If $(\lambda^2, \lambda+1), \lambda \in \mathbb{Z}$ belongs to the region between the lines $x+2y-5=0$ and $3x-y+1=0$ which includes the origin,then the possible number of such points is

Let $R$ be the interior region between the lines $3x-y+1=0$ and $x+2y-5=0$ containing the origin. The set of all values of $a$,for which the points $(a^2, a+1)$ lie in $R$,is :

If the length of the perpendicular from the origin to the line $x/a + y/b = 1$ is $p$,then which of the following is true for $a^2, 4p^2, b^2$?

If $P(\alpha, \beta)$ is a point on the line $3x + y = 0$ such that the point $P$ and the point $Q(1, 1)$ lie on opposite sides of the line $3x - 4y - 8 = 0$,then:

$A$ line $L_1$ passing through the point of intersection of the lines $x-2y+3=0$ and $2x-y=0$ is parallel to the line $L_2$. If $L_2$ passes through the origin and also through the point of intersection of the lines $3x-y+2=0$ and $x-3y-2=0$,then the distance between the lines $L_1$ and $L_2$ is

If a point $(\alpha, \beta)$ on the line $3x + y = 0$ and the point $(3, 4)$ lie on opposite sides of the line $3x - 4y - 8 = 0$,then which of the following is correct?