Compact Questions (Number System)

EXERCISE -1

1) If x= 106 then x(x²- 3x+3)=?   1157626

2) If x= 99 then x(x²+12x+48)=? 1092663
 
3) 1/(³√25 - ³√5 +1) = A ³√25+ B ³√5+ C. Then find A+ B + C.                        1/3

4) 1/(³√9 + ³√3 +1) = A ³√9+ B ³√3+ C. Then find A+ B - C.                                1

5) If x= (7+ 4√3), y= (7- 4√3); then 1/(x+1) + 1/(y+1).                                  1

6) If x= (√3+ √2)⁻³, y= (√3- √2)⁻³ then (x+1)⁻¹ + (y+1)⁻¹ =?                                1

7) If x= 7 + 4√3 then x+ 1/x=?             14

8) If x=14, then x⁵ - 15x⁴ + 15x³ - 15x² + 15x =?                                                     14

9) If x=12, then x⁶- 13x⁵ +13x⁴ - 13x³ + 15x² -13x+5=?                                    281

EXERCISE -2

Recurring Decimal
                                                           _
1) ³√0.037037037... =?                    0.3
          __       __
2) (0.11 + 0.22)×3=?                             1
        __        __       __                             __
3) 3.12+ 5.34+ 2.16=?                   10.62



EXERCISE -3
Number of Factors

1) 240 
a) Find the number of factors.  20
b) Sum of all factors.                          744

2) 300
a) No of factors.                                    18
b) Sum of all factors.                          868

3) 2²× 3¹×5²
a) No of even factor.                               12
b) Sum of even factor.                          744
c) No of odd factor.                                 6
d) Sum of odd factor.                           124

4) 360
a) No of odd factors.                                6
b) Sum of odd factors.                           78
c) Sum of even factors.                      1092

5) 1728
a) no of factors.                                      28

**** Number of prime factor


6) 13²× 7⁵× 3⁸=2+5+8.
a) number of prime factors.                 15

7) 13²×7⁵×15⁸.
a) number of prime factors.                 23




Miscellaneous Exercise(1)

1) Value of
a) 0.55555....                                        5/9
b) 3.242424...                                321/99
c) 5.362362......                          5357/999
d) 0.4357625437624.                 4357625/9999999
            ___
e) 0.43213.
            ___
f) 5.00983

2) For the number 2450 find.
a) The sum & number of all factors.     
b) The sum & number of even factors. 
c) The sum & number of odd factors. 
d) The sum and number of factors divisible by 5.
e) The sum and number of factors divisible by 35.
f) The sum and number of factors divisible by 245.

3) For the number 7200 find
a) The sum & number of all factors. 
b) The sum & number of even factors. 
c) The sum & number of odd factors. 
d) The sum and number of factors divisible by 25.
e) The sum and number of factors divisible by 40.
f) The sum and number of factors divisible by 150.
g) The sum and number of factors not divisible by 75.
h) The sum and number of factors not divisible by 24.

4) Find the number of divisors by 1728.   28
5) Find the number of divisors of 1080 excluding the throughout divisors, which are perfect squares.                             28
6) Find the number of divisors of 544 excluding 1 and 544.                            10
7) Find the number of divisors of 544 which are greater than 3.                     10
8) Find the sum of divisors of 544 which are perfect squares.                             21
9) Find the sum of odd divisors of 544.  18
10) Find the sum of even divisors of 4096.                                         8190
11) Find the sum the sums of divisors of 144 and 160.                                781
12) Find the sum of the sum of even divisors of 96 and the sum of odd divisors of 3600.                            651
                                                                                                                     
Miscellaneous Exercise (2)

Find the number of zeroes in the following:
1) 47!
2) 58!
3) 13×15×22×125×44×35×11
4) 12×15×5×24×13×17
5) 173!
6) 144!×5×15×22×11×44×135
7) 148!
8) 1093!
9) 1132!
10) 1142!×348!×17!

11) n! has 23 zeroes. What is the maximum possible value of n.        nev

12) n! has 13 zeroes. The highest and least Values of n are.                  59, 55

23) Find the number of zeroes in the product 1¹×2²×3³×4⁴×5⁵×6⁶×....×49⁴⁹.   250

24) Find the number of zeroes in:
100¹×99²×98³×97⁴×.....1¹⁰⁰.     1124

25) Find the number of zeroes in:
₁1! x ₂2! x ₃3! x ₄4! x ₅5! x .....₁₀10!.      5!+ 10!

26) 2² x 5⁴x 4⁶ x 10⁸ x 6¹⁰ x 15¹² x 8¹⁴ x 20¹⁶ x 10¹⁸ x 25²⁰.                                 98

27) What is number of zeroes in the following:.
a) 320+1000+40000+32000+15000000. 
b) 3200×1000×40000×32000×1500000.
          3, 18




       

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