If `p ,q ,r` are in A.P. then value of determinant `|a^2+2^(n+1)+2p b^2+2^(n+2)+3q c^2+p2^n+p2^(n+1)2q a^2+2^n+p b^2+2^(n+1)c^2-r|` is 0 (b) Independent from `a , b , c` `a^2b^2c^2-2^n` (d) Independent from `n`

If p ,q ,r are in A.P. then value of determinant |a^2+2^(n+1)+2p b^2+2^(n+2)+3q c^2+p2^n+p2^(n+1)2q a^2+2^n+p b^2+ 2^(n+1)c^2-r| is a) 0 (b) Independent from a , b , c c) a^2b^2c^2-2^n (d) Independent from n

If p ,q ,r are in A.P. then value of determinant |[a^2+2^(n+1)+2p, b^2+2^(n+2)+3q, c^2+p], [2^n+p, 2^(n+1), 2q], [a^2+2^n+p, b^2+2^(n+1), c^2-r]| is (a) 0 (b) Independent from a , b , c (c) a^2b^2c^2-2^n (d) Independent from n

If p ,q ,r are in A.P. then value of determinant |[a^2+2^(n+1)+2p, b^2+2^(n+2)+3q, c^2+p], [2^n+p, 2^(n+1), 2q], [a^2+2^n+p, b^2+2^(n+1), c^2-r]| is (a) 0 (b) Independent from a , b , c (c) a^2b^2c^2-2^n (d) Independent from n

If p ,q ,r are in A.P. then value of determinant |[a^2+2^(n+1)+2p, b^2+2^(n+2)+3q, c^2+p], [2^n+p, 2^(n+1), 2q], [a^2+2^n+p, b^2+2^(n+1), c^2-r]| is (a) 0 (b) Independent from a , b , c (c) a^2b^2c^2-2^n (d) Independent from n

If p,q and r are in AP the value of determinant |{:(a^(2)+2^(n+1)+2p,b^(2)+2^(n+2)+2q,c^(2)+p),(2^(n)+p,2^(n+1)+q,2q),(a^(2)+2^(n)+p,b^(2)+2^(n+1)+q,c^(2)-r):}| is

If p,q and r are in AP the value of determinant |{:(a^(2)+2^(n+1)+2p,b^(2)+2^(n+2)+2q,c^(2)+p),(2^(n)+p,2^(n+1)+q,2q),(a^(2)+2^(n)+p,b^(2)+2^(n+1)+q,c^(2)-r):}| is

If p+q=1, then value of sum_(r=0)^(n)r^(2)C(n,r)p^(r)q^(n-r) is (1)npq(2)np(1+q) (3) n^(2)p^(2)+npq(4)np^(2)+npq

If p/a + q/b + r/c=1 and a/p + b/q + c/r=0 , then the value of p^(2)/a^(2) + q^(2)/b^(2) + r^(2)/c^(2) is: