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

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)

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

x=(sqrt(p^2+q^2)+sqrt(p^2-q^2))/(sqrt(p^2+q^2)-sqrt(p^2-q^2)) then q^2x^2-2p^2x+q^2=? (A)    3    (B)    -1    (C)    -2    (D)    0    

If p_(n+1)=sqrt(1/2(1+p_n)) , then cos(sqrt(1-p_0^2)/(p_1p_2p_3...to oo)) (a)   1    (b)   -1    (c)   p_0    (d)   1/p_0     (e)  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

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 alpha , beta gamma are the roots of the equation x^3+px^2+qx+r=0 , then (1-alpha^2)(1-beta^2)(1-gamma^2) is equal to (a)    (1+q)^2-(p-r)^2    (b)    (1+q)^2+(p+r)^2 (c)    (1-q)^2+(p-r)^2    (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