Showing posts with label Others. Show all posts
Showing posts with label Others. Show all posts

HOW TO ADD 1 TO 1000 NUMBERS VERY EASILY


HOW TO ADD 1 TO 1000 NUMBERS VERY EASILY

If you want to add 1 to 1000 then follow these two steps
Add 1 to last number 

2 Multiply last number and it's next numbers then divide by 2 . And thats it  .

अगर आप 1 से लेकर किसी भी अंतिम संख्या को जोड़ना चाहते हो तो सबसे पहले अंतिम संख्या में एक जोड़ दें फिर अंतिम संख्या और उससे आगे बाली संख्या को गुणा करके 2 से भाग दे दें ,आप इस तरह से कितनी भी शंख्ययाओं का जोड़ एक दम से कर सकते हो

उदाहरण

If we have to add 1st 50 numbers then  Multiply 50 with 51 and divide the product with 2 and it is the sum of 1st 50 natural numbers 

 अगर हम 1 से 50 को जोड़ना चाहें तो 50 और 51 गुना करके 2 से भाग देंगे
1 +2+3+4+5+6+7+……+50 =(50×51)÷2 = 25×51=1275
अगर हम 1 से 100 को जोड़ना चाहें तो 100 और 101 गुना करके 2 से भाग देंगे
1+2+3+4+5+…….+100=( 100×101) ÷2 =50×101=5050
अगर हम 1 से 1000 को जोड़ना चाहें तो 1000 और 1001 गुना करके 2 से भाग देंगे
1+2+3+4+5+…….+1000 =(1000×1001)÷2 = 500×1001= 500500
अगर हम 1 से 2000 को जोड़ना चाहें तो 2000 और 2001 गुना करके 2 से भाग देंगे
1+2+3+4+5+…….+2000=( 2000×2001)÷2 =1000×2001 = 2001000

How-to-check-divisibility-of-given Numbers


FINAL WORDS


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HOW TO RECALL FORGOTTEN PIN OF ATM CARD


Solve this maths in 5 mins


A house wife forgot her 'ATM PIN' which is a four digit number, but luckily she remembers some hints on how to recall this 'PIN'
Here are some of the clues

1. The 1st digit is half of the 2nd
2. The sum of the 2nd and 3rd is 10
3. The 4th is equal to the 2nd plus 1
4. The sum of all digits is 23

What is her ATM PIN?

Solution


Let the four digits PIN be   wxyz, Here 1st ,2nd .3rd and 4th digit are w,x,y and z  respectively .


According  to 1st condition

The 1st digit is half of the 2nd i.e
w = x/2   .......................................... (1 )


 2nd condition

The sum of the 2nd and 3rd is 10 i.e

x + y = 10

This implies   y = 10 - x  .................... ( 2 )



3rd condition


 The 4th is equal to the 2nd plus 1    i . e

z = x + 1     .......................... ( 3 )


According  to 4th condition

 The sum of all digits is 23 . i e .

w  +  x + y + z  = 23 ............ ( 4 )



How to find 2nd digit

1st of all we have to find the value of x .because x is related to all other equations.
Putting the values of w ( from eq1) , y (from eq 2), z( from eq3) in ( 4) we get
x/2   + x + 10 - x + x + 1 = 23,cancelling 'x'

3x/2 +11 = 23
3x/2 =23-11
3x/2 = 12

x = 8 This is our 2nd  digit

Now put the value of x in  (1)
w = 8/2
w = 4  ,This is our 1st  digit

To find 3rd digit Put the value of x in (3)
z = x + 1  
z = 8 + 1
z = 9 This is our 4th  digit
To find 3rd digit Put the value of x in (2)
y = 10 - 8

y = 2  This is our 3rd  digit


So The PIN Would be  wxyz  ➡️4829


Verification



1 The 1st digit is half of the 2nd      ➡️   4  and  8 , definitely 4 is half of 8

2. The sum of the 2nd and 3rd is 10  ➡️ 8+2 =10
3. The 4th is equal to the 2nd plus 1  ➡️ 9 = 8+1
4. The sum of all digits is 23   ➡️ 4 + 8 + 2 + 9 = 23



Conclusion



Thanks for visiting this website and spending your valuable time to read this post regarding How to recall forgotten  PIN of  ATM  .If you liked this post , don't forget to   share it with your friends to benefit them also ,we shall meet in next post , till then bye and take care......

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A QUIZ OF MATHEMATICS FOR YOU ,MATRICES QUESTION PAPERS

A Quiz Of Mathematics For You 






There are Total 10 questions in all . Each question is assigned with 2 marks. Attempt all Question. Matrices question papers, determinant questions and answers, All the questions are from matrices and Determinants . Score will be Displayed at the end of Quiz.




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FINAL WORDS


  Thanks for watching and responding to this quiz based on Matrices and Determinants on Mathematics. 


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If you are a mathematician Don't forget to visit my Mathematics You tube channel ,Mathematics Website and Mathematics Facebook Page , whose links are given below


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C B S E Date sheet for March 2019 Declared



Date Sheet for March 2019




cbse date sheet 2019 class 12,CBSE(  Central Board of Secondary Education) released 10th and  12th Board Exam 2019 Date Sheet on its  cbse.nic.in site. CBSE 's12th Board Examination will begin from  15th February and Class 10th Board exam will commence from 21st February .


cbse date sheet for march 2019


Date sheet released in cbse.nic.in. website


Date sheet of  10th and  12th classes for March 2019 Exam CBSE (Central Board of Secondary Education) released in its site  cbse.nic.in The exam of 12th class will be starting from 15th February 2019  and Class 10th Board exam will be  starting from 21 th February . cbse board exam date 2019 class 10 can be downloaded from  cbse.nic.in.

 Date Sheet of Board examination is prepared based on the subject combinations opted by the students of Class10th and Class10+2th. 
The core examinations  would commence from March 1, 2019 for Class 10th and 10+2th. CBSE Board has also decided to conduct the examination of skill subjects in latter half of Feb, 2019.
Last paper of 10+2 class is of   MULTIMEDIA & WEB INTRO TO HOSP MGMT on   WEDNESDAY,  03rd APRIL 2019 067


Time of  Exam


Answer books would be distributed to candidates between 10.00 - 10.15 A.M. and Question paper will be distributed at 10.15 A.M. Duration of time for each paper has been indicated in the date-sheet. From 10.15 -10.30 A.M.(15 minutes) candidates shall read the question paper . Start Time of paper will be 10:30 Am and concluding time will be different for different subject .

Complete Date sheet along with cbse date sheet 2019 class 12, can be Downloaded from the link given here  cbse.nic.in.  The official circular released by the board on cbse.nic.in, the board states that, CBSE(Central Board of Secondary Education) This time Date Sheet of Boards examination is prepared in view of  subjects combination opted by the students of these two classes .That was the latest news regarding cbse exam date 2019 class 10,cbse 12th date sheet 2019,


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SOME OF MY PUBLISHED POSTS ARE APPEARING HERE IN CHRONOLOGICAL ORDER

In this post I have shown here my some of previous published posts in chronological order.Let us discuss them one by one.

Example :   To Find the Square of Two Digits Numbers Ending with 5



Here I shall show  how square of 35 can be  found quickly.

Step 1 


when unit/(Right most)  place of a number ends with 5 
then place 25 as last two digits (i. e Right most ) of the result.

Step 2 



Take the digit which is on the unit's place and multiply it with its successor (next digit from it), Here in this case the 1st two digits are 12, the product of 3 and its  successor 4. 

Step 3

The result will be  four digit numbers whose first two digits are answer  of step 2 and next two digits are answer of step 1

The square of  35 = (3×4)(25)
                                        = 1225


Example


To find Square of   65   and many more Examples


To find the transpose of matrix 


HOW TO FIND THE TRANSPOSE OF  MATRIX
1st of all shift all the elements which are in 1st row to 1st column as
5
5
2
,then shift the elements which are in      2nd row to 2nd column as  

-1
-3
 7
similarly  shift all the elements which are in 3rd row to 3rd column as
4
2
8

And the matrix so obtained is the transpose matrix. We can  check that same colour row have been  transformed to same colour column
        
HOW TO FIND THE TRANSPOSE OF  MATRIX  WITH AN EASY   METHOD


Now we shall take this  example to find the transpose Matrix 
HOW TO FIND THE TRANSPOSE OF  MATRIX


How to find the multiplication using short cut Method   52324 × 11= ?


1 Place zero at right end of the multiplicand like this 523240

2 Now add 0 to its neighbour 4 as 0 + 4 = 4
3 Now add 4 to its neighbour 2 as 4 + 2 = 6

4 Now add 2 to its neighbour 3 as 2 + 3 = 5
5 Now add 3 to its neighbour 2 as 3 + 2 = 5

6 Now add 2 to its neighbour 5 as 2 + 5 = 7

7 Place left most digit as it is  = 5

8 Write the digits so obtained ( blue coloured) from top to bottom as right to left

So Answer will be 5,75,564

How to  Multiply   543423 × 11= ? and many more  using  short cut Method



How to Multiply  two numbers   98 and  96 nearer to 100 

98 × 96 = (98 - 4)(2×4) = (94)(08) = 9408 (Only in mind )
Step 1 

Consider both the numbers as Num 1 = 98 and Num2 = 96.

Subtract Num 1 from 100 and write its Result 1 as one place .

Also Subtract Num 2 from 100 and write its as Result 2 second place .


Here Result 1 = 100 - 98 = 2
Result 2 = 100 - 96 = 4
Now multiply the results so obtained and mark it as Stepresult1.Stepresult1 = 4*2 = 8 = 08


Shortest method to multiply two  numbers





Step 2 


Subtract the result of  Result 1 (blue Answerfrom Num 2 i. e.(96 ).
Here we have
Stepresult2 = 96-2= 94

Final Answer = (Ist two digits are Stepresult2)(2nd two digits are Stepresult1)

= 9408

The result so obtained i. e. 9408 is the answer of product of two numbers
Shortest method to multiply two  numbers   in 2 seconds


More  Examples like  92 × 91 = ?



 How to Differentiate f(x) = (cos x )sin x


Consider    h(x) = (log cos x) ×(sin x)
then it derivative will be 

 f '(x) = f(x) Diff  (h(x))

⇒ f '(x) = f(x) [(log cos x) . Diff (sin x) + sin x Diff (log cos x)]

Therefore  f '(x) = f(x) [(log cos x) . cos x + sin x (-sin x ) /cos x)]


Therefore  f '(x) =  (cos x )sin x [(log cos x) . cos x - sin x .tan x]



Differentiate w.r.t. 'x' f(x) cos x sin x + (sin x) x 





What is  Matrix


Matrix definition


A Matrix is a set of elements ( Numbers ) arranged in a particular numbers of Rows and columns in a rectangular table. Matrices inside parentheses ( ) or brackets [ ] is the matrix notation.

Here we have an examples of Matrices . 


The elements which are written in horizontal lines are called Row and elements which are written in Vertical lines are called Column. In the matrix A above ↑ the elements 5, 3, -2 are written in Row wise whereas the elements 5,4,3 are written columns wise, Similarly the elements 4,-1,7 are written in Row wise whereas the elements 3,-1,4 are written columns wise .


Order Of a Matrix

If any matrix have "m" number of rows and "n" number of columns , then "m×n" will be the order of that matrix. It is also called matrix dimensions . For  matrices  given below ,

[      5      6    -4    2    ]   This  matrix has 1×4 order,


    3
[  8 ]  Matrix has 3×1 order ,
   -2 

  [  -Matrix has 1×1 order.

And the matrices A,B,C and D  above have 3×3 ,2 ×2 , 3×4 and 3×2  respectively, as Matrix A has 3 rows and 3 columns, matrix B has 2 rows and 2 columns, Matrix C has 3 Rows and 4 Columns Similarly Matrix D has 3 rows and 2 columns.


Elements of a  matrix , Types of matrix  ,

Equality of Matrices And  Determinent 



Condition for Matrix Multiplication


Before multiplication of two matrices we have to check whether multiplication is possible or not , If it is possible then matrices will be multiplied to each other. Necessary condition for multiplication of two matrices is if " The number of columns in the first matrix is the same as the number of rows in the second matrix ". We must know  different types of matrices ,Rows and Column.

Note : The commutation may or may not be possible for multiplication of matrices, That is  in some case AB = BA but In general AB is not equal to BA.


Example 1


1. Multiplication of 2 × matrix with 3 × 4 matrix is possible as number of columns in 1st Matrix is equal to numbers of rows in 2nd Matrix and Resultant matrix will be of 2 × 4 order .

2. Multiplication of 5 × 1 matrix with 1 × 2 matrix is also possible as it gives 5× 2 matrix as resultant Matrix.

3. Multiplication of 4 ×
3 matrix with  2 × 3 matrix is NOT possible. Because red colour numbers 3 and do not match .


How to Multiply Matrices 



To Solve the system  of Linear Equations using 2×2 Matrix Method

x - 5y = 4

2x + 5y = −2


Writing this system of equation in Matrix form

AX = B 


where X = A-1 B------------------------(1)


And A-1 = (1/Det A ) ( Ad joint A)



Where



We need the inverse of   , which we write as   A-1 
To find the inverse 1st find out Co-factor Matrix of A

Ad joint  A  =   (     5    5 -2   1   )


Co factor   A  =   (     5    −2 5   1   )

As we know the Ad joint Matrix of any matrix can be found by taking the transpose of the Co Factor matrix.

Now let us find the determinant of  A


A∣ = 5 − (-10) = 15 , which is non Zero,


Therefore A-1 
 Exists     ,So





Now putting the value of inverse of Matrix A in equation (1)


How to solve system of linear equations







Now putting the elements of Matrix X , and 
By the equality of two Matrices ,their elements in respective positions are equal to each others,


Hence x= 2/3  and y = -2/3



 x  - y + z   = 4
2x + y - 3z  = 0
 x + y + z    = 2
---------------------------------------------------------------------------------
How to multiply Two Matrices 



Matrix Multiplication





Let us take one  example to Multiply 2×3 and 3×2 Matrices ,The order of resultant matrix will be 2 × 2.


How to multiply 3×3 matrix with 3×3 matrix

A11 element will be 4×(-3)+1×5+4×6 =  -12+5+24 =17

A12 element will be   4×1+1×6+4×4  =  4+6+16 = 26

A21 element will be  2×(-3)-5×5+7×6 = -6-25+42 = 11

A22 element will be  2×1+(-5)×6+7×4 = 2-30+28 = 0

Since the resultant Matrix  2× 2   as follows



multiplication of matrices


HOW TO MULTIPLY TWO MATRICES || PRODUCT OF TWO MATRICES

Solving the Quadratic Equation



1 Factorisation Method

2 Completing the Square


3 Quadratic Formula

Completing the Square



1 Shift the constant term to right hand side of equal sign.

2 Complete the square in left side and add the term which is missing and adjust the added term on the right side.

3 Equate the Left hand term to Right hand term.

Let us consider a Quadratic Equation

9x2 – 15x + 6 = 0
To make the complete square add the missing term   (b)2  and  subtract the same term





 (3x)2  – 2*3x *(5/2)+ (5/2)2–  (5/2)2 +6 = 0

 {3x-(5/2)}2 -(25/4)+6 = 0

{3x - (5/2)}2 -(1/4) = 0

{3x-(5/2)}2  = (1/4)                      Taking square roots
3x - (5/2) = (1/2)  or  3x-(5/2) = - (1/2)  
3x = (1/2)+(5/2)  or 3x = -(1/2) + (5/2)
3x = 6/2 or 3x = 4/2
x = 1 or    3x = 2
x = 1 or    x = 2/3

The roots of the given equation are 1 and   2/3





 Learn how to apply Factorisation Method    and      Quadratic Formula



Conclusion



In this post I have discussed some of my post published earlier in chronological order  . If this post helped you little bit, then please share it with your friends to benefit them, comment your views on it and also like this post to boost me and to do better, and also follow me on my Blog .We shell meet in next post till then Bye .
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