If in the expansion of `(1+x)^n ,a ,b ,c` are three consecutive coefficients, then `n=` `(a c+a b+b c)/(b^2+a c)` b. `(2a c+a b+b c)/(b^2-a c)` c. `(a b+a c)/(b^2-a c)` 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))

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

During the transformation of ._(c )X^(a) to ._(d)Y^(b) the number of beta -particles emitted are a. d + ((a - b)/(2)) - c b. (a - b)/(c ) c. d + ((a - b)/(2)) + c d. 2c - d + a = b

If a, b, c are real and x^3-3b^2x+2c^3 is divisible by x -a and x - b, then (a) a =-b=-c (c) a = b = c or a =-2b-_ 2c (b) a = 2b = 2c (d) none of these

If a,b,c gt 0, then (a )/(2a + b +c ) = (b)/(a + 2b +c)= (c )/(a +b + 2c) = ?

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 .

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)

Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a c, b c,c^2):}|