New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Straight Lines and Pair of Straight Lines question

2025 · 28 Jan · Shift 2 · Q31

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Straight Lines and Pair of Straight Lines
2025 · 28 Jan · Shift 2 · Q31

Straight Lines and Pair of Straight Lines question

2025 · 28 Jan · Shift 2 · Q31

JEE MainMathematicsStraight Lines and Pair of Straight LinesMCQ+4 / −1

Two equal sides of an isosceles triangle are along

-x + 2y = 4

and

x + y = 4

. If

m

is the slope of its third side, then the sum, of all possible distinct values of

m

, is:

A
$-2\sqrt{10}$
B
12
C
-6
D
6

More from Straight Lines and Pair of Straight Lines

If A and B are the points of intersection of the circle $x^{2} + y^{2} - 8 x = 0$ and the hyperbola $\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1$ and a point P moves on the line $2 x - 3 y + 4 = 0$ , then the centroid of $Δ P A B$ lies on the line :2025 · MCQ
Let ΔABC be a triangle formed by the lines 7x – 6y + 3 = 0, x + 2y – 31 = 0 and 9x – 2y – 19 = 0. Let the point (h, k) be the image of the centroid of ΔABC in the line 3x + 6y – 53 = 0. Then h2 + k2 + hk is equal to :2025 · MCQ
Let the line x + y = 1 meet the axes of x and y at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB, where O is the origin and the points M and N lie on the lines OB and AB, respectively. If the area of…2025 · MCQ
Let $A B C$ be an isosceles triangle in which $A$ is at $(- 1, 0), ∠ A = \frac{2 π}{3}, A B = A C$ and $B$ is on the positve $x$ -axis. If $BC = 43$ and the line $BC$ intersects the line $y = x + 3$ at $(\alpha,…2024 · Numerical
The lines $L_{1}, L_{2}, \dots, L_{20}$ are distinct. For $n = 1, 2, 3, \dots, 10$ all the lines $L_{2 n - 1}$ are parallel to each other and all the lines $L_{2 n}$ pass through a given point…2024 · Numerical
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…2024 · MCQ
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 $∠ POQ = 9 0^{\circ}$ . If $l = OP^{2} + PQ^{2} + QO^{2}$ …2024 · MCQ
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 $\mathrm{a}…2024 · MCQ