Relative Position of a Point with Respect to a Line

Q. The number of non-negative integral values of $b$ for which the origin and point $(1,1)$ lie on the same side of straight line $a^{2}x+aby+1=0,\forall a\in R-\left\{0\right\},$ is

1. $1$
2. $3$
3. $2$
4. $5$

Q. The position of the point (8, -9) with respect to the lines 2x+3y-4=0 and 6x+9y+8=0 is

1. Point lies on the same side of the lines
2. Point lies on the different sides of the line
3. Point lies on one of the line
4. None of these

Q. The position of the points $(2,3)$ and $(-4,5)$ with respect to the line $3x-4y=8$ is

1. on same side
2. on opposite side
3. lie on the line
4. one point on the line other outside of the line

Q. Let the lines $y-k_{1}x-\beta =0$ and $y-k_{2}x-\beta =0,(k_1\ne k_2),k_1,k_2\in R$ intersect at $P$ and the lines $x-p_{1}y-\alpha =0$ and $x-p_{2}y-\alpha =0,(p_1\ne p_2),p_1,p_2\in R$ intersect at $Q$. If the points $P$ and $Q$ always lies on or inside the triangle formed by the lines $2x-3y-6=0,3x-y+3=0$ and $3x+4y-12=0$, then

1. $\alpha \in [-1,3]$
2. $\alpha \in [-2,4]$
3. $\beta \in [-3,-2)$
4. $\beta \in [-2,3]$

Q. The position of the points $(2,3)$ and $(-4,5)$ with respect to the line $3x-4y=8$ is

1. on same side
2. on opposite side
3. lie on the line
4. one point on the line other outside of the line

Q. If the point $(\alpha ,{\alpha }^2)$ lies between $x+y-2=0$ and $4x+4y=3,$ then the range of $\alpha$ is

1. $(-2,-\frac{3}{2})\cup (\frac{1}{2},1)$
2. $(-2,-\frac{3}{2})\cup (\frac{1}{2},2)$
3. $(2,-\frac{3}{2})\cup (\frac{1}{2},1)$
4. $(-2,-\frac{1}{2})\cup (\frac{1}{2},1)$