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