How many combinations are possible if 3 one rupee coin, 4 fifty paise coin and 2 twenty five paise coin
are available. It is compulsory to select any one of the coin
Out of 3 one rupee coin, total possible combinations are
0 one rupee coin, 1 one rupee coin,
2 one rupee coin, 3 one rupee coin,
Out of 4 fifty paise coin, total possible combinations are
0 fifty paise coin, 1 fifty paise coin, 2 fifty paise coin, 3 fifty paise coin, 4 fifty paise coin,
Similarly out of 2 twenty five paise coin, total possible combinations are
0 twenty five paise coin, 1 twenty five paise coin, 2 twenty five paise coin,
Therefore total number of methods = 4*5*3 – 1= 60-1 = 59
(1 case is deducted because in a case no coin is selected)
6^3 = three power of six = 15 (total letters used in written expression)
Similarly 4^2 = two power of four = 14
8^4 = four power of eight = 16
And 9^5 = five power of nine = 15
For obtaining 31 zeros at last of the number, 31 powers of 5 is necessary. Product 1*2*3*4*5……………upto 125
contain 5, 10 ,15………. 125. These 25 numbers are multiple of 5, besides it 25, 50, 75, 100, 125 contain
a second 5 and 125 contains a third 5 hence total number of 5 = 25+5+1 = 31
A carom board is of size 2.5 m × 2.5 m. Striker is placed on a side at a position 0.5 m from the left corner.
For overcoming the condition of foul it is necessary to touch the queen placed on right side at a position 0.5 m
from the side where striker is placed. If player wants to make a two collision rebound then he should make
an impact on the first side at a distance of
OPtion
1) 0.8 m from corner
2) 1 m from corner
3) 0.5 m from corner
4) 0.75 m from corner
5) 0.6 m from corner
6) 1.25 m from corner
7) 1.4 m from corner
8) 1.3 m from corner
9) 1.5 m from corner
10) 0.25 m from corner
Solution
Let striker makes first impact at a distance x from the corner and second at a distance y from other corner.
First draw a plot for this condition. Then according to plot
x/0.5 = (2.5-x)/y => xy = 0.5(2.5-x) ..... Equation 1
and y/(2.5-x) = (2.5-y)/2 => 2y =(2.5-x) (2.5-y) .....Equation 2
On solving these equations we get x = 0.75 m
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
Tobias Dantzig
Language is remarkable, except under the extreme constraints of mathematics and logic, it never can talk only about what it's supposed to talk about but is always spreading around.