Mathematics for Competitive Exam Success

Mathematics

3D Geometry Applications of Derivatives Binomial Theorem Circles Complex Numbers Conic Sections Coordinate Geometry Differential Equations Differentiation Integration Limits & Continuity Matrices & Determinants Permutations & Combinations Probability Quadratic Equations Sequences & Series Sets & Relations Straight Lines Trigonometry Vector Algebra

Q. How many different 4-digit PINs can be formed using the digits 0-9 without repetition?

A. 5040
B. 9000
C. 10000
D. 1000

Solution

The number of 4-digit PINs is P(10, 4) = 5040.

Correct Answer: A — 5040

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Q. How many different ways can 2 out of 5 different fruits be chosen?

A. 10
B. 15
C. 20
D. 25

Solution

The number of ways to choose 2 from 5 is C(5, 2) = 10.

Correct Answer: A — 10

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Q. How many different ways can 3 boys and 2 girls be seated in a row?

A. 30
B. 60
C. 120
D. 180

Solution

The number of ways to arrange 5 people is 5! = 120.

Correct Answer: C — 120

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Q. How many different ways can 4 different colored balls be arranged in a row? (2020)

A. 12
B. 24
C. 36
D. 48

Solution

The number of arrangements of 4 different colored balls is 4! = 24.

Correct Answer: B — 24

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Q. How many different ways can 4 prizes be distributed among 10 students? (2020)

A. 5040
B. 10000
C. 2100
D. 120

Solution

The number of ways to distribute 4 prizes among 10 students is 10P4 = 10! / (10-4)! = 5040.

Correct Answer: A — 5040

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Q. How many different ways can 6 people be seated in a row? (2020)

A. 720
B. 600
C. 360
D. 480

Solution

The number of arrangements of 6 people is 6! = 720.

Correct Answer: A — 720

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Q. How many different ways can the letters of the word 'BOOK' be arranged? (2014)

A. 12
B. 24
C. 36
D. 48

Solution

The number of arrangements of the letters in 'BOOK' is 4! / 2! = 12.

Correct Answer: B — 24

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Q. How many different ways can the letters of the word 'MATH' be arranged?

A. 12
B. 24
C. 36
D. 48

Solution

The number of arrangements of the letters in 'MATH' is 4! = 24.

Correct Answer: B — 24

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Q. How many ways can 2 boys and 2 girls be selected from 5 boys and 5 girls? (2020)

A. 100
B. 150
C. 200
D. 300

Solution

The number of ways to select 2 boys from 5 is C(5, 2) and 2 girls from 5 is C(5, 2). Total = C(5, 2) * C(5, 2) = 10 * 10 = 100.

Correct Answer: B — 150

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Q. How many ways can 2 boys and 3 girls be selected from 5 boys and 6 girls?

A. 100
B. 150
C. 200
D. 250

Solution

The number of ways is 5C2 * 6C3 = 10 * 20 = 200.

Correct Answer: B — 150

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Q. How many ways can 2 boys and 3 girls be selected from 5 boys and 7 girls? (2020)

A. 210
B. 300
C. 350
D. 400

Solution

The number of ways is 5C2 * 7C3 = 10 * 35 = 350.

Correct Answer: C — 350

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Q. How many ways can 2 boys and 3 girls be selected from 8 boys and 6 girls?

A. 336
B. 280
C. 420
D. 180

Solution

The number of ways is 8C2 * 6C3 = 28 * 20 = 560.

Correct Answer: A — 336

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Q. How many ways can 2 boys and 3 girls be selected from a group of 5 boys and 7 girls? (2018)

A. 210
B. 300
C. 150
D. 100

Solution

The number of ways to select 2 boys from 5 is 5C2 and 3 girls from 7 is 7C3. Total = 5C2 * 7C3 = 10 * 35 = 350.

Correct Answer: A — 210

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Q. How many ways can 2 out of 5 students be selected?

A. 10
B. 15
C. 20
D. 5

Solution

The number of ways to choose 2 from 5 is C(5,2) = 10.

Correct Answer: A — 10

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Q. How many ways can 2 students be selected from a group of 5? (2019)

A. 10
B. 5
C. 15
D. 20

Solution

The number of ways to select 2 students from 5 is given by 5C2 = 10.

Correct Answer: A — 10

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Q. How many ways can 2 students be selected from a group of 8? (2015)

A. 28
B. 56
C. 36
D. 48

Solution

The number of ways to select 2 from 8 is C(8, 2) = 28.

Correct Answer: A — 28

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Q. How many ways can 3 books be selected from a shelf of 10 books? (2022)

A. 120
B. 210
C. 100
D. 30

Solution

The number of ways to select 3 books from 10 is given by 10C3 = 120.

Correct Answer: B — 210

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Q. How many ways can 3 boys and 2 girls be seated in a row?

A. 30
B. 60
C. 120
D. 180

Solution

The number of ways to arrange 5 people is 5! = 120.

Correct Answer: C — 120

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Q. How many ways can 3 different books be chosen from a set of 7?

A. 35
B. 42
C. 49
D. 56

Solution

The number of ways to choose 3 from 7 is C(7, 3) = 35.

Correct Answer: A — 35

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Q. How many ways can 3 different colored balls be arranged in a row? (2022)

A. 6
B. 3
C. 9
D. 12

Solution

The number of arrangements of 3 distinct balls is 3! = 6.

Correct Answer: A — 6

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Q. How many ways can 3 different gifts be given to 5 children if each child can receive more than one gift? (2022)

A. 125
B. 243
C. 60
D. 30

Solution

Each gift can go to any of the 5 children, so the total ways = 5^3 = 125.

Correct Answer: B — 243

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Q. How many ways can 3 different trophies be awarded to 5 students? (2022)

A. 60
B. 100
C. 120
D. 30

Solution

The number of ways to award 3 trophies to 5 students is given by P(5,3) = 5! / (5-3)! = 60.

Correct Answer: C — 120

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Q. How many ways can 3 out of 8 different colored balls be chosen? (2022)

A. 56
B. 24
C. 8
D. 12

Solution

The number of ways to choose 3 balls from 8 is given by 8C3 = 56.

Correct Answer: A — 56

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Q. How many ways can 3 prizes be awarded to 10 students if no student can win more than one prize?

A. 720
B. 1000
C. 1200
D. 100

Solution

The number of ways to award 3 prizes is P(10, 3) = 720.

Correct Answer: A — 720

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Q. How many ways can 3 red balls and 2 blue balls be arranged in a line? (2016)

A. 10
B. 30
C. 60
D. 20

Solution

The number of arrangements is 5! / (3! * 2!) = 10.

Correct Answer: D — 20

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Q. How many ways can 3 students be selected from a group of 10?

A. 120
B. 90
C. 100
D. 80

Solution

The number of ways to select 3 students from 10 is given by 10C3 = 120.

Correct Answer: A — 120

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Q. How many ways can 4 different flags be arranged on a pole? (2021)

A. 24
B. 12
C. 16
D. 20

Solution

The number of arrangements of 4 distinct flags is 4! = 24.

Correct Answer: A — 24

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Q. How many ways can 4 different fruits be selected from 6 available fruits? (2021)

A. 15
B. 30
C. 20
D. 25

Solution

The number of ways to choose 4 fruits from 6 is C(6, 4) = 15.

Correct Answer: C — 20

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Q. How many ways can 4 different fruits be selected from 8 available fruits? (2021)

A. 70
B. 80
C. 90
D. 100

Solution

The number of ways to choose 4 fruits from 8 is given by 8C4 = 70.

Correct Answer: A — 70

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Q. How many ways can 4 different fruits be selected from 8?

A. 70
B. 56
C. 80
D. 90

Solution

The number of ways to select 4 fruits from 8 is given by 8C4 = 70.

Correct Answer: B — 56

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Mathematics

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