Intercept of a Straight Line

Q. Match $\text{List I}$ with the $\text{List II}$ and select the correct answer using the code given below the lists :

Let the line $L:ax+by+c=0$ intersect $x-$axis at $A$ and $y-$axis at $B.$ Let $O$ be the origin.

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(I)}& \text{If}a,b,c\text{are in G.P. with common ratio as}2,\text{then area of}\Delta AOB\text{is}& \text{(P)}& 6\\ \text{(II)}& \text{If}a=1,b=1,c=2\text{and circumradius of}\Delta AOB\text{is}\sqrt{p},p>0\text{, then the value of}3p\text{is}& \text{(Q)}& 4\\ \text{(III)}& \text{If}a=b=c=1\text{and reflection of}O\text{along the line}L\text{is}(\alpha ,\beta ),\text{then}|\alpha +\beta |\text{is}& \text{(R)}& 2\\ \text{(IV)}& \text{If}a=b=1,c=\sqrt{2}\text{and}d\text{is the shortest distance of line}L\text{from}O\text{, then 2}d\text{is}& \text{(S)}& 3\\ & & \text{(T)}& 1\end{array}$

Which of the following is CORRECT combination?

1. $\text{(I)}\to \left(R\right);\text{(II)}\to \left(S\right);\text{(III)}\to \left(Q\right);\text{(IV)}\to \left(P\right)$
2. $\text{(I)}\to \left(Q\right);\text{(II)}\to \left(T\right);\text{(III)}\to \left(P\right)\text{(IV)}\to \left(R\right)$
3. $\text{(I)}\to \left(Q\right);\text{(II)}\to \left(T\right);\text{(III)}\to \left(S\right);\text{(IV)}\to \left(R\right)$
4. $\text{(I)}\to \left(Q\right);\text{(II)}\to \left(P\right);\text{(III)}\to \left(R\right);\text{(IV)}\to \left(R\right)$

Q.

ax + by = ab is the equation of a straight line which makes intercepts a & b on x & y axis respectively. State True or False.

1. True

2. False

Q. The area of triangle formed by the lines x = 0, y = 0 and $\frac{x}{a}+\frac{y}{b}=1$, a and b are positive , is

1. 
2. 
3. 
4. 

Q. Slope of a line which cuts intercepts of equal lengths on the axes is

1. $2$
2. $0$
3. $-1$
4. $\sqrt{3}$

Q. The equation of the straight line which passes through the point (1, - 2) and cuts off equal intercepts from axes, is

1. x+y=1
2. x-y=1
3. x+y+1=0
4. x-y-2=0

Q. A straight line through origin $O$ meets the lines $3y=10-4x$ and $8x+6y+5=0$ at points $A$ and $B$ respectively. Then $O$ divides the segment $AB$ in the ratio:

1. $4:1$
2. $3:4$
3. $2:3$
4. $1:2$

Q. The area enclosed by $2|x|+3|y|\le 6$ is

1. $3$ sq. units
2. $4$ sq. units
3. $12$ sq. units
4. $24$ sq. units

Q. If a line parallel to $2x+6y-7=0$ makes an intercept of $10$ units between the coordinate axes and $y-$ intercept is $\pm \sqrt{k}$, then the value of $k$ is

Q. The equation of line passing through $(3,4)$ and parallel to $5x+9y+12=0$ is

1. $5x-9y+51=0$
2. $5x-9y-51=0$
3. $5x+9y+51=0$
4. $5x+9y-51=0$

Q. The area (in sq. units) of the triangle formed by the coordinate axes and the line $x\left(\tan \theta \right)+y\left(\cot \theta \right)=4$ where $\theta \in (0,\frac{\pi }{2}),$ is