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JEE Main202325 Jan 2023Evening ShiftMathematicsStraight LinesActual

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 is an integer and b is a multiple of a , is _____ .

Correct answer

0

Step-by-step solution

Given: 3 x + 4 y = 60 ⇒ x 20 + y 15 = 1 If x = 1 , y = 57 4 = 14 . 25 So, points are 1 , 1 1 , 2 - 1 , 14    ⇒ 14 points. If x = 2 , y = 27 2 = 13 . 5 So, points are 2 , 2 2 , 4 … 2 , 12    ⇒ 6 points. If x = 3 , y = 51 4 = 12 . 75 So, points are 3 , 3 3 , 6 - 3 , 12    ⇒ 4 points. If x = 4 ,   y = 12 So, points are 4 , 4 4 , 8    ⇒ 2 points. If x = 5 , y = 45 4 = 11 . 25 So, points are 5 , 5 , 5 , 10    ⇒ 2 points. If

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