NIMCET 2025 Paper

Section: Mathematics

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Question : 38 of 120

Marks: +1, -0

The obtuse angle between the lines

2 y=x+1 \;\; \;\text " and "\; \;\; y=3 x+2

is:

$\;{2 π}/{3}$
$\;{5 π}/{6}$
$\;{3 π}/{4}$
$\;{4 π}/{5}$

Solution:

First find the slopes:
Line 1:

2 y=x+1 ⇒ y=\;{x}/{2}+\;{1}/{2}

So

m_1=\;{1}/{2}

Line 2:

y=3 x+2

So

m_2=3 .

Angle between the lines is given by:

\tan θ={| \;{m_2-m_1}/{1+m_1 m_2} |}={| \;{3-{1}/{2}}/{1+\;{3}/{2}} |}=\;{2.5}/{2.5}=1

So the acute angle is:

θ=\;{π}/{4}

The obtuse angle between the lines is:

π-\;{π}/{4}=\;{3 π}/{4}

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