February 8, 2017

# Mathematical Tricks

**Mathematical Tricks**

Trick Number 1

this rule state 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…

L hospital rule

To find value of defined limits questions….

defined mean Limit should not be infinite…

It can apply on exercise 1.3 book number 2

Its more easy then solving algebraically

Numerator and denomerator ka derivative independently laina not by using p/q rule of derivate…..

Or jitni bar numerator ka derivative laina utni bar he denomerator ka laina….

Yeh rule 0/0 form py apply hu gya…….

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

Denum 2x-0

now lim x app -1( 3x^2+2x/(2x) )

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

lazmi nhi ap aik bar derivative lain ap jitni marzi bar bhi ly skty mgr jitni bar uper utni bar nechy

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

Example lim x app 0 (sin7x/x )

taking derivative of num and denum

Independtly

7Cos(7x) /1

now putting limit answer is 7…

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Math trick number 3

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Math trick number 3

#Algebra2

Roots of equation always satisfied 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 apply on difficult equations….. it can also apply

On chapter number 4 of second book

Point on a line or any thing is also a roots of equation and satisfied the equation of that line 60percent chapter4 of book two and 90percent book 1 chapter four can solve by this method……..

Chapter 5th of first chapter can also solve by this technique but its trick will uploaded soon

example number 2

4^x – 3^(1.5x) +11=0

where x is

a) 3 putting =64-27+11not 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

Stay tune for many more

Best Regards :

Talha naqvi

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Math trick number 2

#algebra1

in sentence problem some time we have to face a mcq in ecat….

Such like as

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

ab is question main hm agr isko solve krin gy algebraically to its time consuming

Hm options pr ghor karin gy

Part a) ka sum 40 bnta

Part b) ka sum 40 nhi bta (so yeh hu hi nhi skta)

Part c) ka sum 40 bnta

Part d) ka sum 40 nhi bnta (so yeh bhi possible nhi hay )

Ab hamin sirf two options check krni haain

Aksr ecat main aisy hota hay k sirf aik he mcq pheli condition ko follow kr rha hota or wohe answer hota…..

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 trying

15×15+25×25= 850

2(15×28)=750

850-750=100

This question is little bit tough..

If you can send me question of sentence problem may be its chapter 4.11 or 4.10

i have no book please

send me its question 3to 10 for practice….

You will love this technique thanks

Stay tune for more

Regards :

Talha naqvi

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Math trick number 1

#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 same angle on both side of equations

For example

1)

2Sin(theta)=?

A ) cos 3(theta)

b)sin3(theta)

c

And

D

Now put theeta =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 side equation equal so

Answer is b

I tried it so many time really help full

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

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

Othr wise if in equation there come only sine and cos solutions with 90,0 is more easily

stay tuned for more tricks

Best Regards :

Talha naqvi

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Physic resistance combination

#tricks+#important Notes

any one who wanna practice tomorrow should have to remember the following

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

I.e 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 combinations result

12//6=4

6//3=2

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

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

4)

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

Practices question will be uploaded tomorrow evening

Insha Allah

Remember me in your prayers

Best Regards :

Talha Naqvi

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General physic trick for every one

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General physic trick for every one

#Numerical solving 1

Baaz owqat examination hall k bachon ko numerical ki smjh nhi ati… statement kuch aisi hoti hy k yeh pta nhi lgta k find kia krna hay… ya formula bhol jata hay….

Or question hath sy nikalta nazr Ata hay….

Isi conditions main student ko chahey k answer main given unit ko daikhy

For example unit hay

A) 15kwh b) 16kwh etc…..

Ab is sy pta chalta hay k hamin energy find out krni ya koi bhi Chez jo k p.t k barabr Hay ab apko given conditions sy p ya t nikalna bhi prh skta etc…

Ya for example answer main unit hay

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

Its mean apko pressure find out krna hay ya koi bhi chez jo k F/A sy nikalti hay

Ab may be given conditions sy apko F ya A nikalna prhy pehly…

This trick will help you in Sha Allah

Best Regards :

Talha naqvi

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Physic trick #cross product

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Physic trick #cross product

Math trick number 6

For chapter 7

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

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

So in mcq we can take 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) ans3i+3j+3k d) none

As we know tourqe = rxF

is question main abhi r nhi given points given hain ab aik tu yeh method k pehly r nikalin phr torque using determinant

Lekin mcq main waqt kyu zaya karin solution thori check krwana…..

Ab ap option k sath dot laen force ka… ya r nikal kr uska u r free….

Taking dot of mcq with

For a) 1

for b) -6

for c) 0

so c is the answer

This technique apply on every cross product

Also

F=ILxB

F=q(vxB)

Use this and enjoy

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