Combinatorics and Mathematical Induction

A School library has 75 books on Mathematics, 35 books on Physics. A student can choose only one book. In how many ways a student can choose a book on Mathematics or Physics?
1. 75
2. 110
3. 30
4. none
A Woman wants to select one silk saree and one sungudi saree from a textile shop located at Kancheepuram. In that shop, there are 20 different varieties of silk sarees and 8 different varieties of sungudi sarees. In how many ways she can select her sarees?
1. 150
2. 140
3. 160
4. 0
In a village, out of the total number of people, 80 percentage of the people own Coconut groves and 65 percent of the people own Paddy fields. What is the minimum percentage of people own both?
1. 45
2. 55
3. 65
4. 35
How many strings of length 6 can be formed using letters of the word FLOWER if
either starts with F or ends with R?
1. 186
2. 216
3. 228
4. 256
Find the total number of outcomes when 5 coins are tossed once.
1. 32
2. 16
3. 36
4. 56
In how many ways 5 different balls be distributed among 3 boxes?
1. 153
2. 183
3. 243
4. 273
In how many ways 3 different balls be distributed among 5 boxes?
1. 105
2. 125
3. 625
4. 225
There are 10 bulbs in a room. Each one of them can be operated independently. Find the number of ways in which the room can be illuminated.
1. 64
2. 1023
3. 512
4. 256
Simplify 7!/2!
1. 210
2. 840
3. 2520
4. 5040
If 6!/n!= 6, then find the value of n.
1. 5
2. 6
3. 4
4. 3
If n!+(n − 1)! = 30, then find the value of n.
1. 4
2. 5
3. 6
4. 2
What is the unit digit of the sum 2! + 3! + 4! + ..... + 22!?
1. 3
2. 4
3. 2
4. 1
If (n+2)P₄ = 42 × nP₂, find n.
1. 4
2. 5
3. 6
4. 7
If 10Pᵣ =7Pᵣ₊₂ find r.
1. 3
2. 2
3. 4
4. 1
In how many ways 5 boys and 4 girls can be seated in a row so that no two girls are together.
1. 43200
2. 25000
3. 35468
4. 24105
4 boys and 4 girls form a line with the boys and girls alternating. Find the number
of ways of making this line
1. 1313
2. 1212
3. 1152
4. 145
Find the number of ways of arranging the letters of the word BANANA.
1. 60
2. 30
3. 10
4. 5
For all n ≥ 1,
1² + 2² + 3² + 4² +…+ n² =
1. [n(n+1)(2n+1)]/2
2. n/(n+1)
3. [n(n+1)/2]²
4. None
For all n ∈ N ,1³ + 2³ + 3³ + … +n³ =
1. [n(n+1)(2n+1)]/2
2. n/(n+1)
3. [n(n+1)/2]²
4. (3ⁿ-1)/2
For all n ∈ N ,a + ar + ar²+…+ arⁿ⁻¹ =
1. [r(r+1)(2a+1)]/2
2. a(rⁿ−1)/(r−1)
3. [a(r+1)/2]²
4. (3ⁿ-1)/2

Combinatorics and Mathematical Induction

Quiz