If `S_1`, `S_2` and `S_3`are the sums of first n natural numbers, their squares and their cubes respectively, then show that `9S_2^2 = S_3 (1 + 8S_1)`.

If S_(1) , S_(2) and S_(3) are the sums of first n natural numbers, their squares and their cubes respectively then show that - 9 S_(2) ^(2) = S _(3) (1 + 8 S _(1))

In the S.D. of first N natural number is sqrt2 , then the value of n must be ______.

If S_1 , S_2 and S_3 are respectively the sum of n, 2n and 3n terms of a G.P., then prove that S_1(S_3 - S_2) = (S_2 - S_1)^2 .

If S is the sum, P the product and R the sum of reciprocals of n terms of a G.P., then prove that P^2 = (S/R)^n .

If S_1, S_2, S_3 and S_4 are the solubilities of AgCI in water, in 0.01 M CaCI_2 , in 0.01M NaCl and in 0.05M AgNO_3 respectively at a certain temperature, the correct order of solubilities is

If velocities of 3 molecules are 5 m/s, 6m/s and 7 m/s respectively, then their mean square velocity in m^2/s^2 is

If in a DeltaABC , right angled at B, s - a = 3, s - c = 2, then the values of a and c respectively are

This question has statement 1 and statement 2 . Of the four choice given after the Statement , choose the one that best describe the two Statement . If the spring S_(1) and S_(2) of force constant k_(1) and k_(2) respectively , are streached by the same force , it is found that more work is done on spring S_(1) then on spring S_(2) Statement -1: If statement by the same answer work done on S_(1) work on S_(1) is more then S_(2) Statement - 2 : k_(1) ltk_(2)

Two satellites S1 and S2 revolve round a planet in coplanar circular orbits in the same sense. TI1eir periods of revolution are 2 hours and 16 hours respectively. If the radius of the orbit of S_1 is 10^4 , then the radius of the orbit of S_2 is