Mathematics · 2023
JEE Main · 25 January 2023, Shift 2 · Q87
A triangle is formed by X-axis, Y-axis and the line 3 x+4 y=60. Then the number of points P ( a, b ) which lie strictly inside the triangle, where a…
A triangle is formed by X-axis, Y-axis and the line $\displaystyle 3 x+4 y=60$. Then the number of points $\displaystyle \mathrm{P}(\mathrm{a}, \mathrm{b})$ which lie strictly inside the triangle, where a is an integer and b is a multiple of a , is $\displaystyle \_\_\_\_$.
Official answer
From NTA’s final answer key for this paper.
31
More from Straight Lines
- Consider the lines x(3 λ+1)+y(7 λ+2)=17 λ+5, λ being a parameter, all passing through a point P. One of these lines (say L ) is farthest from the…2025
- Let A B C be an isosceles triangle in which A is at (-1,0), ∠ A=(2 π)/3, A B=A C and B is on the positve x -axis. If B C=4 √3 and the line B C…2024
- Let ABC be a triangle formed by the lines 7 x-6 y+3=0, x+2 y-31=0 and 9 x-2 y-19=0. Let the point (h, k) be the image of the centroid of Δ ABC in the…2025
- If the point (α, (7 √3)/3) lies on the curve traced by the mid-points of the line segments of the lines x cos θ+y sin θ=7, θ ∈(0, (π)/2) between the…2023
- Let the vertex A of a triangle A B C be (1,2), and the mid-point of the side A B be (5,-1). If the centroid of this triangle is (3,4) and its…2026
- 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,…2024
- Let A(6,8), B(10 cos α,-10 sin α) and C(-10 sin α, 10 cos α), be the vertices of a triangle. If L(a, 9) and G(h, k) be its orthocenter and centroid…2025
- Let the area of the triangle formed by a straight line L: x+b y+c=0 with co-ordinate axes be 48 square units. If the perpendicular drawn from the…2025
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.