Evaluate each of the following : ^{3}P_{3}
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^{3}P_{3 }= 3! / (3−3)! = 3! /0! = 3! (Since, 0! = 1) = 6
Evaluate each of the following : ^{9}P_{1}
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^{9}P_{1 }=9! / (9−1)! = 9! /8! =9
Evaluate each of the following : P (10, 2)
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P (10, 2)
it can also be written as ^{10}P_{2.}
^{10}P_{2} = 10! /8! = 10(9) = 90
Evaluate each of the following : ^{5}P_{5}
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^{5}P_{5 }= 5! / (5−5)! = 5! /0! = 5!
(Since, 0! = 1) = 120
Evaluate each of the following : ^{10}P_{1}
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^{10}P_{1 }=10! / (10−1)! = 10! /9! =10
Evaluate each of the following : ^{10}P_{2}
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^{10}P_{2} =10! / (10−2)! = 10! /8! = 9x10 = 90
Evaluate each of the following : P (6, 2)
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P (6, 2)
it can also be written as ^{6}P_{2.}
^{6}P_{2} = 6! /4! = 6(5) = 30
Evaluate each of the following : ^{6}P_{5}
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^{6}P_{5 }= 6! / (6−5)!= 6! /1! = 6!(Since , 0! = 1) = 720
Evaluate each of the following : ^{10}P_{3}
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^{10}P_{3 }=10! / (10−3)!= 10! /7!=10(9) (8) (7!)/7! =10×9×8 = 720
Answer :
^{8}P_{2} =8! / (8−2)! = 8! /6! =8(7) (6!)/ 6! =8×7 = 56
If ^{10}C_{0} = ^{10}C_{r}, find r
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10
If ^{40}C_{20} = ^{20}C_{r}, find r
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20
If ^{10}C_{4} = ^{20}C_{r}, find r
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6
If ^{n}C_{4} = ^{n}C_{6}, find n
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10
If ^{n}C_{4} = ^{n}C_{3}, find n
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7
If ^{n}C_{1} = ^{n}C_{6}, find n
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7
If ^{20}C_{4} = ^{20}C_{r}, find r
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16
If ^{n}C_{4} = ^{n}C_{46}, find n
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50
If ^{n}C_{4} = ^{n}C_{60}, find n
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64
^{20}C_{3} = ^{20}C_{r}, find r
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17
If ^{45}C_{5} = ^{45}C_{r}, find r
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40
If ^{27}C_{7} = ^{27}C_{r}, find r
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20
If ^{24}C_{4} = ^{24}C_{r}, find r
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20
If ^{18}C_{4} = ^{18}C_{r}, find r
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14
There are 5 books on Mathematics and 6 books on Chemistry in a book shop. In how many ways can a students buy a Mathematics book and a Chemistry
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Number of books on mathematics = 5
Number of books on Chemistry = 6
Number of ways of buying a mathematics book = 5
Similarly, number of ways of buying a Chemistry book = 6
By using fundamental principle of multiplication:
Number of ways of buying a mathematics and a Chemistry book = 6×5 = 30
There are 5 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next two have 2 each?
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Number of ways of answering the first three questions = 4 each
Number of ways of answering the remaining three questions = 2 each
∴ Total number of ways of answering all the questions = 4×4×4×2×2 = 256
In how many ways can an examinee answer a set of 9 true/false type questions?
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Number of ways of answering the first question = 2 (either true or false)
Similarly, each question can be answered in 2 ways.
∴ Total number of ways of answering all the 9 questions = 2×2×2×2×2×2×2×2×2= 2^{9} = 512
A coin is tossed 4 times and outcomes are recorded. How many possible outcomes are there?
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Number of outcomes when the coin is tossed for the first time = 2
Number of outcomes when the coin is tossed for the second time = 2
Thus, there would be 2 outcomes, each time the coin is tossed.
Total number of possible outcomes on tossing the coin five times = 2×2×2×2 = 16
There are three parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
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Number of ways of sending 1 parcel via registered post = 5
Number of ways of sending 3 parcels via registered post through 5 post offices = 5×5×5 = 125
A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?
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The first day of the year can be any one of the days of the week, i.e the first day can be selected in 7 ways.
But, the year could also be a leap year.
So, the mint should prepare 7 calendars for the non-leap year and 7 calendars for the leap year.
So, total number of calendars that should be made = 7 + 7 = 14
From Chennai to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Chennai to Delhi via Bombay, how many kinds of routes are there?
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Number of routes from Chennai to Bombay = 2
Number of routes from Bombay to Delhi = 3
Using fundamental principle of multiplication:
Number of routes from Chennai to Delhi via Bombay = 2 × 3 = 6
A person wants to buy one Blue pen, one Black pen and one pencil from a stationery shop. If there are 10 Blue pen varieties, 12 Black pen varieties and 5 pencil varieties, in how many ways can he select these articles?
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Number of blue pen varieties = 10
Number of black pen varieties = 12
Number of pencil varieties = 5
Ways to select a blue pen = 10
Ways to select a black pen = 12
Ways to select a pencil = 5
Ways to select a blue pen, a black pen and a pencil = 10 × 12 × 5 = 600
In a class there are 14 boys and 27 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?
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Answer :
No. of boys in the class = 14
No. of girls in the class = 27
Ways to select a boy = 14
Similarly, ways to select a girl = 27
∴ Number of ways to select 1 boy and 1 girl = 14 × 27 = 378
1 |
^{8}P_{2} |
A |
30 |
2 |
^{10}P_{3} |
B |
6 |
3 |
^{6}P_{1} |
C |
720 |
4 |
P(6,2) |
D |
56 |
Answer :
1-D, 2-C, 3-B, 4-A
1 |
^{10}P_{2} |
A |
120 |
2 |
^{10}P_{1} |
B |
9 |
3 |
^{5}P_{5} |
C |
90 |
4 |
P(9,1) |
D |
10 |
Answer :
1-C, 2-D, 3-A, 4-B
1 |
^{9}P_{1} |
A |
7 |
2 |
^{3}P_{1} |
B |
9 |
3 |
^{6}P_{1} |
C |
3 |
4 |
^{7}P_{1} |
D |
6 |
Answer :
1-B, 2-C, 3-D, 4-A
Find r
1 |
^{10}C_{0} = ^{10}C_{r} |
A |
14 |
2 |
^{18}C_{4} = ^{18}C_{r} |
B |
20 |
3 |
^{24}C_{4} = ^{24}C_{r} |
C |
10 |
Answer :
1-C, 2-A, 3-B
Find n
1 |
^{n}C_{4} = ^{n}C_{6} |
A |
50 |
2 |
^{n}C_{4} = ^{n}C_{3} |
B |
64 |
3 |
^{n}C_{4} = ^{n}C_{60} |
C |
10 |
4 |
^{n}C_{4} = ^{n}C_{46} |
D |
7 |
Answer :
1-C, 2-D, 3-B, 4-A
The GSEB Books for class 10 are designed as per the syllabus followed Gujarat Secondary and Higher Secondary Education Board provides key detailed, and a through solutions to all the questions relating to the GSEB textbooks.
The purpose is to provide help to the students with their homework, preparing for the examinations and personal learning. These books are very helpful for the preparation of examination.
For more details about the GSEB books for Class 10, you can access the PDF which is as in the above given links for the same.