### Contents of SSC CHSL(10+2) TIER 1 COMBINED HIGHER SECONDARY LEVEL ONLINE EXAM 2019 LDC/DEO/PSA

This book contains chapter-wise solutions, topic-wise solutions, exercise-wise solutions, and videos.

#### 75 Chapters

- 1. SSC CHSL Tier-I
- 2. Semantic Analogy
- 3. Symbolic/Number Analogy
- 4. Semantic Classification
- 5. Symbolic/Number Classification
- 6. Semantic Series
- 7. Number Series
- 8. Word Formation
- 9. Logical Sequencing
- 10. Coding-Decoding
- 11. Direction Sense Test
- 12. Venn Diagram
- 13. Mathematical/Numerical Operation
- 14. Symbolic Operation
- 15. Inserting the Missing Character
- 16. Order and Sequence
- 17. Drawing Inferences
- 18. Trends
- 19. Problem Solving
- 20. Figural Analogy
- 21. Figural Classification
- 22. Figural Series
- 23. Punched Hole/Pattern (Folding and Unfolding)
- 24. Figural Pattern (Folding and Completion)
- 25. Embedded Figures
- 26. Critical Thinking
- 27. Emotional Intelligence
- 28. Social Intelligence
- 29. Other Sub-Topics
- 30. Number System
- 31. Square Root and Cube Root
- 32. Surds and Indices
- 33. Number Series
- 34. Average
- 35. Percentage
- 36. Ratio and Proportion
- 37. Partnership
- 38. Profit, Loss and Discount
- 39. Speed, Distance and Time
- 40. Time and Work
- 41. Interest (Simple & Compound)
- 42. Linear Equations
- 43. Alligation and Mixture
- 44. Elementary Algebra
- 45. 2D-Mensuration
- 46. 3D-Mensuration
- 47. Basic Trigonometry
- 48. Height and Distance
- 49. Table
- 50. Problem Based on Ages
- 51. Bar Diagram
- 52. Line Graph
- 53. Pie Chart
- 54. Geometry
- 55. Spotting Errors
- 56. Sentence Improvement
- 57. Voice
- 58. Direct and Indirect Speech
- 59. Idioms and Phrases
- 60. Synonyms
- 61. Antonyms
- 62. One Word Substitution
- 63. Spelling Test
- 64. Sentence Completion
- 65. Rearrangement of Sentences/Words
- 66. Cloze Passage
- 67. Comprehension
- 68. History of India
- 69. Geography
- 70. Indian Polity
- 71. Indian Economy
- 72. General Science
- 73. Miscellaneous
- 74. Environment & Ecology
- 75. Practice Set

#### 4 Topics

19 March, 2018

18 January, 2017

2015

2014

#### 1 Topics

Symbolic/Number Analogy

#### 1 Topics

Word Classification

#### 1 Topics

Symbolic/Number Classification

#### 2 Topics

Single Letter or Group of Letter Series

Continuous Series

#### 2 Topics

Find Out the Next Number

Find Out the Wrong Number

#### 2 Topics

Word Formation of Given Word

Word Formation of Unscrambled Letters

#### 1 Topics

Types of Logical Sequencing

#### 5 Topics

Number Coding

Alphabet Coding

Symbol Coding

Message Coding

Substitution Coding

#### 3 Topics

Finding the Direction

Finding the Distance

Finding Both the Distance and Direction

#### 2 Topics

Identification of Relation Based Venn Diagram

Analysis Based Venn Diagram

#### 2 Topics

Symbol Substitution

Interchange of Signs and Numbers

#### 1 Topics

Symbolic Operation

#### 2 Topics

Number Puzzles

Letter Puzzles

#### 2 Topics

Sequential Order of Arrangement

Position Test

#### 2 Topics

Statement and Conclusion

Syllogism

#### 1 Topics

Figural Classification

#### 1 Topics

Folding and Unfolding

#### 1 Topics

Figural Pattern (Folding and Completion)

#### 2 Topics

Figure Embedded in Option Figures

Figure Embedded in Question Figures

#### 1 Topics

Critical Thinking

#### 1 Topics

Emotional Intelligence

#### 3 Topics

Blood Relations Based on Conversation

Blood Relations Based on Puzzle

Symbolically Coded Blood Relationship

#### 2 Topics

Verbal

Non-Verbal

#### 4 Topics

Classification of Numbers

Divisibility Test

Simplification

Fraction

#### 2 Topics

Square Root

Cube Root

#### 2 Topics

Surds

Indices

#### 4 Topics

Prime Number Series

Multiple Series

Difference or Addition Series

N² Series

#### 2 Topics

Ratio

Proportion

#### 1 Topics

Profit, Loss and Discount

#### 1 Topics

Speed, Distance and Time

#### 2 Topics

Simple Interest

Compound Interest

#### 2 Topics

Linear Equation in One Variable

Linear Equation in Two Variables

#### 1 Topics

Rules of Mixture

#### 1 Topics

Fundamental Operations on Algebraic Expressions

#### 1 Topics

Important Features and Formulae of Different 2D-Figure

#### 1 Topics

Properties and Formulae of Important 3D-Figure

#### 1 Topics

Trigonometric Ratio

#### 1 Topics

Concept of Pythagoras Theorem

#### 1 Topics

Problem Based on Ages

#### 2 Topics

Types of Graph/Chart

Histogram

#### 4 Topics

Basic Definitions

Polygons

Triangle

Circle

#### 9 Topics

Tense

Subject-Verb Agreement

Noun

Pronoun

Adjective

Articles

Adverb

Preposition

Conjunction

#### 1 Topics

Sentence Improvement

#### 1 Topics

Direct and Indirect Speech

#### 1 Topics

Some Important Idioms and Phrases

#### 1 Topics

Some Important One Word Substitutions

#### 1 Topics

Sentence Completion

#### 1 Topics

Rearrangement of Sentences/Words

#### 3 Topics

Ancient India

Medieval India

Modern India

#### 3 Topics

Universe

World Geography

Indian Geography

#### 25 Topics

Framing of the Constitution

Composition of Constituent Assembly

Preamble to the Constitution

Timeline of States and Union Territories

Fundamental Rights

Directive Principles of State Policy

The President

Election

Impeachment [Article 61]

Power

Vice-President

Prime Minister

Parliament of India

Consolidated Fund of India [Article 226]

Contingency Fund of India

Supreme Court of India

Qualification Criterion

The Governor

State Legislature

Legislative Assembly

High Court

Union Public Service Commission [UPSC]

Comptroller and Auditor General of India [CAG] [Article 148]

Election Commission [Article 324]

Panchayati Raj

#### 8 Topics

Features of Indian Economy

National Income Aggregates

Economic Planning in India

Poverty

Banking System in India

Reserve Bank of India

Insurance

Indian Money Market

#### 3 Topics

Physics

Chemistry

Biology

#### 7 Topics

Important Dates

Art and Culture

Indian Defence

India's Atomic Research

United Nations Organisation

Awards and Honours

Sports

#### 5 Topics

Environment

Atmosphere

Ecology and Ecosystem

Biodiversity

Climate Change

#### 3 Topics

Practice Set 1

Practice Set 2

Practice Set 3

## Experience Tests Tailored to Match the Real Exam

## Practise Questions with Solutions from the SSC CHSL(10+2) TIER 1 COMBINED HIGHER SECONDARY LEVEL ONLINE EXAM 2019 LDC/DEO/PSA

- (a)Crude oil prices
- (b)Copper futures prices
- (c)Gold futures prices
- (d)Shipping rate index

**Hint**

The index represents the average trading price in the 25-day Brent Blend, the Forties, Oseberg, Ekofisk (BFOE) market in the relevant delivery month.

**Solution:**

Brent Index is associated with crude oil prices. It is a standard for crude oils.

The index represents the average trading price in the 25-day Brent Blend, the Forties, Oseberg, Ekofisk (BFOE) market in the relevant delivery month.

Thus, option (A) is the correct answer.

- (a)$64$
- (b)$44$
- (c)$36$
- (d)$54$

**Hint**

Consider the question given, square it on both the sides of the question and find out the value.

**Solution:**

$\sqrt{1-\left(\frac{x}{289}\right)}=\frac{15}{17}$

Squaring on both sides,

$\Rightarrow 1-\frac{x}{289}={\left(\frac{15}{17}\right)}^{2}$

$\Rightarrow \frac{289-x}{289}=\frac{225}{289}$

$\Rightarrow x=289-225$

$\therefore x=64$

- (a)$3$
- (b)$0$
- (c)$2$
- (d)$-1$

**Hint**

Solve by using only the first two terms of a given expression.

**Solution:**

Given,

$3x+5(4-3x)>2-4x<3x-\frac{x}{3}$

From the first two terms of given expressions,

$3x+5(4-3x)>2-4x$

$\Rightarrow 3x+20-15x2-4x$

$\Rightarrow 20-12x2-4x$

$\Rightarrow -12x+4x2-20$

$\Rightarrow -8x-18$

$\Rightarrow x\frac{18}{8}$

$\therefore x=2.25=2$

- (a)$Rs.12000$
- (b)$Rs.9360$
- (c)$Rs.10202.4$
- (d)$Rs.13322.4$

**Hint**

The M.R.P. of the washing machine $=\frac{14000\times 100}{91}$

**Solution:**

Let marked price of the machine $=Rs.x$

As given in the question,

$x-\frac{x\times 9}{100}=14000$

$\Rightarrow \frac{91x}{100}=14000$

$\Rightarrow x=\frac{14000\times 100}{91}$

Now, selling price of machine at $22\%$discount $=\frac{14000\times 100}{91}-\frac{14000\times 100}{91}\times \frac{22}{100}$

$=\frac{14000}{91}\left(100-22\right)$

$=\frac{14000\times 78}{91}$

$=\frac{14000\times 6}{7}$

$=2000\times 6$

$=Rs.12000$

Hence, the correct answer is $\u20b912000$.

- (a)$2$
- (b)$3$
- (c)$4$
- (d)$6$

**Hint**

From the given equation, factorise the numbers on both sides and later compare the powers to find the value which is required.

**Solution:**

${4}^{x-1}\times {9}^{2x-6}=5184$

${\left({2}^{2}\right)}^{x-1}\times {\left({3}^{2}\right)}^{2x-6}={\left({2}^{3}\times {3}^{2}\right)}^{2}$

${\left(2\right)}^{2x-2}\times {\left(3\right)}^{4x-12}={2}^{6}\times {3}^{4}$

On comparing,

${2}^{2x-2}={2}^{6}$

$2x-2=6$

$2x=8$

$x=4$

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- (a)Father
- (b)Mother
- (c)Aunt
- (d)Cousin

**Hint**

Analyze the given words in options based on position in family tree. One word is different from logic.

**Solution:**

Except Cousin, all others belong to the same generation. So option (d) is odd one out. Hence, option (d) is correct.

- (a)Cricket
- (b)Hockey
- (c)Billiards
- (d)Fencing

**Hint**

Analyse the given words in options based on the arena where these sports are played. One word is different from logic.

**Solution:**

Cricket, Hockey and Fencing are outdoor games, whereas Billiards is an indoor game.

Cricket is an open-air game that is played on a large field with the help of a bat, a ball and two wickets.

Hockey is a team game played with hooked sticks and a hardball.

Fencing is a sport played with swords.

Billiards is a game played by two people on a billiard table with a cue.

Hence, 'Billiards' is the correct answer.

- (a)Triangle
- (b)Rectangle
- (c)Circle
- (d)Square

**Hint**

Analyse the given words in the option based on the same logic. One word is different from logic.

**Solution:**

Triangle, rectangle and square are made up of straight lines, whereas circle is not made up of straight lines.

Triangle is a two-dimension figure that is made up of three sides and has three angles.

A rectangle is a two-dimension figure that is made up of four sides in which opposite sides are equal.

Square is a two-dimension figure that is made up of four sides in which all the sides are equal.

A circle is a round figure in which the points are always equidistant from a fixed central point.

Hence, 'circle' is the correct answer.

- (a)Advice
- (b)Counsel
- (c)Suggest
- (d)Direct

**Hint**

Analyze the given words in option based on similarity in words. One word is different from logic.

**Solution:**

All are synonyms to each other except Direct. So, option (d) is odd one out. Hence, option (d) is correct.

- (a)Turmeric
- (b)Carrot
- (c)Ginger
- (d)Tomato

**Hint**

Analyze the given words in option based on same logic. One word is different from logic.

**Solution:**

Except Tomato, all others are either modified roots or modified stones. Tomato is sprawling plant. So option (d) is odd one out. Hence, option (d) is correct.

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- (a)20
- (b)22
- (c)23
- (d)26

**Hint**

two series

I. 36, 30, 24

II. 34, 28, 22

**Solution:**

The pattern of the series are as follows

Series 1

Series 2

Its combination of two series and the difference between the term is 6 in each series. So, missing term is 22. Hence, option (b) is correct.

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- (a)$3,4,1,6,2,5$
- (b)$3,5,6,1,4,2$
- (c)$5,3,6,2,4,1$
- (d)$6,2,5,3,4,1$

**Hint**

Meaningful word should be formed by arranging all digits in given order.

**Solution:**

On arranging the letters according to the given digits $\text{'}341625\text{'},$ the Meaningful word 'TOLIRA' is not formed.

On arranging the letters according to the given digits $\text{'}536241\text{'},$ the Meaningful word 'ATIROL' is not formed.

On arranging the letters according to the given digits $\text{'}625341\text{'},$ the Meaningful word 'IRATOL' is not formed.

After careful observation of the letters given in the question, it can be concluded that on arranging the given letters in a meaningful order, the word TAILOR is formed which is obtained by arranging the digits in the order $3,5,6,1,4,2.$

Therefore, option (b) is the correct answer.

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- (a)AJMTVT
- (b)AMJXVS
- (c)MJXVSU
- (d)WXYZAX

**Hint**

D becomes C by subtracting $1$ from its alphabetical position.

**Solution:**

Given:

DELHI can be coded as CCIDD

Here, we can see that one, two, three, four and five are subtracted from the respective alphabetical position of letters in the given word (DELHI) to get the coded form.

The pattern is shown below,

$\mathrm{D}-1=\mathrm{C}\phantom{\rule{0ex}{0ex}}\mathrm{E}-2=\mathrm{C}\phantom{\rule{0ex}{0ex}}\mathrm{L}-3=\mathrm{I}\phantom{\rule{0ex}{0ex}}\mathrm{H}-4=\mathrm{D}\phantom{\rule{0ex}{0ex}}\mathrm{I}-5=\mathrm{D}$

Similarly, Bombay will be coded as

$\mathrm{B}-1=\mathrm{A}\phantom{\rule{0ex}{0ex}}\mathrm{O}-2=\mathrm{M}\phantom{\rule{0ex}{0ex}}\mathrm{M}-3=\mathrm{J}\phantom{\rule{0ex}{0ex}}\mathrm{B}-4=\mathrm{X}\phantom{\rule{0ex}{0ex}}\mathrm{A}-5=\mathrm{V}\phantom{\rule{0ex}{0ex}}\mathrm{Y}-6=\mathrm{S}$So, the code of BOMBAY will be AMJXVS.

Hence, the correct answer is AMJXVS.

- (a)TIATIATIA
- (b)MNUMNUMNU
- (c)IATIATIAT
- (d)ALDALDALD

**Hint**

Some letters of the given words are repeated to form their codes.

**Solution:**

According to the given coding:

BOMBAY is written as MYMYMY.

Here we can see that the letters at the third and sixth places are repeated thrice to code BOMBAY as MYMYMY.

Similarly, the letters at the $3\mathrm{rd},6\mathrm{th}$ and $9\mathrm{th}$ places i.e M, N and U are repeated thrice to code TAMILNADU as MNUMNUMNU.

Hence, the correct answer is MNUMNUMNU.

- (a)SQPZM
- (b)SQMPZ
- (c)SPQZM
- (d)SQPMZ

**Hint**

Use codes of different letters given.

**Solution:**

According to the question,

letters E A R T H code Q P M Z S Therefore,

HEART can be coded as SQPMZ.

Hence, option (d) is correct.

- (a)$12-4-1-25$
- (b)$12-1-4-25$
- (c)$10-1-4-23$
- (d)$12-1-4-22$

**Hint**

Code is the place value of each letter.

**Solution:**

Clearly, each letter is coded by the numeral denoting its position in the English alphabet. Thus, A is coded as $1$, B as $2$, C as $3$, D as $4$, ......, L as $12$, M as $13$, .... , Y as $25$, Z as $26$. So, the code for LADY is $12-1-4-25$.

So, option (b) is correct.

Hence, "$12-1-4-25$" is the correct answer.

- (a)44
- (b)54
- (c)64
- (d)72

**Hint**

Multiplied by 2 in place value.

**Solution:**

Clearly, each letter is assigned a numeral value which is twice the numeral denoting its position in the English alphabet. B, E and T are 2nd, 5th, 20th letters respectively.

So, BET = B + E + T = (2$\times $2) + (5$\times $2) + (20$\times $2) = 54

So, option (b) is correct.

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- (a)East
- (b)North-East
- (c)South
- (d)North-West

**Hint**

standard direction is rotated ${45}^{\mathrm{o}}$ anticlockwise.

**Solution:**

After carefully observing at the given question, it can be concluded that the South-East in the question is called East by rotating ${45}^{\mathrm{o}}$ anti-clockwise, similarly the North-West is called South by rotating ${45}^{\mathrm{o}}$ anti-clockwise and the sequence continues further. Based on the information in the question, it is shown by different diagram below.

Hence it is clear from the diagram that North is called North-West by rotating ${45}^{\mathrm{o}}$ anti-clockwise.

Therefore, option (d) is the correct answer.

- (a)North-East
- (b)North-West
- (c)South-East
- (d)South-West

**Hint**

standard direction sense is rotated ${135}^{\mathrm{o}}$ anticlockwise.

**Solution:**

After carefully observing at the given question, it can be concluded that the South-East in the question becomes North by rotating ${135}^{\mathrm{o}}$anticlockwise, similarly North-East becomes West by rotating ${135}^{\mathrm{o}}$anticlockwise and the sequence continues further. Based on the given information in the question, it is shown by different diagram below.

Hence, it is clear from the diagram that West becomes South-East by rotating ${135}^{\mathrm{o}}$anti-clockwise.

Therefore, option (c) is the correct answer.

- (a)C
- (b)A
- (c)X
- (d)B

**Hint**

draw diagram according to the information given then we clearly see that B is farthest west.

**Solution:**

The information in the given question is shown below through a diagram.

Hence, it is clear from the diagram that B is the farthest West

Therefore, option (d) is the correct answer.

- (a)North-East
- (b)East
- (c)West
- (d)South

**Hint**

take standard direction sense as a refrence and draw diagram from given information.

**Solution:**

The information in the given question is shown below through a diagram.

Hence it is clear from the diagram that M is East of K.

Therefore, option (b) is the correct answer.

- (a)North
- (b)South
- (c)East
- (d)West

**Hint**

Draw diagram according to the information given by taking reference of standard direction.

**Solution:**

The information in the given question is shown below through a diagram.

Hence, it is clear from the diagram that he is facing West and his left hand will be in the North direction.

Therefore, option (a) is the correct answer.

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- (a)Animals, Insects, Cockroaches
- (b)Animals, Males, Females and Hermaphrodites
- (c)States, Districts, Union Territories
- (d)Country, States, Districts

**Hint**

Analyze the elements and find correct relation between them.

**Solution:**

No relation between States and Union Territories. Districts are the part of States.

So, option (c) is the best representation. Hence, option (c) is correct.

- (a)E, A, B, C are in all the three shapes
- (b)F, C, D, B, A are in all the three shapes
- (c)Only B is in all the three shapes
- (d)A and B are in all the three shapes

**Hint**

Analyze the diagram to find the common in all.

**Solution:**

B is the region common to the circle, square and triangle.

So, option (c) is correct.

- (a)
- (b)
- (c)
- (d)

**Hint**

Analyze the elements and find correct relation between them.

**Solution:**

Diagram is:

District comes under State and State comes under Nation. So, option (b) is correct.

- (a)
- (b)
- (c)
- (d)

**Hint**

Analyze the words and try to find which one is part of the other and which one is not related to it.

**Solution:**

Diagram is:

Sparrow is one of the types of birds but Mice is not bird. So, option (c) is correct.

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- (a)$190$
- (b)$180$
- (c)$90$
- (d)$-60$

**Hint**

Change symbols as per the question and calculate the expression.

**Solution:**

Given expression is $=15-2\xf7900+90\times 100$

Using the correct symbols, we get the expression

$=15\times 2+900\xf790-100$

$=30+10-100$

$=-60$

So. option (d) is correct.

- (a)$-2$
- (b)$2$
- (c)$4$
- (d)$8$

**Hint**

Change symbols as per the question and then use BODMAS rule to calculate the expression.

**Solution:**

Given expression is $12+6\xf73-2\times 8$

Using the correct symbols, we have given expression

$12\xf76-3\times 2+8$

$=2-6+8$

$=10-6$

$=4$

So, option (c) is correct.

- (a)$-1$
- (b)$2$
- (c)$4$
- (d)$8$

**Hint**

Change symbols as per the question and calculate the expression.

**Solution:**

Given expression is

$\left(3-15\xf719\right)\times 8+6$

Using the correct symbols, we have given expression

$\left(3\times 15+19\right)\xf78-6$

$=64\xf78-6$

$=8-6$

$=2$

So, option (b) is correct.

- (a)$9$
- (b)$10$
- (c)$19$
- (d)$12$

**Hint**

After changing the symbols, division should be performed first.

**Solution:**

Given expression is:

$16\times 3+5-2\xf74$

According to the question, on replacing the mathematical operations according to the given symbols, we get:

$16+3-5\xf72\times 4$

$=16+3-\left(5/2\right)\times 4$

$=19-10$

$=9$

Hence, the correct answer is '$9$'.

- (a)$5$
- (b)$22$
- (c)$48$
- (d)$52$

**Hint**

Change symbols as per the question, apply BODMAS rule and then calculate the expression.

**Solution:**

The given expression is

$15-3+10\times 5\xf75$

On replacing the symbols according to the question, we get,

$15\times 3-10\xf75+5$

$=45-2+5$

$=48$

Hence, the correct answer is '$48$'.

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- (a)$\xf7,=,\times $
- (b)$\times ,=,\xf7$
- (c)$=,\xf7,\times $
- (d)$=,\times ,\xf7$

**Hint**

Try all options one by one.

**Solution:**

From option (a),

$96\xf76=8\times 2$

$16=16$

So, option (a) is correct.

- (a)$-,\times ,=$
- (b)$-,=,\times $
- (c)$=,\times ,-$
- (d)$\times ,-,=$

**Hint**

Try to eliminate options.

**Solution:**

Given equation $=8*5*9*31$

From option (d),

$8\times 5-9=31$

$40-9=31$

$31=31$

So, option (d) is correct.

- (a)$3\gamma 6\eta 2\delta 8*4\omega 5$
- (b)$3\eta 6\gamma 2\delta 8*4\beta 5$
- (c)$3\gamma 6*2\delta 8\eta 4\alpha 5$
- (d)$3\delta 6*2\gamma 8\eta 4\omega 5$

**Hint**

Try all options one by one.

**Solution:**

Given, $3\delta 6*2\gamma 8\eta 4\omega 5$

Then, replacing signs,

$3+6-2\times 8\xf74=5$

$9-2\times 2=5$

$5=5$

So, option (d) is correct.

- (a)$25$
- (b)$27$
- (c)$29$
- (d)$36$

**Hint**

Use symbols as given in the question.

**Solution:**

Using the correct symbols, we have

$16\$4@5\#72*8$

$=16+4\times 5-72\xf78$

$=16+20-9$

$=36-9$

$=27$

So, option (b) is correct.

- (a)$-\frac{3}{2}$
- (b)$30$
- (c)$32$
- (d)$34$

**Hint**

Place proper value of the symbols.

**Solution:**

Using the proper symbols, we have

$28\mathrm{B}7\mathrm{P}8\mathrm{T}6\mathrm{M}4$

$=28\xf77\times 8-6+4$

$=4\times 8-6+4$

$=32-6+4$

$=36-6$

$=30$

So, option (b) is correct.

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- (a)$1216$
- (b)$2250$
- (c)$8100$
- (d)$11036$

**Hint**

Analyze all numbers and find missing number.

**Solution:**

Pattern of the given numbers,

${4}^{2}\times {3}^{2}=144,{11}^{2}\times {9}^{2}=9801$

So according to this pattern missing number will be

$={15}^{2}\times {6}^{2}$

$=225\times 36$

$=8100$

- (a)$12$
- (b)$21$
- (c)$24$
- (d)$35$

**Hint**

Analyze all numbers and find missing number.

**Solution:**

We have,

$\frac{27+54}{9}=9:\frac{42+84}{14}=9$

Let, the missing number be $\mathrm{X}$.

Then,$\frac{\mathrm{X}+42}{7}=9$

$\mathrm{X}=21$

So, option (b) correct.

- (a)$38$
- (b)$39$
- (c)$40$
- (d)$44$

**Hint**

Squares are being added to previous number to get the next number.

**Solution:**

Given that,

$9+{2}^{2}=13,13+{3}^{2}=22$

So according to this pattern missing number will be $=22+{4}^{2}=38$

- (a)$9$
- (b)$18$
- (c)$24$
- (d)$27$

**Hint**

Analyze all numbers and find missing number.

**Solution:**

Starting from $3$ and moving clockwise, the number in each quadrant is the square of that in the previous quadrant. So, missing number $={3}^{2}=9$

- (a)$10$
- (b)$12$
- (c)$13$
- (d)$15$

**Hint**

Analyze all numbers clockwise and find missing number.

**Solution:**

We have, ${3}^{\mathrm{rd}}$ number is addition of first two numbers.

$1+2=3,2+3=5,3+5=8$

So, missing number $=5+8=13$

So, option (c) is correct.

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- (a)$18$
- (b)$19$
- (c)$31$
- (d)$32$

**Hint**

Use order and ranking concept.

**Solution:**

Rank from last $=$ total students $-$ rank from start $+1=49-18+1=32$

So, Nitin's rank from last is $32$.

So, option (d) is correct.

- (a)$45$
- (b)$46$
- (c)$47$
- (d)$48$

**Hint**

Use the concept of order and ranking.

**Solution:**

Use the below formula,

Total number of students $=$ Top $+$ Bottom $-1=9+38-1=46$

So, option (b) is correct.

- (a)$27$
- (b)$37$
- (c)$38$
- (d)$39$

**Hint**

Use the concept of order and ranking.

**Solution:**

Use the below formula,

Total number of students $=$ left $+$ right $-1=19+19-1=37$.

So, option (b) is correct.

- (a)${6}^{\mathrm{th}}$
- (b)${7}^{\mathrm{th}}$
- (c)${10}^{\mathrm{th}}$
- (d)${12}^{\mathrm{th}}$

**Hint**

Analyze the order and ranking concept.

**Solution:**

Use the formula, Total number of the boys in the row, $\left(12+1+10\right)=23$

Number of boys left of $\mathrm{D}=$ Total $-$ boys right of $\mathrm{D}=23-17=6$

So, $\mathrm{D}$ is $\left(6+1\right)={7}^{\mathrm{th}}$ from the left.

So, option (b) is correct.

- (a)$3$
- (b)$7$
- (c)$12$
- (d)$23$

**Hint**

Use order and ranking concept.

**Solution:**

Total Students $=60$

Girls are twice of Boys so Boys are $20$ and Girls are $40$.

Number of students behind Kamal $=60-17=43$

Number of girls behind Kamal $=40-9=31$

Number of boys behind Kamal $=43-31=12$ boys

So, option (c) is correct.

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- (a)$56,43,32,97,10$
- (b)$89,43,40,12,44$
- (c)$10,75,32,96,78$
- (d)$78,11,12,96,10$

**Hint**

Analyze the matrix and solve question.

**Solution:**

Different sets of words are:

T —

10, 03, 10, 56, 68,78, 89

E — 11, 43, 59,75, 97

M — 21, 31,32, 58, 69, 79

P — 40, 55,96, 99So, correct set of word TEMPT is 10, 75, 32, 96, 78

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- (a)$20$
- (b)$15$
- (c)$10$
- (d)$25$

**Hint**

Use the mathematical concepts for calculating the number of persons in the party and total number of gifts exchanged will be equal to number of persons (number of person $-$ 1).

**Solution:**

Let the total number of persons in the party $=n$

Then, total number of gifts exchanged in the party $=n(n-1)$

According to the question,

$n\left(n-1\right)=600$

${n}^{2}-n=600$

${n}^{2}-n-600=0$

${n}^{2}-25n+24n-600=0$

$n\left(n-25\right)+24\left(n-25\right)=0$

$\left(n\u201425\right)\left(n+24\right)=0$

$n=25$ and $n=-24$

$n=-24$ is rejected because number of persons can't be negative.

So. $n=25$

Therefore, the total number of persons in the party $=n=25$

So, option (4) is correct.

- (a)$14$
- (b)$13$
- (c)$15$
- (d)$16$

**Hint**

The number of handshakes will be ${}^{n}{C}_{2}$ if $n$ persons are shaking hands with each other.

**Solution:**

Let the total number of persons $=n$

Then, according to the question.

${}^{n}{C}_{2}=105$

$\Rightarrow \frac{n(n-1)}{2}=105$

$\Rightarrow {n}^{2}-n=210$

$\Rightarrow {n}^{2}-n-210=0$

$\Rightarrow \left(n-15\right)\left(n+14\right)=0$

So, $n=15$ and $n=-14$

['.' $n$ cannot be negative]

So, $n=-14$ is discarded.

So, $n=15$

Therefore, the total number of persons present at the get-together $=15$

So, option (3) is correct.

- (a)$3$
- (b)$5$
- (c)$7$
- (d)$9$

**Hint**

Analyse the statements given and solve it.

**Solution:**

Draw the position of the ducks as shown below:

We can see that two ducks in front of a duck, two ducks behind a duck and a duck between two ducks. Clearly, the smallest number of ducks is 3.

- (a)17
- (b)9
- (c)Nil
- (d)8

**Hint**

Analyse the statement and solve.

**Solution:**

According to the question, ‘All but nine died'. This statement means that ‘All except nine died' i.e., nine sheep remained alive and others died.

So, the shepherd was left with 9 sheep.

- (a)20
- (b)30
- (c)50
- (d)60

**Hint**

Analyse the problem and solve.

**Solution:**

Let the number of deer and peacocks in the zoo be A and B respectively.

According to the question,

A + B = 80 ..... (1)

4A + 2B = 200

2A + B = 100 .... (2)Subtracting Equation (i) and (ii) we get,

A = 100 - 80 = 20

Putting A = 20 in (i), we get

20 + B = 80

B = 80 - 20 = 60So, the required number of peacocks in the zoo = 60.

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- (a)
- (b)
- (c)
- (d)

**Hint**

Use the figure in the question to find the relationship in the question figure to find the answer.

**Solution:**

In the first pair, the triangle is replaced by a rhombus. In the same way, in the second pair, both triangles will be replaced by two rhombuses. So, option (d) will be the right answer.

- (a)
- (b)
- (c)
- (d)

**Hint**

Use the figure given in the question to find the relation between the figures.

**Solution:**

In the first pair, the first figure gets laterally inverted and the shaded circle becomes unshaded. In the same way and in the second figure, the first figure will get laterally inverted and the shaded circle will become unshaded.

- (a)
- (b)
- (c)
- (d)

**Hint**

Use the figure given in the question to find the relation between the figures.

**Solution:**

In the first pair, both the inner circles of figure (1) are removed and thus figure (2) has been formed. When we establish the same relationship between figures (3) and (4), figure (b) fits properly as the fourth figure.

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- (a)
- (b)
- (c)
- (d)

**Hint**

In this type of questions, each subsequent figure of the series is obtained by addition and/or deletion of designs - in the preceding figures.

**Solution:**

In this question we have to find figures which will continue the same series as given in the problem figures and the logic behind the figural series is that ‘x' moves one step and two steps in anticlockwise direction alternately and a new symbol is added once before and then after the cross alternately. So, option D will be the right answer.

- (a)
- (b)
- (c)
- (d)

**Hint**

In this type of questions, each subsequent figure of the series is obtained by addition and/or deletion of designs - in the preceding figures.

**Solution:**

In this question we have to find figures which will continue the same series as given in the problem figures and the logic behind the figural series is that the symbols change positions and the smaller symbol enlarges while the larger symbol becomes shorter in each step. Also, the symbols are replaced by new ones in every second figure. So, option A will be the right answer.

- (a)
- (b)
- (c)
- (d)

**Hint**

Observe the pattern in changing position of lines.

**Solution:**

In this question we have to find figure which will continue the same series as given in the problem figures and the logic behind the figural series is that here the smallest line at the bottom interchanges positions with other lines sequentially and after reaching the top it again comes back to its initial position.

- (a)
- (b)
- (c)
- (d)

**Hint**

In this type of questions, each subsequent figure of the series is obtained by addition and/or deletion of designs - in the preceding figures.

**Solution:**

In this question we have to find figures which will continue the same series as given in the problem figures and the logic behind the figural series is that the vertical arrow and inverted in the first step, then goes to the other side in the second step and then rotates by 180° in third step, rotates by 180° in the fourth step. The process repeats. Similarly, the horizontal arrow rotates by 180" in first step, rotates by 180° in second step. Laterally gets inverted in third step and moves to the other side in fourth step by the above logic we get figure in option (d) as the right answer.

- (a)
- (b)
- (c)
- (d)

**Hint**

**Solution:**

In this question we have to find figures which will continue the same series as given in the problem figures. The logic behind the figural series is that each figure is rotated in anticlockwise direction, then a similar figure appears after alternate steps. By applying the following logic we obtain option (a) as the right answer.

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- (a)
- (b)
- (c)
- (d)

**Hint**

Analyse the pattern which is formed when a folded piece of paper have been cut in a definite design.

**Solution:**

Answer figure (3) will appear when a piece of paper is folded and cut as shown in the question figure.

So, option (3) is correct.

- (a)
- (b)
- (c)
- (d)

**Hint**

Analyze the pattern which is formed when a folded piece of paper have been cut in a definite design.

**Solution:**

Answer figure (3) will appear when a piece of paper is folded and cut as shown in the question figure.

So, option (3) is correct.

- (a)
- (b)
- (c)
- (d)

**Hint**

When the given paper is unfolded, we get two slant lines, one at each side.

**Solution:**

According to the given figure, there is a cross and two small circles being cut on the paper.

When we open the folded paper, we will get a cross in the centre, four small circles and two slant lines, one on each side.

Hence, the correct answer is

- (a)
- (b)
- (c)
- (d)

**Hint**

Analyse the pattern which is formed when a folded piece of paper have been cut in a definite design.

**Solution:**

Answer figure (4) will appear when a piece of paper is folded and cut as shown in the question figure.

So, option (4) is correct.

- (a)
- (b)
- (c)
- (d)

**Hint**

Analyse the pattern which is formed when a folded piece of paper have been cut in a definite design.

**Solution:**

Answer figure (3) will appear when a piece of paper is folded and cut as shown in the question figure.

So, option (3) is correct.

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- (a)
- (b)
- (c)
- (d)

**Hint**

Analyze the figural pattern.

**Solution:**

Paper folded vertically.

When the transparent sheet is folded at the dotted line, the following pattern appears

So, option (2) is correct.

- (a)
- (b)
- (c)
- (d)

**Hint**

Analyze the figural pattern.

**Solution:**

Paper folded vertically.

When the transparent sheet is folded at the dotted line, the following pattern appears

So, option (3) is correct.

- (a)
- (b)
- (c)
- (d)

**Hint**

Analyze the figural pattern.

**Solution:**

Paper folded vertically.

When the transparent sheet is folded at the dotted line pattern appears

So, option (3) is correct.

- (a)
- (b)
- (c)
- (d)

**Hint**

Analyze the figural pattern.

**Solution:**

Paper folded vertically.

When the transparent sheet is folded at the dotted line pattern appears

So, option (3) is correct.

- (a)
- (b)
- (c)
- (d)

**Hint**

Analyze the figural pattern.

**Solution:**

Paper folded vertically.

When the transparent sheet is folded at the dotted line pattern appears

So, option (4) is correct.

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- (a)
- (b)
- (c)
- (d)

**Hint**

Analyze the embedded figure.

**Solution:**

Hence, answer figure (c) is embedded in the given question figure.

So, option (c) is correct.

- (a)
- (b)
- (c)
- (d)

**Hint**

Analyze the embedded figure.

**Solution:**

Hence, question figure is embedded in answer figure (a).

So, option (a) is correct.

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- (a)New Zealand
- (b)West Indies
- (c)Australia
- (d)India

**Hint**

Analyze the passage and make a table.

**Solution:**

Team India Australia West Indies New Zealand India - 2 - 2 Australia - - 2 - West Indies 2 - - 2 New Zealand - - - - Total Defeat 2 2 2 4 So, New Zealand lost most number of times.

So, option (a) is correct.

- (a)P
- (b)O
- (c)N
- (d)M

**Hint**

Analyze the passage and solve the questions.

**Solution:**

City Person Girls/ Boys Delhi K Girl Short Delhi L Boy Short Bengaluru M Girl Short Bengaluru N Girl Tall Bengaluru O Boy Short Bengaluru P Boy Tall So, N is tha tall girl from Bengaluru.

So, option (c) is correct.

- (a)Jaya
- (b)Seema
- (c)Tanya
- (d)Preeti

**Hint**

Analyze the passage and solve the questions..

**Solution:**

Girls Occupation Geeta Violinist Veena Violinist, Vocal Musician Jaya Vocal Musician Seema Dancer, Vocal Musician Tanya Dancer, Violinist, Vocal Musician Preeti Actress So, Tanya is Dancer and Violinist both.

So, option (c) is correct.

- (a)RU
- (b)RS
- (c)TU
- (d)QR

**Hint**

Analyze the passage and solve the questions.

**Solution:**

New volume - P, Q, S

Old volume - R, T, U

Law reports - P, Q, R

Medical extracts - S, T, U

Green covers - Q, R,

T, UYellow covers - P, S.

So, T and U are old medical extracts and have green covers.

So, option (c) is correct.

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- (a)Try to finish the job as per its requirement
- (b)Tell him that you would do it next day
- (c)Request one of your colleagues to help you
- (d)You will say sorry to him for not to do the work at that time

**Hint**

Analyze the situation and act accordingly.

**Solution:**

If my boss has given me some urgent assignment at the end hour then I will try to finish the job as per its requirement and I can't say sorry or can't delay it.

So, option (a) is correct.

- (a)ignore the uncomfortable glances as it is his job
- (b)just do your work
- (c)subtly convey it to the boss
- (d)tell your seniors clearly that such supervision affects your performance

**Hint**

Analyze the statements and do which is best suitable solution of this situation.

**Solution:**

If my boss has very piercing eyes and spies on my performance all the time then it is very uncomfortable to me and best way out of this is to do your work properly by which things will improve with time.

So, option (b) is correct.

- (a)You talk and work it out with him/her so that both adjust with time.
- (b)You develop an uncaring attitude towards him/her
- (c)You indulge in self-pity and find faults with yourself
- (d)You decide you cannot adjust and therefore think of separation

**Hint**

Analyze the statements and do which is best suitable solution of this situation.

**Solution:**

If my boyfriend/girlfriend has got a new job and is too busy and I feel neglected, then I will understand him/her and will talk to him/her and will sort and we will adjust the timing.

So, option (a) is correct.

- (a)take the friend to the first aid room
- (b)run away from the field
- (c)start discussions with the boy why he came in the way
- (d)blame other friends

**Hint**

Analyze the statements and do which is best suitable solution in this situation.

**Solution:**

While playing cricket when I hit the ball, it strikes one of my friends and blood starts oozing out from the forehead, then I would first take my friend to the first aid room because he may be seriously injured.

So, option (a) is correct.

- (a)hand it over to the bus conductor
- (b)leave the wallet as it is
- (c)try to find his/her contact number and inform the owner
- (d)give the money to the beggar

**Hint**

Analyze the statements and do which is best suitable solution of this situation.

**Solution:**

In a bus, I realize that someone has left his/her wallet, then I would try to find his/her contact number and inform the owner because I should be honest and I would like to return it to the real owner.

So, option (c) is correct.

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- (a)Grandmother
- (b)Mother
- (c)Aunt
- (d)Cannot be determined

**Hint**

Analyze the blood relation and try to make family tree for solving this and remember no information is given about D's father's brother.

**Solution:**

Either Mother of D (if D's father don't have a brother) or Aunt of D (if D's father have a brother) is D's father’s mother’s son’s wife. So, relation is not established. So, Relation can not be determined.

- (a)Cannot be determined
- (b)Sister
- (c)Brother
- (d)Cousin

**Hint**

Analyze the blood relation of by making family tree and father's father will be husband of P's grandmother.

**Solution:**

P's father and Q's mother will be siblings because thier father and mother are spouse to each other. P is cousin of Q.

- (a)Sister
- (b)Cousin
- (c)Niece
- (d)Aunt

**Hint**

A is sister of B who is mother of E.

**Solution:**

+ means male, - means female.

A is sister of B who is mother of D. So, its clear that A is Aunt of D.

So, option(4) is correct.

- (a)A
- (b)C
- (c)F
- (d)K

**Hint**

A is parent of G.

**Solution:**

Diagram is

F is brother of A who is parent of G. So, its clear that F is the uncle of G.

So, option (3) is correct.

- (a)Niece
- (b)Nephew
- (c)Sister in law
- (d)None of these

**Hint**

Analyze the blood relation and try to make the family tree to solve this.

**Solution:**

Diagram is

Neeraj's mother is sister-in-law of Kavita. So, its clear that Neeraj is nephew of Kavita.

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- (a)A
- (b)S
- (c)X
- (d)Z

**Hint**

Try to make a diagram according to it and only one person is left whose description is not given.

**Solution:**

According to the question, the arrangement in the row will be

PXSZRAHence, X is on the right of P.

- (a)1st
- (b)2nd
- (c)3rd
- (d)5th

**Hint**

Try to make arrangement where professor and businessman are on ends and advocate is on right of Student.

**Solution:**

According to the question, the arrangement in the row is

Professor,Student,Advocate, Author,BusinessmanHence, the advocate is third from the left.

- (a)B is to the left of A
- (b)D is third to the left of E
- (c)B is to the right of E
- (d)A is second to the left of C

**Hint**

Analyze the seating arrangement. Where B is in between A and E and C and D are at end position.

**Solution:**

According to the question, the arrangement in the row is

So, D is third left of E.

- (a)A is first
- (b)B is first
- (c)F is sixth
- (d)F is seventh

**Hint**

Analyze the final seating arrangement. Where F is in between C and G.

**Solution:**

According to the question, the arrangement in the row will be:

E/BB/EADCFGSo, F is sixth in arrangement.

- (a)1
- (b)3
- (c)4
- (d)5

**Hint**

Rotate the dices clock-wise to find the opposite number.

**Solution:**

By combining both dice and rotating them clock wise direction.

1 is opposite to number 6

2 is opposite to number 3

4 is opposite to number 5.

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- (a)$10$
- (b)$12$
- (c)$20$
- (d)$15$

**Hint**

The formula for quotient is $\frac{Dividend}{Divisor}=Quotient$

**Solution:**

According to the question, divisor taken by Amit is $12$

The correct divisor is $21$.

Hence, the product of divisor and quotient is $35\times 12=420$

Therefore, the required correct quotient is $\frac{420}{21}=20$.

- (a)$7$
- (b)$8$
- (c)$12$
- (d)$9$

**Hint**

The difference in the value both odd and even consecutive number is given as $\pm 2$

**Solution:**

According to the question, the sum of three consecutive number is more than the first number.

Let the odd numbers are $a,\left(a+2\right),\left(a+4\right)$

The equation formed is:

$a+\left(a+2\right)+\left(a+4\right)=a+20$

$2a+6=20$

$a=7$

Placing the value of $a$ in middle number $\left(a+2\right)$ we get

$a+2=7+2=9$

- (a)$5050$
- (b)$500500$
- (c)$550000$
- (d)$55000$

**Hint**

The formula for even number finite series is $\frac{n\left(n+1\right)}{2}$

**Solution:**

According of the number series

$n\frac{\left(n+1\right)}{2}=1+2+3+4+...+n$

Hence placing the value of $n=1000$ in the series formula of $n\frac{\left(n+1\right)}{2}$, we get the sum of the series as:

$n\frac{\left(n+1\right)}{2}=1000\times \frac{1001}{2}=500500$

- (a)$5$
- (b)$6$
- (c)$7$
- (d)$8$

**Hint**

The formula for unknown two digit number (let's say $xy$) expansion is $10x+y$

**Solution:**

The two-digit numbers are given as $\left(10x+y\right)$

$\Rightarrow \left(10x+y\right)-\left(10y+x\right)=63$

$\Rightarrow 9x-9y=63\Rightarrow 9(x-y)=63$

Therefore, the difference in the digit is given as:

$\Rightarrow \left(x-y\right)=\frac{63}{9}=7$

- (a)$9$
- (b)$36$
- (c)$18$
- (d)$72$

**Hint**

The product of two unknown '$n$' digit numbers can be found by expansion of ${\left(a-b\right)}^{n}-{\left(a+b\right)}^{n}=0$

**Solution:**

Let the two digits taken are $x$ and $y$

The sum of the digits are $x+y=9$

The difference of the digits are $x-y=3$

Let the two-digit numbers are $\left(10x+y\right)$

Now forming equation to find the value of the digit of the numbers

${\left(x+y\right)}^{2}={\left(x-y\right)}^{2}+4xy$

$\Rightarrow {9}^{2}={3}^{2}+4xy$

$\Rightarrow 4xy=81-9=72$

$\Rightarrow xy=\frac{72}{4}=18$

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- (a)$3$
- (b)$4$
- (c)$1$
- (d)$2$

**Hint**

Use the formula and simplify the question.

${\left(a+b\right)}^{2}={a}^{2}+{b}^{2}+2ab$

**Solution:**

According to the given question,

$\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$

Simplifying the roots, we get

$=\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}\phantom{\rule{0ex}{0ex}}=\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{4+3+2\times 2\sqrt{3}}}}\phantom{\rule{0ex}{0ex}}=\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{{2}^{2}+{\left(\sqrt{3}\right)}^{2}+2\times 2\sqrt{3}}}}\phantom{\rule{0ex}{0ex}}=\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{{\left(2+\sqrt{3}\right)}^{2}}}}\phantom{\rule{0ex}{0ex}}=\sqrt{-\sqrt{3}+\sqrt{3+8\left(2+\sqrt{3}\right)}}$

Here,

$=3+8\left(2+\sqrt{3}\right)\phantom{\rule{0ex}{0ex}}=3+16+8\sqrt{3}\phantom{\rule{0ex}{0ex}}{\left(a+b\right)}^{2}={a}^{2}+{b}^{2}+2ab\phantom{\rule{0ex}{0ex}}a=\sqrt{3}b=4$

$=\sqrt{-\sqrt{3}+4+\sqrt{3}}\phantom{\rule{0ex}{0ex}}=\sqrt{4}\phantom{\rule{0ex}{0ex}}=2$

- (a)$\frac{5}{9}$
- (b)$1-\frac{1}{7}$
- (c)$\frac{4}{7}$
- (d)$1-\frac{2}{7}$

**Hint**

To find the fraction value of any number subtracted by $1$ is $=1-\frac{1}{x}=\frac{\left(x-1\right)}{x}$

**Solution:**

Solving the problem given, we first solve the fraction inside the cube root.

$\sqrt[3]{1-\frac{127}{343}}$

$\sqrt[3]{1-\frac{127}{343}}$

$\sqrt[3]{\frac{343-127}{343}}$

$\sqrt[3]{\frac{216}{343}}=\frac{6}{7}=1-\frac{1}{7}$

Hence, the correct answer is $=1-\frac{1}{7}$

- (a)$9.7$
- (b)$9.97$
- (c)$9.997$
- (d)$9.9997$

**Hint**

To find the cube root of the number, first find the factors to the number.

**Solution:**

Simplifying the square roots we get

$\sqrt[3]{1000}+\sqrt[3]{0.008}-\sqrt[3]{0.125}$

$=\sqrt[3]{10\times 10\times 10}+\sqrt[3]{0.2\times 0.2\times 0.2}-\sqrt[3]{0.5\times 0.5\times 0.5}$

$=10+0.2-0.5=9.7$

- (a)$63$
- (b)$61$
- (c)$65$
- (d)$64$

**Hint**

To find the square of any number add the last digit of the number to the number to be squared and attach the last digit's square at the end of the number to be squared.

**Solution:**

Simplifying the given equation,

We get,

$\sqrt{1+\frac{x}{961}}=\frac{32}{31}$

$1+\frac{x}{961}=\frac{1024}{961}$

$\frac{x}{961}=\frac{1024}{961}-1$

$x=1024-961=63$

- (a)$24$
- (b)$2.4$
- (c)$0.024$
- (d)$1.2$

**Hint**

Simplify the decimal number into whole number and then find the square root of the question.

**Solution:**

First let us simplify the equation we get

$\frac{0.324\times 0.081\times 4.624}{1.5625\times 0.0289\times 72.9\times 64}$

$\frac{324\times 81\times 4624}{15625\times 289\times 729\times 64}=\frac{9}{15625}$

Hence, the square root of the value $\sqrt{\frac{9}{15625}}=\frac{3}{125}=0.024$

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- (a)$1$
- (b)${x}^{abc}$
- (c)${x}^{a+b+c}$
- (d)${x}^{bc+ca+ab}$

**Hint**

When solving question related to powers or exponent first form common bases to as to simplify the powers easily

**Solution:**

According to the question given, we first simplify the question.

Multiply the powers of the equation

${x}^{\left(b-c\right)\left(b+c-a\right)}.{x}^{\left(c-a\right)\left(c+a-b\right)}.{x}^{\left(a-b\right)\left(a+b-c\right)}$

Equating the power we get

${x}^{\left({b}^{2}-{c}^{2}+{c}^{2}-{a}^{2}+{a}^{2}-{b}^{2}\right)}.{x}^{-a\left(b-c\right)-b\left(c-a\right)-c\left(a-b\right)}$

${x}^{0}.{x}^{0}=1\times 1=1$

Hence, the correct answer is $1$.

- (a)$0$
- (b)$1$
- (c)${x}^{a-b-c}$
- (d)None of these

**Hint**

In case of when power is in subtraction its equal to its division form ${x}^{a-b}=\frac{{x}^{a}}{{x}^{b}}$

**Solution:**

Let us simplify the equation by taking LCM of the denominator.

$\frac{1}{1+{x}^{b-a}+{x}^{c-a}}+\frac{1}{1+{x}^{a-b}+{x}^{a-c}}+\frac{1}{1+{x}^{b-c}+{x}^{a-c}}$

$\frac{{x}^{a}}{{x}^{a}+{x}^{b}+{x}^{c}}+\frac{{x}^{b}}{{x}^{a}+{x}^{b}+{x}^{c}}+\frac{{x}^{c}}{{x}^{a}+{x}^{b}+{x}^{c}}$

$\frac{{x}^{a}+{x}^{b}+{x}^{c}}{{x}^{a}+{x}^{b}+{x}^{c}}=1$

- (a)$\frac{5}{11}$
- (b)$\frac{11}{5}$
- (c)$\frac{11}{3}$
- (d)$\frac{13}{5}$

**Hint**

When value with power are equated first step is to form common bases on both sides for example:-

$9={3}^{x}\phantom{\rule{0ex}{0ex}}{3}^{2}={3}^{x},\left(3=3\right)$

**Solution:**

Simplifying the equation by getting same bases on both sides, we get

${5}^{x+3}={25}^{3x-4}$

${5}^{x+3}={5}^{2\left(3x-4\right)}$

Equating the power of the number $5$ we get

$x+3=6x-8$

$11=5x$

$x=\frac{11}{5}$

- (a)$0$
- (b)$2$
- (c)$3$
- (d)$4$

**Hint**

When solving power or exponent problem of same multiple but different power first have common bases.

${3}^{n}\times {9}^{m}=27\phantom{\rule{0ex}{0ex}}{3}^{n}\times {3}^{2m}={3}^{3},(3\times 3=3)\phantom{\rule{0ex}{0ex}}$

**Solution:**

On Simplifying the equation we get,

$\frac{{9}^{n}\times {3}^{5}\times {27}^{3}}{3\times {81}^{4}}=27$

${9}^{n}\times {3}^{5}\times {27}^{3}=27\times 3\times {81}^{4}$

${9}^{n}\times {3}^{4}\times {27}^{2}={81}^{4}$

${9}^{n}=\frac{{81}^{4}}{{3}^{4}\times {27}^{2}}$

${9}^{n}=\frac{{\left({3}^{4}\right)}^{4}}{{3}^{4}\times {\left({3}^{3}\right)}^{2}}$

${9}^{n}={9}^{3}$

$n=3$

Hence, the value of $n=3$

- (a)$abc$
- (b)$\sqrt{abc}$
- (c)$\frac{1}{abc}$
- (d)$1$

**Hint**

When multiplying square roots of unknown value it transforms into one unit example $\sqrt{c}\sqrt{b}=\sqrt{cb}$

**Solution:**

Placing the given instruction, we find the product of $\sqrt{{a}^{-1}b}.\sqrt{{b}^{-1}c.}\sqrt{{c}^{-1}a}$

$\sqrt{{a}^{-1}b.{b}^{-1}c.{c}^{-1}a}$

$\sqrt{\frac{1}{a}\times b\times \frac{1}{b}\times c\times \frac{1}{c}\times a}$

$\sqrt{1}=1$

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- (a)$246$
- (b)$182$
- (c)$234$
- (d)$256$

**Hint**

The series has a gap of $+\left(n\times 13\right)$

**Solution:**

The pattern in the series is given as:

$39+\left(1\times 13\right)=52$

$52+\left(2\times 13\right)=78$

$78+\left(3\times 13\right)=117$

$117+\left(4\times 13\right)=169$

$169+\left(5\times 13\right)=234$

Hence, the missing number is $234$

- (a)$12$
- (b)$24$
- (c)$46$
- (d)$70$

**Hint**

The series is formed by decreasing prime numbers from previous terms.

**Solution:**

The given pattern in the series is:

$142-23=119$

$119-19=100$

$100-17=83$

$83-13=70$

$70-11=59$

$59-7=52$

Hence, according to the series, the value $70$ should be placed in place of $60$

- (a)$2$
- (b)$4$
- (c)$6$
- (d)$12$

**Hint**

The series is added by $3$

**Solution:**

The pattern in the series is given as:

$2\times 3=6$

$6\times 3=18$

$18\times 3=54$

$54\times 3=162$

$162\times 3=486$

$486\times 3=1458$

The value $10$ should be replaced by $6$

Hence, the wrong number is $10$

- (a)$70$
- (b)$65$
- (c)$60$
- (d)$75$

**Hint**

The series is formed by adding ${n}^{2},n\in 1,2,3,.....$ with each value

**Solution:**

The given series pattern is written as:

$20+{1}^{2}=21$

$21+{2}^{2}=25$

$25+{3}^{2}=34$

$34+{4}^{2}=50$

$50+{5}^{2}=\left[75\right]$

$75+{6}^{2}=111$

Hence, the missing number is $75$

- (a)$178$
- (b)$96$
- (c)$109$
- (d)$124$

**Hint**

The series has a gap pattern of $\left(+{\mathrm{n}}^{2}\right)$, where n is an even number.

**Solution:**

Given series:

$4,8,24,60,?,224$

The pattern followed in the given series is shown below:$4+{2}^{2}=8$

$8+{4}^{2}=24$

$24+{6}^{2}=60$

$60+{8}^{2}=124$

$124+{10}^{2}=224$

So, the missing number will be $124$.

Hence, the correct answer is $124.$

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- (a)