Class 11 Applied Maths Chapter 8 (Ex – 8.3)

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Class 11 Applied Maths Chapter 8 Solutions

Logical Reasoning

EXERCISE- 8.3

Find odd man out in the following questions (1 to 19) :

Q.1 AC, BD, CE, DG, EG, FH

Ans. Let’s break down the sequence:

• AC: A to C (A is the 1st letter, C is the 3rd letter, so +2 positions)
• BD: B to D (B is the 2nd letter, D is the 4th letter, so +2 positions)
• CE: C to E (C is the 3rd letter, E is the 5th letter, so +2 positions)
• DG: D to G (D is the 4th letter, G is the 7th letter, so +3 positions)
• EG: E to G (E is the 5th letter, G is the 7th letter, so +2 positions)
• FH: F to H (F is the 6th letter, H is the 8th letter, so +2 positions)

The sequence generally follows a pattern of moving +2 positions, except for DG where the shift is +3 positions, making “DG” the odd one out.

Q.2 BCD, CDE, DEF, EFG

Ans. To find the “odd man out” in the sequence of letter groups BCDBCDBCD, CDECDECDE, DEFDEFDEF, and EFGEFGEFG, let’s analyze each group:

1. BCD: Consecutive letters in the alphabet: B → C → D
2. CDE: Consecutive letters in the alphabet: C → D → E
3. DEF: Consecutive letters in the alphabet: D → E → F
4. EFG: Consecutive letters in the alphabet: E → F → G

All groups consist of three consecutive letters in the English alphabet, so, at first glance, all groups seem similar. However, if we consider the alphabetical position of each letter:

• BCD: B (2nd), C (3rd), D (4th)
• CDE: C (3rd), D (4th), E (5th)
• DEF: D (4th), E (5th), F (6th)
• EFG: E (5th), F (6th), G (7th)

Each group follows a sequence where each letter is one step ahead of the previous letter in the alphabet. But if we look closely, BCD starts with B, while the others start with C, D, and E respectively.

So, BCD is the “odd man out” because it is the only group that starts with a letter that is not in sequence with the starting letters of the other groups (BCD starts with B, while the others start with C, D, and E).

Q.3 BDF, GIK, LMN, OQS, TVX

Ans. To find the “odd man out” in the sequence BDF, GIK, LMN, OQS, TVX, let’s analyze the pattern in each set of letters:

1. BDF: The letters B, D, F are all separated by one letter in the alphabet (B → D, D → F).
2. GIK: The letters G, I, K are also separated by one letter in the alphabet (G → I, I → K).
3. LMN: The letters L, M, N are consecutive in the alphabet (no separation between them).
4. OQS: The letters O, Q, S are separated by one letter in the alphabet (O → Q, Q → S).
5. TVX: The letters T, V, X are separated by one letter in the alphabet (T → V, V → X).

Conclusion:

The sequence LMN is the “odd man out” because the letters in this sequence are consecutive without any separation, unlike the other sequences where the letters have a gap of one letter between them.

Q.4 Venus, Jupiter, Mercury, Pluto, Moon, Neptune

Ans. To find the “odd man out” in the sequence Venus, Jupiter, Mercury, Pluto, Moon, Neptune, let’s analyze each item:

1. Venus: A planet in the Solar System.
2. Jupiter: A planet in the Solar System.
3. Mercury: A planet in the Solar System.
4. Pluto: A dwarf planet in the Solar System.
5. Moon: A natural satellite of Earth.
6. Neptune: A planet in the Solar System.

Conclusion:

The “odd man out” is Moon because it is not a planet; it is a natural satellite of Earth, whereas all the other options are planets or dwarf planets in the Solar System.

Q.5 Dog and Bitch, Cock and Hen, Cow and Buffalo, Lion and Lioness

Ans. To find the “odd man out” in the sequence Dog and Bitch, Cock and Hen, Cow and Buffalo, Lion and Lioness, let’s analyze each pair:

1. Dog and Bitch: Male and female counterparts of the same species (dogs).
2. Cock and Hen: Male and female counterparts of the same species (chickens).
3. Cow and Buffalo: Different species (cow is a domestic cattle, while buffalo is a different animal).
4. Lion and Lioness: Male and female counterparts of the same species (lions).

Conclusion:

The “odd man out” is Cow and Buffalo because they are not male and female counterparts of the same species, unlike the other pairs.

Q.6 Peaceful – Quiet, Small – Tiny, Borrow – Land, Want – Desire

Ans. To find the “odd man out” in the sequence Peaceful – Quiet, Small – Tiny, Borrow – Land, Want – Desire, let’s analyze each pair:

1. Peaceful – Quiet: These words are synonyms.
2. Small – Tiny: These words are synonyms.
3. Borrow – Land: These words are not synonyms; they have opposite meanings (Borrow means to take temporarily, while Land (in the context of lending/borrowing) could imply ownership or receiving).
4. Want – Desire: These words are synonyms.

Conclusion:

The “odd man out” is Borrow – Land because they are not synonyms, unlike the other pairs which consist of words with similar meanings.

Q.7 Violet, Indigo, Black, Green, Yellow, Orange, Red

Ans. To find the “odd man out” in the sequence Violet, Indigo, Black, Green, Yellow, Orange, Red\text{Violet, Indigo, Black, Green, Yellow, Orange, Red}Violet, Indigo, Black, Green, Yellow, Orange, Red, let’s analyze the colors:

1. Violet: A color in the visible spectrum (part of the rainbow).
2. Indigo: A color in the visible spectrum (part of the rainbow).
3. Black: Not a color in the visible spectrum; it’s technically the absence of light/color.
4. Green: A color in the visible spectrum (part of the rainbow).
5. Yellow: A color in the visible spectrum (part of the rainbow).
6. Orange: A color in the visible spectrum (part of the rainbow).
7. Red: A color in the visible spectrum (part of the rainbow).

Conclusion:

The “odd man out” is Black because it is not a color in the visible spectrum or part of the rainbow, whereas all the other colors are.

Q.8 City, Town, District, Village, Towel

Ans. The odd man out in the list is “Towel”.

While “City,” “Town,” “District,” and “Village” are all related to geographic or administrative divisions, “Towel” is an object and unrelated to the others.

Q.9 Reader, Writer, Printer, Publisher

Ans. The odd man out in the list is “Printer.”

“Reader,” “Writer,” and “Publisher” are all roles related to the creation and dissemination of content, while “Printer” is a machine or device used to produce physical copies of written or printed material.

Q.10 Attractive, Pretty, Beautiful, Marvelous, Repulsive

Ans. The odd man out in the list is “Repulsive.”

“Attractive,” “Pretty,” “Beautiful,” and “Marvelous” all have positive connotations, describing something that is pleasing or appealing. In contrast, “Repulsive” has a negative connotation, describing something that is unpleasant or off-putting.

Q.11 26, 38, 50, 62, 76, 86, 98

Ans. To find the “odd man out” in the sequence of numbers 26, 38, 50, 62, 76, 86, and 98, let’s analyze the pattern:

Looking at each number, observe the differences between consecutive numbers: 38 − 26 = 12,

50 − 38 = 12,

62 − 50 = 12,

76 − 62 = 14,

86 − 76 = 10,

98 − 86 = 12

From the above differences, we can see:

• The difference between 26 and 38 is 12.
• The difference between 38 and 50 is 12.
• The difference between 50 and 62 is 12.
• The difference between 62 and 76 is 14.
• The difference between 76 and 86 is 10.
• The difference between 86 and 98 is 12.

Most of the differences are 12, except for 76 (where the difference changes to 14 when moving from 62 to 76).

Thus, 76 is the “odd man out” in this sequence because it breaks the pattern of having a consistent difference of 12.

Q.12 67, 65, 62, 60, 57, 55, 53, 50, 47

Ans. The odd man out in the list is “53.”

All the other numbers are decreasing by 2 or 3, but “53” is a prime number and does not follow the consistent pattern of the other numbers.

Q.13 15, 25, 45, 55, 65, 72, 75, 85

Ans. The odd man out in the list is “72.”

All the other numbers are multiples of 5, but “72” is not.

Q.14 2, 5, 10, 17, 26, 37, 50, 64, 82, 101

Ans. The odd man out in the list is “64.”

All the other numbers in the sequence follow the pattern of n^2 + 1:

• 2 = 1^2 + 1
• 5 = 2^2 + 1
• 10 = 3^2 + 1
• 17 = 4^2 + 1
• 26 = 5^2 + 1
• 37 = 6^2 + 1
• 50 = 7^2 + 1
• 64 does not fit this pattern (it is 8^2, not n^2 + 1)
• 82 = 9^2 + 1
• 101 = 101^2 + 1

Q.15 2, 3, 5, 7, 11, 13, 15, 17, 19, 23 17.

Ans. The odd man out in the list is “15.”

All the other numbers are prime numbers, but “15” is not. (15 can be divided by 3 and 5, in addition to 1 and itself.)

Q.16 725, 871, 642, 954, 863, 734, 541

Ans.

Q.17 16, 36, 64, 81, 100, 144, 196

Ans. The odd man out in the list is “81.”

All the other numbers are perfect squares of even numbers:

• 16 = 4^2
• 36 = 6^2
• 64 = 8^2
• 100 = 10^2
• 144 = 12^2
• 196 = 14^2

However, “81” is the square of an odd number:

• 81 = 9^2

This makes “81” the odd one out.

Q.18 231, 352, 473, 524, 682, 781, 891 20.

Ans. The odd man out in the list is “524.”

All the other numbers are formed by reversing the digits of numbers that follow a consistent pattern:

• 231 (reverse of 132)
• 352 (reverse of 253)
• 473 (reverse of 374)
• 682 (reverse of 286)
• 781 (reverse of 187)
• 891 (reverse of 198)

However, “524” is not the reverse of any such number that follows this pattern, making it the odd one out.

Q.19. 7, 26, 63, 124, 217, 342, 511

Ans. All the other numbers are one less than a perfect cube:

• 8 − 1 = 7
• 27 − 1 = 26
• 64 − 1 = 63
• 125 − 1 = 124
• 216 − 1 = 215 (but it was incorrectly listed as “217”)
• 343 − 1 = 342
• 512 − 1 = 511

However, “26” is not a perfect cube minus 1. The correct sequence would include “215” instead of “217.” But considering the provided sequence, “217” is the odd one out.

Q.20 6, 24, 60, 120, 210, 336, 505

Ans. The odd man out in the list is “505.”

All the other numbers are triangular numbers (which can be formed by the sum of the first nnn natural numbers), but “505” is not.

To break it down:

• 6 = 1 + 2 + 3
• 24 = 1 + 2 + 3 + 4 + 5 + 6 + 7
• 60 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
• 120 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15
• 210 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19
• 336 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27
• “505” doesn’t fit this pattern, making it the odd one out.

FAQ’s related to Class 11 Applied Maths Chapter 8 on Logical Reasoning:

Q.1 What is logical reasoning?

Ans. Logical reasoning refers to the process of using a structured and methodical approach to arrive at a conclusion based on given premises or facts. It involves critical thinking and the ability to see the logical connections between ideas.

Q.2 What are the common mistakes to avoid in logical reasoning?

Ans. Common mistakes include:

• Assuming correlation implies causation.
• Overgeneralizing from insufficient evidence.
• Ignoring counterexamples.
• Misinterpreting logical connectives.

Q.3 What is a Venn diagram?

Ans. A Venn diagram is a graphical way to represent sets and their relationships using circles. It is used in logical reasoning to visually illustrate the logical relationships between different sets.

Q.4 How are Venn diagrams used in logical reasoning?

Ans. Venn diagrams are used to:

• Show logical relationships between different sets.
• Solve problems involving set operations such as union, intersection, and difference.
• Visualize logical propositions and their truth values.

Q.5 Can you give an example of a logical reasoning problem and solution?

Ans. If all dogs are mammals and some pets are dogs, can we conclude that some pets are mammals?

Solution: Yes, because if all dogs are mammals, and some pets are dogs, it logically follows that those pets which are dogs must also be mammals. Therefore, some pets are mammals.

These are a few Frequently Asked Questions relating to Class 11 Applied Maths Chapter 8

In Class 11 Applied Maths chapter 8, you will explore fascinating topics that form the backbone of practical problem-solving techniques. Through clear explanations, illustrative examples, and step-by-step solutions, you’ll grasp complex concepts effortlessly. Whether you’re preparing for exams or simply eager to deepen your mathematical understanding, Class 11 Applied Maths Chapter 8 promises an enriching learning experience that will set you on the path to success. Class 11 Applied Maths Chapter 8, we delve deep into advanced mathematical concepts that are crucial for understanding.