Let `A B C` be a triangle such that `/_A C B=pi/6` and let `a` , `b` and `c` denote the lengths of the side opposite to `A , B` ,and `C` respectively. The value(s) of `x` for which `a=x^2+x+1,b=x^2-1,\and\ c=2x+1` is(are) `-(2+sqrt(3))` (b) `1+sqrt(3)` (c)`2+sqrt(3)` (d) `4sqrt(3)`

If the angle A ,Ba n dC of a triangle are in an arithmetic propression and if a , ba n dc denote the lengths of the sides opposite to A ,Ba n dC respectively, then the value of the expression a/csin2C+c/asin2A is (a) 1/2 (b) (sqrt(3))/2 (c) 1 (d) sqrt(3)

In a "Delta"A B C , let a ,b , and c denote the length of sides opposite to vertices A, B, and C respectively. If b=2,c=sqrt(3) and /_B A C=pi/6, then value of circumradius of triangle ABC is- 1/2 (2) 1 (3) 2 (4) 1/4

In a Delta A B C ,if a=2,/_B=60^0a n d/_C=75^0 , then b= (a) sqrt(3) (b) sqrt(6) (c) sqrt(9) (d) 1+sqrt(2)

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

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)

If x^4+1/(x^4)=623 , then x+1/x=? (a)27 (b) 25 (c) 3sqrt(3) (d) -3sqrt(3)

The shortest distance between line y-x=1 and curve x=y^2 is (a) (3sqrt2)/8 (b) 8/(3sqrt2) (c) 4/sqrt3 (d) sqrt3/4

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))

Consider a triangle A B C and let a , ba n dc denote the lengths of the sides opposite to vertices A , B ,a n dC , respectively. Suppose a=6,b=10 , and the area of triangle is 15sqrt(3)dot If /_A C B is obtuse and if r denotes the radius of the incircle of the triangle, then the value of r^2 is

The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot Then (a) a=2sqrt(2) (b) a=1-sqrt(3) (c) a=-1+sqrt(3) (d) a=-4