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Question 1 of 5
1. Question
A question paper consists of two sections having respectively 3 and 5 questions. The following note is given on the paper. “It is not necessary to attempt all the questions” One question from each section is compulsory. In how many ways, a candidate can select the question?
Correct
Ans : b
Here, we have two sections A and B. Section A has 3 questions and B has
5 questions and one question from each section is compulsory according to the given condition.
∴Number of ways selecting one or more than one question from section A
=23-1 = 7
Similarly, from section B = 25-1 = 31
According to the rule of multiplication, the required number of ways in which
Which candidate can select the questions
=7x 31 = 217
Incorrect
Ans : b
Here, we have two sections A and B. Section A has 3 questions and B has
5 questions and one question from each section is compulsory according to the given condition.
∴Number of ways selecting one or more than one question from section A
=23-1 = 7
Similarly, from section B = 25-1 = 31
According to the rule of multiplication, the required number of ways in which
Which candidate can select the questions
=7x 31 = 217
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Question 2 of 5
2. Question
Find the number of combinations that can be formed with 5 oranges, 4 mangoes and 3 bananas, when one fruit of each kind is taken.
Correct
Ans : a
The required number of combinations,
when one fruit of each kind is taken
= 5C1 x 4C1 x 3C1 = 5 x4 x3= 60
Incorrect
Ans : a
The required number of combinations,
when one fruit of each kind is taken
= 5C1 x 4C1 x 3C1 = 5 x4 x3= 60
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Question 3 of 5
3. Question
In how many ways, 12 balls can be divided between 2 boys, one receiving 5 and the other 7 balls?
Correct
Ans: b
Here, order is important, then the number of ways in which 12 different balls can be divided between two boys who receives 5 and 7 balls respectively, is
(12!)/(5!7!) * 2! = 1584
Incorrect
Ans: b
Here, order is important, then the number of ways in which 12 different balls can be divided between two boys who receives 5 and 7 balls respectively, is
(12!)/(5!7!) * 2! = 1584
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Question 4 of 5
4. Question
There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities, is
Correct
Ans : b
There are 10 stations on railway line.
So, the number of different journey tickets between two stations from given 10
stations from one side = 10C2 = (10* 9)/2 = 45
Similarly, number of different journey tickets from other side = 45
∴Total number of tickets to be generated by authorities.
= 45 + 45 = 90
Incorrect
Ans : b
There are 10 stations on railway line.
So, the number of different journey tickets between two stations from given 10
stations from one side = 10C2 = (10* 9)/2 = 45
Similarly, number of different journey tickets from other side = 45
∴Total number of tickets to be generated by authorities.
= 45 + 45 = 90
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Question 5 of 5
5. Question
The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a group consisting of 8 ladies and 7 gentlemen, if Mrs. X refuses to serve in a committee if Mr. Yis its member, is
Correct
Ans: d
If Mrs. X is selected among the ladies in the committee, then Mr. Y is not selected or
if Mrs. X is not selected then Mr. Y can be there in the committee.
So, required number of ways
= 8C3 x 6C4 + 7C3 x 7C4
([8x7x6)/(3 *2)] * [(6 x5)/(2 *1)]+ [(7 x6 x5)/(3 *2)] *[(7x6x5)/(3 *2)]
= 840+ 1225 =2065
Incorrect
Ans: d
If Mrs. X is selected among the ladies in the committee, then Mr. Y is not selected or
if Mrs. X is not selected then Mr. Y can be there in the committee.
So, required number of ways
= 8C3 x 6C4 + 7C3 x 7C4
([8x7x6)/(3 *2)] * [(6 x5)/(2 *1)]+ [(7 x6 x5)/(3 *2)] *[(7x6x5)/(3 *2)]
= 840+ 1225 =2065
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