JEE MAIN - Mathematics (2021 - 18th March Morning Shift - No. 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
2
3
0
Explanation
3x + 4(mx + 1) = 9
$$ \Rightarrow $$ x(3 + 4m) = 5
$$ \Rightarrow $$ $$x = {5 \over {(3 + 4m)}}$$
$$ \Rightarrow $$ (3 + 4m) = $$\pm$$1, $$\pm$$5
$$ \Rightarrow $$ 4m = $$-$$3 $$\pm$$ 1, $$-$$3 $$\pm$$ 5
$$ \Rightarrow $$ 4m = $$-$$4, $$-$$2, $$-$$8, 2
$$ \Rightarrow $$ m = $$-$$1, $$-$$$${1 \over 2}$$, $$-$$2, $${1 \over 2}$$
$$ \therefore $$ Two integral value of m.
$$ \Rightarrow $$ x(3 + 4m) = 5
$$ \Rightarrow $$ $$x = {5 \over {(3 + 4m)}}$$
$$ \Rightarrow $$ (3 + 4m) = $$\pm$$1, $$\pm$$5
$$ \Rightarrow $$ 4m = $$-$$3 $$\pm$$ 1, $$-$$3 $$\pm$$ 5
$$ \Rightarrow $$ 4m = $$-$$4, $$-$$2, $$-$$8, 2
$$ \Rightarrow $$ m = $$-$$1, $$-$$$${1 \over 2}$$, $$-$$2, $${1 \over 2}$$
$$ \therefore $$ Two integral value of m.
Comments (0)
