If `a ,b ,c in R^+, t h e n(b c)/(b+c)+(a c)/(a+c)+(a b)/(a+b)` is always (a)`lt=1/2(a+b+c)` (b)`geq1/3sqrt(a b c)` (c)`lt=1/3(a+b+c)` (d)`geq1/2sqrt(a b c)`

If a ,b ,c in R^+t h e n(a+b+c)(1/a+1/b+1/c) is always (a) geq12 (b) geq9 (c) lt=12 (d)none of these

If a b c = 0, then ({(x^a)^b}^c)/({(x^b)^c}^a) = (a)3 (b) 0 (c) -1 (d) 1

If a+b+c=0 , then (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a b)=?\ (a)0 (b) 1 (c) -1 (d) 3

If a ,\ b ,\ c are positive real numbers, then sqrt(a^(-1)b)\ xx\ sqrt(b^(-1)\ c)\ xx\ sqrt(c^(-1)a) is equal to: (a)\ 1 (b) a b c (c) sqrt(a b c) (d) 1/(a b c)

If a ,b ,a n dc are in H.P., then th value of ((a c+a b-b c)(a b+b c-a c))/((a b c)^2) is ((a+c)(3a-c))/(4a^2c^2) b. 2/(b c)-1/(b^2) c. 2/(b c)-1/(a^2) d. ((a-c)(3a+c))/(4a^2c^2)

If a ,b ,c are positive, then prove that a//(b+c)+b//(c+a)+c//(a+b)geq3//2.

In a triangle A B C , right angled at C ,t a n A+t a n B is equal to a. a+b b. (c^2)/(a b) c. (a^2)/(b c) d. (b^2)/(a c)

If a ,b ,c are in A.P., prove that the following are also in A.P. (i) 1/(b c),1/(c a),1/(a b), (ii) b+c ,c+a ,a+b (iii) a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) (iv) a^2(b+c),b^2(c+a),c^2(a+b) (v) 1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b))

If a >0,b >0 and c >0 prove that (1984, 2M) (a+b+c)(1/a+1/b+1/c)geq9

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