The coordinates of two consecutive vertices `A` and ` B` of a regular hexagon `A B C D E F` are `(1,0)` and `(2,0),` respectively. The equation of the diagonal `C E` is (a)`sqrt(3)x+y=4` (b) `x+sqrt(3)y+4=0` (c)`x+sqrt(3)y=4` (d) none of these

The coordinates of two consecutive vertices A and B of a regular hexagon ABCDEF are (1,0) and (2,0) respectively.The equation of the diagonal CE is:

Given b=2,c=sqrt(3),/_A=30^(0), then inradius of o+ABC is (sqrt(3)-1)/(2) (b) (sqrt(3)+1)/(2) (c) (sqrt(3)-1)/(4) (d) none of these

The equations of the sides A B ,\ B C\ a n d\ C A\ of\ "Delta"A B C\ a r e\ y-x=2,\ x+2y=1\ a n d\ 3x+y+5=0 respectively. The equation of the altitude through B is x-3y+1=0 b. x-3y+4=0 c. 3x-y+2=0 d. none of these

If y=|cos x|+|sin x|, then (dy)/(dx)atx=(2 pi)/(3) is (1-sqrt(3))/(2)(b)0(c)(1)/(2)(sqrt(3)-1) (d) none of these

The value of lim_(x rarr2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2) is (1)/(8sqrt(3))(b)(1)/(4sqrt(3)) (c) 0 (d) none of these

If sin x+sin y=sqrt(3)(cos y-cos x), then sin3x+sin3y=(a)2sin3x( b) 0(c)1(d) none of these

The distance of (0,0) from 2x-3y+5=0 measured parallel to the line 3x-2y=1=0 is (5)/(sqrt(13)) b.(4)/(sqrt(13)) c.sqrt(13) d.none of these

The length of perpendicular from the poit (1,-1,2) on the line (x+1)/2=(2-y)/3=(z+2)/4 is (A) 0 (B) sqrt(6) (C) sqrt(21) (D) none of these

Given that (1+sqrt(1+x))tan y=1+sqrt(1-x) Then sin4y is equal to (a)4x(b)2x(c)x(d) none of these

A circle C of radius 1 is inscribed in an equilateral triangle PQR . The points of contact of C with the sides PQ, QR, RP and D, E, F respectively. The line PQ is given by the equation sqrt(3) +y-6=0 and the point D is ((sqrt(3))/(2), 3/2) . Equation of the sides QR, RP are : (A) y=2/sqrt(3) x + 1, y = 2/sqrt(3) x -1 (B) y= 1/sqrt(3) x, y=0 (C) y= sqrt(3)/2 x + 1, y = sqrt(3)/2 x-1 (D) y=sqrt(3)x, y=0