" (i) "4y^(2)+4sqrt(3)y+3=0

The lines represented by the equation x^2 + 2sqrt(3)xy + 3y^(2) -3x -3sqrt(3)y -4=0 , are

The lines represented by the equation x^2 + 2sqrt(3)xy + 3y^(2) -3x -3sqrt(3)y -4=0 , are

Equation of a circle of radius 2 and touching the circles x^(2)+y^(2)-4|x|=0 is x^(2)+y^(2)+2sqrt(3)y+2=0x^(2)+y^(2)+4sqrt(3)y+2=0x^(2)+y^(2)-4sqrt(3)y+8=0 none of these

An equilateral triangle whose two vertices are (-2, 0) and (2, 0) and which lies in the first and second quadrants only is circumscribed by a circle whose equation is : (A) sqrt(3)x^2 + sqrt(3)y^2 - 4x +4 sqrt(3)y = 0 (B) sqrt(3)x^2 + sqrt(3)y^2 - 4x - 4 sqrt(3)y = 0 (C) sqrt(3)x^2 + sqrt(3)y^2 - 4y + 4 sqrt(3)y = 0 (D) sqrt(3)x^2 + sqrt(3)y^2 - 4y - 4 sqrt(3) = 0

An equilateral triangle whose two vertices are (-2, 0) and (2, 0) and which lies in the first and second quadrants only is circumscribed by a circle whose equation is : (B) sqrt(3)x^2 + sqrt(3)y^2 - 4x - 4 sqrt(3)y = 0 (C) sqrt(3)x^2 + sqrt(3)y^2 - 4y + 4 sqrt(3)y = 0 (D) sqrt(3)x^2 + sqrt(3)y^2 - 4y - 4 sqrt(3) = 0

The equation of a line whose inclination is (5pi)/(6) and which cuts off an intercept of 4 units on negative direction of y-axis is (i) x+sqrt(3)y+4sqrt(3)=0 (ii) x-sqrt(3)y+4sqrt(3)=0 (iii) x+sqrt(3)y-4sqrt(3)=0 (iv) x-sqrt(3)y-4sqrt(3)=0

Solve the following pair of linear equations by the substitution method. (i) x+y=14 ;x- y=4 (ii) s-t=3; s/3+t/2=6 (iii) 3x-y=3;9x-3y=9 (iv) 0. 2 x+0. 3 y=1. 3 ;0. 4 x+0. 5 y=2. 3 (v) sqrt(2)x+sqrt(3)y=0;sqrt(3)x-sqrt(8)y=0 (vi) 3x/2-5y/2=-2;x/3+y/2=13/6

Solve the following pair of linear equations by the substitution method. (i) x+y=14 ;x- y=4 (ii) s-t=3; s/3+t/2=6 (iii) 3x-y=3;9x-3y=9 (iv) 0. 2 x+0. 3 y=1. 3 ;0. 4 x+0. 5 y=2. 3 (v) sqrt(2)x+sqrt(3)y=0;sqrt(3)x-sqrt(8)y=0 (vi)3x/2-5y/2=-2;x/3+y/2=13/6

If cosxdy/dx-y sin x=6x, (0ltxltx/2)and y(pi/3)=0 , then y(pi/6) is equal to (a) pi^(2) /(2sqrt 3) (b) -pi^(2) /(2sqrt 3) (c) -pi^(2) /(4sqrt 3) (d) (c) -pi^(2) /2