`(7-r)(6-r)=6` , find the value of r.

If .^(6)P_(r): .^(6)P_(5) = 1:2 , find the value of r.

If .^(10)P_(r) =5040 , find the value of r

If r is positive real number such that 4sqrt(r)-(1)/(4sqrt(r))= 4, then find the value of 6sqrt(r)+(1)/(6sqrt(r)).

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 a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))

Potential energy in a field is given by U=-A/(r^6)+B/(r^11) then find the value of r for equilibrium position.

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

If (r)/(3)=6 , what is the value of (4s)/(r) ?

If ""^10 P_r=5040 , find the value of r.

If "^10 P_r=5040 , find the value of r .