JEE Main 2021 · 18 March · morning · Single correct · +4 / −1

The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is :

  1. (a) 1
  2. (b) 2
  3. (c) 3
  4. (d) 0
Answer and solution

Answer (b) 2

Solution

Maths sir · 3 steps

Solve for x in terms of m, then ask which values of 3 + 4m can divide 5 exactly.

  1. Find the abscissa. Put y = mx + 1 into 3x + 4y = 9. This gives 3x + 4mx + 4 = 9, so x(3 + 4m) = 5.

    x = 5/(3 + 4m)

  2. Integer condition. If m is an integer, 3 + 4m is an integer. Then x is an integer only when 3 + 4m divides 5, so 3 + 4m must be one of 1, -1, 5, -5.
    3 + 4mmInteger m?x
    1-1/2no5
    -1-1yes-5
    51/2no1
    -5-2yes-1
  3. So. Only m = -1 and m = -2 work, so there are 2 integral values of m.

The idea to keep. When a coordinate comes out as a fraction like k/expression, demanding an integer means the expression must be a divisor of k. List every divisor, negative ones too.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Straight Lines

Asked about 130 times in JEE Main since 2020. This question is from 2021.