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Question Bank for JEE Main 2020 and NEET 2020 released by Gujarat Board
Gujarat Secondary and Higher Secondary Education Board (GSEB) has released a Question Bank that comprises four key subjects, i.e, Physics, Chemistry, Biology and Mathematics common to the official syllabus of all national-level and state-level entrance exams like JEE Main 2020, NEET 2020, GUJCET 2020 and so on. The question bank is released on the official gujrat-education.gov.in website. Students can download the question banks by clicking on the link given below.
Download the question bank in Gujrati here
Download the question bank in English here
Solving the question bank will turn out to be fruitful for all the aspirants who are due to take any of the entrance examinations in the coming months and get desired results. The board has released the question bank in Gujrati and English due to the fact that the majority of students from Gujarat study in either of the two languages. Students can download these question papers in any of the two languages and practice them to increase their chances of securing a rank and get into the top institutions.
How to Download Question Bank?
To download the question bank from the official website of GSEB students need to follow the steps mentioned below:-
- Click on “Question Bank”
- Choose on the language and download the question paper from the links appear on the screen.
Revised schedule released for JEE Main 2020
Owing to the COVID-19 pandemic and the consequent lockdown, JEE Main 2020, like all the other state and national level entrance exams, had been postponed. It was earlier scheduled to be held from 5th to 11th April. However, the exam had to be rescheduled to a later date in order to conform to the norms of the lockdown amidst the outbreak.
On 5th May 2020, Minister Mr. Ramesh Pokhriyal, through a webinar announced the JEE Main 2020 new examination dates. The exam will now be conducted from 18th – 23rd July 2020. Admit Cards will be issued 10 – 14 days prior to the exam.
JEE Main Preparation Module Available for Free on National Digital Library of India (NDLI)
The JEE Main April Session and JEE Advanced examination for the year 2020 has been delayed until June 2020 because of the outbreak of coronavirus (SARS-CoV-2) causing the fatal COVID-19 disease with a daily exponential increase in infected patients. Cases have now crossed over 35,000 and fatalities have been well over 1,000. Multiple authorities from the world as well as India, including the conducting authority NTA, are trying to combat this disease. NDLI is now providing all the required facilities for students within their reach for studying at home.
National Digital Library of India (NDLI) already provided the JEE Advanced Preparation Module compiled by IIT Kharagpur for students last month. Now, NDLI has also provided the JEE Main Preparation Module for students who have been studying at home.
NDLI tweeted, “NDLI Tutor IIT-JEE already has the solutions for IIT-JEE ADVANCED and now keeping in mind the benefit of all aspiring IITians, it has been upgraded with the IIT-JEE MAINS solutions too. Begin preparing from our archives.”
NDLI Tutor IIT-JEE already has the solutions for IIT-JEE ADVANCED & now keeping in mind the benefit of all aspiring IIT-ians, it has been upgraded with the IIT-JEE MAINS solutions too. Begin preparing from our archives at : https://t.co/b9joJoVwqj
#AnytimeLearning #IITJEE #IIT pic.twitter.com/y9t8RbeDet
— NDL India (@NDLIndia) April 25, 2020
Currently, JEE Main Preparation Module only includes JEE Main 5 Years’ Solved Papers by NDLI Tutor.
Steps to access JEE Main Preparation Module
To access JEE Main Preparation Module, students have to follow these steps-
- Head over to the official website of NDLI – ndl.iitkgp.ac.in
- Once the website is loaded, a pop-up will appear.
- Click on “School” button. Students can also click on “Corona Outbreak: Study From Home”.
- A new tab will open.
- Here, students will find JEE Preparation Materials under Video Lectures
- Click on JEE Main 5 Years’ Solved Papers.
- Here, students will find JEE Main Papers from 2014 to 2018 Fully Solved.
How is JEE Main Preparation Module useful?
A few points which prove the usefulness of this JEE Main Preparation Module are given below-
- Candidates can jump from one question to another using the question links provided on the right side of the web module.
- Candidates can download the whole question paper as PDF and use these question papers offline.
- NDLI Application for Android and iOS can also be used to access these modules free of cost.
- Questions are available in English, Hindi and Gujarati similar to the actual examination.
- Solutions are hidden and are visible only when the user clicks on “Solution to Question..” This engages the students to try the questions first, rather than reading the whole solution at first instance.
Candidates are advised to visit NDLI Website to access study material for JEE Main 2020
JEE Main 2020 April Session has been delayed until June 2020 as per the statement by Union HRD Minister Mr Ramesh Pokhriyal. There is uncertainty for the exam being held even in June 2020. Students are anxious as this will delay the entire admission process directly affecting their studies as a result. It is advised that students, must keep calm, and trust the exam authorities. Moreover, exam authorities as well as colleges will consider these extreme situations and will probably relax the regulations for students in this academic year. Ministry of Human Resource Development is also undergoing discussions with other authorities over the situation.
JEE Main Preparation Tips for Mathematics: Important Topics and Strategies
Mathematics is probably the lifesaver for a large number of aspirants of JEE Main. Preparation for JEE Main Mathematics is comparatively easier than the other two sections and due to a foundation based on Sets, Relations and Functions, the learning does not require to start everything from scratch. The first step that comes under the JEE Main Preparation Tips for Mathematics is to be updated with the syllabus of JEE Main Mathematics 2020. Being well informed with the syllabus will definitely help you work upon the most important topics.
Mathematics is yet considered to be hard because of the fear created out of it. In order to overcome your fear, you are advised to start preparing Mathematics pretty well in advance. Candidates are advised to practice a sufficient number of IIT JEE previous year question papers. When you will start regularly solving previous years papers, you will be able to know the type of questions, the patterns that might be present in the upcoming examination and will also be able to figure out your weaknesses and strengths. Let us start with some very basic JEE Main Preparation Tips for Mathematics.
JEE Main Preparation Tips for Mathematics: Basic Rules to Follow
- Revision is Important – Organise your study time and revision time. Revision ensures you are on track with the topics that are not under purview but must be worked on. Take regular breaks and practice previous years’ JEE Main question papers. Revise the topics every alternate day or at least twice a week.
- Topic-wise Mocks– Attempting mock tests and practice papers can actually tell what level of preparation is needed. Solving the question papers enables the candidates to know difficulty levels and their own preparation against it so they can work on their weak areas. With online mocks, a deep analysis is easily available online, to understand accuracy, strong topics, time-consuming topics and weak topics.
- Speedy Calculations – With better practice, students will build speed in core topics. This speed must be maintained during the examination as well. Since there is no sectional timing, ensure that you solve enough questions from each section within 1 and a half hour (90 minutes) such that the score reaches the expected cutoff.
- Accurate Answers – If you follow the speed rule in the first 90 minutes, follow the accuracy rule in the next 90 minutes. Instead of solving maximum questions, try solving what you can, but with accurate answers. This will help build your score and probably help in overall rank considered for IITs.
JEE Main Preparation Tips for Mathematics: Key Pointers
- The trend of questions from previous year question papers can be analysed. Questions come from almost every chapter in the exam.
- Apply for the official JEE Main Mock Test. It will help you overcome the nervousness of exam halls.
- You cannot learn a formula by reading but only through practice. The more you practice, the better you perform.
- Solve online mock tests on a table and chair. It gives an exam hall viewpoint and helps with time management.
- The graphical approach helps a lot in solving Mathematics questions. If you can learn how to create a graph, many questions of calculus and trigonometry could be solved in a blink.
- Hit and trial method works in some questions where reverse calculations might be time-consuming. Use it with care.
- While solving questions, make sure the most common errors of addition, subtraction, multiplication or division do not occur. Marks in JEE Main are only for the right answer, none for steps.
- Strengthen your grip on function theory because it is the foundation for almost each and every topic of class 11th and 12th.
- If solving questions on a rough sheet, use as many sheets as required. Do not scribble over and over on the same sheet. One may never know when the answer might get mixed up with another question.
- As soon as the timer starts on the computer, spend around 5 to 10 minutes searching for easy questions from all the 25 questions. 40% to 50% of JEE Main Mathematics questions are easy and scorable. Around 20% to 30% are moderate and almost 10% to 20% difficult.
- Instead of getting entangled in tough questions, you must try to solve easy questions while giving two to three minutes towards each question. Approximately, 20 questions can be solved in 60 minutes if each question takes a maximum duration of 3 minutes. Every single mark counts. Don’t waste time.
- Focus on the topics you have a good grip over. Pay attention to them. Memorise formulas and concepts of all the major topics.
JEE Main Preparation Tips for Mathematics: Crucial Topics
- Calculus: Calculus is one of the largest topics of mathematics. It is divided into two major studies – Differential and Integral calculus. Key topics to study in differential calculus are – limits and continuity, application of derivatives, differentiation. Key topics from integral calculus are – Indefinite integral, definite integral, the area under curves.
- Coordinate Geometry: Comparatively easy and scorable, coordinate geometry is the study of shapes and curves on a graph. Major topics to be covered under coordinate geometry are – straight lines, hyperbola, parabola, ellipse, circle.
- Trigonometry: Trigonometry has been considered one of the most important topics since class 10th. Students must have a command over the basics of trigonometry. JEE Main and other exams have questions from trigonometric ratios and trigonometric functions. These are scorable and are moderately tough.
- Algebra: This is the vastest topic of Mathematics. Questions from algebra could vary from easy to very hard. It depends on your ability to decipher how long a question can take. Major topics to be covered under algebra are – sets, relations and functions, matrices and determinants, permutations and combinations, complex numbers, probability, differential equations, quadratic equations and expressions, progressions and series, binomial theorem.
How to prepare JEE Main Mathematics by studying at home?
It is a proven fact that when you are at your home, books are the best source of knowledge to study properly. But it is also very important to note that due to the changed exam mode into the computer-based environment, JEE Main is not exactly a pen and paper-based examination. Students also require to learn various tricks over how to increase productivity while attempting the full examination of 3 hours. Given below are some JEE Main Preparation Tips for Mathematics to Study from Home.
Question Papers of JEE Main Mathematics (by Allen Kota)
To begin with the preparation, it is often suggested that Computers and Smartphones are typically contributing to distractions. To end this struggle for students, download these question paper PDFs of JEE Main 2019 Mathematics section prepared by Allen Kota. If possible, it is also suggested to print these papers and solve them offline in a traditional pen and paper mode. Do remember to first use “Papers & Answers” as this pushes you to attempt the questions on your own, rather than copying the whole solution.
Date | Shift | Paper & Answer | Paper & Solutions |
January 9 | Shift 1 | Click Here | Click Here |
Shift 2 | Click Here | Click Here | |
January 10 | Shift 1 | Click Here | Click Here |
Shift 2 | Click Here | Click Here | |
January 11 | Shift 1 | Click Here | Click Here |
Shift 2 | Click Here | Click Here | |
January 12 | Shift 1 | Click Here | Click Here |
Shift 2 | Click Here | Click Here |
Free Online Mock Tests Provided by NTA
The online mock tests provided by NTA (National Testing Agency) are a simulation of the actual exam which will help students understand how to attempt the examination in a computer-based environment. The only disadvantage here is that these are full mock tests and not subject-wise mock tests. Although, students can utilise this portal if they have completed the syllabus for JEE Main Mathematics and now are under revision mode.
- To access the mock tests head over to this website – https://nta.ac.in/quiz.
- After this, just select the examination and paper from 2020, 2019, 2018 and 2017 sessions.
- Once selected, start your mock test.
Latest News Updates
- NTA Re-opens JEE Main Application Form For Candidates, Last Date To Apply Is 24th May
- Turn Lockdown Period Into An Opportunity”, says Anand Kumar of Super 30 to JEE Aspirants
- JEE Main 2020 Syllabus not reduced, says NTA
- JEE Main 2020: Dates announced by the MHRD, Examination to be conducted from July 18 to 23, 2020
- New Batches for IITs and NITs to start in September 2020
NTA Content-Based Lectures (by IIT-PAL)
National Testing Agency has provided video lectures recorded by a few reputed IIT Professors under the nemesis of IIT-PAL on Youtube. These lectures are divided into sub-topics for each chapter to focus only on main topics. There are more than 200 videos of approximately 50 to 60-minute runtime for each video. To access these videos-
- Head over to the official website of NTA – www.nta.ac.in
- Click on the ‘Students’ tab.
- Under the ‘Test Practice’ section, select ‘Content Based Lectures’.
E-Learning Platforms
There are various e-learning platforms which are the best source for preparation of almost each and every competitive examination. In the past few years, the use of smartphones and online courses have increased multiple folds due to decreased cost of the internet in India. A lot of Ed-Tech companies started growing and now provide video lectures, mock tests, study material and a lot more stuff which helps students improve their preparation levels. Given below are some E-learning portals which can help students boost their JEE Main Mathematics Preparation.
- Unacademy – This is the largest learning platform in India with a continuously growing user base. Students can watch completely free lectures on various subjects and topics directly streamed by the toppers of various examinations. Students can also interact with the educators or teachers through the comment section given below the video.
- EduRev – This application is a learning application which provides subject-wise notes and video lectures. It also houses a large number of Mock Tests and topic-wise tests for students to work on their weak topics. Students will also find a large database of questions from previous years provided within the application.
- Khan Academy – This application provides video lectures according to the curriculum of CBSE and for IIT JEE too. Video lectures of Khan Academy are very well explained to understand the topics of JEE Main Mathematics thoroughly. With each video lecture, students are also asked questions on the topic for which they earn points and badges as rewards.
- Vedantu – This application houses all the major resources required for a student. From Solutions of questions from books of major writers to All India Mock Tests and live video lectures, students will find all the necessary resources, completely free! The speciality of this application is their in-house WAVE technology which lets students (or users) interact with a question put-up on the screen by the educator.
Chapter-wise Weightage in JEE Main Mathematics
Given below is the chapter-wise weightage of JEE Main Mathematics which will help you understand what topics should be given more time. It is nonetheless a universal fact that about 30-40% of the syllabus is part of the Calculus which is divided into Limits and Derivatives, Differentiation, Integration, Applications of Calculus, Differential Equations and much more. Students who can complete Calculus build huge confidence to cover other chapters as well.
Topic | Number of Questions |
Sets, Relations and Functions | 1 |
Complex Numbers and Quadratic Equations | 2 |
Matrices and Determinants | 2 |
Permutations and Combinations | 1 |
Mathematical Induction | 1 |
Binomial Theorem and its applications | 1 |
Sequences and Series | 2 |
Limit, Continuity and Differentiability | 1 |
Differential Calculus | 4 |
Integral Calculus | 5 |
Differential Equations | 1 |
Coordinate Geometry | 2 |
Three Dimensional Geometry | 3 |
Vector Algebra | 1 |
Statistics and Probability | 2 |
Trigonometry | 2 |
Mathematical Reasoning | 1 |
Recommended Books for Preparing JEE Main Mathematics
Mathematics section requires comprehensive preparation. The following table represents some of the best books for JEE Main along with their author’s name that students can prefer for their Mathematical exam preparation:
Book | Author |
IIT Mathematics | M.L. Khanna |
Differential Calculus | Das Gupta |
Class XI and XII Mathematics | R.D. Sharma |
Trigonometry, Geometry Books | S.L. Loney |
Integral Calculus for IIT-JEE | Amit Agarwal |
Calculus and Analytic Geometry | Thomas and Finney |
Problems in Calculus of One Variable | I. A. Maron |
Higher Algebra | Hall and Knight |
Basic Sample Questions on Various Topics
Ques. The locus of the point of intersection of the lines xcost+(1-cost)y=asint and xsint-(1+cost)y+asint=0 is
1) x2-y2=a2 3) y2 = ax
2)x2+y2=a2 4) x2 = ay
Ans. Rearranging the above equations, we get
1-cost/sint=a-x/y and 1+cost/sint=a+x/y
multiplying the above equations ,we get x2+y2=a2
Ques. Lines ax+by+c=0, where 3a+2b+4c=0 & a,b,c all belong to the set of real numbers that are concurrent at the point?
1) (3,2) 3) (3,4)
2) (2,4) 4) (3/4, 1/2)
Ans. We know that,
3a+2b+4c =0
which equals (3/4)a+(1/2)b+c=0
So, the line passes through (3/4,1/2)
Ques. If the area of the triangle formed by the equation 8×2-6xy+y2=0 and the line 2x+3y=a is 7 then the value of a is?
1) 14 3) 7
2) 28 4) 17
Ans. Equation of the sides of the given triangle are y=2x, y=4x and 2x+3y=a
So, vertices of the triangle are (a/8,a/4);(a/14,2a/7) and (0,0)
By the determinant method, the area of the triangle formed by these coordinates comes out to be a2/112 which is equal to 7
This gives the value of a as 28.
Ques. If the line x=k; k= 1,2,3,…..,n meet the line y=3x+4 at the points Ak(xk,yk), k= 1,2,3…..,n then the ordinate of the centre of the mean position of points Ak, k= 1,2,3,…..,n is
1) n+1/2 3) 3(n+1)/2
2) 3n+11/2 4) None of the above
Ans. We have yk=3k+4, the ordinate of intersection of x=k and y=3x+4 . So the ordinate of the mean position of the points Ak k= 1,2,3,…..,n is
(1/n){sum of all yk’s} which comes out to be 3n+11/2
Ques. If the point (3,4) lies on the locus of the point of intersection of the lines xcost+ysint =a and xsint-ycost=b, the point (a,b) lies on the line 3x-4y=0 then |a+b|=?
1) 1 3) 7
2) 3 4) 12
Ans. Squaring and adding the given equations of the lines we get
x2+y2=a2+b2 as the locus of the point of intersection of these lines.
Since (3,4) lies on the locus we get
9+16=a2+b2
Also (a,b) lies on 3x-4y=0 so 3a-4b=0
Solving the two equations for a and b, we get |a+b|= 7
Ques. Equation of the circle with centre (-4,3) touching internally and containing the circle x2+y2=1is
1) x2+y2+8x-6y+9=0 3) x2+y2-8x+6y+9=0
2)x2+y2+8x-6y+11=0 4) x2+y2-8x+6y-11=0
Ans. Let the equation of the required circle be (x+4)2+(y-3)2=r2
If the above circle touches the circle x2+y2=1 internally, then the distance between the centres of the circles is equal to the difference of their radii
42+32=r-1
Which implies r=6
So the equation of the circle is x2+y2+8x-6y-11=0
Ques. If the normal chord at a point ‘t’ on the parabola y2=4axsubtends a right angle at the vertex, then the value of t is
1)4 3) 3
2)1 4) 2
Ans. Equation of the normal at ‘t’ to the parabola y2=4ax is y= -tx+2at+at3
The joint equation of the lines joining the vertex to the points of the intersection of parabola and the normal is
y2=4ax[y+tx/2at+t3]
4tx2-(2t+t3)y2+4xy=0
Since these lines are at right angles so the coefficient of x2+y2=0
So, t comes out to be 2.
Ques. The angle between a diagonal of a cube and one of its edges is,
1) cos-1(1/3) 3) /3
2) /4 4) /6
Ans. Let a= a1i, b=a1j ,c=a1k.
Then the vector d= a1(i+j+k) is a diagonal of the cube. The angle between one of the edges a, b or c and the diagonal d is given by,
cos=a.d/|a||d| which comes out to be cos-1(1/3).
Ques. Volume of the tetrahedron with vertices P(-1,2,0) ; Q(2,1,-3) ; R(1,0,1) and S (3,-2,3) is
1) 1/3 3) 1/4
2) 2/3 4) ¾
Ans. Volume of the tetrahedron is given by a scalar triple product,
Volume of tetrahedron= ⅙|PQ.(PR x PS)|
Here PQ, PR and PS are three vectors made from the above provided coordinates.
So, the volume of tetrahedron comes out to be ⅔ after solving the triple product.
Ques. If A,B,C and D are four points in space and |ABxCD+BCxAD+CAxBD|=(area of triangle ABC). Then the value of is-
1) 1 3) 3
2) 2 4) 4
Ans. Let D be the origin of reference and DA=a, DB= b, DC= c
So, |ABxCD+BCxAD+CAxBD|= |(b-a) x (-c) +(c-b) x (-a) + (a-c) x (-b)|
= 2|axb+bxc+cxa|
=2(2 area of ABC)
Hence equals 4
Ques. A unit tangent vector at t=2 on the curve x=t2+2,y=4t3-5,z=2t2-6t is?
Ans. The position vector of any point at t is r=(t2+2)i+(4t3-5)j+(2t2-6t) k
dr/dt=2ti+12t2j+(4t-6)k
At t=2, the above comes out to be 4i+48j+2k, and the unit vector comes out to be (1/580) 2i+24j+k
Ques. Let N be the foot of the perpendicular of length p from the origin to a plane and l,m,n be the direction cosines of ON, the equation of the plane is
1) px+my+nz=l 3) lx+my+pz=n
2) lx+py+nz =m 4) lx+my+nz=p
Ans. The coordinates of N are (pl,pm,pn) and let P(x,y,z) be any point on the plane. The direction cosines of PN are proportional to x-pl, y-pm and z-pm. Since ON is perpendicular to the plane, it is perp. To PN
Hence, l(x-pl)+m(y-pm)+n(z-pm)=0
lx+my+nz=p(l2+m2+n2)=p, which is the locus of P and is the required equation of the plane.
Ques. The image of the point (-1,3,4) in the plane x-2y = 0 is
1) 8,4,4 3) 15,11,4
2) 9/5, -13/5,4 4) 4,4,1
Ans. Required image of the line lies on the line through A(-1,3,4) and perpendicular to x-2y=0 that is on the line
x+1/1 = y-3/-2 = z-4/ 0 =t (say)
So, the coordinates of the image is (t-1,-2t+3,4)
This point also lies on the plane, so t comes out to be 14/5
So, the required image is (9/5, -13/5,4).
Ques. If (2,3,5) is one end of the diameter of the spherex2+y2+z2-6x-12y-2z+20=0 then the coordinates of the other end are
1) 4,9,-3 3) 4,3,3
2) 4,-3,3 4) 4,3,5
Ans. Let the other end of the diameter be (a,b,c) , then the equation of the sphere is (x-2)(x-a)+(y-3)(y-b)+(z-5)(z-c)=0
Which equals x2+y2+z2-(2+a)x-(3+b)y-(5+c)z+2a+3b+5c=0
Comparing the above equations of the sphere with the equation given and comparing the corresponding terms we get,
The required coordinates as (4,9,-3).
Ques. Four Persons independently solve a certain problem correctly with probabilities ½, ¾, ¼ and 1/8. Then the probability that the problem is solved correctly by at least one of them. [JEE Advanced 2013]
Ans. P(Problem solved by at least one of them)=1-P(Problem solved none of them)
=1-½*¼*¾*7/8
=1-21/256
=235/256
Ques. An unbiased coin is tossed. If the result is heads, a pair of unbiased dice is rolled, and the number obtained by adding the number on the two faces are noted. If the result is a tail, a card from a well-shuffled pack of 11 cards numbered 2, 3, 4…. .., 12 is picked & the number on the card is noted. What is the probability that the number noted is 7 or 8?
Ans. Let us define the events:
A : head appears.
B : Tail appears
C : 7 or 8 is noted.
We have to find the probability of C i.e. P (C)
P(C) = P(A) P (C/A) + P(B) P(C/B)
Now we calculate each of the constituents one by one P(A) = probability of appearing head=½
P(C/A) = Probability that event C takes place i.e. 7 or 8 being noted when head has already appeared. (If something has already happened then it becomes certain, i.e. now it is certain that head has appeared we have to certainly roll a pair of unbiased dice).
= 11/36 (since (6, 1) (1, 6) (5, 2) (2, 5) (3, 4) (4, 3) (6, 2) (2, 6) (3, 5) (5, 3) (4, 4) i.e. 11 favorable cases and of course 6 × 6 = 36 total number of cases)
Similarly, P(B) = 1/2
P(B/C) = 2/11 (Two favorable cases (7 and 8) and 11 total number of cases).
Hence, P(C) = ½ × 11/36 + ½ × 2/11 = 193/792 (Ans.)
Ques. Sixteen players P1, P2, ….. P16 play in a tournament. They are divided into eight pairs at random. From each pair, a winner is decided on the basis of a game played between the two players of the pair. Assuming that all the players are of equal strength, the probability that exactly one of the players P1 and P2 is among the eight winners is
(a) 4/15
(b) 5/9
(c) 3/8
(d) 8/15
Ans. Let E1 and E2 denote the event that P1 and P2 are paired or not paired together. Let A denote the event that one of the two players P1 and P2 is amongst the winners.
Since, P1 can be paired with any of the remaining 15 players, so P(E1) = 1/15
and P(E2) = 1 – P(E1) = 1 – 1/15 = 14/15
In case E1 occurs, it is certain that one of P1 and P2 will be among the winners. In case E2 occurs, the probability that exactly one of P1 and P2 is among the winners is
P[(P1 ∩ P2C) ∪ (P1C ∩ P2)] = P(P1 ∩ P2C) + P(P1C ∩ P2)
= P(P1) P(P2C) + P(P1C) P(P2)
= ½ (1 – 1/2) + (1 – 1/2)1/2
= ¼ + ¼
= ½
i.e. P(A/E1) = 1 and P(A/E2) = ½
By the total probability rule,
P(A) = P(E1). P(A/E1) + P(E2) P(A/E2)
= 1/15 (1) + 14/15(1/2)
= 8/15
Ques. In a test an examinee either guesses or copies or knows that answer to a multiple-choice question which has 4 choices. The probability that he makes a guess is 1/3 and the probability that he copies is 1/6. The probability that his answer is correct, given the copied it, is 1/8. Find the probability that he knew the answer to the question, given that he answered it correctly.
Ans.
P(g) = probability of guessing = 1/3
P(c) = probability of copying = 1/6
P(k) = probability of knowing = 1 – 1/3 – 1/6 = ½
(Since the three-event g, c and k are mutually exclusive and exhaustive)
P(w) = probability that answer is correct
P(k/w) = (P(w/k).P(k))/(P(w/c)P(c) + P(w/k)P(k) + P(w/g)P (g)) (using Bayes theorem)
= (1×1/2)/((1/8,1/6) + (1×1/2) + (1/4×1/3) )
= 24/29(Ans.)
Ques. A speaks truth 3 out of 4 times. He reported that Mohan Bagan had won the match. Find the probability that his report was correct.
Ans.
Method 1:
Let T : A speaks the truth
B : Mohan Bagan won the match
Given, P(T) = 3/4
.·. P(TC) = 1 – 1/3 = 1/4
A match can be won, drawn or loosen
.·. P(B/T) = 1/3 P(B/TC) = 2/3.
Using Bayes theorem we get
P(T/B) = (P(T).P(B/T))/(P(T).P(B/T) + P(TC)P(B/TC))
= 3/4×1/3)/(3/4×1/3 + 1/4×2/3) = (1/4)/(5/12)
=3/5
Method 2:
Let, T : The man speaks truth
A : Mohan Bagan won the match
B : He reported that Mohan Bagan has won.
P(A) = 1/3(the match may also end in a draw)
P(T) = ¾
P(B) = P(A) P(T) + P(AC) P(TC)
= 1/3×3/4 + 2/3×1/4
= ¼ + 1/6
= (3+2)/12 = 5/12
P(T/B) = (P(B/T).P(T))/(P(B)) = (1/3×3/4)/(5/12)
= 3/5 (Ans.)
JEE Main 2020 Syllabus
Mathematics: Sets, relations and functions, complex numbers and quadratic equations, matrices and determinants, permutations and combinations, mathematical signs, binomial theorems, etc.
Physics: Kinematics, Laws of Motion, Functions, Gravity, Solids and Liquids, Thermodynamics, Energy and Power, Rotating Motion etc.
Chemistry: Basic concepts of chemistry, chemical bonds and molecular structures, chemical kinetics, chemical thermodynamics, states of substances etc.
Mathematics can be easily scorable if you know the tricks and short methods for harder calculations. Remember that in a board examination marks are given for each step but in competitive exams like JEE Main, each question has 4 marks only. Now that question can take 10 steps or it can take 2 steps. That choice is the smart decision which brings out the toppers.
Keep revising your topics and maintain a small handbook for the basic formulae of trigonometry, calculus and other major sections. Mathematics is a mixture of hard work and smart work. You cannot just rely on one of them to ensure a good score. Work on your weak topics but even more on strong topics to give you an edge on them.
JEE Main 2020 Toppers: Tips and Strategies
India is at the pinnacle of producing engineers every year. With intense competition around, it is a given to be among the top to survive the contest of becoming engineers. The path to follow to reach your goal is JEE Main. So if you want to be a topper in JEE Main, then you are on the right page. So let’s go through some tricks and tips to crack the exam and delve deep into the details.
Currently, NTA is conducting JEE main in two sessions. The first session completed in January: and the second session has been postponed due to the recent outbreak of COVID-19. The exam has two papers to be solved, which is mostly computer-based. Students appearing for B.Arch papers have to attempt pen and paper-based mode of questions.
JEE Main Preparation Tips by JEE Main Toppers
JEE main toppers from the JEE Main 2020 January session have shared their preparation strategy.
Chagari Koushal Kumar Reddy
- JEE Main 2020 NTA Score: 100 Percentile
- Prep Strategy: To have a clear grasp of the basics of Physics, Chemistry, and Mathematics by following NCERT with other books for solving higher-level problems.
Landa Jitendra
- JEE Main 2020 NTA Score: 100 Percentile
- Prep Strategy: Study material provided by the coaching and mastering the concepts of NCERT books fetched him this score. The school and coaching helped him to manage well between board exams and JEE Main 2020 preparation.
Divyanshu Agarwal
- JEE Main 2020 NTA Score: 100 Percentile
- Prep Strategy: Self-study in a day for 8-9 hours is his mantra, which helped him in scoring the highest marks.
Nishant Agarwal
- JEE Main 2020 NTA Score: 100 Percentile
- Prep Strategy: He has been preparing from the very start to get a very good score in JEE Main. Mentors played a pivotal role in clearing all the doubts and motivated him to do well in the exam.
Kunwar Preet Singh
- JEE Main 2020 NTA Score: 99.99 Percentile
- Prep Strategy: Regular studies and revision was his game plan and it paved well; which helped him score well in JEE Main. Appearing in computer-based mock tests will also help to perform well in the exam.
Check JEE Main Preparation Tips
Topic-wise Recommended Books
Physics
Book Title | Author |
Concepts of Physics Volume I and II | H.C.Verma |
Fundamentals of Physics | Halliday, Resnick and Walker |
Problems in General Physics | I.E.Iridov |
Mathematics
Book Title | Author |
Trigonometry | S.L.Loney |
Higher Algebra | Hall and Knight |
Maths XI and XII | NCERT |
Co-ordinate Geometry | S.L.Loney |
Problems in Calculus of One Variable | I.A.Maron |
Chemistry
Book Title | Author |
Numerical Chemistry | P.Bahadur |
Organic Chemistry | Morrison and Boyd |
Organic Chemistry | Paula Brice |
Inorganic Chemistry | J.D.Lee |
Latest News Updates
- NTA Re-opens JEE Main Application Form For Candidates, Last Date To Apply Is 24th May
- Turn Lockdown Period Into An Opportunity”, says Anand Kumar of Super 30 to JEE Aspirants
- JEE Main 2020 Syllabus not reduced, says NTA
- JEE Main 2020: Dates announced by the MHRD, Examination to be conducted from July 18 to 23, 2020
- New Batches for IITs and NITs to start in September 2020
Weightage of Topics in each Paper is as follows
Physics
Name of the Topic | Expected Number of Questions in JEE Main April 2020 | Expected Marks |
Optics | 2 | 08 |
SHM & Waves | 3 | 12 |
Heat & Thermodynamics | 4 | 16 |
Modern Physics | 3 | 12 |
Mechanics | 5 | 20 |
Electrodynamics | 8 | 32 |
Chemistry
Name of the Chapter | Topics to be Covered | Expected Number of Questions | Expected Marks |
Organic Chemistry | Oxidation & Hydrolysis, Reduction, Grignard Reagent, Environmental Chemistry, Carbonyl Compounds, Polymers, Amino Acids, Carbohydrates, Biomolecules, Aromatic Compounds, Reaction Mechanism | 10 | 40 |
Physical Chemistry – 1 | Thermochemistry, Thermodynamics, Mole Concept, Ionic Equilibrium, Nuclear Chemistry, Atomic Structure | 07 | 28 |
Physical Chemistry – 2 | Surface Chemistry, Solution & Colligative Properties, Solid State, Electrochemistry, Chemical Kinematics | 05 | 20 |
Inorganic Chemistry | S-Block, Periodic Table & Periodicity in Properties, Chemical Bonding | 05 | 20 |
Mathematics
Name of the Topic | Expected Number of Questions | Expected Marks |
Trigonometry | 02 | 08 |
Matrix and Determinants | 02 | 08 |
Probability | 02 | 08 |
Matrix and Determinants | 02 | 08 |
Co-Ordinate Geometry | 02 | 08 |
Integral Calculus | 04 | 16 |
Differential Calculus | 07 | 28 |
Single questions from the following topics to be expected-
- Trigonometric Ratios
- Parabola
- Complex Numbers
- Integration
- Vector Algebra
- Probability and Statistics
- 3D Geometry
- Sequence and Series
- Circles and Family of Circles
- Inverse Trigonometric Functions
JEE Main 2020 – Toppers of January session
JEE main conducted in January 2020 produced 9 toppers with 100 percentile.
S. No. | Candidates Name | State Code of Eligibility |
1. | Landa Jitendra | Andhra Pradesh |
2. | Thadavarthi Vishnu Sri Sai Sankar | Andhra Pradesh |
3. | Nishant Agarwal | Delhi (NCT) |
4. | Nisarg Chadha | Gujarat |
5. | Divyanshu Agarwal | Haryana |
6. | Akhil Jain | Rajasthan |
7. | Parth Dwivedi | Rajasthan |
8. | Rongala arun Siddhartha | Telangana |
9. | Chagari Koushal Kumar Reddy | Telangana |
JEE Main Preparation Tips by Experts
Know the layout of the battle-field- Try solving as many mock papers as possible. It will provide an insight into which topics the student can solve and the sessions that need extra work. Thus the students can find their Achilles heel and turn it into armor. Students can attempt JEE Main mock tests from 9:00 a.m to 12:00 p.m and from 2:00 p.m to 5:00 p.m.
Repetition is the key to success– More you solve the question papers; proportionately your confidence will grow in facing the exams and facing it. To help the students practice, NTA has setup Test Practice centers.
Revisit and Revise- Inculcating knowledge is what a student stresses on. But what they forget is, it is equally important to be able to recall and reproduce it. Set the weekends aside to repeat the study of topics covered during the week and revise it. End of the month, evaluate how well you have studied and understood the topics covered. Hence, it will enable the student to recall well and apply the right knowledge in the exam.
Less is more- With less hand in time, it is slightly tedious to cover voluminous books with exams at the corner. Flashcards and short notes are a student’s best friend at this point. Summarizing the topics, in brief, will enable students to revise well and also cover formulas and other important topics. This handy tool will prove to be a smart choice of revision at the last stage of preparation for the exam.
Health is wealth- One key component to being kept in mind is health. In the throes of preparation, health is in a back burner. Students tend to ignore that a sound body leads to a sound mind. Eating the right food and hydrating yourself provides good fuel to the brain. Negative stress has never been any good and never will be. Practice meditation and visualizing your destination for a smooth and happy journey.
Know your enemy, know your sword– What syllabus the exam entails is tackling half the battle. Familiarize yourself with the contents of JEE Main 2020. Categorize your strengths and weakness based on the outlined course of study. Deciding how much time to be spent on a topic would be easy.
Bow and arrow– Knowing the syllabus will not suffice. Prepare yourself with the exam pattern in mind. Candidates appearing for this exam have to surf through the earlier question papers to be mentally prepared. So, knowing the syllabus and exam pattern will set you ahead in the battle.
Game Plan- The books we refer will be the game-changer. Humans are confusing souls. Too many options and our brain will go hazy. Sticking to a few reference books is the goal here. Starting with basics is the first step, and there’s only one way to go about this. It is NCERT. I can’t stress enough the importance of NCERT. NCERT is the basic template on which you can elevate by studying additional reference books.
Read through and perfect the running notes which you have jotted down. If you have a coaching center material, then it is a bonus.
Knowing topic-wise weightage will save a lot of time. It will be a great help for students to chart out their study plan and follow it through and through.
Online Lectures by IIT Professors for JEE Main 2020 Uploaded on nta.ac.in
NTA (National Test Agency) has launched online content lecture series for aspirants of JEE Main 2020 and NEET 2020 delivered by faculty from IITs. This videos are part of the IIT PAL (Professor Assisted Learning) initiative which is another in line of major efforts taken by NTA and MHRD to facilitate students’ preparations using free and self-sustained coaching methods for JEE Main Preparation.
Several lectures are provided by IIT professors on various topics in accordance with the syllabus of exam. Lectures are dispensed on Maths, Physics, Chemistry and Biology.
With this initiative, students would have an easy reach to different topics from the portion of JEE Main and NEET 2020 syllabus. The lectures can be obtained from the official website of NTA i.e. nta.ac.in.
Benefits of Starting JEE Main Preparation Early
JEE Main 2020 Official Schedule is finally out now, and now we know that the exam is going to be held in the months of January and April. JEE Main is among the most competitive exam in the world which sees a participation of approximately 1 million candidates every year. To get a seat in NITs or IITs through JEE requires a lot of effort and one has to supersede huge competition to succeed. So, what’s the ideal time to start JEE Main Preparation?
Chapters for JEE Main 2020 Last Minute Preparation
If you are appearing for the April session of JEE Main 2020 then you might be in the final lap of your preparation. With approximately one month time left for the April session of JEE Main 2020, it’s important to brush up on important concepts and formulas to deliver your best on the D-day. JEE Main 2020 is scheduled from April 05 to April 11, 2020 in online mode only.
Now, the question arises before aspirant about how to choose topics for revision or say how to prioritize among topics from the huge syllabus of JEE Main.
Well, you don’t need to worry anymore. To facilitate you in making the most out of last-minute JEE Main 2020 preparation and devise an effective strategy, we have put together a comprehensive list of important chapters to be covered from each subject.