23, జులై 2014, బుధవారం

Mallapragada's Mathematics (Numbers)

                                                                               
Tirumala Tirupati, Andhrapradesh, India 
                                                                               
   Om Sri Ram          Om Sri Ram                            Om Sri Ram
  PREFACE
THE MATHEMATICS HAS BEEN PUBLISHED IN MY BLOG TO HELP STUDENTS TO TEST THEIR KNOWLEDGE. AND ALSO USEFUL FOR D.S.E.R.T,  N.C.E.R.T., B.S.R.B. S.S.C., U.P.S.C., K.P.SC, OTHER COMPETITIVE EXAMINATIONS.AND QUIZ PROGRAM MES.

SUGGESTIONS AND CRITICISMS ARE MOST WELCOME FOR FURTHER IMPROVEMENT.

          By.
                    Mallapragada ramakrishna, B.Sc.
Asst. Treasury Officer 
                           Telugu writer and Mathematics Master .                                             

OBJECTIVE TYPE QUESTIONS for   Competitions   (Paper-1)  ( NUMBERS)

1.       8888+888+88+8                      =

2.       10000-5000-3000                     =

3.       ?- 10000  = 3000                      =  

4.       ? + 123456 =654321                =                            

5.       10000-5000+5000-10000        =  

6.       7014+6134+5978                     =                                                                                                                  
7.       7589 _ ?    =  3434                    =

8.      32  +  42  +  52 + 62                              =                                                                                                                                                 
 9.       521 + 522 + 523 + 524                  =   

10.   431 + 432 + 433 + 434                        =    

11.   Simplify : 57934 x 9999               =

12.   Simplify: 12345 x 999                  =

13.   Simplify : 839478 x625                =                                                                                            
14.   Simplify: 505 x 505                      =

15.   Simplify: 1605 x 1605                  =   

16.   Simplify:495 x495                         = 

17.   Simplify: 1595 x 1595                   =

18.   Evaluate: 213 x 213 + 113 x 113  =

19.   Evaluate: 313x313 + 287 x287  =,

20.   Evaluate: 313x313 - 287 x287   =

21.   10000+1000+100+10      = 

22.   123456789  x  72                = 

23.   2014 x 1986                          = 

24.   200 x200 +100 x 100 + 2 x 200 x 100  =

25.   200 x 200 + 100 x 100 – 2 x 200 x 100 =

26.   (475 +425)2 – 4 x 475 x 425                   =

27.   3000 + 2000 – a100 = 4000

28. Find the decimal value i.e. 1/2 = ?

29. Express 7/16,2/3 and 10/7 in decimal form  ?

30. Express 3.28 in the form of P/Q

31. Express 1.62 in the p/q32.  Show that 67920574 is divisible 4  =



32.  Show that 67920562 is divisible 4 


33.  Show that 67920574 is divisible 11  =



34     Show that 4832718 is divisible 11  =


 35.   Show that 4832715 is divisible 2  =


 36.  Show that 4832715 is divisible 3  =


 37.  Show that 4832715 is divisible 5  =


38.  Show that 4832715 is divisible 6  =


   39. Show that 35256 is divisible 6  =


40.  show that 35257 is divisible 8  =



 41.   how that 35360 is divisible 8  =


42.   is 52563744 divisible by 24   =



43.   what least valuemust be assigned to (*) so that the    
        number 197*5462 is divisible by 9 ?

     
        























                                                      

Om Sri Ram    Om Sri Ram   Om Sri Ram

SALVED ABOVE (PAPER -1)
OBJECTIVE TYYPE QUESTINS   (Paper -1) ( NUMBERS)

1.       8888+888+88+8                                 = ?    9872

2.       10000-5000-3000                               = ?                               
          10000-(5000+3000)=2000

3.       ?- 10000  = 3000                                = ?                                               let x-10000 = 3000  x = 3000 + 10000=13000

4.       ? + 123456 =654321                         = ?                                             let x+123456=654321   : x= 654321 + 123456     
           =    777777                             

5.       10000-5000+5000-10000                = ?    0

6.       7014+6134+5978                           = 19126                                                                                                                                         
 7.       7589 _ ?    =  3434                         = ?                                                  7589   - X   = 3434 , -X = 3434-7589= -4155 
            X=4155

8.       32  +  42  +  52   +  62                       =  ?                                                9 +16+25+36 = 86

9.       521 + 522 + 523 + 524                        = ?                                               520   (1+5+52+53) =  520  X (1+5+25+125) = 
           520 X 156

10.   431 + 432 + 433 + 434                             =                                                   430 (1+4+42+43  =  430  X 340 (WHICH IS 
         CLEARLY   DEVISIBLY BY 10) 

11.   Simplify : 57934 x 9999                    =                                   
        57934 (1000-1) , 57934000 – 57934 =59876066

12.   Simplify: 12345 x 999                       =                              
         12345(1000 – 1) , 12345000 – 12345 =12332655

13.   Simplify : 839478 x625                      
        = 839478 x 54 = 8394780000 / 16 = 524673750

14.   Simplify: 505 x 505                           =                                     
        (505)2, = (500+5)2 ,= 5002 + 52 + 2x500x5
         =2500+25+1000=   3525

 15.   Simplify: 1605 x 1605                      =                                     

         (1605)2 , =(1600 + 5 )2, =(1600)2 + 52  +
          2x1600x5      
                                                           
          =2560000+25+16000=2576025

 16.   Simplify:495 x495                           =                                   

         (500)2, = (500-5)2 ,= 5002 + 52 - 2x500x5
          =2500+25-1000=  

17.   Simplify: 1595 x 1595                      =                                        
         (1595)2 , =(1600 - 5 )2, =(1600)2 + 52 - 2x1600x5     
                                                                      
           =2560000+25-16000=2400025
 18     Evaluate: 213 x 213 + 113 x 113  =                              
          (213)2 + (113) 2= ½ {(a+b)2 + (a-b)2}
                  ½ (213 +113)2  + (213-113)2 = ½{(326)2+(100)2)
                    =(106276+10000)/2 = 1630000
19   Evaluate: 313x313 + 287 x287 =                                      
        (313)2 + (287) 2= ½ {(a+b)2 + (a-b)2}
                ½ (313 +287)2  + (313-287)2 = ½{600)2 +(26)2
                 =1/2 (360000 +676) =180338
20. Evaluate: 313x313 - 287 x287     =                                   
       (313)2 – (287)2 = (313+287) x 
                                                            
      (313-287)=600x26=15600
       
 21.  10000+1000+100+10                   =11110                                                                                         --   
       
 22.  123456789  x  72                =                                        
        123456789(100-28) = 12345678900 – (123456789 x 28)
        12345678900 –(123456789 x (30-2),
                                                                   
        12345678900-370370370 + 24691358 = 
             888888888        

23     2014 x 1986                         = (2000+14) x  (2000-14), 
         (2000)2 – (14)2  = 4000000-196 
         =3999804

24     200 x200 +100 x 100 + 2 x 200 x 100  =                                  
           200 + 100)2 = (300)2  = 90000

25     200 x 200 + 100 x 100 – 2 x 200 x 100 =                              
          (200 - 100)2 = (100)2  =10000

26     (475 +425)2 – 4 x 475 x 425                   =                              
         (a-b)2  = (a+b)2 -4ab 
         (475 – 425 )2  = (50)2    =2500

27     3000 + 2000 – a100 = 4000                                                     
          -a100 = 4000 –(3000+2000),                                                                -a100 = -1000    ..      a = 10 


28. Find the decimal value i.e. 1/2 = ?
      Ans. 0.5
   
29. Express 7/16,2/3 and 10/7 in decimal form  ?
       Ans.  7/16= 0.4375, 10/7 = 1.428571, 2/3=0.666

30. Express 3.28 in the form of P/Q
       328/100 = 2(164)/2(50) = 82/25 = (NUMERATOR AND 
        DENOMINATOR ARE CO-PRIMES)

31. Express 1.62 in the p/q
       let x = 1.6262.....................(1)
       multipling both sides of equation (1) b 100 weget
       100 x = 162.62...................(2)
       Submiting (2) from (1) we get 
       100 x = 162.62..
              x =      1.62..
           ----------------
          99x = 161
      -------------------
              x = 161/99

      There fore 1.6262 = 161/99



32.   Show that 67920574 is divisible 4  =
 
The Last two digits number is 74, which is not devisible  by 4



33.Show that 67920562 is divisible 4 

The Last two digits number is 72, which is  devisible  by 4



34  Show that 67920574 is divisible 11  =

{(Sum of digits at add place( – ( sum of digits at even places)}(4+5+2+7) – (7+0+9+6) = (18 – 22)  is not divisible by 11



35 S how that 4832718 is divisible 11  =
           {(Sum of digits at add place( – ( sum of digits at even 
            places)}(8+7+3+4) – (1+2+8) = (22 – 11)  is  divisible   
           by 11

36.   Show that 4832718 is divisible 2  =
If units digits is any of 0,2,4,6,8 is divisible by two

37.     Show that 4832715 is divisible 3  =
     A number is divisible by  3 , if the sum of the digits is 
     divisibe by 3

    (4+8+3+2+7+1+6)=30 is not  divisible by 3

38.     Show that 4832715 is divisible 5  =
        If units digits is any of  0,5 is  divisible by five
        i.e. lost disit number is 5  divisible

39.     Show that 4832715 is divisible 6  =
        A number is divisible b 6 if it is divisible b both 2  
         and 3 
                    The lost number is 5 it is not devisible b 2 & 3, 
                    hence not divisible by  6

40.   Show that 35256 is divisible 6  =
   A number is divisible by 6 if it is divisible by  both 2   
   and 3 
                The lost number is 6 it is devisible b 2  the sum of the 
               disits (3+5+2+5+6)=21
   21     divisible by 3, now givin number is divisible by 6

41. show that 35257 is divisible 8  =
     Thelast 3 disits number is 257  is not divisibele  by 8

42 how that 35360 is divisible 8  =
The last 3 disits number is 360  is  divisibele  by 8

43     is 52563744 divisible by 24   =
the last 3 disit number is 744 which is divisible by 8 and 3 now 24 is divisible

44     what least valuemust be assigned to (*) so that the number 197*5462 is divisible by 9 ?
let the missing disit is x
sum of digits = 1+9+7+*+5+4+6+2 = 34+*= 34+2=36 is divisible 9 now x is 2