(A) The triangle is bounded by $x > 0$,$y > 0$,and $3x + 4y < 60$. Since $b$ is a multiple of $a$,let $b = ka$ for some integer $k \ge 1$.For a fixed

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(A) The triangle is bounded by $x > 0$,$y > 0$,and $3x + 4y For a fixed $x = a$,we have $3a + 4y Since $y = ka$,we have $ka For $a=1$: $k For $a=2$: $k For $a=3$: $k For $a=4$: $k For $a=5$: $k For $a=6$: $k For $a=7$: $k For $a=8$: $k For $a \ge 9$: $k Total points $= 14 + 6 + 4 + 2 + 2 + 1 + 1 + 1 = 31$.

Class 11 Mathematics Linear Inequalities Word problem of Linear inequalities

Difficult

$A$ triangle is formed by the $X$-axis,$Y$-axis,and the line $3x + 4y = 60$. 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 $...........$

JEE MAIN 2023 All JEE MAIN

A
$31$
B
$30$
C
$28$
D
$56$

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Linear Inequalities

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Word problem of Linear inequalities

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$A$ triangle is formed by the $X$-axis,$Y$-axis,and the line $3x + 4y = 60$. 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 $...........$

Similar Questions

Solve $\frac{1 - |x|}{2 - |x|} \ge 0$.

How many points having integer coordinates are there in the feasible region of the inequalities $3x + 4y \leq 12$,$x \geq 0$,and $y \geq 1$?

Find all pairs of consecutive even positive integers,both of which are larger than $5$,such that their sum is less than $23$.

$A$ container is filled with $1120 \text{ litres}$ of a solution containing $40 \%$ acid. How many litres of acid must be added so that the resulting mixture contains more than $40 \%$ but less than $50 \%$ water?

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