# Free Objective Test 02 Practice Test - 11th and 12th

### Question 1

The number of ways in which 8 boys be seated at a round table so that two particular boys are next to each other is

#### SOLUTION

Solution :C

The number of ways in which this can be done = 6! 2!

### Question 2

The number of ways of arranging 6 players to throw the hand ball so that the oldest player may not throw first is

#### SOLUTION

Solution :B

The number of ways in which this can be done = 6! – 5! = 600

### Question 3

m men and n women are to be seated in a row so that no two women sit together. If m > n, then the number of ways in which they can be seated is

#### SOLUTION

Solution :D

The number of ways in which they can be seated = m!.m+1Pn

### Question 4

The number of ways that a volley ball 6 can be selected out of 10 players so that 2 particular players are excluded is

#### SOLUTION

Solution :D

The number of ways selecting 6 out of 10 so that 2 particular players are always excluded is 10−2C6

### Question 5

The number of permutations that can be made out of the letters of the word “EQUATION” which start with a consonant and end with a consonant is

#### SOLUTION

Solution :B

Consonants occupy 2 ends in 3P2 ways remaining 6 letters occupy 6 places in 6! Ways

So the required number of arrangements = 3P2.6!=3!6!

### Question 6

If m parallel lines in plane are intersected by n parallel lines, then number of parallelograms formed is

#### SOLUTION

Solution :C

mC2. nC2

### Question 7

The number of four digit even numbers that can be formed with 0,1,2,3,7,8, is

#### SOLUTION

Solution :D

If 0 is in units place no. of ways = 5P3=60

If 2 or 8 is in units place no. of ways = 2(5P3−4P2)=96

Total : 60 + 96 = 156

### Question 8

The number of nine digit numbers that can be formed with different digits is

#### SOLUTION

Solution :C

Required number numbers = total - the number of numbers begining with 0 = 10!–9!=9.9!

### Question 9

The number of permutations of n dissimilar things taken not more than ‘r’ at a time, when each thing may occur any number of times is

#### SOLUTION

Solution :A

n+n2+⋯⋯⋯+nr=n(nr−1)n−1

### Question 10

There are 5 doors to a lecture room. The number of ways that a student can enter the room and leave it by a different door is

#### SOLUTION

Solution :A

A student can enter the room in 5 ways but he can leave the room in 4 ways.

The total number of ways in which this can be done = 5 × 4 = 20

### Question 11

Total 4 digit odd numbers that can be formed, if the digits used is not to be repeated again is

#### SOLUTION

Solution :A

The number of four digit numbers which satisfy the above condition = 8×8×7×5=2240

### Question 12

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

#### SOLUTION

Solution :D

By fundamental theorem of Multiplication = 4 × 3 × 2

### Question 13

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

#### SOLUTION

Solution :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 × 14 = 210

### Question 14

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

8

16

24

28

#### SOLUTION

Solution :D

The number of straight lines is 8C2 = 28

### Question 15

The number of diagonals in an octagon will be

28

20

10

16

#### SOLUTION

Solution :B

Number of diagonals in an Octagon = 8C2−8 = 20