In triangle `A B C ,` if `r_1=2r_2=3r_2,` then `a : b` is equal to `5/4` (b) `4/5` (c) `7/4` (d) `4/7`

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

Let D be the middle point of the side B C of a triangle A B Cdot If the triangle A D C is equilateral, then a^2: b^2: c^2 is equal to 1:4:3 (b) 4:1:3 (c) 4:3:1 (d) 3:4:1

In triangle A B C , if sinAcosB=1/4 and 3t a n A=t a n B ,t h e ncot^2A is equal to (a)2 (b) 3 (c) 4 (d) 5.

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

If in triangle A B C ,sumsinA/2=6/5a n dsumI I_1=9 (where I_1,I_2a n dI_3 are excenters and I is incenter, then circumradius R is equal to (15)/8 (b) (15)/4 (c) (15)/2 (d) 4/(12)

If in a triangle ABC , a=5,b=4 ,A = (pi)/( 2) +B then C

With usual notations, in triangle A B C ,acos(B-C)+bcos(C-A)+c"cos"(A-B) is equal to(a) (a b c)/R^2 (b) (a b c)/(4R^2) (c) (4a b c)/(R^2) (d) (a b c)/(2R^2)

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to 3/7 (b) 2/7 (c) 5/7 (d) 3/5

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

In triangle ABC, if A-B=120^@ and R=8r, where R and r have their usual meanings, then cos C equal (a) 3/4 (b) 2/3 (c) 5/6 (d) 7/8