(a) 2:1 (6) 1:2 (c) 1:1 af (x + y) : (x - y) = 4:1 21, 1 (x2 + y2) : (x2 - y2) = ? . (a) 25:9 (6) 16:1 (C) 8:1

If (2x + y + 2)/(5) = ( 3x - y + 1)/( 3 ) = ( 2 x + 2y + 1 )/(6) then

If sqrt(y)=4x, then (x^(2))/(y) is (a) 2 (b) (1)/(16) (c) (1)/(4) (d) 4

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

Solve : 8 ^(x+1) = 16 ^(y+2) and ( (1)/(2)) ^(3+x) = ((1)/(4))^(3y)

Tangent are drawn from two points (x_1, y_1) and (x_2, y_2) to xy = c^2 . The conic passing through the two points and through the four points of contact will be circle if (A) x_1 x_2 = y_1 y_2 (B) x_1 y_2 = x_2 y_1 (C) x_1 y_2 + x_2 y_1 = 4c^2 (D) x_1 x_1 + y_1 y_2 = 4c^2

If the image of the point (x_1, y_1) with respect to the mirror ax+by+c=0 be (x_2 , y_2) then. (a) (x_2-x_1)/a = (a x_1 + b y_1+ c)/(a^(2)+b^(2)) (b) (x_2-x_1)/a = (y_2 - y_1)/b (c) (x_2-x_1)/a = -2 ((a x_1 + b y_1+ c)/(a^(2)+b^(2))) (d) None of these

Consider the two curves C_1 ; y^2 = 4x , C_2 : x^2 + y^2 - 6x + 1 = 0 then :

The centres of the circles x ^(2) + y ^(2) =1, x ^(2) + y^(2)+ 6x - 2y =1 and x ^(2) + y^(2) -12 x + 4y =1 are