Intercept of a Straight Line

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

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

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

Q. Let the line $\frac{x}{a}+\frac{y}{b}=1$ where $ab>0,$ passes through $P(\alpha ,\beta ),$ where $\alpha \beta >0.$ If the area formed by the line and the coordinate axes is $S,$ then the least value of $S$ is

1. $\alpha \beta$
2. $4\alpha \beta$
3. $2\alpha \beta$
4. $\frac{\alpha \beta }{2}$

Q. If $a,c,b$ are in G.P. and the area formed by the coordinate axes and the line $ax+by+c=0$ is $A\text{sq. units},$ then the value of $4A$ is

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 equation of the straight line which passes through the point $P(-4,3)$ such that the portion of it between the $x$-axis and $y$-axis is divided by the point $P$ in the ratio $1:2$ respectively, is

1. $\frac{x}{6}-\frac{y}{9}=1$
2. $\frac{x}{9}-\frac{y}{6}=1$
3. $\frac{y}{9}-\frac{x}{6}=1$
4. $\frac{y}{9}+\frac{x}{6}=1$

Q.

Find the equation of the straight line passing through the point of intersection of $2x+y-1=0$ and $x+3y-2=0$ and making with the coordinate axes a triangle of area $\frac{3}{8}$ sq. units.

Q.

The equation of the plane which is parallel to y-axis and cuts off intercepts of length 2 and 3 from x-axis and z-axis is

1. 

2. 

3. 

4. 

Q. Find the equation of the line which is passing through the point $(–4,3)$ with slope $\frac{1}{2}.$

Q.

Find the equation of a line passing through the point $\left(2,4\right)$ and intersecting the line $2x+3y+6=0$ on the $X-axis$.

Q. If the $X-$coordinate of a point ${}^{\prime }{P}^{\prime }$ on the segment joining $Q(2,2,1)\text{and}R(5,1,-2)$ is $4,$ then $Z-$ coordinate is:

1. $-1$
2. $0$
3. $1$
4. $2$

Q. True or false : If complex numbers $Z_1,Z_2\text{and}{Z}_3$ represent the vertices of an equilateral triangle such that $|Z_1|=|Z_2|=|Z_3|$, then $Z_1+Z_2+Z_3=0$.

Q. The equation of the plane through $(1,2,-3)$ and $(2,-2,1)$ and parallel to $X-$ axis is

1. $y-z+1=0$
2. $y-z-1=0$
3. $y+z-1=0$
4. $y+z+1=0$

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. 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.

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 number of arrangements of the letters of the word NAVA NAVA LAVANYAM which begin with N and end with M is

1. 
2. 
3. 
4. 

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. 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 straight line passing through the point of intersection of the straight lines
$x-3y+1=0$ and $2x+5y-9=0$
and having infinite slope and and at a distance 2 units from the origin has the equation

1. $x=2$
2. $3x+y-1=0$
3. $y=1$
4. None of these

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. In a right angled isosceles $△ABC$, where $A$ is at origin and side lengths $AB$ and $AC$ are equal to $a$ units. If point $B$ and $C$ are produced to $P$ and $Q$ respectively such that $BP\cdot CQ=A{B}^2$, then the locus of the midpoint of $PQ$ is

1. $\frac{1}{x}+\frac{1}{y}=\frac{4}{a}$
2. $\frac{1}{x}+\frac{1}{y}=\frac{1}{2a}$
3. $\frac{1}{x}+\frac{1}{y}=\frac{1}{a}$
4. $\frac{1}{x}+\frac{1}{y}=\frac{2}{a}$

Q. If area enclosed by the simultaneous inequations $x-2y^2\ge 0$ and $1-x-\left|y\right|\ge 0$ is $A$ sq. units, then the value of $12A$ is

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. Find the equation of a line having the angle of inclination ${45}^{\circ }$ and $y-$ intercept $2$

Q. The two lines $x=ay+b,z=cy+d$ and $x=a{}^{\prime }y+b{}^{\prime },z=c{}^{\prime }y+d{}^{\prime }$ are perpendicular to each other if

1. $aa{}^{\prime }+cc{}^{\prime }=-1$
2. $aa{}^{\prime }+cc{}^{\prime }=1$
3. $\frac{a}{a{}^{\prime }}+\frac{c}{c{}^{\prime }}=1$
4. $\frac{a}{a{}^{\prime }}+\frac{c}{c{}^{\prime }}=-1$

Q. At what point, the slope of the curve $\text{y}=-{\text{x}}^3+3{\text{x}}^2+9\text{x}-27$ is maximum? Also find the maximum slope

Q.

Find the equation of the plane through the intersection of the planes $\overrightarrow{r}.(\hat{i}+3\hat{j})-6=0$ and $\overrightarrow{r}.(3\hat{i}-\hat{j})-4\hat{k}=0$, whose perpendicular distance from origin is unity.

Q.

The equation of the line joining origin to the points of intersection of the curve $x^2+y^2=a^2$ and $x^2+y^2-ax-ay=0$ is

1. 

2. 

3. 

4. 

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. $5x+9y-51=0$