Permutations And Combinations(11th Grade > Mathematics ) Questions and answers for exam Preparation

11th Grade > Mathematics

PERMUTATIONS AND COMBINATIONS MCQs

Total Questions : 30 | Page 2 of 3 pages

Question 11.

There are 16 points in a plane out of which 6 are collinear, then how many lines can be drawn by joining these points

Discuss Question

Answer: Option A. -> 106
:
A

Required number of lines

= $^{16} C_{2} -^{6} C_{2}$ +1 = 120 -15+1 = 106

Question 12.

The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line is

Discuss Question

Answer: Option A. -> 185
:
A

Required number of ways = $^{12} C_{3} -^{7} C_{3}$

= 220 - 35 = 185

Question 13.

An auto mobile dealer provides motor cycles and scooters in 3 body patterns and 4 different colours each. The number of choices open to customer is

$^{5} C_{3}$
$^{4} C_{3}$
$12$
$24$

Discuss Question

Answer: Option D. ->

24

:
D
By fundamental theorem of Multiplication = 4

\times

\times

Question 14.

The number of diagonals in an octagon will be

Discuss Question

Answer: Option B. -> 20
:
B

Number of diagonals in an Octagon = $^{8} C_{2} - 8$ = 20

Question 15.

The number of integers greater than 6000 that can be formed using the digits 3, 5, 6, 7 and 8 without repetition is

Discuss Question

Answer: Option B. -> 192
:
B

The integer greater than 6000 may be of 4 digits or 5 digits. So, here two cases arise.
Case I When number is of 4 digits.
Four digit number can start from 6, 7 or 8.

Thus, total number of 4-digit numbers, which are greater than
$6000 = 3 \times 4 \times 3 \times 2 = 72$
Case II When number is of 5 digits.
Total number of five digit numbers which are greater than 6000 = 5! = 120
$∴$ Total number of integers = 72 + 120 = 192

Question 16.

The number of straight lines joining 8 points on a circle is

Discuss Question

Answer: Option D. -> 28
:
D

The number of straight lines is $^{8} C_{2}$ = 28

Question 17.

15 busses fly between Hyderabad and Tirupathi.The number of ways can a man go to tirupathi from Hyderabad by a bus and return by a different bus is

Discuss Question

Answer: Option C. -> 210
:
C
The number of ways in which a man travel from Hyderabad to Triupati is 15 and back to Hyderabad is 14 and hence the total number of ways =15

\times

14 = 210

Question 18.

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friend. Number of ways in which X & Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is ?

Discuss Question

Answer: Option A. -> 485
:
A
Given, X has 7 friends, 4 of them are ladies and 3 are men while Y has 7 friends, 3 of them are ladies and 4 are men.

∴

Total number of required ways

^{3} C_{3} \times^{4} C_{0} \times^{4} C_{0} \times^{3} C_{3} +^{3} C_{2} \times^{4} C_{1} \times^{4} C_{1} \times^{3} C_{2} +^{3} C_{1} \times^{4} C_{2} \times^{4} C_{2} \times^{3} C_{1} +^{3} C_{0} \times^{4} C_{3} \times^{4} C_{3} \times^{3} C_{0} = 1 + 144 + 324 + 16 = 485

Question 19.

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include atmost one boy, the number of ways of selecting the team is ?

Discuss Question

Answer: Option A. -> 380
:
A
We have, 6 girls and 4 boys. To select 4 members (atmost one boy)
i.e. (1 boy and 3 girls) or (4 girls)

=^{6} C_{3} .^{4} C_{1} +^{6} C_{4}

.....(i)
Now, selection of captain from 4 members (including the selection of a captain, from these 4 members)

(^{6} C_{3} .^{4} C_{1} +^{6} C_{4})^{4} C_{1} = (20 \times 4 + 15) \times 4 = 380

Question 20.

Let $T_{n}$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n + 1} - T_{n} = 10$ , then the value of N is