We have probably all heard about how doing well in the JEE is about hard work. But those who do the best aren’t necessarily the hardest workers–or even the smartest candidates. They simply know the best tricks and shortcuts to employ so they can solve what looks like unsolvable questions quickly and efficiently.

In this post, I’m going to cover some tricks and shortcuts that will give you an immediate boost. Know these and you’ve accelerated your JEE studies manifold!

## 1) Some Cool Mathematics Tricks

### Graphical Analysis

In my opinion, this is one of the best techniques to approach a JEE Maths problem. What I mean by graphical analysis is to plot the graphs roughly, and then analyze its properties visually. You can solve some of the most complex problems in no time. So if you find it difficult to follow, let me show it to you.

How many value(s) of x satisfy the given equation x^{3} — 3x^{2} — x + 3 = e^{x} + e^{–x}?

A) 1

B) 2

C) 3

D) 4

The equation, as you see, seems very difficult to solve analytically. The best way to find the number of x’s that satisfy the above equation is to look for points where the LHS and the RHS intersect.

To put it explicitly, plot the graph for e^{x} + e^{–x} = 0. For the second graph x^{3} — 3x^{2} — x + 3 = 0, you will find it is cubic with roots x = 1, –1, 3. By plotting the two graphs, you can see that they intersect at only two points. Hence, the answer is B).

A good book to develop your graphical intuition is “Play with Graphs” by Amit M. Aggarwal.

### Hit and Trial

It is a fundamental trick that you can use to solve problems with the general solution. Start with putting values to the variable and check which of the options give you the answer. This JEE Main trick will fetch you easy marks and is suitable for problems that sport complex orientation.

Here is a quick example.

Given that a^{3}x^{4} = b^{3}y^{4} and a^{2} < b^{2}, then

A) a^{3}x^{2} > b^{3}y^{2}

B) a^{3} > y^{4}

C) b^{3} < y^{4}

D) a^{3}x^{2} < b^{3}y^{2}

What you can do for the above problem is to assume some values for a, b, x, and y such that the above conditions are satisfied. For a = 2, b = 3 and x = 3, you will get y approximately equal to 2.2. Putting in these values, you will find that D) is the correct choice.

This JEE Main shortcut proves useful even in those questions where you are asked to find the nth general term for a given sequence or series.

Let’s try one.

Given a series T_{n} = 1^{4} + 2^{4} + 3^{4} + ………. + n^{4}. Find T_{n}.

A) (n + 1)(n + 2)(n — 1)(n — 2)

B) (n + 1)(2n + 1)(3n^{2} + 3n — 1)

C) (n + 2)(2n + 1)(3n^{2} + 3n — 1)

D) (n + 1)(2n + 1)(n + 2)(2n + 2)

Now, you can see that for T1 = 1 and T2 = 17. Putting n = 1 and n = 2 in all the four options will show you that option B) is the correct answer.

A good way to excel in maths is to practice problems methodically as much as possible. This will give you some idea about what values to put to ease your calculation and get quick results.

### Remember the Series Expansion

Most of the problems in JEE Main Mathematics have a quick and neat solution that does not require more than a few lines. The well-known methods for such problems may be cumbersome and time-consuming. In a few cases, series expansion may come in handy. Keep them in the back of your mind.

Also, it would help you a lot if you practice trigonometry and its related formulas during the last few months of your preparation. Look up the formulas frequently, so that you don’t forget them. Deriving these formulas during exam time will be futile, and nothing will serve you better than your memory.

## 2) How to Make an ‘Intelligent’ Guess

JEE Main does not require you to submit any working or procedure of how you arrived at your answer. It only awards you on the merit of your choice. As a result, there is a scope for intelligent guesses.

Personally, I would not advise you to rely completely on guesswork if you wish to crack the JEE Main! But at times, a few correct guesses can boost your rank a long way up.

### Stay Away from Extremes

Some of the questions in JEE Main have numerical answers. In such cases, it is often a good idea that you stay away from the maximum and minimum values. In almost 65% of cases, the answer would be one of the two closest values.

### Narrow Down Your Options

At times, the options can be very confusing. In such scenarios, you can systematically strike out those options which are completely unlikely. Questions that have ‘All of these’ as one of its options can be approached by eliminating the wrong choices, thus, reducing to only two viable possibilities.

Here is an example.

Both lithium and magnesium display several similar properties due to the diagonal relationship, however, the one which is incorrect, is:

A) Both form nitrides

B) Nitrates of both Li and Mg yield NO_{2} and O_{2} on heating

C) Both form basic carbonates

D) Both form soluble bicarbonates

You can easily rule out option A) and D) as Li forms Li_{3}N and Mg forms Mg_{3}N_{2} and most of the group I bicarbonates exist only in solution form. We also know that the nitrates of both Li and Mg decompose to give out NO_{2} and O_{2} on heating. This leaves us with option C), which is indeed the correct answer.

In case you are wondering about the above facts, the equations for them are given below:

6 Li + N_{2} → 2 Li_{3}N

3 Mg + N_{2} → Mg_{3}N_{2}; at 800 ℃

4 LiNO_{3} → 2 Li_{2}O + 4 NO_{2} + O_{2}

2 Mg(NO_{3})_{2} → 2 MgO + 4 NO_{2} + O_{2}

### Units and Values

Another common shortcut you should use during your JEE Main exam is examining the unit and the value of each option. JEE frequently plays around with it. If you are stuck on a similar problem and solving it seems out of the question, choose the unit and the value with maximum occurrences.

Let me make myself clear with an example. Assume there is a question which has the following options:

A) 10 mm

B) 60 cm

C) 10 cm

D) 80 cm

For the above choices, it would be wise if you go with option C). It has the value 10 which occurs most frequently. Also, its unit is cm, which appears in three options.

Keep in mind that it is a dangerous route and should be avoided if there is the slightest chance of solving the question directly.

### Dimensional Analysis

Dimensional Analysis can help you out in some of the most terrible situations. Not only will it save you a large chunk of time but will also steer you away from possible mistakes you may commit during tedious calculations.

Suppose, you have been asked to calculate the radius of curvature of a charged particle under the influence of a magnetic field. The options are:

A) mv/qB

B) mq/vB

C) Bm/qv

D) Bv/qm

You already know the dimension of each of the quantities above:

m — [M^{1}L^{0}T^{0}A^{0}]

v — [M^{0}L^{1}T^{-1}A^{0}]

q — [M^{0}L^{0}T^{-1}A^{1}]

B — [M^{1}L^{0}T^{-2}A^{-1}]

Now, when you calculate the dimension of each of the four options, you will find that only the first option has dimension [M^{0}L^{1}T^{0}A^{0}] which is the dimension of the radius and hence, is your answer.

A straightforward approach would be to calculate the force on the particle and equate it with centrifugal force, yielding mv^{2}/r = qBv => r = mv/qB.

For this particular question, the direct method is simple and easy to execute. Had the concepts been more involving, the dimensional analysis method would surely turn out to be a better and quicker approach. What makes it so helpful is that you can arrive at the correct answer without knowing the correct concepts involved.

### Reverse Engineering

This is one of the most popular tricks that can be used to save time during your JEE Main exam. Instead of steering your way forward, take a step backward and try to build back the question using the options available to you. Try out each option and see if they satisfy the conditions provided in the question.

### Example #1

Given the equation x^{4} – 4x^{3} – 18x^{2} + 108x -135, which of the following is its possible root?

A) 7

B) — 3

C) 5

D) — 5

In the above question, you can check which of the four options satisfy the given fourth order polynomial. Putting the values, you will find that x = — 5 satisfies the equation. Hence, D) is the correct answer.

The direct approach would be to factorize the equation which will yield (x — 3)^{3} (x + 5). It would take relatively longer to factorize it. Therefore, reverse engineering the problem should be preferred.

### Example #2

What is the Moment of Inertia of a rod of mass m and length l along an axis inclined at an angle passing through the center of the rod?

A) ml^{2}sin θ cos^{2} θ/12

B) ml^{2}cos^{2} θ/12

C) ml^{2}sin^{2} θ/12

D) ml^{2}sin^{2} θ cos θ/12

It is known that the moment of inertia of a rod about its length is zero. Now, this condition is equivalent to θ = 0. When we put θ = 0, option B) turns out ml^{2}/12 which is not zero. Hence, it can be ruled out.

For θ = 90, the axis is perpendicular to the rod. We know that moment of inertia about a perpendicular axis is ml^{2}/12. When we put θ = 90, option A) and D) become zero. Therefore, they can be ruled out. Finally, we are left with option C) which is indeed the correct answer.

### A Few Things to Keep in Mind

There are a few things to keep in mind when you reverse engineer the problem.

Time is an essential factor that decides how much you score in your JEE Main examination. If the time it takes to check all of the four options is considerably more than directly solving the problem, you are surely wasting your time.

It is advisable to use this shortcut when the calculations involved to solve the problem is tedious and prone to errors. You can also resort to it when you do not know how to approach the question, but you’re pretty sure about the other way round.

## 3) Develop a Strategy

JEE Main is not only a test of your skills in Mathematics, Chemistry, and Physics–but it also tests your resolve and resilience. Develop a strategy to maximize your output during your examination. Haphazardly attempting the paper may backfire, and you will not perform to your full potential.

Attempting Chemistry first is a good choice as you can finish it within 35-45 minutes. You can devote the rest of your time to Mathematics and Physics which are relatively more time-consuming. I personally liked to attempt Maths first as it maximized my accuracy and left me with sufficient time for other sections.

Do what suits you but be prepared with a secondary plan. The section you like to do first may be the most difficult section. In such a case, you can resort to plan B. Fix a bar on the time you spend on each section and try not to cross it.

In this article you learned about some JEE Main tricks and shortcuts that will surely help boost your JEE Main score. Hope you found them useful!

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