**Tricks For Entry Test**

**L hospital rule**

To find value of defined limits questions….Defined mean Limit should not be infinite…It can be applied on exercise 1.3 book number 2.This rule states that we can take derivative of algebraic equation or polynomials present in the form of p/q to simplify it and then putting the limit we can get result…Its more easy then solving algebraically

Both the derivative of numerator and denominator are taken separately.

This rule can also be applied to 0/0 form i.e Indeterminent form.

For example

lim x___>-1 (x^3+x^2/(x^2-1) )

Now by putting x=-1 we get 0/0 form

Now taking derivative of num 3x^2+2x

Denominator 2x-0

now applying -1( 3x^2+2x/(2x) )

by putting limit 3-2/(-2) =-1/2

You can take derivative as many time as you want.

sometime after 1st derivative again 0/0 comes then u must have to again take derivative.

Example lim x approaches 0 (sin7x/x )

taking derivative of numerator and denominator Separately.

7Cos(7x) /1

now putting limit answer is 7…

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**Roots of equation always satisfy their equation**

**it is better to put that’s root in equation else calculating it**

For example

find the roots of quadratic equation

2X^2-4x-16=0

- a) 2,4 putting= -16,0
- b) 1,2 putting = -18,-16
- C) -2,4 putting = 0,0 both roots satisfied the equation
- D) 1,4 putting = -18,0

so c is the right answer

Although it is an easy equation but this method can be applied on difficult equations….. it can also be applied

On chapter number 4 of second book

Point on a line or any thing is also a root of the equation and satisfies the equation of that line. Most of the chapter 4 of book two and book 1 chapter four canbe solved by this method……..

Chapter 5th of first Book can also solved by this technique.

example

4^x – 3^(1.5x) +11=0

where x is

- a) 3 putting =64-27+11 not equal to zero

b)2 putting =16-27+11=0 so its answer

- C) 1 putting =4-7+11 Not equal to zero
- D) 0 putting =11 Not equal to zero

So b is right answer

This is very useful trick. try it

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**Tricks For Entry Test**

In statement problems sometimes we have to face a mcqs in ECAT….

Like

1)

divide 40 into two parts such that the sum of their squares is greater than 2 times their product by 100

a)12,28 b)14,16 c)15,25 d)12,30

This question is too much time consuming when solved algebrically.

We will look all the options

Sum of part a) is 40

Sum of Part b) is not 40 so excluding this one

Sum of Part c) is also 40

Sum of Part d) is not 40 so excluding this one too.

Now we are left with two options.

Sometimes only one option follows the questions so that becomes our answer.

For part a) 144+(28×28)=928

2(28×12)=672

928-672 is not equal to 100

2nd condition false so

Answer is c)

No need to solve but here we are solving

15×15+25×25= 850

2(15×28)=750

850-750=100

You will love this technique thanks

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**?#?trignometry**

**You can put any value from the domain of a trigonometric function to solve an identity or any trigonometric equation**

**If you forget in exams then don’t solve just put an angle on both side of equations.**

For example

**2Sin(theta)=?**

A ) cos 3(theta)

b)sin3(theta)

c

And

D

Now put theta =30

2 sin30=2(1/2)=1

Now put this 30 in all options

Part a

Cos3(30)=0

Part b

Sin 3(30)=1

since both sides of the equation are equal so our Answer is b.

Especially in 9.3 9.4 and 10.3,4 also in chapter 13,14

Where a long equation comes to solve practice it… but remember the domain and try it that a function should not become undefined as tan90 and cot0 etc…

Otherwise if in equation there comes only sine and cos , solutions with 90,0 are more easy.

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**Physics resistances combination**

**1)**Parallel(//)** combination of two equal resistance is half of any individual of **them..

E.g 10//10=10/2=5

20//20=20/2=10

6//6=6/2=3

5//5=5/2=2.5

No need to use any formula of combination.

2)

remember this two parallel combination’s result

12//6=4

6//3=2

these two are very common so no need to use a formula just remember these….

3) if two resistors are such that both head and tail are connected to each other than this is in parallel combination….

4)

if two resistors are connected such that the tail of first is connected to head of second and providing a single path for flow of current then this combination is series combination

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Sometimes the statement of the question is very confusing and students get confused.They feel that it is very difficult and lose hope.

### In such conditions , look at the units of the answers.

For example the unit is

- A) 15kwh b) 16kwh etc…..

these units give us the idea that we have to find out the energy using the given conditions.

For example the unit is

- a) 4N/m^2 b) 3N/m^2

This gives us the hint that we have to find pressure or anything that is solved by F/A.

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**For chapter 7**

The solution of vector product is comparatively tough…. determinant method and other methods are very long…

As we know the result of vector product is also a vector and its perpendicular to both the vectors..

So in such MCQs we can take the dot product of any one given vector to the option… the option in which we get 0 result is the right answer as both are perpendicular i.e theeta=90 Cos90=0

for example….

given force F=2i+j-3k acting at a point A(1,-2,1) find moment of force about point B(2,0,-2)

A) 3i+4j+3k b) 3i+3j+5k c) 3i+3j+3k (correct) d) none

As we know torque = rxF

in this question r is not given.One can first find r then solve this but its too time consuming.

Now take the dot product of force with the option… this will gice you the r.

This technique can be applied on every cross product.

Also

F=I(LxB)

F=q(vxB)

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Sir!

I’m having my NET on 4th April for NBS. Please let me know from where should i prepare for it.

You just need to prepare at home.

What books to use ? I have the SAT Books . Are these enough?