{"id":196046,"date":"2022-06-17T18:11:14","date_gmt":"2022-06-17T12:41:14","guid":{"rendered":"https:\/\/www.aakash.ac.in\/blog\/?p=196046"},"modified":"2023-03-25T23:58:38","modified_gmt":"2023-03-25T18:28:38","slug":"jee-main-maths-previous-year-questions-with-solutions","status":"publish","type":"post","link":"https:\/\/www.aakash.ac.in\/blog\/jee-main-maths-previous-year-questions-with-solutions\/","title":{"rendered":"JEE Main Maths Previous Year Questions With Solutions"},"content":{"rendered":"<p><a href=\"https:\/\/www.aakash.ac.in\/jee-mains-results?utm_source=seobanner&amp;utm_medium=jeemain&amp;utm_campaign=jeemain2023result\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2023\/02\/1300x420-1140x368.jpg\" alt=\"jee main exam\" width=\"100%\" data-entity-type=\"file\" data-entity-uuid=\"d4e023ef-9ff8-4b8f-b582-b9892a7d2953\" \/><\/a><br \/>\n<span style=\"font-weight: 400;\">JEE is a common entrance exam for students who wish to pursue their engineering higher studies in India&#8217;s most prestigious institutions, such as IITs and NITs.<\/span><\/p>\n<p><a href=\"https:\/\/www.aakash.ac.in\/answers-solutions\/jee-mains\/\"><span style=\"font-weight: 400;\">JEE Main<\/span><\/a><span style=\"font-weight: 400;\"> has three sections for BE\/B. Tech students are in Mathematics, Physics, and Chemistry. Each section carries 30 questions, which would add up to a total of 90 questions. In that, the candidates are obliged to write 75 questions. The total mark for this examination is 300.\u00a0<\/span><\/p>\n<p>Also See:\u00a0<a href=\"https:\/\/www.aakash.ac.in\/blog\/jee-main-2022-session-1-day-2-exam-live-updates-paper-analysis-difficulty-level-student-reactions\/\" data-wpel-link=\"internal\">JEE Main 2022 Exam Live Updates<\/a><\/p>\n<p><span style=\"font-weight: 400;\">Mathematics<\/span><span style=\"font-weight: 400;\"> is one of the sections in <a href=\"https:\/\/www.aakash.ac.in\/jee-main-exam\">JEE Main 2022<\/a>. The Maths section in JEE will contain 20 Multiple Choice Questions and 10 numerical questions. They are divided into Sections A and B. Every correct answer will be awarded 4 marks, while 1 mark will be deducted for wrong answers. Unattended questions will neither be awarded nor be deducted any mark.<\/span><\/p>\n<h2><a href=\"https:\/\/www.aakash.ac.in\/jee-crash-courses\">Click Here to Register for JEE Main Crash Courses 2023 at Aakash Byju&#8217;s<\/a><\/h2>\n<p><span style=\"font-weight: 400;\">This article lets us see what maths questions are asked in <\/span><span style=\"font-weight: 400;\"><a href=\"https:\/\/www.aakash.ac.in\/jee-main-previous-year-question-papers\">JEE Main Previous year&#8217;s question papers.<\/a><\/span><\/p>\n<h2>Previous Year Questions &#8211; JEE Mathematics<\/h2>\n<p><span style=\"font-weight: 400;\">Given-below is the most commonly asked questions in previous years&#8217; question papers:<\/span><\/p>\n<p><b>Q1. <\/b><span style=\"font-weight: 400;\">The number of integral values of m so that the abscissa of point of intersection of lines <\/span><span style=\"font-weight: 400;\">3x + 4y = 9 and y = m x + 1<\/span><span style=\"font-weight: 400;\"> is also an integer is:<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ul>\n<li aria-level=\"1\"><span style=\"font-weight: 400;\">1<\/span><\/li>\n<\/ul>\n<ul>\n<li aria-level=\"1\"><span style=\"font-weight: 400;\">2<\/span><\/li>\n<\/ul>\n<ul>\n<li aria-level=\"1\"><span style=\"font-weight: 400;\">3<\/span><\/li>\n<\/ul>\n<ul>\n<li aria-level=\"1\"><span style=\"font-weight: 400;\">5<\/span><\/li>\n<\/ul>\n<p><b>Answer: Option B &#8211; 2<\/b><\/p>\n<p><b>Q2.<\/b><span style=\"font-weight: 400;\"> Choose the correct statement about two circles whose equations are given below:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + <\/span><span style=\"font-weight: 400;\">y<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 10 x \u2013 10 y + 41 = 0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + <\/span><span style=\"font-weight: 400;\">y<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 22 x \u2013 10 y + 137 = 0<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ul>\n<li aria-level=\"1\"><span style=\"font-weight: 400;\">circles have the same centre<\/span><\/li>\n<\/ul>\n<ul>\n<li aria-level=\"1\"><span style=\"font-weight: 400;\">circles have no meeting point<\/span><\/li>\n<\/ul>\n<ul>\n<li aria-level=\"1\"><span style=\"font-weight: 400;\">circles have only one meeting point<\/span><\/li>\n<\/ul>\n<ul>\n<li aria-level=\"1\"><span style=\"font-weight: 400;\">circles have two meeting points<\/span><\/li>\n<\/ul>\n<p><b>Answer: Option C &#8211; circles have only one meeting point<\/b><\/p>\n<p><b>Q3.<\/b><span style=\"font-weight: 400;\"> Let <\/span><span style=\"font-weight: 400;\">\u00a0 <\/span><span style=\"font-weight: 400;\"> be the real roots of the equation, <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\"> + a<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + bx + c = 0<\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\">(a, b, c\u00a0 R<\/span><span style=\"font-weight: 400;\"> and <\/span><span style=\"font-weight: 400;\">a, b\u00a0 0)<\/span><span style=\"font-weight: 400;\">. If the system of equations (in, <\/span><span style=\"font-weight: 400;\">u, v,w<\/span><span style=\"font-weight: 400;\">) given by <\/span><span style=\"font-weight: 400;\"> u +\u00a0 v +\u00a0 w = 0, \u00a0 u +\u00a0 v +\u00a0 w = 0;\u00a0 u +\u00a0 v +\u00a0 w = 0<\/span><span style=\"font-weight: 400;\"> has non-trivial solution, then the value of 2 a b is:<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">3<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option B &#8211; 3<\/b><\/p>\n<p><b>Q4.<\/b><span style=\"font-weight: 400;\"> The equation of one of the straight lines which passes through the point (1,3) and makes an angles <\/span><span style=\"font-weight: 400;\">(<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">)<\/span> <span style=\"font-weight: 400;\"> with the straight line, <\/span><span style=\"font-weight: 400;\">y+1=3 <\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> x<\/span><span style=\"font-weight: 400;\"> is:<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4 <\/span><span style=\"font-weight: 400;\">2 x<\/span><span style=\"font-weight: 400;\"> + 5 y &#8211; <\/span><span style=\"font-weight: 400;\">15 + 4<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = 0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">5 <\/span><span style=\"font-weight: 400;\">2 x<\/span><span style=\"font-weight: 400;\"> + 4 y &#8211; <\/span><span style=\"font-weight: 400;\">15 + 4<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = 0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4 <\/span><span style=\"font-weight: 400;\">2 x<\/span><span style=\"font-weight: 400;\"> + 5 y &#8211; 4 <\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">= 0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4 <\/span><span style=\"font-weight: 400;\">2 x<\/span><span style=\"font-weight: 400;\"> &#8211; 5 y &#8211; <\/span><span style=\"font-weight: 400;\">5 + 4<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = 0<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option A &#8211; <\/b><span style=\"font-weight: 400;\">4 <\/span><span style=\"font-weight: 400;\">2 x<\/span><span style=\"font-weight: 400;\"> + 5 y &#8211; <\/span><span style=\"font-weight: 400;\">15 + 4<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = 0<\/span><\/p>\n<p><b>Q5.<\/b><span style=\"font-weight: 400;\"> If <\/span><span style=\"font-weight: 400;\"> x<\/span> <span style=\"font-weight: 400;\">\u00a0&#8211; x<\/span> <span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">3<\/span> <span style=\"font-weight: 400;\"> is equal to L, then the value of (6L + 1) is<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1\/6<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">3\/7<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option D &#8211; 2<\/b><\/p>\n<p><b>Q6.<\/b><span style=\"font-weight: 400;\"> A vector <\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\"> has components 3p and 1 with respect to a rectangular Cartesian system. This system has been rotated through a certain angle (about its origin) in the anticlockwise direction. If, with respect to the new system, <\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\"> has components <\/span><span style=\"font-weight: 400;\">p + 1<\/span><span style=\"font-weight: 400;\"> and <\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\">, then a value of p is equal to:<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">3<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">&#8211; 4<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">12<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">&#8211; 1<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option D &#8211; &#8211; 1<\/b><\/p>\n<p><b>Q7.<\/b><span style=\"font-weight: 400;\"> For the four circles M, N, O and P, given below are the four equations :<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Circle M: <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + <\/span><span style=\"font-weight: 400;\">y<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = 1<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Circle N: <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + <\/span><span style=\"font-weight: 400;\">y<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2 x = 0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Circle O: <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + <\/span><span style=\"font-weight: 400;\">y<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2x \u2013 2y + 1 = 0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Circle P: <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + <\/span><span style=\"font-weight: 400;\">y<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2y = 0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">If the centres of the M and N circles are joined together, further centres of the circles N and O are joined together. Moreover, the centres of the circles O and P are joined together. Finally, the centres of the circles P and M are joined together; then, these lines form the sides of a:<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Rhombus<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Square<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Parallelogram<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Rectangle<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option B &#8211; Square<\/b><\/p>\n<p><b>Q8.<\/b><span style=\"font-weight: 400;\"> If <\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\"> are natural numbers such that <\/span><span style=\"font-weight: 400;\">100 \u03b1 &#8211; 199 \u03b2 = <\/span><span style=\"font-weight: 400;\">100<\/span> <span style=\"font-weight: 400;\">100<\/span><span style=\"font-weight: 400;\"> + <\/span><span style=\"font-weight: 400;\">99<\/span> <span style=\"font-weight: 400;\">101<\/span><span style=\"font-weight: 400;\"> + <\/span><span style=\"font-weight: 400;\">98<\/span> <span style=\"font-weight: 400;\">102<\/span><span style=\"font-weight: 400;\"> + \u2026 + <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\"> (199)<\/span><span style=\"font-weight: 400;\">, then will be the slope of the line passing through <\/span><span style=\"font-weight: 400;\">()<\/span><span style=\"font-weight: 400;\"> and origin?<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">510<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">550<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">560<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">590<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option B &#8211; 550<\/b><\/p>\n<p><b>Q9.<\/b><span style=\"font-weight: 400;\"> The real-valued function <\/span><span style=\"font-weight: 400;\">f <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">=<\/span><span style=\"font-weight: 400;\">cose<\/span><span style=\"font-weight: 400;\">c<\/span><span style=\"font-weight: 400;\">-1<\/span><span style=\"font-weight: 400;\"> x<\/span><span style=\"font-weight: 400;\">x-<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">, where [x] indicates the greatest integer less than or equal to x, is defined for all x belonging to:<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">all reals except integers<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">all non-integers except the interval [\u2013 1, 1]<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">all integers except 0, \u2013 1, 1<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">all reals except the interval [\u2013 1, 1]<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option B &#8211; all non-integers except the interval [\u20131, 1]<\/b><\/p>\n<p><strong>Also Read:<\/strong><\/p>\n<p><a href=\"https:\/\/www.aakash.ac.in\/blog\/tips-to-crack-jee-main\/\">How to Prepare for JEE Main 2022? Top 5 Tips to Crack the exam<\/a><\/p>\n<p><a href=\"https:\/\/www.aakash.ac.in\/blog\/1-month-preparation-plan-for-every-jee-aspirant\/\">JEE Mains in 30 Days: 1 Month Preparation Plan For Every JEE Main 2022 Aspirant<\/a><\/p>\n<p><b>Q10.<\/b><span style=\"font-weight: 400;\"> If the functions are defined as <\/span><span style=\"font-weight: 400;\">f <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"> and as <\/span><span style=\"font-weight: 400;\">g <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">1 -x<\/span><span style=\"font-weight: 400;\">, then identify the common domain of the below-specified functions:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0192 + g,\u00a0 \u0192\u00a0 \u2013 g, <\/span><span style=\"font-weight: 400;\">\u0192<\/span><span style=\"font-weight: 400;\">g<\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\">g<\/span><span style=\"font-weight: 400;\">\u0192<\/span><span style=\"font-weight: 400;\">,\u00a0 g \u2013 \u0192 where (\u0192 \u00b1 g) (x) = \u0192 (x) \u00b1 g(x),\u00a0 <\/span><span style=\"font-weight: 400;\">\u0192<\/span><span style=\"font-weight: 400;\">g<\/span><span style=\"font-weight: 400;\">(x)<\/span> <span style=\"font-weight: 400;\">f <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">g <\/span><span style=\"font-weight: 400;\">x<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">0 \u2264x \u22641<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">0 \u2264x &lt;1<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">0 &lt;x &lt;1<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">0 &lt;x \u22641<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option C &#8211; <\/b><span style=\"font-weight: 400;\">0 &lt;x &lt;1<\/span><\/p>\n<p><b>Q11.<\/b><span style=\"font-weight: 400;\"> What will be the sum of all the 4-digit distinct numbers formed with the digits 1, 2, 2 and 3?<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">26664<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">122664<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">22264<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">122234<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option A &#8211; 26664<\/b><\/p>\n<p><strong>Watch our video on Learn with the Best JEE Experts &#8211; JEE Mission 2022<\/strong><\/p>\n<div class=\"jeg_video_container jeg_video_content\"><iframe loading=\"lazy\" title=\"NEET Biology 2022 Important Questions and Answers (Part C) - Smart Mock Test 5 | NEET 2022 Zoology\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/zNp-YEcRiqc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/div>\n<p><b>Q12.<\/b><span style=\"font-weight: 400;\"> Which of the ones mentioned below is logically equivalent to <\/span><span style=\"font-weight: 400;\">(p q) ( ~p\u00a0 q)<\/span><span style=\"font-weight: 400;\">?<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">p q<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">(p ^ q)<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">~p q<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">p ^ ~q<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option A &#8211; <\/b><span style=\"font-weight: 400;\">p q<\/span><\/p>\n<p><b>Q13.<\/b><span style=\"font-weight: 400;\"> If the coefficient of <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">7<\/span><span style=\"font-weight: 400;\"> and <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">-7<\/span><span style=\"font-weight: 400;\"> in the expansion of <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">b x<\/span><span style=\"font-weight: 400;\">11<\/span><span style=\"font-weight: 400;\"> and <\/span><span style=\"font-weight: 400;\">x + <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">b <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">11<\/span><span style=\"font-weight: 400;\">respectively are equal, then what will be the value b:<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">&#8211; 1<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">0<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option A &#8211; 1<\/b><\/p>\n<p><b>Q14.<\/b><span style=\"font-weight: 400;\"> If the mean and variance of the following eight observations: 10, 13, 6, 7, a, 12, b, 12 are 9 and 37\/4, respectively, what will be the value of <\/span><span style=\"font-weight: 400;\">a-b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">?<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">20<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">54<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">16<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">49<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option C &#8211; 16<\/b><\/p>\n<p><b>Q15.<\/b><span style=\"font-weight: 400;\"> If <\/span><span style=\"font-weight: 400;\">\u03b1<\/span><span style=\"font-weight: 400;\"> and <\/span><span style=\"font-weight: 400;\">\u03b2<\/span><span style=\"font-weight: 400;\"> are the roots of the equation <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 <\/span><span style=\"font-weight: 400;\">20<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">4<\/span><span style=\"font-weight: 400;\"> x + <\/span><span style=\"font-weight: 400;\">5<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = 0<\/span><span style=\"font-weight: 400;\">, then the value of <\/span><span style=\"font-weight: 400;\">8<\/span><span style=\"font-weight: 400;\"> + <\/span><span style=\"font-weight: 400;\">8<\/span><span style=\"font-weight: 400;\"> is equal to:<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">25<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">50<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">75<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">100<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option B &#8211; 50<\/b><\/p>\n<p><b>Q16.<\/b><span style=\"font-weight: 400;\"> Let n be a 2-digit natural number. If n is selected at random, what will be the probability that <\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> \u2013 2<\/span><span style=\"font-weight: 400;\"> is a multiple of 3?<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1\/3<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2\/3<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1\/2<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">0<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option C &#8211; 1\/2<\/b><\/p>\n<p><b>Q17.<\/b><span style=\"font-weight: 400;\"> If tangents to the circle <\/span><span style=\"font-weight: 400;\">x \u2013 1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + <\/span><span style=\"font-weight: 400;\">y \u2013 3<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = 22<\/span><span style=\"font-weight: 400;\"> are drawn from the point (\u20131, 1) such that the tangents\u2019 points of contact are A and B. Also, if a point P lies on the circle such that AB = AP, what will be the area of <\/span><span style=\"font-weight: 400;\">\u0394<\/span><span style=\"font-weight: 400;\">ABP?<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1\/4<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">7<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option C &#8211; 4<\/b><\/p>\n<p><b>Q18.<\/b><span style=\"font-weight: 400;\"> If <\/span><span style=\"font-weight: 400;\">sec<\/span> <span style=\"font-weight: 400;\">y<\/span> <span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">dy<\/span><span style=\"font-weight: 400;\">dx<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">sin<\/span> <span style=\"font-weight: 400;\">\u00a0(x + y)<\/span> <span style=\"font-weight: 400;\">\u00a0+ (x &#8211; y)<\/span> <span style=\"font-weight: 400;\">; <\/span><span style=\"font-weight: 400;\">y <\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\"> = 0<\/span><span style=\"font-weight: 400;\">, then what will be value of <\/span><span style=\"font-weight: 400;\">5 <\/span><span style=\"font-weight: 400;\">y<\/span><span style=\"font-weight: 400;\">&#8216;<\/span> <span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">?<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">3<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option C \u2013 2<\/b><\/p>\n<p><b>Q19.<\/b><span style=\"font-weight: 400;\"> A circle with a centre <\/span><span style=\"font-weight: 400;\">(2, 3) <\/span><span style=\"font-weight: 400;\">passes through the origin. A diameter MN is such that it is perpendicular to the line that joins the centre of the circle and its origin. What are the coordinates of points M and N?<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">(\u2013 1, 5) &amp; (5, 1)<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">(\u2013 2, 5) &amp; (\u2013 5, 1)<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">(3, 6) &amp; (5, 1)<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">(\u2013 1, 1) &amp; (5, \u2013 1)<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option A &#8211; (\u2013 1, 5) &amp; (5, 1)<\/b><\/p>\n<p><b>Q20. <\/b><span style=\"font-weight: 400;\">The area bounded by the curve <\/span><span style=\"font-weight: 400;\">y = <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> and the line <\/span><span style=\"font-weight: 400;\">y \u2013 x = 2<\/span><span style=\"font-weight: 400;\"> is:<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">7\/2<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">9\/2<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">6\/5<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4\/3<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option B &#8211; 9\/2<\/b><\/p>\n<p><b>Q21.<\/b><span style=\"font-weight: 400;\"> A circle that touches the y-axis at (0, 6) and contains an x-intercept equal to <\/span><span style=\"font-weight: 400;\">6 <\/span><span style=\"font-weight: 400;\">5<\/span><span style=\"font-weight: 400;\">, what will be the circle&#8217;s radius?<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">9<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">19<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option C &#8211; 9<\/b><\/p>\n<p><b>Q22.<\/b><span style=\"font-weight: 400;\"> Three vectors <\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\">b<\/span><span style=\"font-weight: 400;\">,\u00a0 and <\/span><span style=\"font-weight: 400;\"> c<\/span><span style=\"font-weight: 400;\"> with magnitudes <\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">, 1 and 2 respectively follow the given relation <\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">= <\/span><span style=\"font-weight: 400;\">b<\/span><span style=\"font-weight: 400;\">*<\/span><span style=\"font-weight: 400;\">b<\/span><span style=\"font-weight: 400;\">* <\/span><span style=\"font-weight: 400;\">c<\/span><span style=\"font-weight: 400;\">. The acute angle between the vectors <\/span><span style=\"font-weight: 400;\">b<\/span><span style=\"font-weight: 400;\"> &amp; <\/span><span style=\"font-weight: 400;\">c<\/span> <span style=\"font-weight: 400;\">is <\/span><span style=\"font-weight: 400;\">\u03b8<\/span><span style=\"font-weight: 400;\">. What will be the value of <\/span><span style=\"font-weight: 400;\">(1+<\/span><span style=\"font-weight: 400;\">tan<\/span> <span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\">?<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">9<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">13<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option A &#8211; 2<\/b><\/p>\n<p><b>Q23.<\/b><span style=\"font-weight: 400;\"> If two sides of a parallelogram are given as: <\/span><span style=\"font-weight: 400;\">4x + 5y = 0<\/span><span style=\"font-weight: 400;\"> and <\/span><span style=\"font-weight: 400;\">7x + 2y = 0<\/span><span style=\"font-weight: 400;\">. If one of the diagonals is <\/span><span style=\"font-weight: 400;\">11x + 7y = 9<\/span><span style=\"font-weight: 400;\">, then what will be the other diagonal pass through the point?<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\">, &#8211;<\/span><span style=\"font-weight: 400;\">4<\/span><span style=\"font-weight: 400;\">3<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1, 1<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">,<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">4<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2, 3<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option B &#8211; (1, 1)<\/b><\/p>\n<p><b>Q24.<\/b><span style=\"font-weight: 400;\"> The point <\/span><span style=\"font-weight: 400;\">P <\/span><span style=\"font-weight: 400;\">a, b<\/span><span style=\"font-weight: 400;\"> undergoes the below-mentioned transformation to a new coordinate <\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\">&#8216;<\/span> <span style=\"font-weight: 400;\">&#8211; <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\">7<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Reflection about <\/span><span style=\"font-weight: 400;\">y = x<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Translation through 2 units in the +ve direction of the x-axis<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Rotation through an angle <\/span><span style=\"font-weight: 400;\">4 <\/span><span style=\"font-weight: 400;\"> in an anticlockwise sense about the origin<\/span><\/li>\n<\/ul>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">9<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option D &#8211; 9<\/b><\/p>\n<p><b>Q25.<\/b><span style=\"font-weight: 400;\"> For an ellipse E, the centre lies at the point <\/span><span style=\"font-weight: 400;\">(3, \u2013 4), <\/span><span style=\"font-weight: 400;\"> one of the vertices is at <\/span><span style=\"font-weight: 400;\">(5, \u2013 4)<\/span><span style=\"font-weight: 400;\"> and one of its foci is at <\/span><span style=\"font-weight: 400;\">(4, \u2013 4)<\/span><span style=\"font-weight: 400;\">. If the equation of tangent on the ellipse E is <\/span><span style=\"font-weight: 400;\">m x \u2013 y = 4 (m &gt; 0)<\/span><span style=\"font-weight: 400;\">, what is the value of <\/span><span style=\"font-weight: 400;\">5 <\/span><span style=\"font-weight: 400;\">m<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">?<\/span><\/p>\n<p><b>Options:<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">3<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">5<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">7<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">9<\/span><\/li>\n<\/ol>\n<p><b>Answer: Option A &#8211; 3<\/b><\/p>\n<h2>Conclusion<\/h2>\n<p><span style=\"font-weight: 400;\">To secure maximum marks in the Maths section of the <\/span><a href=\"https:\/\/www.aakash.ac.in\/jee-coaching-centers\"><span style=\"font-weight: 400;\">JEE examination<\/span><\/a><span style=\"font-weight: 400;\">, it is essential to go through and solve the problems given in previous years&#8217; question papers. It will help the candidates enhance their time-management and problem-solving skills.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">In this article, we have given 25 questions that were asked in previous year&#8217;s papers along with their answers. The students can make use of it while they prepare for their examinations.<\/span><\/p>\n<h2>FAQs about JEE Main Maths Previous Year Questions With Solutions<\/h2>\n\t\t<div class=\"wp-faq-schema-wrap\">\n\t\t\t\t\t\t<div class=\"wp-faq-schema-items\">\n\t\t\t\t\t\t\t\t\t<h3>1. Is JEE Main Maths hard?<\/h3>\n\t\t\t\t\t<div class=\"\">\n\t\t\t\t\t\t<p>Compared to the other sections in JEE Main, Maths is the hardest one. It is completely analytical and involves numerous formulae; it is quite hard to get all the answers right and very time-consuming. Each question takes a significant amount of time to answer. However, if you prepare for it enough, you can easily score good marks.<\/p>\n<p>Furthermore, the students should know the important topics and beware of the most frequently asked questions.<\/p>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t<h3>2. What are the tips one can use to study effectively?<\/h3>\n\t\t\t\t\t<div class=\"\">\n\t\t\t\t\t\t<p>The following are tips for students to help them study effectively:<\/p>\n<p>- Create a timetable<br \/>\n- Set a time limit for each chapter<br \/>\n- Use flashcards. They are as useful as taking notes<br \/>\n- Practice regularly<br \/>\n- Do not listen to songs while preparing<br \/>\n- Avoid using social media while studying<br \/>\n- Study in a good environment<br \/>\n- Take necessary amounts of breaks<br \/>\n- Be productive with time<\/p>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\n","protected":false},"excerpt":{"rendered":"<p>JEE is a common entrance exam for students who wish to pursue their engineering higher studies in India&#8217;s most prestigious institutions, such as IITs and NITs. JEE Main has three sections for BE\/B. Tech students are in Mathematics, Physics, and Chemistry. Each section carries 30 questions, which would add up to a total of 90 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":196055,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3719],"tags":[],"class_list":["post-196046","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-jee"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>JEE Main Maths Previous Year Questions With Solutions<\/title>\n<meta name=\"description\" content=\"JEE Main Maths Previous Year Questions With Solutions: This article lets us see what questions are asked in past year&#039;s question papers in JEE Mathematics.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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