Homogenization

Q.

The lines joining the points of intersection of line x + y = 1 and curve $x^2+y^2-2y+\lambda =0$ to the origin are perpendicular, then the value of $\lambda$ will be

1. 1/2

2. -1/2

3. 

4. 0

Q.

The equation of pair of straight lines joining the point of intersection of the curve $x^2+y^2=4$ and y - x = 2 to the origin, is

1. 

2. 

3. 

4. 

Q. Factorize the equation $50a^3-2a$

1. $2a(a+1)(1-a)$
2. $2a(5a+1)(5a+6)$
3. $2a(5a+1)(5a-1)$
4. $2a(a+1)(a+1)$