Find the co-ordinates of the points on `bar(AB)` which divide it into 'n' congruent parts if A is `(1, 2) and B` is `(n+1, n+2)`. [Ans.: `P(r + 1, r + 2); r = 1, 2,..... (n - 1)]`

The greatest positive integer which divides n (n+1)(n+2)….. (n+r-1), AA n in N is

The greatest positive integer which divides n(n+1)(n+2)......(n+r-1),AA n in N is

Given that C(n, r) : C(n,r + 1) = 1 : 2 and C(n,r + 1) : C(n,r + 2) = 2 : 3 . What is P(n, r) : C(n, r) equal to ?

If sum _(r =1) ^(n ) T _(r) = (n +1) ( n +2) ( n +3) then find sum _( r =1) ^(n) (1)/(T _(r))

Given that P(n, r)=n(n-1)(n-2) ….to r factors If P(n, 4) = 20 P(n, 2), find n

Prove that sum_(r = 1)^(n+1) (2^(r +1) C_(r - 1) )/(r (r + 1)) = (3^(n+2) - 2n - 5)/((n+1)(n+2))

Prove that sum_(r = 1)^(n+1) (2^(r +1) C_(r - 1) )/(r (r + 1)) = (3^(n+2) - 2n - 5)/((n+1)(n+2))

There are two long co-axial solenoids of same length l. The inner and other coils have redii r_(1) and r_(2) and number of turns per unti length n_(1) and n_(2) respectively .The reatio of mutual inductance to the self - inductance of the inner- coil is : (A) n_(1)/n_(2) (B) n_(2)/n_(1).r_(1)/r_(2) (C) n_(2)/n_1.r_2^2/r_1^2 (D) n_(2)/n_(1)