वोट

वोट उसी को दीजिये जिसका दामन साफ |
वर्ना आने वाली पीढ़ी नहीं करेगी माफ़ ||

वोट उसी  को दीजिये जिसका दमन साफ | 

वर्ना आने वाली पीढ़ी नहीं करेगी माफ़ ||

Limit

What is the limit? Question can strike in mind for those who study mathematics in senior secondary level. Answer to the question is quite simple but not clear. When a function f(x) is undefined at a point say x = a, then we try to find its value very very close to that point. If this value exist, we say it limiting value of f(x) at a.
                                               

Geometric Progression

A sequence obtained by successive multiplication of a fixed term to the first term is called in geometric progression. In other words " If ratio of any two consecutive terms of a sequence is constant called in G.P."
Example:  1, 2, 4, 8, .......
                  1, 3, 9, 27, 81, .........

Symmetry

                                           

Symmetry in nature always attracted people.  It develops beauty in nature. There are plenty of things available in nature which has linear symmetry. Symmetry in English alphabets, Symmetry in birds, symmetry in flowers and symmetry in human being. 

           Due to symmetry, flowers are so beautiful


Beauty in human being is Due to symmetry 

           











                   
        Mathematical figures also look nice Due to symmetry

Symmetry in Alphabets

सुखार्थिनः कुतो विद्या …… 

सच है सुख की कामना रखने वालों विद्या की प्राप्ति कैसे हो सकती है ? सुख पूर्वक समय बिताने वाला सफलता के ऊँचे पायदान पर अपना कदम कैसे रख सकता है ? माना ज़माना बदल गया परन्तु कठिन परिश्रम और लगन से अध्ययन  करने वाला हीं सफल हो कर समाज में अपनी पहचान बना सकता है ।  Facebook , internet , mobile , T.V. , ए. सी. , कूलर,  फैन्सी ड्रेस  यहां तक  कि चटपटे भोजन की कामना रखने वालों को असफलता अविलम्ब अपने साथ लगा  लेती है ।  

पाना चाहो जीवन में कुछ , ना करना विश्राम । 

जैसी करनी करोगे प्यारे , वैसे पाओ परिणाम ॥

Check for accuracy of a product

Subject:  How to check for the accuracy of product of two numbers.
                   Example           123476
                                              x 654879
                                            7645983254
      Now to check for the accuracy no need to go to the actual product. Follow the following simple steps.
1.    add all the digits of the first number i.e. 1+2+3+4+7+6= 23
2.  divide it by 9 and record the remainder i.e. 23 /9 , remainder = 5
3. add all the digits of second number 6+5+4+8+7+9 = 39
4.  divide it by 9 and record the remainder i.e. 39 /9 , remainder = 3
5.  multiply the two remainders i.e. 5x3 = 15
6.  divide the number obtained in step 5 by 9 and record the remainder. i.e. 15/9, remainder = 6
7.  add all the digits of the product of two numbers i.e. 7645983254 you get
      7+6+4+5+9+8+3+2+5+4= 53
8.  divide it by 9 and record the remainder i.e. 53 /9 , remainder = 8
Conclusion: If remainders obtained in step 6 and 8 are equal then your product is correct otherwise wrong.
Clearly above product is wrong. As remainder in step 6 is and that in step 8 is 8 , unequal.