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 the equation a x^2+b x+c=0,a ,b ,c , in R have none-real roots, then a. c(a-b+c)>0 b. c(a+b+c)>0 c. c(4a-2b+c)>0 d. none of these

If alpha,beta are the roots of the equation a x^2+b x+c=0, then the value of aalpha^2+c//aalpha+b+(abeta^2+c)//(abeta+b) is (b(b^2-2a c))/(4a) b. (b^2-4a c)/(2a) c. (b(b^2-2a c))/(a^2c) d. none of these

If a,b,c,d be four consecutive coefficients in the binomial expansion of (1+x)^(n) , then value of the expression (((b)/(b+c))^(2)-(ac)/((a+b)(c+d))) (where x gt 0 and n in N ) is

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

If (x^2+p x+1) is a factor of (a x^3+b x+c),t h e n a. a^2+c^2=-a b b. a^2-c^2=-a b c. a^2-c^2=a b d. none of these

If a , b and c are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

If z(1+a)=b+i ca n da^2+b^2+c^2=1, then [(1+i z)//(1-i z)= A. (a+i b)/(1+c) B. (b-i c)/(1+a) C. (a+i c)/(1+b) D. none of these

The area of a parallelogram formed by the lines a x+-b x+-c=0 is (a) (c^2)/((a b)) (b) (s c^2)/((a b)) (c) (c^2)/(2a b) (d) none of these

C F is the internal bisector of angle C of A B C , then C F is equal to (2a b)/(a+b)cosC/2 (b) (a+b)/(2a b)cosC/2 (c) (b sinA)/(sin(B+C/2)) (d) none of these

If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmetic means between a ,b ,a n db ,c , then the value of a/x+c/y is 1 b. 2 c. 1//2 d. none of these