`cosA+cosB+cosC` is equal to (A) `r/R` (B) `R/r` (C) 1` (D) `1+r/R`

In A B C ,(a b-r_1r_2)/(r_3),w h e r ea ,b ,r_1r_2, r_3, Ra n dr have usual meanings, is equal to (A) R (B) 2R (C) r (D) none of these

If sum_(r=0)^(n-1)log_(2)((r+2)/(r+1)) =prod_(r=10)^(99)log_(r) (r+1), then 'n' is equal to (A) 4 (B) 3 (C) 5 (D) 6

If a /_\ ABC, if r=r_2+r_3-r_1 and /_Agt pi/3 then the range of S/a is equal to (A) (1/2, 2) (B) (1/2,∞) (C) (1/2,3) (D) (3,∞)

In triangle A B C , if cosA+cosB+cosC=7/4, t h e n R/r is equal to 3/4 (b) 4/3 (c) 2/3 (d) 3/2

If in a triangle A B C ,(1+cosA)/a+(1+cosB)/b+(1+cosC)/c =(k^2(1+cosA)(1+cosB)(1+cosC)/(a b c) , then k is equal to (a) 1/(2sqrt(2)R) (b) 2R (c) 1/R (d) none of these

In A B C ,cotA/2+cotB/2+cotC/2 is equal to Delta/(r^2) (b) ((a+b+c)^2)/(a b c)2R (c) Delta/r (d) Delta/(R r)

In any triangle, the minimum value of r_1r_2r_3//r^3 is equal to (a) 1 (b) 9 (c) 27 (d) none of these

A B C is an equilateral triangle of side 4c mdot If R , r, a n d,h are the circumradius, inradius, and altitude, respectively, then (R+r)/h is equal to (a) 4 (b) 2 (c) 1 (d) 3

In a triangle A B C ,(r_1+r_2)/(1+cosC) is equal to (2a b)/(c"Delta") (b) ((a+b))/(c"Delta") (a b c)/(2"Delta") (d) (a b c)/("Delta"^2)

In a A B C , S/R is equal to s in A+s in B+s in C (b) 4cosA/2cosB/2cosC/2 4s in A\ s in B\ s in C (d) ( s)/(a b c)