riyakhilnani7 wrote:1) How many 10 digit numbers can be formed using 3 and 7 only?

10 digit no , each digit can can be either 3 or 7 => each digit can be occupied by 2 numbers

_ _ _ _ _ _ _ _ _ _

2 2 2 2 2 2 2 2 2 2

=>

2^10 numbers riyakhilnani7 wrote:2) How many 5 digit numbers can be formed which are divisible by 3 using the numerals 0,1,2,3,4,5 (without repitition)

for the number to be divisible by 3 , the sum of its digits should be divisble by 3

0+1+2+3+4+5 = 15

therefore the digits in the number can be either

01245 (sum of its digits = 12)

or

12345 (sum of its digits = 15)

If digits are 12345, there can be 5!=120 numbers without repetition of the digits

If digits are 01245, there can be 4x4x3x2x1 = 96 numbers without repetition of the digits

because _ _ _ _ _

4 4 3 2 1

the 1st digit cant be zero otherwise it will be 4 digit no.

total 120+96 =

216 numbersriyakhilnani7 wrote:3) Everyone shakes hands with everyone else in a room. Total number of handshakes is 66. Number of persons=?

Suppose n people are there. When n people are taken 2 at a time there are 66 handshakes so

nC2 = 66

n!/[2!x(n-2)!] = 66

=>

n = 12riyakhilnani7 wrote:4) The number of parallelograms that can be formed from a set of FOUR parallel straight line intersecting a set of THREE parallel straight lines=?

We can assume there are 4 horizontal parallel lines ,3 vertical parallel lines

parallelogram is made by 2 horizontal parallel lines and 2 vertical parallel liness

so

4C2 x 3C2 =

18 parallelograms