Let a,b,c,d be the foru cosecutive coefficients int eh binomial expansion `(1+x)^n` On the basis of above information answer the following question: ((bc+ad)(b-c))/(ac^2-b^2d)=` (A) `1/2` (B) 1 (C) -1 (D) 2

Let a,b,c,d be the foru cosecutive coefficients int eh binomial expansion (1+x)^n On the basis of above information answer the following question: a/(a+b), b/(b+c), c/(c+d) are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

Let a,b,c,d be the foru cosecutive coefficients int eh binomial expansion (1+x)^n On the basis of above information answer the following question: The value of n is (A) (2ac-b(a+c))/(b^2-ac) (B) (2ac+b(a+c))/(b^2-ac) (C) (2ac)/(a+c)-b (D) (b^2-ac)/(2ac+b(a+c)

If the four consecutive coefficients in any binomial expansion be a, b, c, d, then prove that (i) (a+b)/a , (b+c)/b , (c+d)/c are in H.P. (ii) (bc + ad) (b-c) = 2(ac^2 - b^2d)

If the four consecutive coefficients in any binomial expansion be a,b,c and d then (A) (a+b)/a,(b+c)/b,(c+d)/c are in H.P. (B) (bc+ad)(b-c)=2(ac^2-b^2d) (C) b/a,c/b,d/c are in A.P. (D) none of these

If a,b,c be the three consecutive coefficients in the expansion of a power oif (1+x), prove that the index power is ( 2ac+b(a+c)/(b^2-ac))

Comprehension 1 Let a^((log)_b x)=c w h e r e a , b , c & x are parameters. On the basis of above information, answer the following questions: If a=2 x=a^((log)_5 25)& c=sqrt(2) , then b is- a.2 b. 16 c. 12 d. 2

If n is a positive integer then ^nC_r+^nC_(r+1)=^(n+1)^C_(r+1) Also coefficient of x^r in the expansion of (1+x)^n=^nC_r. In an identity in x, coefficient of similar powers of x on the two sides re equal. On the basis of above information answer the following question: If n is a positive integer then ^nC_n+^(n+1)C_n+^(n+2)C_n+.....+^(n+k)C_n= (A) ^(n+k+1)C_(n+2) (B) ^(n+k+1)C_(n+1) (C) ^(n+k+1)C_k (D) ^(n+k+1)C_(n-2)

if a,b,c and d are the coefficient of four consecutive terms in the expansion of (1+x)^(n) then (a)/(a+b)+(C) /(c+d)=?

If a,b,c and d are any four consecutive coefficients in the expansion of (1 + x)^(n) , then prove that (i) (a) /(a+ b) + (c)/(b+c) = (2b)/(b+c) (ii) ((b)/(b+c))^(2) gt (ac)/((a + b)(c + d)), "if " x gt 0 .