JEE Main Straight Lines and Pair of Straight Lines Practice Questions With Solutions

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JEE Main Mathematics Straight Lines and Pair of Straight Lines Practice Questions

Question 1.

A variable line $L$ passes through the point $(3, 5)$ and intersects the positive coordinate axes at the points $A$ and $B$ . The minimum area of the triangle $OAB$ , where $O$ is the origin, is :

Question 2.

A ray of light coming from the point $P (1, 2)$ gets reflected from the point $Q$ on the $x$ -axis and then passes through the point $R (4, 3)$ . If the point $S (h, k)$ is such that $P Q R S$ is a parallelogram, then $h k^{2}$ is equal to:

Question 3.

If the line segment joining the points $(5, 2)$ and $(2, a)$ subtends an angle $\frac{π}{4}$ at the origin, then the absolute value of the product of all possible values of $a$ is :

Question 4.

The equations of two sides $AB$ and $AC$ of a triangle $ABC$ are $4 x + y = 14$ and $3 x - 2 y = 5$ , respectively. The point $(2, - \frac{4}{3})$ divides the third side $BC$ internally in the ratio $2 : 1$ , the equation of the side $BC$ is

x + 6 y + 6 = 0

x - 3 y - 6 = 0

x + 3 y + 2 = 0

x - 6 y - 10 = 0

Question 5.

If the locus of the point, whose distances from the point $(2, 1)$ and $(1, 3)$ are in the ratio $5 : 4$ , is $a x^{2} + b y^{2} + c x y + d x + e y + 170 = 0$ , then the value of $a^{2} + 2 b + 3 c + 4 d + e$ is equal to :

- 27

437

Question 6.

Let a variable line of slope $m > 0$ passing through the point $(4, - 9)$ intersect the coordinate axes at the points $A$ and $B$ . The minimum value of the sum of the distances of $A$ and $B$ from the origin is

Question 7.

Let $A (- 1, 1)$ and $B (2, 3)$ be two points and $P$ be a variable point above the line $AB$ such that the area of $△ PAB$ is 10. If the locus of $P$ is $a x + by = 15$ , then $5 a + 2 b$ is :

- \frac{12}{5}

- \frac{6}{5}

Question 8.

Let two straight lines drawn from the origin $O$ intersect the line $3 x + 4 y = 12$ at the points $P$ and $Q$ such that $△ OPQ$ is an isosceles triangle and $∠ POQ = 90^{\circ}$ . If $l = {OP}^{2} + {PQ}^{2} + {QO}^{2}$ , then the greatest integer less than or equal to $l$ is :

Question 9.

The vertices of a triangle are $A (- 1, 3), B (- 2, 2)$ and $C (3, - 1)$ . A new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to origin is :

- x + y - (2 - \sqrt{2}) = 0

x + y - (2 - \sqrt{2}) = 0

x + y + (2 - \sqrt{2}) = 0

x - y - (2 + \sqrt{2}) = 0

Question 10.

Let $A (a, b), B (3, 4)$ and $C (- 6, - 8)$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $P (2 a + 3, 7 b + 5)$ from the line $2 x + 3 y - 4 = 0$ measured parallel to the line $x - 2 y - 1 = 0$ is

\frac{17 \sqrt{5}}{6}

\frac{15 \sqrt{5}}{7}

\frac{17 \sqrt{5}}{7}

\frac{\sqrt{5}}{17}

Question 1.

Let $α, β, γ, δ \in Z$ and let $A (α, β), B (1, 0), C (γ, δ)$ and $D (1, 2)$ be the vertices of a parallelogram $ABCD$ . If $A B = \sqrt{10}$ and the points $A$ and $C$ lie on the line $3 y = 2 x + 1$ , then $2 (α + β + γ + δ)$ is equal to

Question 2.

If $x^{2} - y^{2} + 2 h x y + 2 g x + 2 f y + c = 0$ is the locus of a point, which moves such that it is always equidistant from the lines $x + 2 y + 7 = 0$ and $2 x - y + 8 = 0$ , then the value of $g + c + h - f$ equals

Question 3.

A line passing through the point $A (9, 0)$ makes an angle of $30^{\circ}$ with the positive direction of $x$ -axis. If this line is rotated about A through an angle of $15^{\circ}$ in the clockwise direction, then its equation in the new position is :

\frac{y}{\sqrt{3} + 2} + x = 9

\frac{x}{\sqrt{3} + 2} + y = 9

\frac{x}{\sqrt{3} - 2} + y = 9

\frac{y}{\sqrt{3} - 2} + x = 9

Question 4.

Let $A$ be the point of intersection of the lines $3 x + 2 y = 14, 5 x - y = 6$ and $B$ be the point of intersection of the lines $4 x + 3 y = 8, 6 x + y = 5$ . The distance of the point $P (5, - 2)$ from the line $AB$ is

\frac{13}{2}

\frac{5}{2}

Question 5.

The distance of the point $(2, 3)$ from the line $2 x - 3 y + 28 = 0$ , measured parallel to the line $\sqrt{3} x - y + 1 = 0$ , is equal to

3 + 4 \sqrt{2}

6 \sqrt{3}

4 + 6 \sqrt{3}

4 \sqrt{2}

Question 6.

In a $△ A B C$ , suppose $y = x$ is the equation of the bisector of the angle $B$ and the equation of the side $A C$ is $2 x - y = 2$ . If $2 A B = B C$ and the points $A$ and $B$ are respectively $(4, 6)$ and $(α, β)$ , then $α + 2 β$ is equal to

Question 7.

Let $R$ be the interior region between the lines $3 x - y + 1 = 0$ and $x + 2 y - 5 = 0$ containing the origin. The set of all values of $a$ , for which the points $(a^{2}, a + 1)$ lie in $R$ , is :

(- 3, 0) \cup (\frac{2}{3}, 1)

(- 3, 0) \cup (\frac{1}{3}, 1)

(- 3, - 1) \cup (\frac{1}{3}, 1)

(- 3, - 1) \cup (- \frac{1}{3}, 1)

Question 8.

The portion of the line

4 x + 5 y = 20

in the first quadrant is trisected by the lines

L_{1}

and

L_{2}

passing through the origin. The tangent of an angle between the lines

L_{1}

and

L_{2}

is :

\frac{30}{41}

\frac{8}{5}

\frac{2}{5}

\frac{25}{41}

Question 9.

(α, β)

is the orthocenter of the triangle

ABC

with vertices

A (3, - 7), B (- 1, 2)

and

C (4, 5)

, then

9 α - 6 β + 60

is equal to :

Question 10.

Let $(α, β)$ be the centroid of the triangle formed by the lines $15 x - y = 82, 6 x - 5 y = - 4$ and $9 x + 4 y = 17$ . Then $α + 2 β$ and $2 α - β$ are the roots of the equation :

x^{2} - 7 x + 12 = 0

x^{2} - 13 x + 42 = 0

x^{2} - 14 x + 48 = 0

x^{2} - 10 x + 25 = 0

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JEE Main Straight Lines and Pair of Straight Lines Practice Questions With Solutions

JEE Main Mathematics Straight Lines and Pair of Straight Lines Practice Questions

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

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