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`

The value of |[1, 1 ,1],[\ ^n C_1,\ ^(n+2)C_1,\ ^(n+4)C_1],[\ ^n C_2,\ ^(n+2)C_2,\ ^(n+4)C_2]| is (a) 2 (b) 4 (c) 8 (d) n^2

The value of determinant |[ ^n C_(r-1), ^n C_r, (r+1)^(n+2)C_(r+1)],[ ^n C_r, ^n C_(r+1),(r+2)^(n+2)C_(r+2)],[ ^n C_(r+1), ^n C_(r+2), (r+3)^(n+2)C_(r+3)]| is n^2+n-2 b. 0 c. ^n+3C_(r+3) d. ^n C_(r-1)+^n C_r+^n C_(r+1)

Let P(n):2^n a. 1 b. 2 c. 3 d. 4

If l n(a+c),l n(a-c) and l n(a-2b+c) are in A.P., then (a) a ,b ,c are in A.P. (b) a^2,b^2, c^2, are in A.P. (c) a ,b ,c are in G.P. (d) a ,b ,c are in H.P.

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:

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a/c+c/a

If p+q=1, then show that sum_(r=0)^n r^2^n C_rp^r q^(n-r)=n p q+n^2p^2dot

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

If the n^(t h) term of an A.P. is 2n+1 , then the sum of first n terms of the A.P. is n(n-2) (b) n(n+2) (c) n(n+1) (d) n(n-1)

If a 1 , a 2 , a 3 , , a 2 n + 1 are in A.P., then a 2 n + 1 − a 1 a 2 n + 1 + a 1 + a 2 n − a 2 a 2 n + a 2 + + a n + 2 − a n a n + 2 + a n is equal to a. n ( n + 1 ) 2 × a 2 − a 1 a n + 1 b. n ( n + 1 ) 2 c. ( n + 1 ) ( a 2 − a 1 ) d. none of these