Question

KSHI
1. REAL NUMBERS
1. The prime factor of 2×7×11×17×23+23 is ____
2. A Physical Education Teacher wishes to distribute 60 balls and 135
bats equally among a number of boys. The greatest nu-mber
receiving the gift in this way are___
3. The Values of X and Y in the given figure are ____
4. If the LCM of 12 and 42 is 10m+4, then the value of 'm' is ____
5. π is ____
6. log20152015 = ____
7. The reciprocal of two irrational numbers is ____
8. The decimal expansion of 17/18

Answer 1

2.60=2.3.2.5
   135=3.3.3.5

required no is HCF
HCF =product of least powers of common factors
       =3.5=15
so,highest possible value is 15

Answer 2

1)  prime factors of  2 * 7 * 11 * 17 * 23  +  23
                N   =  ( 2 * 7 * 11 * 17 + 1)  * 23 = 2619 * 23
       2619 is divisible by 3.  so  N = 3 * 873 * 23 = 3 * 3 * 291 * 23
             = 3 * 3 * 3 * 97 * 23
===================
2)
   60 balls must be distributed / divided among N boys equally.
   135 bats must be distributed / divided among N boys equally.
           So N is the higher common factor of 60 and 135.
             60 = 5 * 2 * 2 * 3
           135 =  5 * 3 *  3 * 3
       HCF = 5 * 3 = 15              =>  N  = 15
             so each boys will get  4 balls and 7 bats.
===============================
3)  there is no diagram given.
============================
4.        12 = 2 * 2 * 3          and     
           42 = 2 * 3 * 7
     LCM  of 12 and 42 is = 2 * 2 * 3 * 7 = 84
           10 m + 4 = 84    =>  10 m = 80    =>  m = 8
===========================
5) π = 22/7    about.    Pi is the ratio of circumference of a circle to its diameter.
==================
6)  Log 20152015  = 7.304  by calculation.
          = Log (2015 * 10001)
          = Log 2015 + log 10001
          = Log (5 * 13 * 31) + log 10001
           = Log 5 + log 13 + log 31 +Log 10001
=================================
7)  reciprocal of an irrational number is also irrational number.
       Ration of two irrational numbers can be rational or irrational.
   what is meant by the reciprocal of two irrational numbers. ??
==============================
8)    0.9444..

 decimal expansion of  17/18 =
          18  ) 1 7. 0 0 0 0 ( 0.944..
                 1 6  2
               ========
                       8 0
                       7 2
                      ====
                         8 0
                         7 2
                     ======