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Published on: 03/10/2019
Permutation and Combination
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Questions + Answers key
Take MCQ Mathematics Test
1.
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
2.
7 points lie on a circle . How many chords can be drawn by joining these points?
3.
Evaluate 20C5 + \(\sum _{ r=1 }^{ 5 }\) 25-rC4
4.
If 28C2r : 24C2r-4 = 225 : 11 , find r
5.
How many different words can be formed with the letters of the word 'HARYANA'? How many of these begin with H and end with N?
6.
Prove that 35! is divisble by 212. What is the largest integer n such that 35! is divisible by 2n?
7.
How many different words can be formed with the letters of the word 'HARYANA'? How many of these have H and N together?
8.
How many numbers greater than 1000, but not greater than 4000 can be formed with the digits 0, 1, 2, 3, 4, if
(i) repetition of digits is alllowed?
(ii) repetition of digits is not allowed?
9.
How many natural numbers less than 1000 can be formed with the digits 1, 2, 3, 4, and 5, if repetition of digits is allowed?
10.
Five persons entered in the lift cabin on the ground floor of an 8-floor house. Suppose each of them can leave the cabinindependently at any floor begining with the first. Find the total number of ways in which each of the five persons can leave the cabin
(i) at anyone of the 7 floor.
(ii) at different floors.
1.
When a coin is tossed once, the number of outcomes is 2 (Head and tail) i.e., in each throw, the number of ways of showing a different face is 2.
Thus, by multiplication principle, the required number of possible outcomes is 2 × 2 × 2 = 8
2.
Required number of chords = 7C2
3.
42504
4.
Use nCr = \(\frac {n!}{r!(n-r)!}\) and simplify
Ans. 7
5.
Ans. 840; 20
6.
n=32
7.
Ans. 840; (i) 240
8.
Thousand's place can be filled either by 1 or 2 or 3, i.e. thousand's place can be filled in 3 ways.
Ans. (i) 375
(ii) 72
9.
Required numbers will be of 1-digit, 2-digit or 3-digit.
Ans. 155
10.
(i) Each person can leave the cabin at anyone of the seven floors. So, each person can leave the cabin in 7 ways.
Ans. 75
(ii) First person can leave the cabn at anyone of the seven floors. Second person can leave the cabin at anyone of the remaining 6 floors. Similarly, we can calculate for other.
Ans. 2520
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