1.
Two trains whose respective lengths are 240 m and 360 m cross each other in
30 seconds when they are moving in opposite directions and in 1 minute 40
seconds when they are moving in the same direction. What is the speed of the
faster train (kmph)

a. 39.2 b.
36.6 c. 46.8 d. 33.33
e. 49.2

Solution: let speeds are x and y

In opposite direction, Relative
speed is (x+y)

x+y= (240+360)/30 = 20 m/sec ---- (1)

In Same direction, Relative speed is
(x-y)

x-y= (240+360)/100 = 6 m/sec --- (2)

Solving (1) and (2)

X= 46.8 kmph

2. A five digit
number is formed with the digits 0,1,2,3 and 4 without repetition. Find the
chance that the number is divisible by 5.

a. 2/7 b. ¼ c. 1/5
d. 3/5 e. 11/19

Solution: Probability = (favorable cases)/(total cases)

Total cases = forming 5 digit number

_
_ _ _ _

First place can be occupied by any one of these digits 1,2,3,4 = 4 ways

Second place can be occupied by 0,
any three digits remaining from above 4 digits= 4 ways

Third = 3 ways

Fourth = 2 ways

Fifth = 1 way

So total cases = 4* 4!

Favorable cases= 5 digit number divisible by 5

_
_ _ _ _

Fifth place have to occupy by 0 only
as number should be divisible by 5 = 1 way

Remaining 4 places any 4 digits
(1,2,3,4 ) so 4! Ways

Favorable cases = 4!

Probability= 4!/(4 * 4!) = ¼

3. How many words of 11letters could be formed with all the
vowels present only in the even places, and the consonants only in the odd places,
using letters of English alphabet each letter may appear only once the vowels
are A E I O U and consonants are remaining letters of the alphabet .in the
answers n! denotes n factorial

a)21! B)26!/5! C) 21! /(5! * 5! ) d)21!* 5!/15!

Solution:

_ _
_ _ _
_ _ _
_ _ _

1
2 3 4
5 6 7
8 9 10 11

First place vowels at even places. As
there are 5 even places and 5 vowels so we can arrange in 5! Ways

Remaining odd places, total 6 need
to be filled with 21 consonants

First place can be filled with 21
ways

Third place can be filled with 20
ways

5

^{th}place can be filled with 19 ways
7

^{th}place can be filled with 18 ways
9

^{th}place can be filled with 17 ways
11

^{th}place can be filled with 16 ways
So odd places can be filled in 21*20*19*18*17*16
ways= 21!/15!

So Total = (21! * 5! )/ 15!