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Phrases Previous Year Questions (PYQs)

Phrases Ellipse PYQ

Phrases PYQ
List I List II
A. Kailash Satyarthi I. Chemistry
B. Abhijit Banerjee II. Peace
C. Vinkatraman Ramakrishnan III. Physics
D. Subrahmanyan Chandrasekhar IV. Economics






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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

List I List II
A. Kailash Satyarthi II. Peace
B. Abhijit Banerjee IV. Economics
C. Venkatraman Ramakrishnan I. Chemistry
D. Subrahmanyan Chandrasekhar III. Physics
Phrases PYQ
Let $E$ be the ellipse $\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$ and $C$ be the circle $x^2+y^2=9$. Let $P(1,2)$ and $Q(2,1)$ respectively. Then





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

For $P(1,2)$: Circle: $1^2+2^2=5<9$ ⇒ inside $C$ Ellipse: $\dfrac{1}{9}+\dfrac{4}{4}= \dfrac{1}{9}+1=\dfrac{10}{9}>1$ ⇒ outside $E$ So, $P$ lies inside $C$ but outside $E$.
Phrases PYQ
The length of major axis and coordinate of vertices for the ellipse $3x^{2}+2y^{2}=6$ respectively are:





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Phrases Previous Year PYQ Phrases CUET 2025 PYQ

Solution

Given ellipse: $3x^{2}+2y^{2}=6 \;\;\Rightarrow\;\; \dfrac{x^{2}}{2}+\dfrac{y^{2}}{3}=1$.  
Here $a^{2}=3,\; b^{2}=2 \;\Rightarrow\; a=\sqrt{3}$.  
Major axis length $=2a=2\sqrt{3}$, vertices $=(0,\pm \sqrt{3})$.  

{Answer:} $2\sqrt{3},\;(0,\pm\sqrt{3})$

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