JEE Advanced · Mathematics · 9. Straight Lines
Lines \(L_1: y-x=0\) and \(L_2: 2 x+y=0\) intersect the line \(L_3: y+2=0\) at \(P\) and \(Q\), respectively. The bisector of the acute angle between \(L_1\) and \(L_2\) intersects \(L_3\) at \(R\).
Statement I The ratio \(P R: R Q\) equals \(2 \sqrt{2}: \sqrt{5}\).
Statement II In any triangle, bisector of an angle divides the triangle into two similar triangles.
- A Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I
- B Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I
- C Statement I is true, Statement II is false
- D Statement I is false, Statement II is true
Answer & Solution
Correct Answer
(B) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I
Step-by-step Solution
Detailed explanation
In \(\triangle O P Q\)
Clearly,
\[
\frac{P R}{R Q}=\frac{O P}{O Q}=\frac{2 \sqrt{2}}{\sqrt{5}}
\]
Clearly,
\[
\frac{P R}{R Q}=\frac{O P}{O Q}=\frac{2 \sqrt{2}}{\sqrt{5}}
\]
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Mathematics
- Let be a continuous function such that for all Then, which of the following statement(s) is (are) TRUE?JEE Advanced 2018 Hard
- The value of \(\lim _{x \rightarrow 0} \frac{1}{x^3} \int_0^x \frac{t \log (1+t)}{t^4+4} d t\) isJEE Advanced 2010 Easy
- For any real numbers and , let , be the solution of the differential equation Let . Then which of the following functions belong(s) to the set ?JEE Advanced 2021 Hard
- Let and be two biased coins such that the probabilities of getting head in a single toss are and , respectively. Suppose is the number of heads that appear when is tossed twice, independently, and suppose is the number of heads that appear when is tossed twice, independently. Then the probability that the roots of the quadratic polynomial are real and equal, isJEE Advanced 2020 Medium
- The value of is equal toJEE Advanced 2016 Medium
- Let \(\mathbb{R}\) denote the set of all real numbers. Let \(a_{\mathrm{i}}, b_{\mathrm{i}} \in \mathbb{R}\) for \(\mathrm{i} \in\{1,2,3\}\).
Define the functions \(f: \mathbb{R} \rightarrow \mathbb{R}, g: \mathbb{R} \rightarrow \mathbb{R}\), and \(h: \mathbb{R} \rightarrow \mathbb{R}\) by
\(\begin{aligned} & f(x)=a_1+10 x+a_2 x^2+a_3 x^3+x^4, \\ & g(x)=b_1+3 x+b_2 x^2+b_3 x^3+x^4, \\ & h(x)=f(x+1)-g(x+2) .\end{aligned}\)
If \(f(x) \neq g(x)\) for every \(x \in \mathbb{R}\), then the coefficient of \(x^3\) in \(h(x)\) isJEE Advanced 2025 Easy
More PYQs from JEE Advanced
- For every integer \(n\), let \(a_{n}\) and \(b_{n}\) be real numbers. Let function \(f: I R \rightarrow I R\) be given by
\(f(x)=\left\{\begin{array}{lll}
a_{n}+\sin \pi x, & \text { for } & x \in[2 n, 2 n+1] \\
b_{n}+\cos \pi x, & \text { for } & x \in(2 n-1,2 n)
\end{array}\right.\)
for all integers \(n\). If \(f\) is continuous, then which of the following hold \((s)\) for all \(n\) ?JEE Advanced 2012 Hard - The number of neutrons emitted when \({ }_{92}^{235} \mathrm{U}\) undergoes controlled nuclear fission to \({ }_{54}^{142} \mathrm{Xe}\) and \({ }_{38}^{90} \mathrm{Sr}\) isJEE Advanced 2010 Medium
- Among the following, the correct statement(s) for electrons in an atom is(are)JEE Advanced 2024 Easy
- The nitrogen containing compound produced in the reaction of withJEE Advanced 2016 Medium
- Statement 1 For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.
and Statement 2 If the observer and the object are moving at velocities \(\overrightarrow{\mathbf{v}}_{\mathbf{1}}\) and \(\overrightarrow{\mathbf{v}_2}\) respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is \(\overrightarrow{\mathbf{v}_2}-\overrightarrow{\mathbf{v}_1}\).JEE Advanced 2008 Easy - The correct statement(s) about and is (are)
[Atomic number of Cr = 24 and Mn = 25]JEE Advanced 2015 Easy