The ratio in which the line segment joining points `A(a_1,\ b_1)` and `B(a_2,\ b_2)` is divided by y-axis is ` a_1: a_2` (b) `a_1: a_2` (c) `b_1: b_2` (d) `-b_1: b_2`

If the points (a_1, b_1),\ \ (a_2, b_2) and (a_1+a_2,\ b_1+b_2) are collinear, show that a_1b_2=a_2b_1 .

If the equation of the locus of a point equidistant from the points (a_1,b_1) and (a_2,b_2) is (a_1-a_2)x+(b_2+b_2)y+c=0 , then the value of C is

If the tangent and normal to xy=c^2 at a given point on it cut off intercepts a_1, a_2 on one axis and b_1, b_2 on the other axis, then a_1 a_2 + b_1 b_2 = (A) -1 (B) 1 (C) 0 (D) a_1 a_2 b_1 b_2

In direct proportion a_1/b_1 = a_2/b_2

If the line a_1 x + b_1 y+ c_1 = 0 and a_2 x + b_2 y + c_2 = 0 cut the coordinate axes in concyclic points, prove that : a_1 a_2 = b_1 b_2 .

The number of ways in which ten candidates A_1, A_2, ...., A_(10) can be ranked so that A_1 is always above A_2 is

For two linear equations , a_1x + b_1y + c_1=0 and a_2x + b_2y + c_2 = 0 , the condition (a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2) is for.

The capacitance of the capacitors of plate areas A_1 and A_2(A_1 lt A_2) at a distance d is

Let bi gt 1 for i = 1, 2, ...., 101 . Suppose log_e b_1, log_e b_2, ...., log_e b_101 are in Arithmetic Progression (A.P.) with the common difference log_e 2 . Suppose a_1, a_2, ....., a_101 are in A.P. such that a_1 = b_1 and a_51 = b_51 . If t = b_1 + b_2 + .... + b_51 and s = a_1 + a_2 + .... + a_51 , then .

Find the coefficient of x in the determinant |((1+x)^(a_1 b_1),(1+x)^(a_1 b_2),(1+x)^(a_1 b_3)),((1+x)^(a_2 b_2),(1+x)^(a_2 b_2),(1+x)^(a_2 b_3)),((1+x)^(a_3 b_3),(1+x)^(a_3 b_2),(1+x)^(a_3 b_3))|=0.