If `l` is the length of a diagonal of a cube of volume V, then (a) `3V=l^3` (b) `sqrt(3)\ V=l^3` (c) `3sqrt(3)\ V=2l^3` (d) `3sqrt(3)\ V=l^3`

If l is the length of a diagonal of a cube of volume V, then 3V=l^(3)( b) sqrt(3)V=l^(3)3sqrt(3)V=2l^(3)( d) 3sqrt(3)V=l^(3)

Volume V of a cube of edge lcm is given by V=(l xx l xx l)cm^(3).

In the given figure A B is the diameter of the circle, centred at Odot If /_C O A=60^0,A B=2r ,A C=d , and C D=l , then l is equal to (a) dsqrt(3) (b) d//sqrt(3) (c) 3d (d) sqrt(3) d /2

Let L L ' be the latus rectum through the focus of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and A ' be the farther vertex. If A ' L L ' is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes). (a) sqrt(3) (b) sqrt(3)+1 (c) ((sqrt(3)+1)/(sqrt(2))) (d) ((sqrt(3)+1))/(sqrt(3))

Relation between length (l), area (A), volume (V) is

If a line lies in the octant OXYZ and it makes equal angles with the axes, then: a) l=m=n=(1)/(sqrt(3)) b) l=m=n=pm(1)/(sqrt(3)) c) l=m=n=-(1)/(sqrt(3)) d) l=m=n=pm(1)/(sqrt(2))

Let L L ' be the latus rectum through the focus of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and A ' be the farther vertex. If A ' L L ' is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes). (a) sqrt(3) (b) sqrt(3)+1 ((sqrt(3)+1)/(sqrt(2))) (d) ((sqrt(3)+1))/(sqrt(3))

Let L L ' be the latus rectum through the focus of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and A ' be the farther vertex. If A ' L L ' is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes). sqrt(3) (b) sqrt(3)+1 ((sqrt(3)+1)/(sqrt(2))) (d) ((sqrt(3)+1))/(sqrt(3))

A straight line L passes through (3,-2) also inclined at an angle 60^@ to the line sqrt(3x)+y=1.If L also intersects the x-axis, then the equation of L is: (A) y+sqrt(3x)+2-3sqrt3=0 (B) y-sqrt(3x)+2+3sqrt3=0 (C) sqrt(3y)-x+3+2sqrt3=0 (D) sqrt(3y)+x-3+2sqrt3=0