Class 11 Straight Lines Exemplar 9 1 Exemplar Solutions

Q1

If the line $\frac{x}{a} + \frac{y}{b} = 1$ passes through the points $(2, -3)$ and $(4, -5)$, then $(a, b)$ is

(a) $(1, 1)$
(b) $(-1, 1)$
(c) $(1, -1)$
(d) $(-1, -1)$

Q2

The distance of the point $(2, 3)$ from the line $2x - 3y + 9 = 0$ measured along the line $x - y + 1 = 0$ is

(a) $\sqrt{2}$
(b) $2\sqrt{2}$
(c) $3\sqrt{2}$
(d) $4\sqrt{2}$

Q3

A line passes through $P(1, 2)$ such that its intercept between the axes is bisected at $P$. The equation of the line is

(a) $x + 2y = 5$
(b) $x - y + 1 = 0$
(c) $2x + y - 4 = 0$
(d) $2x - y = 0$

Q4

The inclination of the line $x - y + 3 = 0$ with the positive direction of the $x$-axis is

(a) $45^\circ$
(b) $135^\circ$
(c) $60^\circ$
(d) $30^\circ$

Q5

If the lines $3x + 4y - 9 = 0$ and $6x + 8y + 15 = 0$ are tangents to the same circle, then the radius of the circle is

(a) $\frac{33}{10}$
(b) $\frac{33}{20}$
(c) $\frac{33}{40}$
(d) $\frac{11}{20}$

Q6

If $p$ is the length of perpendicular from the origin on the line $\frac{x}{a} + \frac{y}{b} = 1$ and $a^2, p^2, b^2$ are in A.P., then $a^2 + b^2$ is equal to

(a) $ab$
(b) $2ab$
(c) $a^2 b^2$
(d) none of these

Q7

The equations of the lines passing through $(1, 2)$ and making an angle of $45^\circ$ with the line $2x + 3y = 10$ are

(a) $5x - y = 3$ and $x + 5y = 11$
(b) $5x + y = 7$ and $x - 5y = -9$
(c) $x - 5y = 3$ and $5x - y = 11$
(d) none of these

Q8

The image of the point $(3, 8)$ with respect to the line $x + 3y = 7$ assuming the line to be a plane mirror is

(a) $(-1, -4)$
(b) $(-1, 4)$
(c) $(1, -4)$
(d) $(2, -5)$

Q9

The acute angle between the lines $y = (2 - \sqrt{3})x + 5$ and $y = (2 + \sqrt{3})x - 7$ is

(a) $30^\circ$
(b) $45^\circ$
(c) $60^\circ$
(d) $90^\circ$

Q10

The coordinates of the foot of the perpendicular drawn from the point $(2, 3)$ on the line $3x - y + 4 = 0$ is

(a) $\left(-\frac{1}{10}, \frac{37}{10}\right)$
(b) $\left(\frac{1}{10}, \frac{37}{10}\right)$
(c) $\left(-\frac{1}{10}, -\frac{37}{10}\right)$
(d) $\left(\frac{2}{5}, \frac{16}{5}\right)$

Q11

If the lines $2x + y - 3 = 0$, $5x + ky - 3 = 0$ and $3x - y - 2 = 0$ are concurrent, then the value of $k$ is

(a) $-2$
(b) $3$
(c) $-1$
(d) $2$

Q12

The equation of the line passing through $(-3, 5)$ and perpendicular to the line joining $(2, 5)$ and $(-3, 6)$ is

(a) $5x - y + 20 = 0$
(b) $5x + y + 10 = 0$
(c) $x - 5y + 28 = 0$
(d) $5x - y - 20 = 0$

Q13

The points $(a, 0)$, $(0, b)$ and $(1, 1)$ are collinear if

(a) $\frac{1}{a} + \frac{1}{b} = 1$
(b) $\frac{1}{a} - \frac{1}{b} = 1$
(c) $\frac{1}{a} + \frac{1}{b} = 0$
(d) $a + b = 1$

Q14

The distance between the parallel lines $9x + 6y - 7 = 0$ and $3x + 2y + 6 = 0$ is

(a) $\frac{19}{2\sqrt{13}}$
(b) $\frac{25}{3\sqrt{13}}$
(c) $\frac{25}{\sqrt{13}}$
(d) $\frac{5}{\sqrt{13}}$

Q15

The area of the triangle formed by the lines $y = 0$, $x = 0$ and $3x + 4y = 12$ is

(a) $6$ sq units
(b) $12$ sq units
(c) $24$ sq units
(d) $3$ sq units

Chapter 9 - Straight Lines

Overview

Objective Type Questions (MCQs)