Match List I with List II LIST I LIST II (A) The angle between the straight lines, 2x 2 +3y 2 -7xy = 0 is (i) tan - 1 3 5 (B) The circles x 2 + y 2 + x + y =0 x 2 +y 2 +x+y = 0 and x 2 +y 2 +x-y = 0 intersect at angle (ii) 25 π (C) The area of circle centred at (1, 2) and passing through (4, 6) is (iii) π /4 (D) The parabolas y 2 = 4x y 2 =4 x and x 2 = 32y x 2 =32 y intersect at point (16, 8) at angle (iv) π /2 Choose the correct answer from the options given below:

A-III, B-IV, C-II, D-I Explanation: Coordinate Geometry Solving A. Angle between straight lines Ye ek pair of straight lines ka equation hai ( ). Yahan . Formula: Match: (iii) B. Intersection angle of circles and Dono circles ke centers aur hain aur radii hain. Intersection angle ka formula: Yahan . Match: (iv) C. Area of circle centred at passing through Pehle radius ( ) nikalte hain distance formula se: Area of circle: Match: (ii) 25\pi \tan \theta = \left| \frac{m_2 - m_1}{1 + m_1m_2} \right| \tan \theta = \left| \frac{1 - 1/4}{1 + (1)(1/4)} \right| = \frac{3/4}{5/4} = \frac{3}{5} \implies \theta = \tan^{-1}\left(\frac{3}{5}\right)$$ Match: (i) Final Matching Summary List-I List-II (A) Angle between (iii) (B) Intersection of circles (iv) (C) Area of circle (ii) (D) Intersection of parabolas (i) Sahi Option Sequence: A-iii

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CUET PG 2023 Mathematics PYQ — Match List I with List II LIST I LIST II (A) The angle between th… | Mathem Solvex

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CUET PG 2023 Mathematics PYQ — Match List I with List II LIST I LIST II (A) The angle between th… | Mathem Solvex | Mathem Solvex

Explanation

Coordinate Geometry Solving

A. Angle between straight lines $2x^2 + 3y^2 - 7xy = 0$

Ye ek pair of straight lines ka equation hai ( $ax^2 + 2hxy + by^2 = 0$ ). Yahan $a=2, b=3, h=-7/2$ .

Formula:

\tan \theta = \left| \frac{2\sqrt{h^2 - ab}}{a+b} \right|

\tan \theta = \left| \frac{2\sqrt{(-7/2)^2 - (2)(3)}}{2+3} \right| = \frac{2\sqrt{49/4 - 6}}{5}

\tan \theta = \frac{2\sqrt{25/4}}{5} = \frac{2(5/2)}{5} = 1 \implies \theta = \frac{\pi}{4}

Match: (iii) $\frac{\pi}{4}$

B. Intersection angle of circles $x^2+y^2+x+y=0$ and $x^2+y^2+x-y=0$

Dono circles ke centers $C_1(-1/2, -1/2)$ aur $C_2(-1/2, 1/2)$ hain aur radii $r_1 = r_2 = 1/\sqrt{2}$ hain.

Intersection angle $\cos \theta$ ka formula:

\cos \theta = \left| \frac{d^2 - r_1^2 - r_2^2}{2r_1r_2} \right|

Yahan $d^2 = (-1/2 - (-1/2))^2 + (1/2 - (-1/2))^2 = 1$ .

\cos \theta = \left| \frac{1 - 1/2 - 1/2}{2(1/\sqrt{2})(1/\sqrt{2})} \right| = \frac{0}{1} = 0 \implies \theta = \frac{\pi}{2}

Match: (iv) $\frac{\pi}{2}$

C. Area of circle centred at $(1, 2)$ passing through $(4, 6)$

Pehle radius ( $r$ ) nikalte hain distance formula se:

r = \sqrt{(4-1)^2 + (6-2)^2} = \sqrt{3^2 + 4^2} = 5

Area of circle:

\text{Area} = \pi r^2 = \pi (5)^2 = 25\pi

Match: (ii) $< s p an c l a ss = " ma t h - in l in e " d a t a - ma t h = " \frac{25 π}{4} " d a t a - in d e x - in - n o d e = "117" >$ 25\pi $ D. Intersection angle of  and at Dono curves ko differentiate karke slopes () nikalte hain: <ol start="1" data-path-to-node="21"> <li> </li> <li> Angle formula: <div data-path-to-node="21,1,1"> <div class="math-block" data-math="\tan \theta = \left| \frac{m_2 - m_1}{1 + m_1m_2} \right|">$ \tan \theta = \left| \frac{m_2 - m_1}{1 + m_1m_2} \right| $< / d i v >< / d i v >< d i v d a t a - p a t h - t o - n o d e = "21, 1, 2" >< d i v c l a ss = " ma t h - b l oc k " d a t a - ma t h = " tan θ = \frac{1 - 1/4}{1 + ( 1 ) ( 1/4 )} = \frac{3/4}{5/4} = \frac{3}{5} ⟹ θ = tan^{- 1} (\frac{3}{5}) " >$ \tan \theta = \left| \frac{1 - 1/4}{1 + (1)(1/4)} \right| = \frac{3/4}{5/4} = \frac{3}{5} \implies \theta = \tan^{-1}\left(\frac{3}{5}\right)$$

Match: (i) $\tan^{-1}\left(\frac{3}{5}\right)$

Final Matching Summary

List-I List-II

(A) Angle between $2x^2 + 3y^2 - 7xy = 0$ (iii) $\frac{\pi}{4}$

(B) Intersection of circles (iv) $\frac{\pi}{2}$

(C) Area of circle (ii) $\frac{25\pi}{4}$

(D) Intersection of parabolas (i) $\tan^{-1}\left(\frac{3}{5}\right)$

Sahi Option Sequence: A-iii, B-iv, C-ii, D-i
Explanation
Coordinate Geometry Solving

A. Angle between straight lines $2x^2 + 3y^2 - 7xy = 0$

Ye ek pair of straight lines ka equation hai ( $ax^2 + 2hxy + by^2 = 0$ ). Yahan $a=2, b=3, h=-7/2$ .

Formula:

$\tan \theta = \left| \frac{2\sqrt{h^2 - ab}}{a+b} \right|$

$\tan \theta = \left| \frac{2\sqrt{(-7/2)^2 - (2)(3)}}{2+3} \right| = \frac{2\sqrt{49/4 - 6}}{5}$

$\tan \theta = \frac{2\sqrt{25/4}}{5} = \frac{2(5/2)}{5} = 1 \implies \theta = \frac{\pi}{4}$

Match: (iii) $\frac{\pi}{4}$

B. Intersection angle of circles $x^2+y^2+x+y=0$ and $x^2+y^2+x-y=0$

Dono circles ke centers $C_1(-1/2, -1/2)$ aur $C_2(-1/2, 1/2)$ hain aur radii $r_1 = r_2 = 1/\sqrt{2}$ hain.

Intersection angle $\cos \theta$ ka formula:

$\cos \theta = \left| \frac{d^2 - r_1^2 - r_2^2}{2r_1r_2} \right|$

Yahan $d^2 = (-1/2 - (-1/2))^2 + (1/2 - (-1/2))^2 = 1$ .

$\cos \theta = \left| \frac{1 - 1/2 - 1/2}{2(1/\sqrt{2})(1/\sqrt{2})} \right| = \frac{0}{1} = 0 \implies \theta = \frac{\pi}{2}$

Match: (iv) $\frac{\pi}{2}$

C. Area of circle centred at $(1, 2)$ passing through $(4, 6)$

Pehle radius ( $r$ ) nikalte hain distance formula se:

$r = \sqrt{(4-1)^2 + (6-2)^2} = \sqrt{3^2 + 4^2} = 5$

Area of circle:

$\text{Area} = \pi r^2 = \pi (5)^2 = 25\pi$

Match: (ii) $< s p an c l a ss = " ma t h - in l in e " d a t a - ma t h = " \frac{25 π}{4} " d a t a - in d e x - in - n o d e = "117" >$ 25\pi $ D. Intersection angle of  and at Dono curves ko differentiate karke slopes () nikalte hain: <ol start="1" data-path-to-node="21"> <li> </li> <li> Angle formula: <div data-path-to-node="21,1,1"> <div class="math-block" data-math="\tan \theta = \left| \frac{m_2 - m_1}{1 + m_1m_2} \right|">$ \tan \theta = \left| \frac{m_2 - m_1}{1 + m_1m_2} \right| $< / d i v >< / d i v >< d i v d a t a - p a t h - t o - n o d e = "21, 1, 2" >< d i v c l a ss = " ma t h - b l oc k " d a t a - ma t h = " tan θ = \frac{1 - 1/4}{1 + ( 1 ) ( 1/4 )} = \frac{3/4}{5/4} = \frac{3}{5} ⟹ θ = tan^{- 1} (\frac{3}{5}) " >$ \tan \theta = \left| \frac{1 - 1/4}{1 + (1)(1/4)} \right| = \frac{3/4}{5/4} = \frac{3}{5} \implies \theta = \tan^{-1}\left(\frac{3}{5}\right)$$

Match: (i) $\tan^{-1}\left(\frac{3}{5}\right)$

Final Matching Summary

List-I List-II

(A) Angle between $2x^2 + 3y^2 - 7xy = 0$ (iii) $\frac{\pi}{4}$

(B) Intersection of circles (iv) $\frac{\pi}{2}$

(C) Area of circle (ii) $\frac{25\pi}{4}$

(D) Intersection of parabolas (i) $\tan^{-1}\left(\frac{3}{5}\right)$

Sahi Option Sequence: A-iii, B-iv, C-ii, D-i
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TopicAll "Coordinate Geometry" PYQs →SubjectMore Mathematics Questions →YearCUET PG 2023 Paper →All CUET PG Questions →📄 Download CUET PG PYQ Papers →📝 Preparation Tips & Articles →

LIST I		LIST II
(A)	The angle between the straight lines, 2x²+3y²-7xy = 0 is	(i)	$tan^{- 1}! (\frac{3}{5})$
(B)	The circles x²+y²+x+y = 0 and x²+y²+x-y = 0 intersect at angle	(ii)	$25 π$
(C)	The area of circle centred at (1, 2) and passing through (4, 6) is	(iii)	$\frac{π}{4}$
(D)	The parabolas y²= 4x and x²= 32y intersect at point (16, 8) at angle	(iv)	$\frac{π}{2}$

CUET PG 2023 — Mathematics PYQ

Choose the correct answer:

Explanation

Coordinate Geometry Solving

Final Matching Summary

Explanation

Coordinate Geometry Solving

Final Matching Summary

List-I	List-II
(A) Angle between $2x^2 + 3y^2 - 7xy = 0$	(iii) $\frac{\pi}{4}$
(B) Intersection of circles	(iv) $\frac{\pi}{2}$
(C) Area of circle	(ii) $\frac{25\pi}{4}$
(D) Intersection of parabolas	(i) $\tan^{-1}\left(\frac{3}{5}\right)$