Q1.
33! is divisible by _____________________ .
(a) 233 (b) 241 (c) 230
(d) 239
Solution.
(c) 230
E2(33!) = E2(1.2.3.4------------.32.33)
= 16 + E2
(1.2.3---------.15.16)
= 16 + 8 + E2 (1.2.3.4------.8)
= 16 + 8 + 4 + E2(1.2.3.4) =
16 + 8 + 4 + 3 = 31
Note : 33! is divisible by 2n , n is integer having largest value 31 .
Solution
Q2.
Convert the product into factorials 6.7.8.9.10.11.12 .
Solution
=
12!/5!
=
12 x 11 x 10 x -----x 7 x 6 x 5!/5!
= 12 x 11 x 10 x -----x 7 x 6
Solution
Q3.
(10 + 4)! = 10! + 4! (True/False).
Solution.
False
Solution
Q4.
(n + 1)! = 30(n - 1)! find n.
Solution.
(n + 1)n(n - 1)! = 30(n - 1)!
(n + 1)n = 30
n = 5
Solution
Q5.
8 women and 4 men are going to sit in a row so that men will occupy the even places . How many such arrangements are possible .
Solution.
In this case all 12 persons are to be seated in a row.
2nd , 4th , 6th , 8th ,
10th and 12th are even places which is filled by 4 men in 6 p4 ways . 8 women will cover remaining
8 places 8p8 ways so , all possible arrangement are
6 p4 . 8p8
Solution
Q6.
How many different signals can be made by 2 flags from 6 flags of different colours .
Solution.
6p
2 =
6!/4!
=
6 x 5 = 30
Solution
Q7.
How many four digit numbers can be created with distinct digits .
Solution.
There are 10 digits which are to be used
0,1,2,3,,4,5,6,7,8,9,10
= 10 p4 - 9p3
9p3 is the total number of numbers having 0 at thousands place .
Solution
Q8.
How many diagonals are there in a decagon.
Solution.
There are 10 sides in a decagon
so,no. of diagonals = nc2 - n
10c2 - 10 = 45 - 10 = 35
Solution
Q9.
How many 3 digits even numbers can be formed using the digits 0,1,2,3,4,5 (when repetition is not allowed)
Solution.
As we know, in even number unit place should be even .
(a) number with 4 at unit place 4 x 4 x 1 = 16
(b) number with 2
at unit place 4 x 4 x 1 = 16
(c) number with 0 at unit place 4 x 5 x 1 = 20
Total even numbers of 3 digits
are 52 .
Solution
Q10.
400c90 + 400c91 = 401cr find r .
Solution.
ncx + ncx + 1 = n + 1cx + 1
r = 91
Solution
