Find r if `.^(5)P_(r )=2 .^(6)P_(r-1)`

Find r if .^(5)P_(r )= .^(6)P_(r-1)

Find r, if 5""^(4)P_(r)=6""^(5)P_(r-1)

Find r, if 5 xx ""^(4)P_(r) = 6 xx ""^(5)P_(r - 1) .

Find the value of r, if (i) .^(11)P_(r)=990 (ii) .^(8)P_(5)+5*.^(8)P_(4)=.^(9)P_(r)

If .^(9)P_(5)+5 .^(9)P_(4)=.^(n)P_(r) then n+r equals

Let a_(n) be the nth term of an A.P. If sum_(r=1)^(100) a_(2r) = alpha and sum_(r = 1)^(100) a_(2r-1) = beta , then the common difference of the A.P. is :

If^(12)P, = ^(11)P_(6)+6.^(11)P_(5), then r is equal to

Let r_(1),r_(2),r_(3), . . .,r_(n) be the position vectors of points P_(1),P_(2),P_(3), . . .,P_(n) relative to an origin O. show that if then a similar equation will also hold good with respect to any other origin O'. If a_(1)+a_(2)+a_(3)+ . . .+a_(n)=0 .

If .^(n+1)C_(r+1):^(n)C_(r):^(n-1)C_(r-1)=11:6:3 , find the values of n and r.

If t_(1)=1,t_(r )-t_( r-1)=2^(r-1),r ge 2 , find sum_(r=1)^(n)t_(r ) .