Polygons

Hello Friends, Today i am posting few very easy formulas and tips to solve question related with polygons.

First let me tell you the meaning of polygon- Polygon is a plane figure which is started from a particular point after drawing any shape by the lines, ends on the same point.Friends it's not a definition of polygon - i just explained it so you can understand.

Its means as we are learned about triangle,rectangle,square etc in our school days, All these are polygons.

Polygons can be divided into two parts:-
1.) Polygon:-This can be again divided into two parts-

      a.)Convex :- If all the external angles are Greater than 180º.
      b.)Concave:- If any one or all angles are less than 180º.

2.)Regular Polygon:- If sides and internal angles are same it is called regular polygon.

Why polygons are used 

We normally leanr formulas to find its area with 3 sides or 4 sides but it is not necessary that a shape can be formed only with 3 or 4 sides, it can has more sides like 5,6,7,8 etc. So than we use these formulas to find it's area and all.


Few Important Notes regarding Polygons:-

1.)Some of all external angles of polygon is 360º:- Yes friends it means the sum of all external angles will be 360º ,It doesn't matter that how many sides it has.

2.)Sum of all internal angles of a polygon with 'n' sides is (n-2)*180º ,here (*=multiply)

Example:

Question:What is the sum of all the angles of a rectangular polygon?
Solution:

Friends as we have learned the sum of all the angles of a rectangle is 360º so now we will check that this formula can calculate or not

So there are 4 sides in a rectangle, Means the value of 'n' is 4

(4-2)*180
=2*180
=360    (hence proved)



3.)No. of Diagonals:-

n(n-3)/2 

Example :

How many diagonals  can be formed in a rectangle?

Solution

Friends as we know only 2 diagonals can be formed in a rectangle So let's check through the formula-

Same here n= 4

So, 4(4-3)/2

=4*1/2

=2     (hence proved)

 

# Regular Polygon:-

1.)Each interior angle of a regular polygon is 

(n-2)180/n

2.)Each exterior angle of a regular polygon is

360/n

 

3.)Area of regular polygon with 'n' sides of dimension 'S'.

n/4*S^2*Cotπ/n

{In this formula the no of sides will be divided by 4 and than multiply with the square of dimensions and than again multiply with the cot with angle (it will be taken as 180º) will be divided by the no. of sides.  }    [^= Power and *= multiply ]

Names of Polygons:-

Which has 5 Sides- Pentagon
Which has 6 Sides - Hexagon
Which has 7 Sides - Heptagon
Which has 8 Sides- Octagon
Which has 9 Sides - Nonagon
Which has 10 Sides - Decagon


Question:- Find the area of Hexagon with side of length 3m.
Answer:-
n/4*S^2*Cotπ/n

6/4*3*3*Cot 180/6

27/2*1/3*Cot 30

9√3/2

Friends this was the simple concept of polygon, by these formulas you can solve all problems asked in your exams related with polygon.

And as always don't forget to comment your Doubt and suggestion's.

Thank you☻

Trigonometry Part-2

Hello Friends, This is the Second Part of trigonometry So if you didn't checked Part-1 Than please check it first.Link is given in the end of this Article.

Friends Today we will learn few basic concepts of trigonometry.which are taught us by our teachers in Our School Time. Ok Let's see-

 In the above figure there you can see there are 4 quadrants

1st - (0°-90°)
2nd- (90°-180°)
3rd- (180°-270°)
4th- (270°- 360°)

• If the Value of θ lies between 0 to 90 than the element lies in 1st Quadrant and in first Quadrant every elements get converted in to a positive element.
• If the Value of θ lies between 90 to 180 than the element lies in 2nd Quadrant and in that Quadrant ,Only Sin and Cosec get converted in Positive Elements and rest are negative.
• If the Value of θ lies between 180 to 270 than the element lies in 3rd Quadrant and in that Quadrant ,Only Tan and Cot get converted in Positive Elements and rest are negative.
•  If the Value of θ lies between 270 to 360 than the element lies in 4th Quadrant and in that Quadrant ,Only Cos and Sec get converted in Positive Elements and rest are negative.

For More Clarification Check the Table given below:

(90-θ)	(90+θ)
Sin(90-θ)      = Cosθ	Sin(90+θ)      = Cosθ
Cos(90-θ)     = Sinθ	Cos(90+θ)     = -Sinθ
Tan(90-θ)     = Cotθ	Tan(90+θ)     = -Cotθ
Cot(90-θ)     = Tanθ	Cot(90+θ)     = -Tanθ
Sec(90-θ)     = Cosecθ	Sec(90+θ)     = -Cosecθ
Cosec(90-θ) = Secθ	Cosec(90+θ) = Secθ

{Note:- By this table make sure which element is converted in which element.because i didn't explained it before and nor i will do. Untill it is asked by anyone}
Few Important Notes

1. As you can see In case of 90-θ value will lie in 1st Quadrent So all the Elements are converted in a Possitive elements.And in case of 90+θ ,All Elements are in Second Quadrent So we just converted Sin and Cosec in the possitive elements and rests are negative.
2. And the other important point is that as you can see Sin get converted in Cos and Cos get converted in Sin and so on ,These elements are get converted only if it is -
   
   (90-θ) and (90+θ)
   Or
   (270-θ) and (270+θ)
   And in all other cases like (180-θ) and (180+θ) or (360-θ) and (360+θ) the elements remains same means Sin will be converted in Sin, it will not be converted in Cos.In that case you just have to check the Quadrant for the positive or negative Sign.

Important Formulas For Trigonometry

1.)Sin(A±B) = SinACosB±SinBCosA

2.)Cos(A±B) =CosACosB±SinACosB

3.)Tan(A±B)= TanA±TanB / 1± TanATanB

4.) Sin2A = 2SinACosA = 2TanA / 1+Tan^2A   (^2 means Square)

5.)Cos2A = 2Cot^2A-1 = 1-2Sin^2A = Cos^2A-Sin^2A = 1-Tan^2A / 1+Tan^2A

6.) Tan2A = 2TanA / 1-Tan^2A

Few more Basic and important Formulas if you Don't Know Just Check it

1.)Sin^2A+Cos^2A = 1

2.)Sec^2A-Tan^2A = 1

3.)Cosec^2A- Cot^2A =1

That's it friends i don't think you need to learn more formulas and if it will be needed i will explain it when we will start solving question's.

Don't miss the 3rd Part to learn how to apply these formulas and use of Quadrant properly.

And if you have any doubt regarding the material provided to you feel free to comment below.

Thank You☺

Trigonometry Part-1

Trigonometry is yet another scoring section of CGL. Most questions can be resolved with Jugad.

Like algebra, where we considered the values ​​of the variable, in the trigonometry we would consider the value of 'live'. And just like algebra, make sure that the value you are assuming for the target will not be denominator zero.
How to value -
1. When you do not have to deal with the differences then you can say Θ = 90 or 0
Like (acosΘ - bsinΘ)
2. So when is the numerator and Θ = 90 or 0 enter denominator remains zero, you can go with Θ = 45.
3. Do not assume value for Gita, on which the trigonometric function is not defined. As when tan is given, you can not accept Θ = 9 0.
4. When you consider two angles, go with A = 60 and B = 30
Note: These are not hard and fast rules and you can assume your preferred value, but make sure denominator ≠ 0. Sometimes when you consider ass, you ended up with two options (A and B say) Those who are giving similar results (but two options will still end, i.e., C and D) Now change the value of Directa and check only A and B.

You only have to remember the values ​​of sin, anguish and tan (Θ = 0, 30, 45 and 60). The value of kausak, sek and coat can be obtained by mutually receiving sin, kos and tan respectively.
Solve CGL questions now

Q. 1.

let Θ = 9 0
X = A (1 + 0) = A
Y = B (1 - 0) = B
Then x2 / a2 + y2 / b2 = 2
Answer: C

Some complex questions can be solved by considering the value of the goat
Q. 2.

Then say Θ = 0
Then a * 1 + b * 0 = core A = C
You will get the value of acosΘ - bsin होगा
acosΘ - bsinΘ = -b (since Θ = 9 0)
Now put a = c in all 4 options so that it can check which '-b' can be output as
Answer: D

Q. 3

Let Θ = 45
One (tan45 + cot45) = 1
So a = 1/2
sin45 + cos45 = b
Then b = √2
Take a = 1/2 and b = √2 all the options and check to see what's right in 4 equations (ie LHS should equal RHS)
Answer: A (LHS and RHS both equal 1)

Let Θ = 45
(TanA - secA - 1) / (tanA + secA + 1) = -√2 / (2 + √2) = -1 / (√2 + 1) = 1 - √2 (rational)
Place Θ = 45 in all 4 options and check which output will give (1 - √2) as
A) √2 - 1
B) √2 + 1
C) 1 - √2
D) √2 - 1
Answer: C

Sometimes you have to accept two angles

Q. 4

Let's do A = 60 and B = 30
Then N = 3 and M = √3
cos2a = 1/4 (since A = 60)
Now enter N = 3 and M = √3 in all the options and check which 1/4 will give
Answer: B


There is a type of question that is often asked by SSC -


Q. 5.

When you see secA + tanA = (let's say 'P') ... (1)
You can say, secA - tanA = 1 / p ... (2)
Add Now (1) and (2)
2secA = P + 1 / P
secA = (P2 + 1) / 2p [you can remember this formula]
tanA = (P2 - 1) / 2p

In the above question, P = 2
So secA = 5/4
Now we have to meet sina. The best way to determine the value of the trigonometric function is to create a triangle when the value of another function is given.
secΘ = Hypotenuse / Base
Here seca = 5/4, hence hypotenuse = 5 and base = 4, which means Vertical = 3
sinA = vertical / hypotenuse = 3/5 = 0.6
Answer: C

Tricks for Making your Calculation Fast

 Tricks for Making your Calculation Fast 

1. Squaring a number with lightning fast speed
Well you might have come across various tricks to find the square of a number, but I can bet you that my trick is the simplest and the fastest :)
Firstly memorize squares of numbers upto 25. I think many of you might be knowing it already, but for those who don't, please mug it. Now this trick will help you in squaring numbers upto 125 and trust me, for SSC you need this much only.


(a) For numbers close to 50
(i) Numbers less than 50
(ii) Numbers greater than 50


The process is almost same - Compute (N - 50)
Add this difference to 25
E.g. 56*56=
1. 56 - 50 = 6
2. Last two digits = 6 * 6 = 36
3. First two digits = 25 + 6 = 31
Therefore, 56 * 56 = 3136
(b) Numbers close to 100
(i) Numbers less than 100
(ii) Numbers greater than 100
The process is almost same - Compute (N - 100)
Add this difference to N
E.g. 107*107=
1. 107 - 100 = 7
2. Last two digits = 7 * 7 = 49
3. First three digits = 107 + 7 = 114
Therefore, 107 * 107 = 11449


2. Squaring a number containing only '1'. E.g. 111, 1111, 1111111, etc.
Just count the number of ones. Like in 1111, there are 4 ones. So the square of 1111 is 1234321 (go from 1 to 4 and then back). Similarly, the square of 111111 = 12345654321


3. Finding product of two numbers of the form ab and ac, such that b+c=10. E.g. product of 43 and 47 Last two digits = 3*7 = 21
First two digits = 4*(4+1) = 20
Hence 43*47 = 2021


4. Finding product of two numbers close to 100
(a) 103*109
Last two digits = 3*9 = 27
First three digits = (103 + 9) or (109 + 3) = 112
So 103*109 = 11227
(b) 92*97
Last two digits = 8*3 = 24 [100 - 92 = 8 and 100 - 97 = 3]
First two digits = (92 - 3) or (97 - 8) = 89
Hence 92*97 = 8924
Bonus Hack :
A very common question asked in SSC -
I will tell you a formula that no 'paramount' will tell you.
Note : Always take the difference between numerator and denominator as positive.
Answer : 3/(4-3) * 20 = 60 minutes
Next question -
Rakesh runs at 5/4 of his usual speed and reaches the playground 5 minutes earlier. What is his usual time?
Answer : 5/(5-4) * 5 = 25 minutes

Friends if you have any doubt or suggestion feel free to comment below.

Thank You😀

Profit And Loss

                 Hello Friends, Today i am posting Short Notes for "Profit And Loss" .This is the one of the most important topic of Quantitative aptitude section. All the times we can find Atleast 2 to 3 questions from this topic. And these kind of questions are little lengthy which means they will take more time to solve and for competative exams time is most important tool to clear your exam with good marks.So today i will tell you few short tricks by which you can save your time and can solve these problems within a few seconds.

                  First of all i would like to tell you that i am not telling the basic cause its very difficult to explain every single thing. So i will tell you the type of question and then tell you the direct formula to solve those problems.


*If the cost price of x articles equals the selling price of w articles, find percent profit/loss?

*If a Person gains x% when he sells an article for Rs. z . What would be the profit or loss per cent if he sold it for Rs. w ?

*A man buys certain quantity of an article for Rs. z. He sells Mth part  of the stock at a loss of x%. At what per cent gain should he sell the remaining stock so as to make an overall profit of y% on the transaction.?

And If we have to find the Overall

* A man invests Rs. z in shares. He sells Mth part at a profit of x% and the remaining part at a loss of y% .Find the overall percent profit or loss.

Profit % = [ mx - (1 - m)y ]% 

*A reduction of x% in the price of an article enables a person to buy y Kg. more for Rs. z . Find the reduced and the original price per Kg. of the article.

*A man purchased m oranges at x a rupees and n oranges at a y rupees. He mixed them together and sold them at z a rupees .what is his percent loss or gain ?What happens when m=n?

When m = n

*A man sells two articles at the same price Rs. P and makes a profit of x% on the first while a loss of y% on the second. Find the overall percent gain or loss? What happens when x equals y?

when x = y

Friends i tried to cover all type of questions form this topic which are again and again asked by the examiner.If you found any difficulty or have any doubt feel free to ask me by the comment box.

And also give your suggestions and topics for the next topic. So i can help you in a right way.

Thank You ☺

SSC Maths Book By Kiran Publication

Hello friends,Today i am posting an e-Book names as SSC Mathematics 2017 Edition published by Kiran publication under the guidence of Sh.S.N.Parsad . Friends as per my Knowledge this is the best book for you to score maximum marks in your exams.Because as i have seen all the times questions are directly asked from this book in your exams or sometimes they ask with a few changes.


For Beginner's
Friends if you are beginner and not taking classes from anywhere than still i will suggest you to go for this book. Because this book is well formed in the starting of this book you can find few important tips ....sometimes those tips can be hard to understand or there can be problem with your basic knowledge of Maths so don't worry you just try to start solving its problem and you will find that those qustions are so easy because as i told you this book is designed in a good way so when you starts there are very easy questions are given in the beginning so you can solve it and can build your basic knowledge for that particular topics...after doing few question's you will find the level of difficulty increased and you are not able to solve those problems than you have to go for the solution given in the end of that chapter and you can see the full solution.

For others 
Friends this book is very helpful for your exam preparation because it contains high level questions too which will take your practice and basic knowledge on a next level.that will make you master about that topic and you will be able to solve any kind of problem from that topic within minimum time which will help you in your exam and you will score good marks in your exams.And the other profit is that if you found any difficulty in solving any question, you can check its solution from the back side as you are already experienced guy so you will be able to catch the tips very easily so it will also help you to improve your basic knowledge.

Details about book

Content

1. Number System
2. LCM and HCF
3. Simplification
4. Power, Indices and Surds
5. Average
6. Ratio and Proportion
7. Percentage
8. Profit and Loss
9. Discount
10. Simple Interest
11. Compound Interest
12. Time and Work
13. Pipe and Cistern
14. Time and Distance
15. Boat and Stream
16. Sequence and Series
17. Algebra
18. Trigonometry
19. Geometry
20. Mensuration
21. Statistics & Data Interpretation
22. Miscellaneous

File Size:- 23.9 MB
Quality  :- Full clear

Friends i will recommend you to buy this book from market.My purpose to upload this book is only to show you how this book looks like and to check all the points as i mentioned above.If you also find this book useful please buy this from market.

To Download this book please Copy the Link given Below:-

https://drive.google.com/file/d/1N1Z4-NwhCSxOSc1WsU-_w1dpYpLwsfrn/view?usp=sharing