Suppose the union of sets S1 and S2 is X and S1, S2 have the same number of elements. If elements S1, S2 are chosen randomly it was found that by exchanging two elements of S1 with two elements of S2, every element of S1 was greater than that of S2. Find the no. of sets S1 that can be formed.

Q. Consider two charged metallic spheres

S_{1} and S_{2}

of radii

R_{1} and R_{2}

, respectively. The electric fields

E_{1} (on S_{1}) and E_{2} (on S_{2})

on their surfaces are such that

E_{1} / E_{2} = R_{1} / R_{2}

. Then the ratio

\frac{V_{1} (on S_{1})}{V_{2} (on S_{2})}

of the electrostatic potentials on each sphere is:

Q. Let X be the set of first 100 natural numbers. Sets S1 and S2 are subsets of X such that each of them has more than zero elements and no common element. If the maximum number of elements in S1 = x1, in S2 = y1 and minimum no. of elements in S1 = x2, in S2 = y2 then:
Suppose the union of sets S1 and S2 is X and S1, S2 have the same number of elements. If elements from S1 and S2 are chosen randomly, it was found that by exchanging two elements of S1 with two elements of S2, every element of S1 was greater than that of S2. Find the no. of sets S1 that can be formed.

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S1 and S2 are two spheres of equal masses. S1 runs down a smooth inclined plane of length 5 cm and of height 4 cm. S2 falls vertically down by 4 cm. the work done by all forces acting on S1

The correct option is A and on S2 are same and non zeroUsing energy balance we see that potential energy which only depends on the height changes to kinetic energy at the bottom. Thus the work done in both the cases is same. If friction were present work done would have been different.

$S_{1}$ and $S_{2}$ are two spheres of equal masses. $S_{1}$ runs down a smooth inclined plane of length 5 cm and of height 4 cm. $S_{2}$ falls vertically down by 4 cm. the work done by all forces acting on $S_{1}$

The correct option is A and on $S_{2}$ are same and non zero
Using energy balance we see that potential energy which only depends on the height changes to kinetic energy at the bottom. Thus the work done in both the cases is same. If friction were present work done would have been different.