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 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 y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these

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

If a ,b ,c ,d in R^+ and a ,b ,c,d are in H.P., then (a) a+d > b+c (b) a+b > c+d (c) a+c > b+d (d)none of these

If a^2+b^2=1 t h e n (1+b+i a)/(1+b-i a)= 1 b. 2 c. b+i a d. a+i b

("lim")_(xvec0)(x^asin^b x)/(sin(x^c)) , where a , b , c in R ~{0},exists and has non-zero value. Then, (a) a+c (b) 1 (c) -1 (d) none of these

If cos^2A+cos^2B+cos^2C=1,t h e n A B C is (a)equilateral (b) isosceles (c)right angles (d) none of these

If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,t h e nf(2x)-f(x) is divisible by (a) a (b) b (c) c ,d ,e (d) none of these

If the lines a x+y+1=0,x+b y+1=0, and x+y+c=0(a , b , c being distinct and different from 1) are concurrent, then (1/(1-a))+(1/(1-b))+(1/(1-c))= (a)0 (b) 1 (c) 1/((a+b+c)) (d) none of these

In A B C , if the orthocentre is (0,0) and the circumcenter is (1,2), then centroid of A B C) is (a) (1/2,2/3) (b) (1/3,2/3) (c) (2/3,1) (d) none of these