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

A. 8!2!
B. 7!2!
C. 6!2!
D. 6!

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
 

A. 720
B. 600
C. 120
D. 480

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

A. m!n!       
B. m!mPn        
C. n!mPn        
D. m!m+1Pn        

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 

A. 56
B. 55
C. 27
D. 28

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

A. 2!6!
B. 3!6!
C. 3!5!
D. 2!5!

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

A. m!n!(2!)2
B. m!n!(m−2)!(n−2)!
C. m!n!(2!)2(m−2)!(n−2)!
D. (m+n)!(m+n−2)!2!

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
 

A. 180
B. 175
C. 160
D. 156

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
 

A. 9.8!      
B. 8.9!
C. 9.9!
D. 10!

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

A. n(nr−1)n−1)
B. n(nn−nr)n−1)
C. nP1+nP2+⋯⋯+nPr
D. n(n−1)rn−1

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

A. 20
B. 16
C. 19
D. 25

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

A. 2240
B. 2420
C. 2440
D. 2520

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

A. 5C3
B. 4C3
C. 12
D. 24

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

A. 15
B. 150
C. 210
D. 225

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

 

A.

8

B.

16

C.

24

D.

28

SOLUTION

Solution : D

The number of straight lines is 8C2 = 28

Question 15

The number of diagonals in an octagon will be

A.

28

B.

20

C.

10

D.

16

SOLUTION

Solution : B

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

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