Find the value of `r` if (i) `16.rP_3=13.(r+1)P_3`

Find the value of r if (i) 16.PP_(3)=13.(r+1)P_(3)

Find the value of r if 5P_r = 6P_(r-1)

Find the value of r if P(5,r+1) = P(6,r)

Find the value of 'r' if ""^(5)P_(r )=""^(6)P_(r-1) .

Find the value of r if "^(n-1)P_r : ^nP_r = 2:3 and "^nC_r :^(n+1)C_r = 9:13 , then find n and r

(i) If ""^(15)P_(r)=2730, find the value of r. (ii) If ""^(10)P_(r)=5040, find the value of r.

If p = 4,q = -3 and r = 2, find the value of : p^(3)+q^(3)-r^(3)-3pqr

If p = -2, q = - 1 and r = 3, find the value of (i) p^(2) + q^(2) - r^(2) (ii) 2p^(2) - q^(2) + 3r^(2) (iii) p - q - r (iv) p^(3) + q^(3) + r^(3) + 3 pqr (v) 3p^(2) q + 5pq^(2) + 2 pqr (vi) p^(4) + q^(4) - r^(4)

In triangle RTK , P is a point on RK such that R-P-K. RP:PK=3:2, then find the value of A(triangle TRP):A(triangle TPK)