Let `y=1/(2+1/(3+1/(2+1/(3+.....))))` the value of `y` is:
a.    `+-(sqrt(15)-3)/2`
b.    `(sqrt(15)-3)/2`
c.    `(sqrt(15)+3)/2`
d.    None of these

The ratio of the area of the largest triangle that can be inscribed in a circle of radius 7 cm to the area of the largest triangle that can be inscribed in semicircle of radius 7 cm is: a.   (2sqrt(3))/3 b.   (3sqrt(3))/4 c.   (2sqrt(3))/5 d.   None of these

If abx^2=(a-b)^2(x+1) , then the value of 1+4/x+4/x^2 is: a.     (a+b)/(a-b) b.     (a+b)^2/(a-b)^2 c.     (a+b)/(a-b)^2 d.     1

If x=3-sqrt(5) , then sqrt(x)/(sqrt(2)+sqrt(3x-2))=_ A.     1/sqrt(5) B.     sqrt(5) C.     sqrt(3) D.     1/sqrt(3)

Given a solid cylinder of radius 10 cm and length 1000 cm a cylinder hold is made into it to obtain a cylindrical shell of uniform thickness and having a volume equal to one-fourth of original volume. The thickness of the cylindrical shell is: a.     sqrt(5)-2 cm b.     5sqrt(5) cm c.     4(sqrt(5)-2) cm d.     5(2-sqrt(3) cm

Let the roots of the equation (3x^3-x^2+x-1)/(3x^3-x^2-x+1)=(4x^3+7x^2+x+1)/(4x^3+7x^2-x-1) be x_1 , x_2 and x_3 , then the value of x_1+x_2+x_3 is a.    0 b.    1 c.    -1 d.   None of these

If sin(theta + alpha)=cos(theta+alpha), then the value of tan theta is: a.    1-tan alpha b.    (1-tan alpha)/(1+tan alpha) c.    1+tan alpha d.    None of these

A solid cube whose edges are 12 cm each has been cut by a plane such that the plane bisects 3 edges meeting at a corner . The surface area of the remaining part of the cube after the small piece is removed will be: a.    81+10sqrt(3) b.    810+10sqrt(3) c.    810-10sqrt(3) d.    810+18sqrt(3)

The simplified form of [((a+1)^2/(a-1)^2+3)/((a-1)^2/(a+1)^2+3)]/((a^3+1)/(a^3-1)-(2a)/(a-1)] is: a.    a-1 b.    1-a c.    -1 d.   None of these

The number of integral pairs (x,y) satisfying the equation (x-y)^2+2y^2=27 is: a.    8 b.    7 c.    6 d.    5

The distance of the point (2,3) from the line x-2y+5=0 measured in a direction parallel to the line x -3y=0 is: (A)   2sqrt(10)     (B)   sqrt(10)     (C)   2sqrt(5)     (D)   None of these