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Classification: Definition, Practice Questions, Examples, Types

Classification: Definition, Practice Questions, Examples, Types

Edited By Deependra Verma | Updated on Jul 23, 2024 07:40 AM IST

Classification is the process of grouping various terms based on their common properties or characteristics such as size, colour, shape etc. and determining the odd term. Questions from this topic have been asked in various competitive exams such as SSC, Railways, Insurance, Defence, Entrance exams etc. This topic is asked in the exams to check the evaluation ability of a candidate.

The Approach to Classification

To find out the odd one, identify the terms except one, follow a specific pattern or rule or terms that have some common characteristics between them or one which is odd doesn’t have common characteristics.

Types of Classification

There are four types of Classification-

1) Word-based odd one
2) Number based odd one
3) Letter based odd one
4) Mixed odd one

Let’s understand all of the above types of classification in detail

1) Word-based Odd one

In this type of question, four meaningful words or word pairs are given. It is a process to determine the odd word or odd word pair from the various given words or word pairs. The question based on word-based classification can be asked from general knowledge and English vocabulary.
Example:
A) Rage B) Soothe C) Calm D) Forbear
Solution:
To solve the classification question first recall the meaning of each word given in the question and then determine the odd one.
Here, the words soothe, calm and forbear are antonyms of anger whereas rage is a synonym for anger. Therefore, rage is the odd one among the given words.
Hence, the first option is correct.
Example:
A) Bitter-Sweet B) Afraid-Brave C) Vertical-Horizontal D) Large-Huge
Solution:
In the above-given word pairs, all pairs have opposite meanings except the fourth pair. It consists of same-meaning words. Therefore, the fourth option is the odd one.
Hence, the fourth option is correct.

2) Number-based odd one

It is a process to determine the odd number or odd pair of numbers from the various numbers according to common features like they are even numbers, odd numbers, prime numbers, multiples of 5 or multiples of any other number and divisible by a certain number.

Example:
A) 13 B) 99 C) 108 D) 236
Solution:
In the above-given numbers except 13, all other numbers are divisible by certain numbers. Only, 13 is a prime number. Therefore, 13 is an odd one.
Hence, the first option is correct.
Example:
A) 121-144 B) 1444-1521 C) 1024-1156 D) 441-484
Solution:
In the above-given pairs, all pairs are squares of natural numbers.
First Option: 121-144; (11 x 11) (12 x 12)
Second Option: 1444-1521; (38 x 38) (39 x 39)
Third Option: 1024-1156; (32 x 32) (34 x 34)
Fourth Option: 441-484; (21 x 21 ) (22 x 22)
All number pairs are squares of consecutive numbers except option third as in the third option a square of 34 is given instead of a square of 33.

Hence, the third option is correct.

3) Letter-based odd one

In this type of question, four random letters or letter clusters following specific rules are given. To solve letter-based questions one should have learned the positional values of the letters from left to right end and from right to left end. It is a process to find the odd letter or group of odd letters by determining the positional values of the letters or according to the consonants and vowels.

Example:
A) HIJK B) QRST C) MNQP D) EFGH
Solution:
In the above-given group of letters, all groups consist of consecutive letters except option third. Therefore, MNQP is an odd one.
Hence, the third option is correct.
Example:
A) HS B) KP C) LO D) GH
Solution:
In the above-given pairs, letters are opposite to each other except, in the fourth option as it consists of consecutive letters. Therefore, the fourth pair is the odd one.
Hence, the fourth option is correct.

4) Mixed odd one

In this type of question, pairs consist of letters and numbers following a pattern or some specific rules as discussed in the letter-based and number-based classification. To solve the mixed odd one classification one should apply the logic on letters as well as numbers to find the odd term.

Example:
A) AC4 B) GI16 C) KM23 D) EG12
Solution:
The above-given pairs consist of letters as well as numbers. The numbers are the sum of the positional values of the alphabet.
First Option: AC4; (1 + 3 = 4)
Second Option: GI; (7 + 9 = 16)
Third Option: KM23; (11 + 13 = 24)
Fourth Option: EG12; (5 + 7 = 12)
All options except option third numbers are the sum of the positional values but in the third pair the number is 23 instead of 24. Therefore, the third option is the odd one.
Hence, the third option is correct.

Things to Remember for Solving Classification Questions

1) You must be well-versed in the English vocabulary and general terms of daily science.
2) You must know types of numbers such as whole numbers, natural numbers, prime numbers, even numbers, odd numbers etc.

3) Practice is key to success.
4) When you have done several questions with the techniques mentioned above, you will be able to attempt any classification question in less than a minute.

Practice and Resources

Following are the recommended sources for the practice of the questions of classification -
a) A Modern Approach to Verbal & Non-Verbal Reasoning by R.S. Aggarwal

b) Analytical Reasoning by M.K. Pandey

c) Logical and Analytical Reasoning by A.K. Gupta

d) Test of Reasoning by Edgar Thorpe

Question Weightage of Classification in Competitive Exams

The number of questions based on classification varies from exam to exam -
1) Classification questions asked in SSC exams i.e. SSC MTS, SSC CGL, SSC CHSL, SSC CPO, Steno - 5 to 6 questions.
2) Classification questions asked in the Railways exam i.e. Group D, NTPC, JE, ALP etc - 3 to 4 questions.

3) Classification questions asked in CUET, NPAT and other college entrance exams - 2 to 3 questions.

Sometimes questions based on classification can be seen in CSAT and IB exams as well.

Practice Questions For Word-Based Classification

1) Directions: Three of the following words are alike in a certain way and one is different. Pick the word that is different from the rest.

1) Sarangi
2) Telephone

3) Saxophone

4) Xylophone

Hint:

Identify the term that is not a musical instrument.

Solution:

Let's check each option –

First option: Sarangi; It is a musical instrument.

Second option: Telephone; It is not a musical instrument.

Third option: Saxophone; It is a musical instrument.

Fourth option: Xylophone; It is a musical instrument.

So, only the second option is different from the other three options as Television is not a musical instrument. Hence, the second option is correct.

2. Directions: In the following question, find the odd letter cluster from the given alternatives.

1) TOP

2) COP

3) MOP

4) JOP

Hint:
Check the meaning of the given words.

Solution:

Let's check the options –

First option: TOP; TOP means surface.

Second option: COP; COP means Police officer.

Third option: MOP; MOP is used for surface cleaning.

Fourth option: JOP; There is no meaning of JOP.

So, the fourth option is different from the other three options because there is no meaning of JOP. Hence, the fourth option is correct.
3. Directions: Find the odd word pair from the given responses.

1) Bangkok

2) Yangon (Rangoon)

3) Jeddah

4) Kabul

Hint:

Check the relationship between the country and its capital.

Solution:

Let's check the options

First option: Bangkok; Bangkok is the capital of Thailand.

Second option: Yangon (Rangoon); Yangoon (Rangoon) is the capital of Myanmar.

Third option: Jeddah; Jeddah is not the capital of any country.

Fourth option: Kabul; Kabul is the capital of Afghanistan.

So, only the third option is different from the other three options as Jeddah is not the capital of any country. Hence, the third option is correct.

4. Directions: Find the odd word pair from the given responses.
1) Happiness

2) Honesty

3) Deceive

4) Truth

Hint:

Determine the meaning of the words and find the odd one.

Solution:

Let's check the options –

First option: Happiness ⇒ The state of being happy.
Second option: Honesty ⇒ Righteousness; being truthful.

Third option: Deceive ⇒ Deliberately cause (someone) to believe something untrue.

Fourth option: Truth ⇒ The quality or state of being true.

So, deceive is the antonym of the other three options. Hence, the third option is correct.

5. Directions: Find the odd word from the given responses.

1) Ink

2) Paper

3) Office

4) Pen

Hint:

Think of the stationary objects.

Solution:

Let's check the options –

First option: Ink; Ink is a stationery item.

Second option: Paper; Paper is a stationery item.

Third option: Office; Office is not a stationery item.

Fourth option: Pen; Pen is a stationery item.

So, from the given words, except office, all others are stationery items. Hence, the third option is correct.

Practice Questions For Word Pairs Based Classification

1. Directions: In the following question, select the odd word pair from the given alternatives.

1) Sugarcane – Jaggery

2) Sack – Jute

3) Road – Asphalt

4) Wall – Brick

Hint:

Determine the things and materials used for them.

Solution:

Let's check each option –

First option: Sugarcane – Jaggery; Jaggery is made from sugarcane but sugarcane is not made from jaggery.

Second option: Sack – Jute; Jute is used to make the sack.

Third option: Road – Asphalt; Asphalt is used to construct roads.

Fourth option: Wall – Brick; Brick is used to create a wall.

So, the first option is different from the other options. Hence, the first option is correct.

2. Directions: In the following question, select the odd word pair from the given alternatives.

1) Question – Answer

2) Pencil – Rub

3) Cup – Saucer

4) Chair – Table

Hint:

Think about two words that are typically related to each other.

Solution:

Let's check each option –

First option: Question – Answer; A question is generally followed by an answer and directly related to each other in a supportive way.

Second option: Pencil – Rub; Rub is used to remove pencil marks, but not related to pencil in a direct supportive way.

Third option: Cup – Saucer; A cup is generally placed on a saucer and directly related to each other in a supportive way..

Fourth option: Chair – Table; A chair is generally paired with a table and directly related to each other in a supportive way..

So, only the second option is different from the other three options. Hence, the second option is correct.

3. Directions: Three of the four groups of words are alike in some manner. Select the odd group of words.

1) (Car, Truck, Road)

2) (Chair, Table, Stool)

3) (Choreographer, Editor, Carpenter)

4) (Shirt, Trouser, Saree)

Hint:

Determine the category of the given terms.

Solution:

Let's check each option –

First option: (Car, Truck, Road); Car and Truck are used for transportation but the road is not a type of transport.

Second option: (Chair, Table, Stool); Chair, Table, and Stool are types of the furniture.

Third option: (Choreographer, Editor, Carpenter); Choreographer, Editor, and Carpenter are types of profession.

Fourth option: (Shirt, Trouser, Saree); Shirt, Trouser, and Saree are types of clothes.

So, the first option is different from the other options. Hence, the first option is correct.

4. Directions: In the following question, select the odd word pair from the given alternatives.

1) China – Yuan

2) Thailand – Baht

3) Lira – Turkey

4) Japan – Yen

Hint:

Think about the order of the country and its currency.

Solution:

Let's check each option –

First option: China – Yuan; The currency of China is the Yuan.

Second option: Thailand – Baht; The currency of Thailand is the Baht.

Third option: Lira – Turkey; The currency of Turkey is the Lira, but here order is different.

Fourth option: Japan – Yen; The currency of Japan is the Yen.

So, the third option is different from the others as in this option first term is currency and the second term is country. Hence, the third option is correct.
5. Directions: Find the odd word pair from the given responses.

1) Long – Short

2) Black – White

3) Head – Cap

4) Friend – Foe

Hint:

The given word pairs are the antonyms of each other.

Solution:

Let's check the given options –

First option: Long – Short; Long and short are antonyms of each other.

Second option: Black – White; Black and White are the antonyms of each other.

Third option: Head – Cap; Cap is worn on the head. They are not antonyms of each other.

Fourth option: Friend – Foe; Friend and Foe are the antonyms of each other.

So, the words in the third option are not the antonyms of each other. Hence, the third option is correct.

Practice Questions For Number-Based Classification

1. Directions: In the following question, find the odd number from the given alternatives.

1) 5125

2) 8564

3) 7343

4) 6216

Hint:

Find the cube of the first digit to establish a relation with other digits.

Solution:

Let's check the options –

First option: 5125

Here, the first digit is 5. (5)3 = 125→So, the number formed is 5125.

Second option: 8564

Here, the first digit is 8. (8)3 = 512→So, the number formed should be 8512.

Third option: 7343

Here, the first digit is 7. (7)3 = 343→So, the number formed is 7343.

Fourth option: 6216

Here, the first digit is 6. (6)3 = 216→So, the number formed is 6216.

In the second option, the number should be 8512 instead of 8564. Hence, the second option is correct.

2. Directions: In the following question, find the odd number from the given alternatives.

1) 529

2) 549

3) 731

4) 525
Hint:

Determine the perfect square in the given options.

Solution:

Let's check the options –

First option: 529; 529 = 232; 529 is a perfect square.

Second option: 549; 549 is not a perfect square.

Third option: 731; 731 is not a perfect square.

Fourth option: 525; 525 is not a perfect square.

So, the first option 529 is different from the other options as it is a perfect square while others are not. Hence, the first option is correct.

3. Directions: In each of the following questions, select the one that is different from the other three alternatives.

1) 357

2) 581

3) 698

4) 784

Hint:

Check whether the given numbers are multiples of 7 or not.

Solution:

Let's check the options –

First option: 357; 357 ÷ 7 = 51 (multiple of 7)

Second option: 581; 581 ÷ 7 = 83 (multiple of 7)

Third option: 698; 698 ÷ 7 = 99.7 (not a multiple of 7)

Fourth option: 784; 784 ÷ 7 = 112 (multiple of 7)

So, only the third option is different from the other three options. Hence, the third option is correct.
4. Directions: In the following question, find the odd number from the given alternatives.

1) 361

2) 441

3) 784

4) 876

Hint:

Check whether the numbers in the given options are perfect squares.

Solution:

Let's check the options –

First option: 361; 361 = (19)2

Second option: 441; 441 = (21)2

Third option: 784; 784 = (28)2

Fourth option: 876 is not a square of any number.

The fourth option does not follow the pattern. Hence, the fourth option is correct.

5. Directions: In the following question, find the odd number from the given alternatives.

1) 253

2) 473

3) 143

4) 633

Hint:

Check the divisibility of the given numbers by 11.

Solution:

Let's check the options –

First option: 253; 253 ÷ 11 = 23

Second option: 473; 473 ÷ 11 = 43

Third option: 143; 143 ÷ 11 = 13

Fourth option: 633; 633 is not divisible by 11.

The fourth option does not follow the pattern of the other three. Hence, the fourth option is correct.

Practice Questions For Number Pair-Based Classification

1. Directions: Select the odd group of numbers. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g.13 – operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

1) (15 – 220 – 215)

2) (10 – 100 – 95)

3) (20 – 400 – 395)

4) (25 – 625 – 620)

Hint:

For each set, the second number is the square of the first number, and subtract 5 from the second number to get the third number.

Solution:

Let's check the options –

First option: (15 – 220 – 215)→(15)2 = 225 ≠ 220

Second option: (10 – 100 – 95)→(10)2 = 100; 100 – 5 = 95

Third option: (20 – 400 – 39)→(20)2 = 400; 400 – 5 = 395

Fourth option: (25 – 625 – 620)→(25)2 = 625; 625 – 5 = 620

So, only the first option does not follow the same pattern as followed by the given set of numbers. Hence, the first option is correct.

2. Directions: In the following question, select the one that is different from the other three alternatives.

1) (37 – 74)
2) (26 – 52)

3) (47 – 84)

4) (44 – 88)

Hint:

For each pair, multiply the first number by 2 to get the second number.

Solution:

Let's check the options –

First option: (37 – 74)→37 × 2 = 74

Second option: (26 – 52)→26 × 2 = 52

Third option: (47 – 84)→47 × 2 = 94 ≠ 84

Fourth option: (44 – 88)→44 × 2 = 88

So, only in the third option, on multiplying the first number by 2, the resultant is 94 instead of 84. Hence, the third option is correct.

3. Directions: In each of the following questions, select the one that is different from the other three alternatives.

1) 20, 16, 18

2) 18, 14, 16

3) 16, 12, 14

4) 14, 11, 13

Hint:

Subtract 4 and add 2 in the first and the second number to get the second and the third number respectively.

Solution:

Let's check each option –

First option: 20, 16, 18→20 – 4 = 16; 16 + 2 = 18

Second option: 18, 14, 16→18 – 4 = 14; 14 + 2 = 16

Third option: 16, 12,14→16 – 4 = 12; 12 + 2 = 14

Fourth option: 14, 11, 13→14 – 3 = 11; 11 + 2 = 13

So, the fourth option is different as the difference in the first and the second term is 3 instead of 4. Hence, the fourth option is correct.

4. Directions: In each of the following questions, select the one that is different from the other three alternatives.

1) 392 – 21

2) 483 –15
3) 602 – 42

4) 917 – 35

Hint:

Find the difference and determine the odd one.

Solution:

Let's check the options –

First option: 392 – 21 = 371

Second option: 483 –15 = 468

Third option: 602 – 42 = 560

Fourth option: 917 – 35 = 882

So, only the first option has an odd number as the final result. Hence, the first option is correct.

5. Directions: In each of the following questions, select the one that is different from the other three alternatives.

1) 120 – 560

2) 91 – 299

3) 78 – 169

4) 104 – 429

Hint:

Determine the multiple of 13, to get the odd one out.

Solution:

Let's check each option –

First option: 120 – 560→120 ÷ 13 = 9.23; 560 ÷ 13 = 43.07 (Both are not the multiples of 13.)

Second option: 91 – 299→91 ÷ 13 = 7; 299 ÷ 13 = 23 (Both are multiples of 13.)

Third option: 78 – 169→78 ÷ 13 = 6; 169 ÷ 13 = 13 (Both are multiples of 13.)

Fourth option: 104 – 429→104 ÷ 13 = 8; 429 ÷ 13 = 33 (Both are multiples of 13.)

So, the first option is different from the other three options as the numbers are not multiples of 13. Hence, the first option is correct.

Practice Questions For Letter Based Odd One

1. Directions: Three of the following letter clusters are alike in some manner and hence, form a group. Which letter cluster does not belong to that group?

1) WDLF

2) YBXR

3) PKSM

4) IRMT (correct)

Hint: Determine the odd term by using opposite letter pairs and subtraction in the place value of the last two letters.

Solution -

Let's check each option –

First option: WDLF; W and D are opposite pairs; L – 6 = F

Second option: YBXR; Y and B are opposite pairs; X – 6 = R

Third option: PKSM; P and K are opposite pairs; S – 6 = M

Fourth option: IRMT; I and R are opposite pairs; M + 7 = T

So, only the fourth option is different from the other three options as the difference between the position values of the letter is different. Hence, the fourth option is correct.

2. Directions: Three of the following letter clusters are alike in some manner and hence, form a group. Which letter cluster does NOT belong to that group?

1) EVS

2) IRP (correct)

3) VEB

4) GTQ

Hint: The first two letters are opposite letters and subtract 3 from the place value of the second letter, to get the third letter.

Solution:

Let's check each option –

First option: EVS; E and V are opposite pairs; V – 3 = S

Second option: IRP; I and R are opposite pairs; R – 2 = P

Third option: VEB; V and E are opposite pairs; E – 3 = B

Fourth option: GTQ; G and T are opposite pairs; T – 3 = Q

So, only the second option is different from the other three options as the difference between the position values of the letter is different. Hence, the second option is correct.

3. Directions: In the following question, select the odd letter/letters from the given alternatives.

1) RTW

2) FHK

3) SVY (correct)

4) KMP

Hint: Check the difference between the place values of the letters of the given options.

Solution:

Let's check the options –

First option: RTW; R + 2 = T; T + 3 = W

Second option: FHK; F + 2 = H; H + 3 = K

Third option: SVY; S + 3 = V; V + 3 = Y

Fourth option: KMP; K + 2 = M; M + 3 = P

So, only the third option is different from the other three options as the difference between the place values of the letter is different. Hence, the third option is correct.

4. Directions: In the following question, select the odd letter/letters from the given alternatives.

1) JJG

2) FFC

3) XXT (correct)

4) PPM

Hint: Add 0 to the place value of the first letter and subtract 3 from the place value of the second letter.

Solution:

Let's check the options –

First option: JJG; J + 0 = J; J – 3 = G

Second option: FFC; F + 0 = F; F – 3 = C

Third option: XXT; X + 0 = X; X – 4 = T

Fourth option: PPM; P + 0 = P; P – 3 = M

So, only the third option is different from the other three options as the difference between the place values of the letter is 4 instead of 3. Hence, the third option is correct.

5. Directions: In the following question, select the odd letter/letters from the given alternatives.

1) VWYB

2) LMOR

3) QSVY (correct)

4) ABDG

Hint: Check the difference between the place values of the letters.

Solution:

Let's check each option –

First option: VWYB; V + 1 = W; W + 2 = Y; Y + 3 = B

Second option: LMOR; L + 1 = M; M + 2 = O; O + 3 = R

Third option: QSVY; Q + 2 = S; S + 3 = V; V + 3 = Y

Fourth option: ABDG; A + 1 = B; B + 2 = D; D + 3 = G

The third option is different from the other three options because the difference in the position values of the letters is different. Hence, the third option is correct.

Classification Questions for BITSAT/ CUET

1. Directions: In the following question, select the one which is different from the other three alternatives.
1) CPBO
2) BODQ
3) ANHU
4) ESGT

Solution:
Determine the difference between the letters to find the odd one.
Let's check each option –
First option: CPBO; P – C = 13 and O – B = 13
Second option: BODQ; O – B = 13 and Q – D = 13
Third option: ANHU; N – A = 13 and U – H = 13
Fourth option: ESGT; S – E = 14 and T – G = 12
So, the fourth option is different from the other three options because the difference in the positional values of the letters is 14 and 12 instead of 13 and 13. Hence, the fourth option is correct.

2. Directions: In each of the following questions, select the one that is different from the other three alternatives.
1) 6 – 36
2) 8 – 64
3) 5 – 25
4) 4 – 16

Solution:
Think about the square of even and odd numbers.
Let's check each option –
First option: 6 – 36; 36 is the square of 6 and both are even numbers.
Second option: 8 – 64; 64 is the square of 8 and both are even numbers.
Third option: 5 – 25; 25 is the square of 5 and both are odd numbers.
Fourth option: 4 – 16; 16 is a square of 4 and both are even numbers.
So, the third option is different from the others as both of the numbers are odd. Hence, the third option is different.

Classification Questions for SSC/ RRB exams

1. Directions: In the following question, select the one which is different from the other three alternatives.
1) PQ
2) AU
3) CD
4) RS

Solution:
Determine the odd term by using the difference between the letters.
Let's check each option –
First option: PQ; P + 1 = Q
Second option: AU; A + 1 = B ≠ U
Third option: CD; C + 1 = D
Fourth option: RS; R + 1 = S
So, the second option is different from the other three options because the difference in the positional value of the letters is different. Hence, the second option is correct.

2. Directions: Find the odd word pair from the given responses.
1) Foreword
2) Text
3) Index
4) Preface

Solution:
Determine the meaning of the given terms.
Let's check each option –
First option: Foreword; It is a short introduction to a book.
Second option: Text; The main written part of a book, newspaper, or document but it does not include pictures.
Third option: Index; An alphabetical list of names, subjects, etc. about the pages on which they are mentioned.
Fourth option: Preface; An introduction to a book, typically stating its subject, scope, or aims.
So, the index is different from the others as it is the type of list. Hence, the third option is correct.

3. Directions: Find the odd word pair from the given responses.
1) Wool
2) Feather
3) Hair
4) Grass

Solution:
Determine the source of the given terms.
Let's check each option –
First option: Wool; Wool is obtained from sheep.
Second option: Feather; Feather is obtained from birds.
Third option: Hair; Hair is obtained from animals or birds.
Fourth option: Grass; Grass is obtained from plants.
So, the fourth option does not belong to the group as all the other things are obtained from animals or birds. Hence, the fourth option is correct.


About the Faculty
Tanu Gupta, with over a decade of experience as a reasoning faculty, specializes in preparing students for various entrance examinations and career development. Her extensive work with multiple educational platforms and institutions has honed her expertise in logical and analytical thinking. Her dedication to innovative teaching methods ensures these articles provide practical insights and expert guidance.

Frequently Asked Question (FAQs)

1. How many types of questions from classification are asked in the examinations?

There are a total of six types of classification in verbal reasoning i.e. word-based, word pair-based, letter-based, set-based, number pair-based and mix classification. The number of questions of a particular type of classification is not fixed for any exam. So, the examiner can ask any of these types of classification-based questions in an exam.

2. What will be the level of the questions asked from classification?

The level of the questions of classification has been seen as easy to moderate in the examinations

3. What is the weightage of the questions of classification in the exams?

In the SSC exams around 3-4 questions have been asked every year whereas in other exams like Railways, CUET or Defence mostly 2-3 questions have been asked.

4. How to ace the topic classification?

Work on your English Language, Mathematics and General Knowledge basics to ace the classification. Also, practice the questions of classification from offline or online resources.

5. Is there any short trick to solve the questions based on classification?

No, there is no short trick to solve the questions based on classification. However, a good practice of the questions based on classification can increase the percentage of accuracy and the speed of solving the question.

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