+1/(sqrt(b))tan^(-1)((c x+d)/(sqrt(11)))+k , then the value of 2a+b+c+d is 15 b. 26 c. (29)/2 d. 13

If 4\ cos^(-1)x+sin^(-1)x=pi , then the value of x is (a) 3/2 (b) 1/(sqrt(2)) (c) (sqrt(3))/2 (d) 2/(sqrt(3))

The discriminant of the quadratic equation 4x^2 - 6x +3 = 0 is (A) 12 (B) 84 (C) 2 sqrt3 (D) -12