JEE Exam > JEE Notes > Mathematics (Maths) for JEE Main & Advanced > Parabola: JEE Mains Previous Year Questions (2021-2024)
Parabola: JEE Mains Previous Year Questions (2021-2024) | Mathematics (Maths) for JEE Main & Advanced PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1 Previous Year Questions (2021-24): Parabola Q1 - 2024 (27 Jan Shift 1) If the shortest distance of the parabola ?? 2 = 4?? from the centre of the circle ?? 2 + ?? 2 - 4?? - 16?? + 64 = 0 is d, then d 2 is equal to : (1) 16 (2) 24 (3) 20 (4) 36 Q2 - 2024 (29 Jan Shift 2) Let P( ?? , ?? ) be a point on the parabola y 2 = 4x. If P also lies on the chord of the parabola ?? 2 = 8?? whose mid point is ( 1, 5 4 ) . Then ( ?? - 28) ( ?? - 8) is equal to Q3 - 2024 (30 Jan Shift 1) The maximum area of a triangle whose one vertex is at ( 0,0) and the other two vertices lie on the curve ?? = -2?? 2 + 54 at points ( ?? , ?? ) and ( -?? , ?? ) where y > 0 is: (1) 88 (2) 122 (3) 92 (4) 108 Answer Key Q1 (3) Q2 (192) Q3 (4) Page 2 Previous Year Questions (2021-24): Parabola Q1 - 2024 (27 Jan Shift 1) If the shortest distance of the parabola ?? 2 = 4?? from the centre of the circle ?? 2 + ?? 2 - 4?? - 16?? + 64 = 0 is d, then d 2 is equal to : (1) 16 (2) 24 (3) 20 (4) 36 Q2 - 2024 (29 Jan Shift 2) Let P( ?? , ?? ) be a point on the parabola y 2 = 4x. If P also lies on the chord of the parabola ?? 2 = 8?? whose mid point is ( 1, 5 4 ) . Then ( ?? - 28) ( ?? - 8) is equal to Q3 - 2024 (30 Jan Shift 1) The maximum area of a triangle whose one vertex is at ( 0,0) and the other two vertices lie on the curve ?? = -2?? 2 + 54 at points ( ?? , ?? ) and ( -?? , ?? ) where y > 0 is: (1) 88 (2) 122 (3) 92 (4) 108 Answer Key Q1 (3) Q2 (192) Q3 (4) Solutions Q1 Equation of normal to parabola ?? = ???? - 2?? - ?? 3 this normal passing through center of circle ( 2,8) 8 = 2?? - 2?? - ?? 3 ?? = -2 So point P on parabola ? ( am 2 , -2am )= ( 4,4) And C = ( 2,8) PC = v4 + 16 = v20 d 2 = 20 Q2 Parabola is ?? 2 = 8?? Chord with mid point ( x 1 , y 1 ) is T = S 1 ? xx 1 - 4( y + y 1 )= x 1 2 - 8y 1 ? ( x 1 , y 1 )= ( 1, 5 4 ) ? x - 4 ( y + 5 4 )= 1 - 8 × 5 4 = -9 ? x - 4y + 4 = 0 … ( ?? , ?? ) lies on (i) \ & also on ?? 2 = 4?? ? ?? - 4?? + 4 = 0 … ( ???? ) &?? 2 = 4?? … (iii) Solving (ii) \ & (iii) Page 3 Previous Year Questions (2021-24): Parabola Q1 - 2024 (27 Jan Shift 1) If the shortest distance of the parabola ?? 2 = 4?? from the centre of the circle ?? 2 + ?? 2 - 4?? - 16?? + 64 = 0 is d, then d 2 is equal to : (1) 16 (2) 24 (3) 20 (4) 36 Q2 - 2024 (29 Jan Shift 2) Let P( ?? , ?? ) be a point on the parabola y 2 = 4x. If P also lies on the chord of the parabola ?? 2 = 8?? whose mid point is ( 1, 5 4 ) . Then ( ?? - 28) ( ?? - 8) is equal to Q3 - 2024 (30 Jan Shift 1) The maximum area of a triangle whose one vertex is at ( 0,0) and the other two vertices lie on the curve ?? = -2?? 2 + 54 at points ( ?? , ?? ) and ( -?? , ?? ) where y > 0 is: (1) 88 (2) 122 (3) 92 (4) 108 Answer Key Q1 (3) Q2 (192) Q3 (4) Solutions Q1 Equation of normal to parabola ?? = ???? - 2?? - ?? 3 this normal passing through center of circle ( 2,8) 8 = 2?? - 2?? - ?? 3 ?? = -2 So point P on parabola ? ( am 2 , -2am )= ( 4,4) And C = ( 2,8) PC = v4 + 16 = v20 d 2 = 20 Q2 Parabola is ?? 2 = 8?? Chord with mid point ( x 1 , y 1 ) is T = S 1 ? xx 1 - 4( y + y 1 )= x 1 2 - 8y 1 ? ( x 1 , y 1 )= ( 1, 5 4 ) ? x - 4 ( y + 5 4 )= 1 - 8 × 5 4 = -9 ? x - 4y + 4 = 0 … ( ?? , ?? ) lies on (i) \ & also on ?? 2 = 4?? ? ?? - 4?? + 4 = 0 … ( ???? ) &?? 2 = 4?? … (iii) Solving (ii) \ & (iii) ?? 2 = 4( 4?? - 4)? ?? 2 - 16?? + 16 = 0 matho ? ?? = 8 ± 4v3 and ?? = 4?? - 4 = 28 ± 16v3 ? ( ?? , ?? ) = ( 28 + 16v3, 8 + 4v3) & ( 28 - 16v3, 8 - 4v3) ? ( ?? - 28) ( ?? - 8)= ( ±16v3) ( ±4v3) matho = 192 Q3. Area of ? = 1 2 | 0 0 1 x y 1 -x y 1 | ? | 1 2 ( xy+ xy ) | = |xy | Area ( ?)= |xy | = |x( -2x 2 + 54) | d( ?) dx = |( -6x 2 + 54) | ? d? dx = 0 at x = 3 Area = 3( -2 × 9 + 54)= 108 January 2023 Q1 - 24 January - Shift 1 The equations of the sides AB and AC of a triangle ABC are ( ?? + 1) ?? + ???? = 4 and ???? + ( 1 - ?? ) ?? + ?? = 0 respectively. Its vertex ?? is on the ?? - axis and its orthocentre is ( 1,2) . The length of the tangent from the point ?? to the part of the parabola ?? 2 = 6?? in the first quadrant is Page 4 Previous Year Questions (2021-24): Parabola Q1 - 2024 (27 Jan Shift 1) If the shortest distance of the parabola ?? 2 = 4?? from the centre of the circle ?? 2 + ?? 2 - 4?? - 16?? + 64 = 0 is d, then d 2 is equal to : (1) 16 (2) 24 (3) 20 (4) 36 Q2 - 2024 (29 Jan Shift 2) Let P( ?? , ?? ) be a point on the parabola y 2 = 4x. If P also lies on the chord of the parabola ?? 2 = 8?? whose mid point is ( 1, 5 4 ) . Then ( ?? - 28) ( ?? - 8) is equal to Q3 - 2024 (30 Jan Shift 1) The maximum area of a triangle whose one vertex is at ( 0,0) and the other two vertices lie on the curve ?? = -2?? 2 + 54 at points ( ?? , ?? ) and ( -?? , ?? ) where y > 0 is: (1) 88 (2) 122 (3) 92 (4) 108 Answer Key Q1 (3) Q2 (192) Q3 (4) Solutions Q1 Equation of normal to parabola ?? = ???? - 2?? - ?? 3 this normal passing through center of circle ( 2,8) 8 = 2?? - 2?? - ?? 3 ?? = -2 So point P on parabola ? ( am 2 , -2am )= ( 4,4) And C = ( 2,8) PC = v4 + 16 = v20 d 2 = 20 Q2 Parabola is ?? 2 = 8?? Chord with mid point ( x 1 , y 1 ) is T = S 1 ? xx 1 - 4( y + y 1 )= x 1 2 - 8y 1 ? ( x 1 , y 1 )= ( 1, 5 4 ) ? x - 4 ( y + 5 4 )= 1 - 8 × 5 4 = -9 ? x - 4y + 4 = 0 … ( ?? , ?? ) lies on (i) \ & also on ?? 2 = 4?? ? ?? - 4?? + 4 = 0 … ( ???? ) &?? 2 = 4?? … (iii) Solving (ii) \ & (iii) ?? 2 = 4( 4?? - 4)? ?? 2 - 16?? + 16 = 0 matho ? ?? = 8 ± 4v3 and ?? = 4?? - 4 = 28 ± 16v3 ? ( ?? , ?? ) = ( 28 + 16v3, 8 + 4v3) & ( 28 - 16v3, 8 - 4v3) ? ( ?? - 28) ( ?? - 8)= ( ±16v3) ( ±4v3) matho = 192 Q3. Area of ? = 1 2 | 0 0 1 x y 1 -x y 1 | ? | 1 2 ( xy+ xy ) | = |xy | Area ( ?)= |xy | = |x( -2x 2 + 54) | d( ?) dx = |( -6x 2 + 54) | ? d? dx = 0 at x = 3 Area = 3( -2 × 9 + 54)= 108 January 2023 Q1 - 24 January - Shift 1 The equations of the sides AB and AC of a triangle ABC are ( ?? + 1) ?? + ???? = 4 and ???? + ( 1 - ?? ) ?? + ?? = 0 respectively. Its vertex ?? is on the ?? - axis and its orthocentre is ( 1,2) . The length of the tangent from the point ?? to the part of the parabola ?? 2 = 6?? in the first quadrant is (1) v 6 (2) 2v 2 (3) 2 (4) 4 Q2 - 24 January - Shift 2 The urns A, B and C contain 4 red, 6 black; 5 red, 5 black and ?? red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn C is 0.4 then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola y 2 = ?? x with one vertex at the vertex of the parabola is Q3 - 24 January - Shift 2 The distance of the point ( 6, -2v 2) from the common tangent y = mx+ c, m > 0, of the curves x = 2y 2 and x = 1 + y 2 is (1) 1 3 (2) 5 (3) 14 3 (4) 5v 3 Q4 - 30 January - Shift 1 If P( h, k) be point on the parabola x = 4y 2 , which is nearest to the point Q( 0,33) , then the distance of P from the directrix of the parabola ?? 2 = 4( ?? + ?? ) is equal to : (1) 2 (2) 4 (3) 8 (4) 6 Q5 - 30 January - Shift 2 Let A be a point on the x-axis. Common tangents are drawn from A to the curves ?? 2 + ?? 2 = 8 and ?? 2 = 16x. If one of these tangents touches the two curves at ?? and ?? , then ( ???? ) 2 is equal to (1) 64 (2) 76 (3) 81 (4) 72 Page 5 Previous Year Questions (2021-24): Parabola Q1 - 2024 (27 Jan Shift 1) If the shortest distance of the parabola ?? 2 = 4?? from the centre of the circle ?? 2 + ?? 2 - 4?? - 16?? + 64 = 0 is d, then d 2 is equal to : (1) 16 (2) 24 (3) 20 (4) 36 Q2 - 2024 (29 Jan Shift 2) Let P( ?? , ?? ) be a point on the parabola y 2 = 4x. If P also lies on the chord of the parabola ?? 2 = 8?? whose mid point is ( 1, 5 4 ) . Then ( ?? - 28) ( ?? - 8) is equal to Q3 - 2024 (30 Jan Shift 1) The maximum area of a triangle whose one vertex is at ( 0,0) and the other two vertices lie on the curve ?? = -2?? 2 + 54 at points ( ?? , ?? ) and ( -?? , ?? ) where y > 0 is: (1) 88 (2) 122 (3) 92 (4) 108 Answer Key Q1 (3) Q2 (192) Q3 (4) Solutions Q1 Equation of normal to parabola ?? = ???? - 2?? - ?? 3 this normal passing through center of circle ( 2,8) 8 = 2?? - 2?? - ?? 3 ?? = -2 So point P on parabola ? ( am 2 , -2am )= ( 4,4) And C = ( 2,8) PC = v4 + 16 = v20 d 2 = 20 Q2 Parabola is ?? 2 = 8?? Chord with mid point ( x 1 , y 1 ) is T = S 1 ? xx 1 - 4( y + y 1 )= x 1 2 - 8y 1 ? ( x 1 , y 1 )= ( 1, 5 4 ) ? x - 4 ( y + 5 4 )= 1 - 8 × 5 4 = -9 ? x - 4y + 4 = 0 … ( ?? , ?? ) lies on (i) \ & also on ?? 2 = 4?? ? ?? - 4?? + 4 = 0 … ( ???? ) &?? 2 = 4?? … (iii) Solving (ii) \ & (iii) ?? 2 = 4( 4?? - 4)? ?? 2 - 16?? + 16 = 0 matho ? ?? = 8 ± 4v3 and ?? = 4?? - 4 = 28 ± 16v3 ? ( ?? , ?? ) = ( 28 + 16v3, 8 + 4v3) & ( 28 - 16v3, 8 - 4v3) ? ( ?? - 28) ( ?? - 8)= ( ±16v3) ( ±4v3) matho = 192 Q3. Area of ? = 1 2 | 0 0 1 x y 1 -x y 1 | ? | 1 2 ( xy+ xy ) | = |xy | Area ( ?)= |xy | = |x( -2x 2 + 54) | d( ?) dx = |( -6x 2 + 54) | ? d? dx = 0 at x = 3 Area = 3( -2 × 9 + 54)= 108 January 2023 Q1 - 24 January - Shift 1 The equations of the sides AB and AC of a triangle ABC are ( ?? + 1) ?? + ???? = 4 and ???? + ( 1 - ?? ) ?? + ?? = 0 respectively. Its vertex ?? is on the ?? - axis and its orthocentre is ( 1,2) . The length of the tangent from the point ?? to the part of the parabola ?? 2 = 6?? in the first quadrant is (1) v 6 (2) 2v 2 (3) 2 (4) 4 Q2 - 24 January - Shift 2 The urns A, B and C contain 4 red, 6 black; 5 red, 5 black and ?? red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn C is 0.4 then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola y 2 = ?? x with one vertex at the vertex of the parabola is Q3 - 24 January - Shift 2 The distance of the point ( 6, -2v 2) from the common tangent y = mx+ c, m > 0, of the curves x = 2y 2 and x = 1 + y 2 is (1) 1 3 (2) 5 (3) 14 3 (4) 5v 3 Q4 - 30 January - Shift 1 If P( h, k) be point on the parabola x = 4y 2 , which is nearest to the point Q( 0,33) , then the distance of P from the directrix of the parabola ?? 2 = 4( ?? + ?? ) is equal to : (1) 2 (2) 4 (3) 8 (4) 6 Q5 - 30 January - Shift 2 Let A be a point on the x-axis. Common tangents are drawn from A to the curves ?? 2 + ?? 2 = 8 and ?? 2 = 16x. If one of these tangents touches the two curves at ?? and ?? , then ( ???? ) 2 is equal to (1) 64 (2) 76 (3) 81 (4) 72 Q6 - 01 February - Shift 1 Let ?? be the set of all ?? ? ?? such that the area of the triangle formed by the tangent at the point P( b, c) , b, c ? N, on the parabola y 2 = 2ax and the lines x = b, y = 0 is 16 unit 2 , then ? a?S ?a is equal to $ \qquad $ Q7 - 01 February - Shift 2 If the ?? -intercept of a focal chord of the parabola ?? 2 = 8?? + 4?? + 4 is 3 , then the length of this chord is equal to . Answer Key (As per Official NTA Key released on 2 Feb) Q1 (2) Q2 (432) Q3 (2) Q4 (4) Q5 (4) Q6 (146) Q7 (16) Solutions Q1 (2) AB : ( ?? + 1) x + ?? y = 4 ???? : ???? + ( 1 - ?? ) ?? + ?? = 0 Vertex ?? is on ?? -axis ? x = 0Read More
|
209 videos|443 docs|143 tests
|
FAQs on Parabola: JEE Mains Previous Year Questions (2021-2024) - Mathematics (Maths) for JEE Main & Advanced
| 1. What is a parabola and how is it defined in terms of its focus and directrix? |  |
Ans. A parabola is a conic section curve formed by the intersection of a right circular cone and a plane parallel to one of the cone's generating lines. It is defined as the set of all points in a plane that are equidistant from a fixed point called the focus and a fixed line called the directrix.
| 2. How can the equation of a parabola be written in standard form for a vertical or horizontal orientation? | |
Ans. For a parabola with a vertical orientation and vertex at (h, k), the equation in standard form is (x - h)^2 = 4p(y - k), where p is the distance between the vertex and the focus. For a parabola with a horizontal orientation and vertex at (h, k), the equation in standard form is (y - k)^2 = 4p(x - h).
| 3. What is the relationship between the focal length and the distance from the vertex to the focus in a parabola? | |
Ans. The focal length of a parabola is equal to the distance from the vertex to the focus. It is denoted by the letter 'p' in the standard form of the parabolic equation.
| 4. How can the focus and directrix of a parabola be determined from its equation in standard form? | |
Ans. For a parabola with equation (x - h)^2 = 4p(y - k) or (y - k)^2 = 4p(x - h), the focus is located at the point (h, k + p) and the directrix is the horizontal line y = k - p for a vertical parabola or the vertical line x = h - p for a horizontal parabola.
| 5. How can the axis of symmetry of a parabola be identified from its equation? | |
Ans. The axis of symmetry of a parabola is the vertical line passing through its vertex. For a parabola in standard form, the axis of symmetry is given by the equation x = h for a vertical parabola or y = k for a horizontal parabola, where (h, k) is the vertex of the parabola.
Related Exams
About this Document
|
Nov 21, 2024 Last updated |
Document Description: Parabola: JEE Mains Previous Year Questions (2021-2024) for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation.
The notes and questions for Parabola: JEE Mains Previous Year Questions (2021-2024) have been prepared according to the JEE exam syllabus. Information about Parabola: JEE Mains Previous Year Questions (2021-2024) covers topics
like and Parabola: JEE Mains Previous Year Questions (2021-2024) Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Parabola: JEE Mains Previous Year Questions (2021-2024).
Introduction of Parabola: JEE Mains Previous Year Questions (2021-2024) in English is available as part of our Mathematics (Maths) for JEE Main & Advanced
for JEE & Parabola: JEE Mains Previous Year Questions (2021-2024) in Hindi for Mathematics (Maths) for JEE Main & Advanced course.
Download more important topics related with notes, lectures and mock test series for JEE
Exam by signing up for free. JEE: Parabola: JEE Mains Previous Year Questions (2021-2024) | Mathematics (Maths) for JEE Main & Advanced
Description
Full syllabus notes, lecture & questions for Parabola: JEE Mains Previous Year Questions (2021-2024) | Mathematics (Maths) for JEE Main & Advanced - JEE | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) for JEE Main & Advanced | Best notes, free PDF download
Information about Parabola: JEE Mains Previous Year Questions (2021-2024)
In this doc you can find the meaning of Parabola: JEE Mains Previous Year Questions (2021-2024) defined & explained in the simplest way possible. Besides explaining types of
Parabola: JEE Mains Previous Year Questions (2021-2024) theory, EduRev gives you an ample number of questions to practice Parabola: JEE Mains Previous Year Questions (2021-2024) tests, examples and also practice JEE
tests
|
209 videos|443 docs|143 tests
|
Download as PDF
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
MCQs
,mock tests for examination
,Free
,Previous Year Questions with Solutions
,Important questions
,shortcuts and tricks
,Objective type Questions
,ppt
,past year papers
,Exam
,Summary
,Viva Questions
,video lectures
,Parabola: JEE Mains Previous Year Questions (2021-2024) | Mathematics (Maths) for JEE Main & Advanced
,study material
,Extra Questions
,practice quizzes
,Parabola: JEE Mains Previous Year Questions (2021-2024) | Mathematics (Maths) for JEE Main & Advanced
,Parabola: JEE Mains Previous Year Questions (2021-2024) | Mathematics (Maths) for JEE Main & Advanced
,Semester Notes
,Sample Paper
;
Additional Information about Parabola: JEE Mains Previous Year Questions (2021-2024) for JEE Preparation
Parabola: JEE Mains Previous Year Questions (2021-2024) Free PDF Download
The Parabola: JEE Mains Previous Year Questions (2021-2024) is an invaluable resource that delves deep into the core of the JEE exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Parabola: JEE Mains Previous Year Questions (2021-2024) now and kickstart your journey towards success in the JEE exam.
Importance of Parabola: JEE Mains Previous Year Questions (2021-2024)
The importance of Parabola: JEE Mains Previous Year Questions (2021-2024) cannot be overstated, especially for JEE aspirants.
This document holds the key to success in the JEE exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Parabola: JEE Mains Previous Year Questions (2021-2024) Notes
Parabola: JEE Mains Previous Year Questions (2021-2024) Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Parabola: JEE Mains Previous Year Questions (2021-2024).
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Parabola: JEE Mains Previous Year Questions (2021-2024) Notes on EduRev are your ultimate resource for success.
Parabola: JEE Mains Previous Year Questions (2021-2024) JEE
The "Parabola: JEE Mains Previous Year Questions (2021-2024) JEE Questions" guide is a valuable resource for all aspiring students preparing for the
JEE exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Parabola: JEE Mains Previous Year Questions (2021-2024) on the App
Students of JEE can study Parabola: JEE Mains Previous Year Questions (2021-2024) alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Parabola: JEE Mains Previous Year Questions (2021-2024),
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Parabola: JEE Mains Previous Year Questions (2021-2024) is prepared as per the latest JEE syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup