Sample QuestionsPART - 2 CH - 9 Straight Lines questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The line joining points $(1,0)$ and $(-2, \sqrt{3})$ makes an angle $\theta$ with $x$-axis, the value of $\tan \theta$ is :
- A
$\sqrt{3}$
- B
$-\sqrt{3}$
- C
$\frac{1}{\sqrt{3}}$
- ✓
$\frac{1}{-\sqrt{3}}$
Answer: D.
View full solution →The length of perpendicular drawn from origin $(0,0)$ to line $x \sec \theta+y \operatorname{cosec} \theta=a$ is given by :
- ✓
$a \sin \theta \cos \theta$
- B
$a \cos \theta \operatorname{cosec} \theta$
- C
$a \operatorname{cosec} \theta \sec \theta$
- D
$a$
Answer: A.
View full solution →If line passing through point $(4,3)$ and $(2, k)$ is perpendicular to the line $y=2 x+3$, then $k$ equals to :
Answer: C.
View full solution →The image of point $(3,8)$ in line $x+2 y-7=0$ is given by:
- A
$(-1,-4)$
- ✓
$(-3,-8)$
- C
$(1,-4)$
- D
$(3,8)$
Answer: B.
View full solution →Equation of line perpendicular to straight line $3 x-4 y$ $+7=0$ and passing through point $(1,-2)$ is given by :
- A
$4 x+3 y-2=0$
- ✓
$4 x+3 y+2=0$
- C
$4 x-3 y+2=0$
- D
$4 x-3 y-2=0$
Answer: B.
View full solution →The distance of point $\left(x_1, y_1\right)$ from line $a x+b y+c=$ 0 is given by
$d=\frac{a x_1+b y_1+c}{\sqrt{a^2+b^2}}$
View full solution →Equation of line passing through points ( $\left.x_1, y_1\right)$ and $\left(x_2\right.$, $\left.y_2\right): y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$
View full solution →Equation of line passing through point $\left(x_1, y_1\right)$ having slope $m$ is given by $y-y_1=m\left(x-x_1\right)$.
View full solution →Equation of line perpendicular to $x$-axis and at a distance $b$ unit from y-axis $x=b$ or $x=-b$.
View full solution →The equation of a line parallel to $x$-axis at a distance ' $a$ ' is either $x=a$ or $x=-a$.
View full solution →The equation of $x$-axis is. _____________
View full solution →The distance between lines $Ax + B y+ C _1=0$ and $A x$ $+ B y+ C _2=0$ is _____________
View full solution →If two lines are mutually perpendicular, then their slopes are _____________
If lines $l_1$ and $l_2$ are parallel then their slopes are _____________
View full solution →The angle made by line $l$ with positive $x$-axis is called _____________
View full solution →Write the equation of line perpendicular to line $-3 x+$ $2 y+4=0$.
View full solution →If one of the line in given lines is parallel to $x$-axis, then calculate the angle between the lines, which is made by the second lines with $x$-axis.
View full solution →Write the equation of line passing through point ( -4 , -3 ) and parallel to $x$-axis.
View full solution →Find the equation of line perpendicular to line $3 x-5 y$ $+7=0$ and passing through point $(1,5)$.
View full solution →Find the distance between parallel lines $2 x+3 y+4$ $=0$ and $2 x+3 y-2=0$.
View full solution →Prove that lines $7 x-5 y+20=0$ and $5 x+7 y+$ $19=0$ are mutually perpendicular to each other.
View full solution →Find the equation of a line passing through point of intersection of lines $2 x+y=5$ and $x-2 y=$ 0 which makes an angle $45^{\circ}$ with $x$-axis.
View full solution →Find the equation of straight lines which passes through point of intersection of lines $y-3 x+5$ $=0$ and $y-2 x+2=0$ and is at a distance of $7 / \sqrt{2}$ unit from origin.
View full solution →Find the distance of point $(1,2)$ from straight line $3 x+y+4=0$, when it is drawn parallel to line $3 x-4 y+8=0$.
View full solution →Find the equation of the straight line which meets the foot of perpendicular drawn from the origin to the lines $3 x-4 y=25$ and $3 x+5 y=17$.
View full solution →Prove that perpendiculars drawn from any point taken on line $7 x+4 y=3$ to the lines $3 x-4 y=$ 2 and $5 x-12 y=4$ are equal in length.
View full solution →Find the equation of lines passing through point $(0, a)$ on which the perpendicular drawn from the point $(2 a, 2 a)$ is of length $a$.
View full solution →| Part (A) | Part (B) |
| 1. The slope of line passing through points $(3,-5)$ and $(1,2)$ | (a) $x=2$ |
| 2. Equation of line parallel to $x$-axis and passing through point $(3,-5)$ | (b) $-\frac{7}{2}$ |
| 3. Equation of line parallel to $x$-axis and is at equal distance from lines $x=-2$ and $x=6$ | (c) $y=2 x+3$ |
| 4. Equation of line having slope 2 and which cuts $y$-intercept as 3 . | (d) $y=-5$ |
| 5. Equation of line passing through point $(6,2)$ having slope -3 | (e) $3 x+y-20=0$ |
| Part (A) | Part (B) |
| 1. The angle between the lines$2 x-y+3=0$ and $x+2 y+3=0$ | (a) $-\frac{7}{2}$ |
| 2. The image of point $(4,-13)$ in line $5 x+y+6=0$ | (b) $(-1,-14)$ |
| 3. Point at equal distance from lines $4 x+3 y-10-0$, $5 x-12 y+26=0$ and $7 x+24 y-50=0$ | (c) $90^{\circ}$ |
| 4. If slope of line passing through points $(2,5)$ and $(x, 3)$ is 2 , then the value of $x$ is | (d) $(0,0)$ |
| 5. The slope of line passing through points $(3,-5)$ and $(1,2)$ | (e) 1 |