 1] Find the total no of 10 digits whose sum is 4

 4 = 4 + 0 (one 4 & 9 zeroes) i.e. 1 4 = 3 + 1 (one 3,one 1 & 8 zeroes) i.e. 2 * 9! / 8! = 18 4 = 2 + 2 (two 2’s & 8 zeroes) i.e. 9 4 = 1 + 1 + 2 (two 1’s & one 2) i.e. 9! / 7! + 9! / (7! * 2!) = 72 + 36 = 108 4 = 1 + 1 + 1 + 1 (four 1’s) i.e. 9! / ( 6! * 3!) = 84 Total number of 10 digits numbers whose sum is 4  are 1 + 18 + 9 + 108 + 84 = 220

2] Next number in the series is 1 , 2 , 4 , 13 , 31 , 112 , ?

 224 No number has digits more than 4. All of them are 1 , 2, 4, 8 , 16 , 32 , 64 converted to numbers in base 5.

3] BE * BE = ACB.
A, B, C, E are non zero numbers. Find B, E.

 B=1 E=9.

4] Three friends divided some bullets equally.
After all of them shot 4 bullets the total number of bullets remaining is equal to the bullets each had after division. Find the original number divided.

 18 Initially  all have x bullets After shooting (x-4) Equation is 3x-12 = x

5] A man loses his way in a thick jungle. At random he walks from his camp but mathematically in an interesting fashion. First, he walks one mile East then half a mile to North. Then 1/4 mile to West, then 1/8 mile to South and so on making a loop. Finally how far he is from his camp and in which direction.

 Distance travelled in north and south directions 1/2 – 1/8 + 1/32 – 1/128 + 1/512 – and so on = 1/2/((1-(-1/4)) Similarly in east and west directions 1- 1/4 + 1/16 – 1/64 + 1/256 – and so on = 1/(( 1- ( – 1/4)) Add both the answers

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