SSC CHSL Previous Paper 31 (Held On: 21 Oct 2020 Shift 1) (Previous Year Paper)

The correct answer is Complacent.

Key Points

• Let's look at the meaning of the marked option:
• Complacent- showing smug or uncritical satisfaction with oneself or one's achievements
• Let's look at the meanings of the other given options: 
• Beneficent- (of a person) generous or doing good
• Innocent- not guilty of a crime or offense
• Adolescent- (of a young person) in the process of developing from a child into an adult
• Hence, from the given meanings, we find that Complacent is the correct one-word substitute.

The correct answer is To wait before making a decision.

Key Points

• Let's look at the meaning of the given idiom:
• Sleep on it- delay making a decision on something until the following day
• Example: 
• Don’t give me an answer now – sleep on it and tell me whenever you’re ready.
• ​Thus from the explanation given above, we find that the 4^th option is the correct choice.

 ​​​​

Additional Information  

• Let's look at the origin of the idiom:
• It is not known where this idiom originated from but people often believe that if they do not have the solution to a problem straight away, good sleep will help.

The correct answer is Deceitful.

Key Points

• Let's look at the meanings of the given word and marked option:
• Fraudulent (कपटी)- obtained, done by, or involving deception, especially criminal deception
• Deceitful (भ्रमकारी)- guilty of or involving deceit; deceiving or misleading others
• ​​​Let's look at the meanings of the other given options: 
• Repellent (प्रतिकर्षी)- able to repel a particular thing; impervious to a particular substance
• Prevalent (प्रचलित)- widespread in a particular area or at a particular time
• Genuine (असली)- truly what something is said to be; authentic
• Hence from the given meanings, we find that Fraudulent and Deceitful are synonyms.

The correct answer is pull away.

Key Points

• Let's look at the meanings of the given options: 
• look into- to try to discover the facts about something such as a problem or a crime
• sit in- attend a meeting or discussion without taking an active part in it
• pull away- to draw oneself back or away
• put off- postpone something
• As per the context of the sentence, the subject had to draw himself away from his family sometimes because of work pressures.
• Hence, from the given meanings, we find that the 3^rd option i.e. pull away is the correct choice.

​Correct Sentence: My family is my priority but there were times when I had to pull away because of work pressures.

The correct answer is dialogues.

Key Points

• Let's look at the meanings of the given options:- 
• prologue- a separate introductory section of a literary or musical work. (एक साहित्यिक या संगीत कार्य का एक अलग परिचयात्मक खंड)
• epilogue- a section or speech at the end of a book or play that serves as a comment on or a conclusion to what has happened. (किसी पुस्तक या नाटक के अंत में एक खंड या भाषण जो उस पर टिप्पणी या निष्कर्ष के रूप में कार्य करता है कि क्या हुआ है)
• monologues- a long speech by one actor in a play or movie, or as part of a theatrical or broadcast program. (एक नाटक या फिल्म में या एक नाटकीय या प्रसारण कार्यक्रम के हिस्से के रूप में एक अभिनेता द्वारा एक लंबा भाषण)
• dialogues- a conversation between two or more people as a feature of a book, play, or movie. (एक किताब, नाटक या फिल्म की विशेषता के रूप में दो या दो से अधिक लोगों के बीच बातचीत।)
• ​As per the possible context of the sentence, the above-mentioned novel contained conversations in simple language.
• Hence, from the given meanings, we find that the 4^th option i.e. dialogues is the correct choice in the 5^th blank.

The correct answer is- to read.

Key Points​

• There are some verbs/nouns/adjectives which are followed by fixed preposition given below:
• ​Exonerate from, refrain from, accused of, able to do something, aptitude for, inured to, accused of, predilection for, respite from, vexed at, etc.
• Example:
• ​After spending some time on the island, they were able to explore it properly.​
• ​Hence, according to the phrases given above, 'to read' will be the correct choice as the 4^th blank is preceded by 'able'.
• The given phrase 'able to do something' means having the power, skill, means, or opportunity to do something.

The correct answer is attractive.

Key Points​

• Let's look at the meanings of the given nouns: 
• attraction (noun)- the action or power of evoking interest, pleasure, or liking for someone or something.
• attract (verb)- cause to come to a place or participate in a venture by offering something of interest, favorable conditions, or opportunities.
• attractive (adjective)- (of a thing) pleasing or appealing to the senses.
• ​Thus the blank must contain an adjective which qualifies the noun 'book cover'.
• Hence, from the given meanings, we find that the 3^rd option i.e. attractive is the correct choice in the 3^rd blank.

The correct answer is picked up.

Key Points

• Let's look at the meanings of the given options:- 
• Pick up- to buy or get something.
• Pick on- to bully or to single one person out.
• Pick at- to irritate, to bother.
• ​As per the possible context of the sentence, the subject bought the book as the book cover was fascinating.
• Hence, from the given meanings, we find that the 2^nd option i.e. picked up is the correct choice in the 2^nd blank.

The correct answer is local.

Key Points​

• Let's look at the meanings of the given nouns:- 
• local (adjective)- belonging or relating to a particular area or neighborhood.
• location (noun)- a particular place or position.
• localize (verb)- restrict (something) to a particular place or part of the body.
• locals (noun)- an inhabitant of a particular area or neighborhood.
• The given blank is succeeded by a noun i.e. bookshop.
• Thus the blank must contain an adjective which qualifies the noun 'bookshop'.
• Hence, from the given meanings, we find that the 1^st option i.e. local is the correct choice in the 1^st blank.

The correct answer is a bit longer​.

Key Points

• The three words—good, better, and best—are examples of the three forms of an adjective or adverb: positive, comparative, and superlative.
• The positive form of an adjective or adverb is the basic form listed in a dictionary.
• The comparative form (followed by 'than') is used when there is a comparison between two or more things.
• The superlative form is used for a thing which is better than any other of the same category.
• Example:
• She is a good Cricketer.
• Rohit is a better human being than his brother.
• He is the best singer in our class.
• Since there is a comparison (as suggested by the usage of the word 'than') being made in the given question, the comparative form of the given adjective i.e. longer must be used.
• As the required structure is followed in the given question, the 4^th option will be the correct choice.

Correct Sentence: The film by itself was good but a bit longer than I had expected.

The correct answer is CDAB.

Key Points

• While arranging the parts of the passage, we should find some grammatical or contextual connections between them:
• Sentence C introduces us to the movie 'Aani Maani'. It is the introductory sentence and will be put in the first place.
• Sentence D tells us about the origin of the title of the above-mentioned movie. It will be put in second place.
• Sentence A tells us further about the game and how it is played. It will be put in third place.
• The last sentence is B as it mentions the comparison made with Sufi dervish.

Thus, the correct order is - Fahim Irshad has made a film called ‘Aani Maani’. The movie title is based on a game popular among little children in Uttar Pradesh. It is played by turning around while reciting a rhyme. The circling motion is like that of a Sufi dervish.

The correct answer is Gloomy.

Key Points

• Let's look at the meanings of the given word and marked option:
• Buoyant- cheerful and optimistic (हंसमुख और आशावादी)
• Gloomy- feeling distressed or pessimistic (व्यथित या निराशावादी महसूस करना)
• ​​Let's look at the meanings of the other given options: 
• Cheerful- noticeably happy and optimistic (उल्लेखनीय रूप से खुश और आशावादी)
• Neutral- not helping or supporting either side in a conflict, disagreement (संघर्ष, असहमति में किसी भी पक्ष की मदद या समर्थन नहीं करना)
• Bouncy- bouncing or causing things to bounce ( )
• Hence from the given meanings, we find that Buoyant and Gloomy are antonyms.

The correct answer is The researcher said that it is a fact that kids model parental behaviour.

Key Points

• Let's look at the steps to change the sentence from direct to indirect speech:
• When the direct speech is in an assertive form, we follow the steps given below:
• The reporting verb said will remain the same.
• Connector 'that' is used in place of comma and inverted commas.
• In the case of a general truth or universal fact (general truth in this case), there will be no change in the tense of reported speech.
• At last line up the remaining part.

​

Following these steps, we finally get - The researcher said that it is a fact that kids model parental behaviour.

Additional Information  ​​​​

• In the case of a permanent state or condition, there will be no change in the tense of reported speech.

The correct answer is Deterent.

Key Points

• Let's look at the correct spelling and meaning of the marked option:
• Deterrent- a thing that discourages or is intended to discourage someone from doing something
• Example: 
• Some people say that capital punishment acts as a deterrent.​

Let's look at the meanings of the other given options:

• Irreverent- not feeling or showing respect
• Different- not the same as another or each other; unlike in nature, form, or quality
• Transparent- (of a material or article) allowing light to pass through so that objects behind can be distinctly seen

The correct answer is Complement.

Key Points

• Let's look at the meaning of the marked option:
• Complement- a thing that completes or brings to perfection
• Let's look at the meanings of the other given options: 
• Attainment- the action or fact of achieving a goal toward which one has worked
• Impediment- a hindrance or obstruction in doing something
• Deportment- a person's behavior or manners
• Hence, from the given meanings, we find that Complement is the correct one-word substitute.

The correct answer is who commuting long distances​.

Key Points

• The simple present tense is used when an action is happening right now, to state or ask about things in general, or when it happens regularly or unceasingly.
• The structure is given below:
• Subject + V1 + object.
• The verb will take 's/es' if the given noun/pronoun (3^rd person) is singular.
• Example:
• ​He plays badminton daily.​
• Since a regular action is being talked about in the question, 'commute' will replace 'commuting' in the part given in the 4^th option.

Correct Sentence: People with full-time sedentary jobs who commute long distances, may have sleep problems due to lack of exercise.

Additional Information

• Certain verbs used only in the simple present tense are given below:
• ​verbs of perception (see, hear, smell, etc.), think, know, has/have, possess, like, want, desire, hate, seem, imagine, etc.
• Example:
• ​My brother is owning a car. (incorrect)
• ​My brother owns a car. (correct)

The correct answer is Invincible.

Key Points

• Let's look at the meanings of the given word and marked option:
• Indomitable- impossible to subdue or defeat
• Invincible- too powerful to be defeated or overcome
• ​​​Let's look at the meanings of the other given options: 
• Justifiable- able to be shown to be right or reasonable; defensible
• Changeable- able to change or be changed
• Accessible- (of a place) able to be reached or entered
• Hence from the given meanings, we find that Indomitable and Invincible are synonyms.

The correct answer is To remain cool.

Key Points

• Let's look at the meaning of the given idiom:
• Keep your shirt on- said to tell someone to stop being so angry or upset
• Example: 
• Keep your shirt on! Your car isn't even scratched!
• ​Thus from the explanation given above, we find that the 2^nd option is the correct choice.

 ​​​​

Additional Information  

• Let's look at the origin of the idiom:
• This idiom originated in America in the 1800s. At that time, clothes were expensive and men often only owned one or two shirts.
• Therefore, they would remove their shirt before getting into a fight to stop it from getting ruined.

The correct answer is Kind.

Key Points

• Let's look at the meanings of the given word and marked option:-
• Caustic- sarcastic in a scathing and bitter way.
• Kind- having or showing a friendly, generous, and considerate nature.
• ​​Let's look at the meanings of the other given options: -
• Scary- frightening.
• Sarcastic- marked by or given to using irony in order to mock or convey contempt.
• Bitter- painful or unpleasant to accept or contemplate.
• Hence from the given meanings, we find that Caustic and Kind are antonyms.

The correct answer is CBDA.

Key Points

• While arranging the parts of the passage, we should find some grammatical or contextual connections between them:
• Sentence C introduces us to the subject 'Vinay Pathak'. It is the introductory sentence and will be put in the first place.
• Sentence B tells us about the play 'Equus'. It will be put in second place.
• Sentence D tells us the effect the above-mentioned play had on the subject. It will be put in third place.
• The last sentence is A as it mentions the career chosen by the subject.

Thus, the correct order is- Vinay Pathak was pursuing MBA in New York. While studying there, he saw ‘Equus,’ a play that changed his life forever. He decided to change tracks and study drama. Since then, Pathak has performed in several plays and films.

The correct answer is a longest and healthy life​.

Key Points

• The three words—good, better, and best—are examples of the three forms of an adjective or adverb: positive, comparative, and superlative.
• The positive form of an adjective or adverb is the basic form listed in a dictionary.
• The comparative form is used when there is a comparison between two or more things.
• The superlative form is used for a thing that is better than any other of the same category.
• Example:
• She is a good Cricketer.
• Rohit is a better human being than his brother.
• He is the best singer in our class.
• Since there is no comparison whatsoever made in the given question, 'long' will be used instead of 'longest' in the 2^nd part.

Correct Sentence: According to a recent study, drinking green tea thrice a week is associated with a long and healthy life.

Additional Information

• Whenever we see the structure like 'as....as' and 'so....as', we will use a positive degree of adjective/adverb.

• For example:

• The thief ran as faster as he could.

• The thief ran as fast as he could.

The correct answer is Circueteous.

Key Points

• Let's look at the correct spelling and meaning of the marked option:
• Circuitous- (of a route or journey) longer than the most direct way
• Example: 
• The canal followed a circuitous route.

Let's look at the meanings of the other given options:

• Delicious- highly pleasant to the taste
• Momentous- (of a decision, event, or change) of great importance or significance, especially in its bearing on the future
• Courteous- polite, respectful, or considerate in manner

The correct answer is sustained.

Key Points

• Let's look at the meanings of the given options:- 
• sustained- strengthen or support physically or mentally.
• ordained- make (someone) a priest or minister; confer holy orders on.
• maintained- cause or enable (a condition or state of affairs) to continue.
• pertained- be appropriate, related, or applicable.
• As per the context of the sentence, a team of doctors operated on an injury sustained by the subject who is a 12-year-old archer.
• Hence, from the given meanings, we find that the 1^st option i.e. sustained is the correct choice.

​Correct Sentence: Shivangini, the 12-year-old archer who sustained an injury has been successfully operated on by a team of doctors at A.I.I.M.S.

The correct answer is Patients were advised to try out a new medicine for migraine by Dr. Verma.

Key Points

• The given sentence is in an active voice form, hence we need to convert it into a passive voice form.
• Find the subject (Dr. Verma) and object (Patients) of the sentence and exchange their places.
• The given sentence is in the simple past tense. The passive verb form for simple past is: 
• was/were + past participle form of the verb.
• So, 'advised' changes to 'were advised'.
• At last line up the remaining part.

​

Following these steps, we get - Patients were advised to try out a new medicine for migraine by Dr. Verma.

The correct answer is where​.

Key Points​​

• ​The pronoun that connect a clause or phrase to a noun or a pronoun, is called a relative pronoun.
• The most common relative pronouns are:
• who, whom, whose, where, which, that.
• Example:
• We don’t know the person who donated this money.
• You need to tick the box which says yes.​
• ​We use 'who' in relative clauses to refer to people, and sometimes to pet animals. (refer to the above example)
• We use 'which' in relative clauses to refer to animals and things, to introduce defining and non-defining relative clauses.
• We use 'where' to find out the place or position.
• ​As 'place' is being talked about in the question, 'where' will be used in the underlined part of the sentence.

​Correct Sentence: I like the place where I live but it would be wonderful to live in the mountains.

​​​

Additional Information  ​​

• ​We use the objective case of pronoun after all the prepositions.
• Example:
• I believe in him. (Him-Objective case of 'He')

Except for DHLN, in all other set of letters, a letter is the fourth successor of the previous letter as per the English alphabetical series as shown below:

In the case of DHLN, 

Hence, DHLN is difference from the others.

6 × 6 × 7 = 252

Similarly,

5 × 5 × 6 = 150

Hence, 150 is related to 5 the same way 252 is related to 6.

Alternate Method

6² + 6³ = 36 + 216 = 252

Similarly,

5² + 5³ = 25 + 125 = 150

The given series: BK, FJ, JI, NH, ?, VF

Clearly, RG will come in place of the question mark to complete the series.

The given figure:

As shown in the image below, the second image is hidden in the given figure:

Hence, the second figure is hidden in the given image.

Rectangle: A rectangle is a four-sided figure or shape and all angles should be right angle.

Square: A square, there are 4 sides and all the four angles are right angles.

Right Angle:** A right angle is an angle of exactly 90°, The angle bounded by two lines perpendicular to each other.

A square is a special type of rectangle because it possesses all the properties of a rectangle. Similar to a rectangle, a square has:

• Opposite sides that are parallel and equal.
• Two diagonals that bisect each other and are equal.

Thus, a square is a rectangle.

The given figure:

The rectangles in the figure: 1, 2, 3, 4, 5, (1, 2)

Hence, there are 6 rectangles in the figure.

Additional Information

Squares are a subset of rectangles, hence, all squares are also rectangles.

The given figure: 

The triangle in the middle is rotated by 90 degrees in the clockwise direction, also, the position of the four shapes at the corners are interchanged diagonally with respect to the previous figure each time. Thus, in the next figure, the triangle in the middle will be facing the west direction as shown below.

Hence, the fourth figure is the answer figure.

The given series: 386, 401, 417, 434, ?

Hence, the next term in the series is 452.

The logic follows here is:

In rows:

(3^rd number ÷ 1^st number) + (1^st number - 1) = middle number

In 1^st row,

(18 ÷ 2) + (2 - 1) = 9 + 1 = 10

In 2^rd row,

(84 ÷ 3) + (3 - 1) = 28 + 2 = 30

In 3^rd row,

(? ÷ 4) + (4 - 1) = 68

? ÷ 4 = 68 - 3  = 65

? = 65 × 4 = 260

Hence, "260" is the correct answer.

The least possible Venn Diagram for the given data:

Conclusions:

1. No printer is keyboard → it is possible but not definite, hence false.

2. Some printers are mouse → true

3. All printers are mouse → it is possible but not definite, hence false.

4. No keyboards are printer → it is possible but not definite, hence false.

Hence, only conclusion 2 follows.

The family tree diagram for the given data:

Clearly, Rohit is the son-in-law of Vijay.

The given figure: 

If we place a mirror to the right of the image then in the reflection, the shapes will be rotated by 180 degrees on their vertical axis and the resultant will look like the image below:

Hence, the third figure is the reflection of the given figure.

• When an equal digit is on an equal surface, the remaining equal surface is opposite each other.
• When no common numbers/symbols in 2 dices, the equal surface is opposite to each other

The given position of the dice:

In the second and the third figure, 'e', 'd', 'g', and 'h' are adjacent to 'f'. Thus, 'a' must be opposite 'f' as it is the only left.

Hence, 'a' is opposite 'f'.

In the First Dice and Second dice, 

Number d is common.

The left letter will be opposite to each other writing them clockwise starting from d.

Hence, the correct answer is "a".

• Dices are of two types :

1. Standard Dice
2. Non-Standard Dice.

• Dice has:-

1. faces = 6
2. sides = 12
3. corners = 8

• Two opposite faces are never seen together.
• Adjacent faces are never opposite to each other.

The given series: EB, HC, KD, NE, QF, ?

Clearly, TG will be the next term in the series.

We first sow the seeds then the wheat plants come out from which we get wheat which finally gives us bread or 'roti'.

Hence, the logical order is 3, 1, 4, 2.

As shown below, except for 309 : 17, in all other pairs, the first number is the product of the second number and its successor.

13 ×14 = 182

12 × 13 = 156

11 × 12 = 132

17 × 18 = 306

Hence, 309 : 17 is different from the other three.

Shoes are made from leather, similarly, paper is made from wood.

Hence, 'wood' is related to 'paper' the same way 'leather' is related to 'shoe'.

The given figure:

When we will unfold the paper for the first time, we will get a rhombus and a circle. When we will unfold it for the second time, we will get two circles and two rhombus as shown below.

Hence, the fourth figure is the answer figure.

The given series: 0, 2, 10, 30,?, 130, 222

0³ + 0 = 0

1³ + 1 = 2

2³ + 2 = 10

3³ + 3 = 30

4³ + 4 = 68    

5³ + 5 = 130

6³ + 6 = 222 ​ 

Hence, 68 is the missing term.

Except for Peas, all other vegetable grow underground.

Hence, 'Peas' is different from the other three.

The given series:

Logic: Row → First number + 3 = Second Number × 4 = Third number

9 + 3 = 12 → 12 × 4 = 48

17 + 3 = 20 → 20 × 4 = 80

33 + 3 = 36 → 36 × 4 = 144

Hence, 144 is the missing term.

The given equation: 5 × 4 + 12 - 3 ÷ 6 = 18

On interchanging + and -, we get:

5 × 4 - 12 + 3 ÷ 6 = 18

⇒ 8 + 0.5 = 18 (false)

On interchanging ÷ and ×, we get:

5 ÷ 4 + 12 - 3 × 6 = 18

⇒ 1.25 - 6 = 18 (false)

On interchanging × and +, we get:

5 + 4 × 12 - 3 ÷ 6 = 18

⇒ 5 + 48 - 0.5 = 18 (false)

On interchanging ÷ and -, we get:

5 × 4 + 12 ÷ 3 - 6 = 18

⇒ 20 + 4 - 6 = 18

⇒ 18 = 18

Hence, we need to interchange ÷ and - to make the situation correct.

The given series: AG, GL, MQ, S?, ?A

Clearly, V and Y will replace the question marks.

Devanagari is a script while Hindi and Sanskrit are languages which are written in Devanagari script. 

Hence, the second Venn Diagram best represents the relationship between Devanagari, Hindi and Sanskrit.

Except for Pascal, all others are the units of temperature. Pascal is the unit of pressure.

Hence, 'Pascal' is different from the others.

Employees in the IT department = 125

Employees in the HR department = 125 ÷ 5 = 25

Employees in the Helpdesk department = 125 + 25 - 20 = 130

Total number of employees in the company = 125 + 25 + 130 = 280

Hence, there are 280 employees in the company.

Given 

x = $\sqrt[3]{5} + 2$

Formula Used

(a + b)³ = a³ + b³ + 3a²b + 3ab²

Calculation

⇒ x = ∛5 + 2 

⇒ x - 2 = ∛5  

⇒ (x- 2)³ = (∛5)³ 

⇒ x³ - 6x² + 12x - 8 = 5

⇒ x³ - 6x² + 12x - 13 = 0 

⇒ x3 - 6x2 + 12x - 13 + 1 = 1

⇒ x3 - 6x2 + 12x - 12 = 1  

∴ The answer is 1.

From Pie chart,

⇒ English teacher = 26% of total number of teacher 

⇒ (26/100) × 1650 = 429

⇒ Maths teacher = 14% of total number of teacher 

⇒ (14/100) × 1650 = 231

⇒ Physics teacher = 18% of total number of teacher 

⇒ (18/100) × 1650 = 297

⇒ Total number of teacher of English, Maths and Physics = 429 + 231 + 297 = 957

∴ Total number of teachers teaching English, Maths and Physics is 957

Given

AB= 7 cm 

AC = 25 cm

Concept Used 

we know the triplet of the right angle triangle 

Calculation 

⇒ we know the some triplet of right angle triangle are 

⇒ (3,4,5), (6, 8, 10) , (5, 12, 13), (7, 24, 25) 

⇒ In Question , we have already two side of triangle i.e. 7 and 25

⇒ so, third side is 24 cm 

∴ the length of BC is 24 cm

Given 

Number = 4432A43B

Concept used 

divisibility rule of 9 = sum of all digit should be divisible by 9, then whole number will be divide by 9 

divisibility rule of 5 = unit digit should be 0 and 5 , whole number will be divide by 5

Calculation 

⇒ according to rule of divisibility of 5 , then B = 0 or 5 

⇒ sum of digit when B = 0, sum = 4 + 4 + 3 + 2 + A + 4 + 3 + 0 = 20 + A

⇒ sum of digit , when B = 5 , sum = 4 + 4 + 3 + 2 + A + 4 + 3 + 5 = 25 + A

⇒ we need sum of digit is 27 to divide by 9 

⇒ so, sum A and B = 7

Given

Train cover distance in 2 minutes = 2 km 

Formula Used 

Speed = Distance/time 

Calculation 

⇒ Actual speed of train = (2/2) × 60 = 60 km/hr 

⇒ Speed of train decreases by = 5 km/hr

⇒ Now speed of train = 55 km/hr 

⇒ Time taken by train to cover 22 km = (22/55) × 60 = 24 minutes 

∴ Time taken by train to cover 22 km is 24 minutes

Given 

$\frac{sin θ + cosθ}{sin θ - cosθ}=3$

Calculation 

⇒ $\frac{sin θ + cosθ}{sin θ - cosθ}=3$

⇒ By using componendo and dividendo 

⇒ 2 sinθ /2 cosθ = 4/2 

⇒ sin θ /cosθ = 2

⇒ so sinθ : cosθ = 2 : 1 

⇒ $\frac{3sin \theta + 4 cos \theta }{8cos \theta - 3 sin \theta }$ = {3(2) + 4}/{8(1) - 3(2)} 

⇒ 10/2 = 5 

∴ the value of $\frac{3sin \theta + 4 cos \theta }{8cos \theta - 3 sin \theta }$ is 5

Given 

The ratio of present age A and B = 1 : 3 

Calculation 

Let the present age of A and B be x and 3x 

After 10 years 

⇒ (x + 10)/(3x + 10) = 2/5 

⇒ 5x + 50 = 6x + 20 

⇒ x = 30 

⇒ Present age of B = 3 × 30 = 90 

∴ the present age of B is 90 years

Given 

A can do work = 15 days 

B can do work = 10 days 

Formula

Work = time × Efficiency 

Calculation 

⇒  Take LCM of (10,15) = 30 

⇒ Let the total work be 30 

⇒ Efficiency of A = 30/15 = 2 

⇒ Efficiency of B = 30/10 = 3 

⇒ A and B can do work in 4 days = 5 × 4 = 20

⇒ Remaining work = 30 - 20 = 10 

⇒ Fraction of the left work = 10/30 = 1/3 

∴ The fraction of the remaining work is 1/3

Given 

$x(5 - \frac{2}{x}) = \frac{5}{x}$

Formula Used 

If x - 1/x =a 

then $x^2 + \frac{1}{x^2}$ = a² + 2 

Calculation 

⇒ 5x - 2 = 5/x 

⇒ x - 1/x = 2/5 

⇒ then , x² + 1/x² = (2/5)² + 2 

⇒ (4/25) + 2 = 54/25 = $2\frac{4}{25}$

Given 

Perimeter of rectangle = 80 cm 

Area of rectangle = 375 cm²

Formula Used 

Perimeter of rectangle = 2(l + b) 

Area of rectangle = length × breadth 

Calculation 

⇒ Let the length and breadth of rectangle be l and b 

⇒ perimeter = 80 

⇒ 2(l + b) = 80 

⇒ l + b = 40 ----(i)

⇒ area = 375 

⇒ l× b = 375 -----(ii)

⇒ From (i) and (ii) 

⇒ l = 25 , b = 15 

⇒ so difference between the length and breadth = 25 - 15 = 10

Given 

sin 7 x = cos 11x

Calculation 

⇒ If sin A = cos B 

⇒ then A + B = 90° 

⇒ from Question 

⇒ 7x + 11x = 90°  

⇒ x = 5° 

⇒ tan 9x = tan 45° = 1 

∴ the value of tan 9x is 1

Given 

AB = 24 cm 

AC = 7 cm 

Formula Used 

(Hypotnuese)² = (perpendicular)² + (base)²

Calculation 

⇒ we now that tangent makes a right angle with radius 

⇒so, ΔABC is right angle triangle 

⇒ (BC)² = (AB)² + (AC)² 

⇒ BC = √(24² + 7²) 

⇒BC = √625 = 25 

∴ The length of BC is 25 cm

From the Bar Graph

⇒ Birth rate of country A = 20/thousand

⇒ Birth rate of country E = 36/thousand

⇒ Percentage = (birth rate of country E)/(birth rate of country A) × 100 

⇒ Percentage = (36/20) × 100 = 180%

∴ The Birth rate of country E is 180% of birth rate of country A

Given 

The average of A, B and C = 18 years 

The average of C, D and E = 12 years 

Formula Used 

Average = (sum of observation)/(No. of observation)

Calculation 

⇒ Total age of A, B and C = 18 × 3 = 54  -----(i)

⇒ Total age of C, D and E = 12 × 3 = 36  ------(ii)

⇒ E + F = 13 ---(iii)

⇒ E + C = 7 ----(iv)

⇒ from iii and iv 

⇒ F - C = 6 -----(v) 

⇒Adding (i), (ii) and (v) 

⇒ A + B + C + C + D + E + F - C = 54 + 36 + 6 

⇒ A + B + C + D + E + F = 96 

⇒ the average = 96/6 = 16 

∴ the average of A, B, C, D, E and F is 16 years

Given 

$a^2 + \frac{1}{a^2} = 98$

Formula Used 

If a² + 1/a² = b 

then a + 1/a = √(b + 2) 

Calculation 

 ⇒ $a^2 + \frac{1}{a^2} = 98$

⇒ then a + 1/a = √(98 + 2) = √100 = 10 

⇒ a + 1/a = x, then a³ + 1/a³ = x³ - 3x 

⇒ so,  a3 + 1/a3 = 100³ - 3 × 10 = 970

From the pie chart, 

⇒ Number of teacher of chemistry = 24% of total number of teacher  

⇒ (24/100) × 1650 = 396 

⇒ NUmber of teacher of biology = 12% of total number of teacher 

⇒ (12/100) × 1650 = 198 

⇒ Total number of teacher teaching chemistry and biology = 396 + 198 = 594 

∴ the total number of teachers teaching chemistry and biology is 594

Given 

Selling price of article at x% profit = Rs 720 

Selling price of article at (x + 5)% profit = Rs 750 

Formula Used 

Profit % = (profit/cp) × 100 

Profit = sp - cp 

Calculation 

⇒ difference in profit = 5% 

⇒ [(750 - cp)/cp] - [(720 - cp)/cp] = 5/100

⇒ 30/cp = 5/100 

⇒ cp = Rs 600 

⇒ x = (720 - 600)/600 × 100 

⇒ x = 20% 

∴ the value of x is 20

Given 

PT = 10 cm 

PA = 5 cm 

Formula Used 

PT² = AP × PB

(Hypotnuese)² = (Perpendicular)² + (Base)²

Calculation 

⇒ PB = PA + AB = 5 + x 

⇒ 100 = 5 × (5 + x) 

⇒ x = 15 

⇒ PB = 20 

⇒ In ΔPTB is right angle triangle (tangent makes a right angle with diameter of circle) 

⇒  ∠PTB = 90° 

⇒ 20² = 10² + BT²

⇒ BT = 10√3 

⇒ Radius of circle = BT/2 = 5√3 

∴ the radius of circle is 5√3

Given 

Δ ABC is an isosceles triangle

AB = AC = 13 cm 

AD is median , AD = 12 cm 

Formula Used 

(Hypotnuese)² = (perpendicular)² +(Base)²

Median and Altitude is same in isosceles triangle 

Calculation 

Let the length of BC = 2x

⇒ so, BD = CD = x

⇒ AD is altitude also , Δ ADC is right angle triangle 

⇒ AC² = AD² + CD²

⇒ 13² = 12² + x²

⇒ x = 5 

⇒ 2x = 10 

∴ the length of BC is 10 cm

Calculation 

⇒ cos A/(cosec A + 1) + cosA/(cosecA - 1) = 2 

⇒ [cos A(cosec A - 1) + cos A(cosec A + 1)]/[cosec² A - 1] = 2 

⇒ (2 cos A cosec A)/cot² A = 2

⇒ cos A cosec A/(cos²/sin A) = 1 [ cot A = cos A/sin A] 

⇒ tan A = 1 

⇒ tan A = tan 45° 

⇒ A = 45°

Shortcut Trick

The 30% discount on the Marked Price is equivalent to the value of the free pen.

⇒ 30% of Marked Price = ₹60

⇒ 1% of Marked Price = ₹2

Arun pays 100% − 30% = 70% of the Marked Price for the book.

⇒ Amount paid = 70 × 2 = ₹140.

∴ The correct answer is ₹140.

Alternate Method

Given: Discount % = 30%, Discount Value = ₹60 (Value of the free pen).

Formula Used: Selling Price (SP) = Marked Price (MP) − Discount; Discount = (Discount% ÷ 100) × MP.

⇒ Discount = 30% of MP = 60

⇒ (30 ÷ 100) × MP = 60

⇒ MP = (60 × 100) ÷ 30

⇒ MP = ₹200

⇒ Amount paid (SP) = MP − Discount

⇒ Amount paid = 200 − 60 = ₹140

∴ The correct answer is ₹140.

Additional Information

Marked Price (MP)

It is the price printed on the label of an article. Discount is always calculated on this price.

Selling Price (SP)

The actual price paid by the customer after deducting the discount from the MP. SP = MP × (100 − D%) ÷ 100.

Discount Percentage

The ratio of discount to the marked price expressed as a percentage. Discount % = (Discount ÷ MP) × 100.

Net Profit with Discount

Profit = SP − CP. If an item is marked up by M% and discounted by D%, net profit % = M − D − (MD ÷ 100).

Given 

$\frac{{\frac{1}{5} ÷ \frac{1}{5} × \frac{1}{5}}}{{\frac{1}{5} ÷ \frac{1}{5}of\frac{1}{5}}} - 4 \frac{1}{5} ÷ 105$

Concept Used 

Using BODMAS Rule , 

B - bracket , O - of , D- divide, M - multiplication, A - addition , S - substraction 

Calculation 

⇒ $\frac{{\frac{1}{5} ÷ \frac{1}{5} × \frac{1}{5}}}{{\frac{1}{5} ÷ \frac{1}{5}of\frac{1}{5}}} - 4 \frac{1}{5} ÷ 105$

⇒ (1 × 1/5)/(1/5 ÷ 1/25) - 21/5 ÷ 105

⇒ 1/25 - 21/5 ÷ 105 

⇒ 1/25 - 1/25 = 0

Given 

Amount after 5 years = Rs 7500

Amount after 7 years = Rs 8500

Formula Used 

Simple Interest = principal × rate × time/100

Amount = Principal + (n) S.I { n = no. of years)

Calculation

Let the principal and simple interest for one year be x and y respectively 

⇒ 7500 = x + 5y -----(i)

⇒ 8500 = x + 7y ------(ii) 

⇒ Substract eq (ii) and (i) 

⇒ 2y = 1000 

⇒ y = 500

⇒ Put the value of y in eq (i) 

⇒ x = 5000 

⇒ 500 = 5000 × r × 1/100 

⇒ r = 10% 

∴ the rate of interest per annum is 10%

Given 

Bala donated money = Rs 1800

Formula Used 

Percentage = (required/actual) × 100 

Calculation 

⇒ Let the Bala's salary is 100x  

⇒ he decide to donate his salary  = 10% of 100x = 10x 

⇒But, he donate money = 60% of 10x = 6x 

⇒ 6x = Rs1800 

⇒ x = 300

⇒ 100x = 100 × 300 = Rs 30000

∴ the Bala's salary is Rs 30000

Given 

From the graph , birth rate of country D = 18/ thousand 

Formula Used 

Percentage = (required no. /actual no) × 100 

Calculation 

⇒ let the birth rate of country which is 50% more than birth rate of country D be x 

⇒ 150 = (x/18) × 100 

⇒ x = 27 

∴ the  birth rate of country C is 27 which is 50% more than birth rate of country D

The correct answer is IIT Madras.

Key Points

• IIT Madras launched the country’s first indigenously designed standing wheelchair in collaboration with Phoenix Medical Systems.
• A ‘standing wheelchair’ called ‘Arise’, was developed at the TTK Center for Rehabilitation Research and Device Development (R2D2) at the Indian Institute of Technology, Madras.
• Arise was formally launched by Thaawarchand Gehlot, Union Minister for Social Justice and Empowerment, at IIT-Madras Research Park.
• The price of the wheelchair 'Arise' is about Rs. 15,000.

Additional Information

• There are a total of 23 IITs in India of which 16 IITs are established after 2004.
• According to QS ranking 2021, IIT Bombay is among the top 50 Engineering Institutes of the world.
• IIT Delhi Develops EV Charging Station with Inbuilt Solar PV Interface Capability.

The correct answer is Haryana.

Key Points

• This dance is named so because the word **Loor** means girl in the Bhangra area of Haryana.
• It is specially performed during the Holi festival.
• Performance-Girls usually participate in this dance wearing their traditional dress of Ghagra, Kurti, Chundri, and Chunda.
• Girls perform the Loor during the month of **Phalguna** (February/March).
• This dance marks the arrival of the pleasant spring season and with it the harvesting of the Rabi crops in the farms.

Additional Information

Some important dances of other states:

The correct answer is High-Level Language.

Key Points

• Computer programming languages are broadly categorized into 2 types namely – High-Level Language and Low-Level Language.
• The abbreviation for High-Level Language is HLL and Low-Level Language is LLL.
• A high-level language (HLL) is a programming language such as C, FORTRAN, or Pascal that enables a programmer to write programs that are more or less independent of a particular type of computer.
• Such languages are considered high-level because they are closer to human languages and further from machine languages.

​

Important Points

• Lisp, Prolog, Python, and R are the main AI programming languages that are best suited for development and design for different kinds of software.
• C language is developed by Dennis M. Ritchie in the early 1970s.
• Father of Computer - Charles Babbage
• Mother of Computer - Ada Lovelace
• The first computer programming language was created in 1883 by Ada Lovelace.

The correct answer is Shillong.

Key Points

• India International Cherry Blossom Festival celebrated in Shillong.
• The 4^th edition of India International Cherry Blossom Festival, 2019 was celebrated in Shillong, Meghalaya from 13 to 16 November 2019.
• It was inaugurated by Meghalaya Chief Minister, Conrad K Sangma.
• The festival is a great example of how natural resources and sustainable tourism can be utilized in an effective manner and create the value of something which already exists.
• The festival celebrates the unique autumn flowering of Himalayan Cherry Blossoms with several cultural events.

Important Points

Some other important festivals celebrated in North-East India:

• Losar - Arunachal Pradesh
• Saga Dawa - Sikkim
• Ambubachi Mela - Assam
• Dree Festival - Arunachal Pradesh
• Anthurium - Mizoram

The correct answer is Jhilli Dalabehera.

Key Points

• Jhilli Dalabehera, Odisha weightlifter has been awarded the 27^th Ekalabya Award 2019, the annual award organized by Indian Metals Public Charitable Trust (IMPaCT)
• This award was managed by IMFA (Indian Metals and Ferro Alloys limited) group.
• The award comprises a cash prize of Rs.5 lakhs along with citation.
• She has won two gold, three silver, and a bronze medal in different International weightlifting events held between April 1, 2017, and March 31, 2019.

Additional Information

• The award is given to encourage and inspire young sportspersons to perform on National and International platforms.
• Ekalabya award was instituted in 1993.

The correct answer is isochrones.

Key Points

• Isobronts - A line drawn through geographical points at which a given phase of thunderstorm activity occurred simultaneously.
• Isohaline - These are the lines (or contours) that join points of equal salinity in an aquatic system.
• Isochrones -Lines joining places located at the equal travel time from a common centre

​

Important Points

• Iso-Seismal Line -  An isoseismal (line) is a contour or line on map bounding points of equal intensity fo.r a particular earthquake.
• Home-Seismal Line - Line on the Earth's surface connecting points where the seismic wave arrives, generated by an earthquake, at the same time.
• Seismic gap - It is a gap of places in a seismic zone where no earthquake occurs.
• Isogonal line - It is a line joining places with the same magnetic declination.

The correct answer is Relief Map.

Key Points

• A raised-relief map or terrain model is a three-dimensional representation, usually of terrain, materialized as a physical artefact.
• When representing terrain, the vertical dimension is usually exaggerated by a factor between five and ten.
• This facilitates the visual recognition of terrain features.

Additional Information

• Political Map -  A Political Map represents countries, states, and towns. Often they are painted in different colours so we can see them better. This map shows names and boundaries.
• Topographic Map - Topography concerns the shape and character of the Earth's surface, and maps were among the first artefacts to record these observations.
• Thematic Map - A thematic map is a type of map that portrays the geographic pattern of a particular subject matter (theme) in a geographic area like temperature, language, or population.

Source:

https://ncert.nic.in/ncerts/l/fess204.pdf

The correct answer is Tamil Nadu.

Key Points

• The top-ranked state – Tamil Nadu
• The top-ranked district – Peddapalli (Telangana),
• Top state with the maximum citizen participation – Uttar Pradesh

Additional Information

• This Swachh Survekshan Grameen Award felicitated on the occasion of World Toilet Day at Pravasi Bhartiya Kendra, New Delhi.
• World Toilet Day - 19 November
• The theme of World Toilet Day 2020 - Sustainable sanitation and climate change
• Corporates were also felicitated for their contribution under the Swachhata Hi Seva campaign this year, for their efforts towards effective plastic waste management.

The correct answer is Shafali Verma.

Key Points

• Shafali Verma became the youngest Indian cricketer to score a half-century in international cricket(2019)
• She is only 15 years old when she scored a half-century.
• She scored 49-ball 73 in the first T20 International against West Indies surpassing Sachin Tendulkar's 30-year-old record.

Important Points

• Kushal Malla is the youngest cricket who scored a half-century in men's International cricket.
• He scored a half-century in 15 years and 340 days of age.
• Sachin Tendulkar is the youngest cricketer who scored a century in Test cricket.
• Sachin Tendulkar was 18 years 256 days old when he scored test century.

The correct answer is Sudarsan Pattnaik.

Key Points

• Acclaimed Indian sand artist Sudarsan Pattnaik has been conferred the Italian Golden Sand Art Award, 2019 at a ceremony in Rome.
• Becoming the first Indian to win the prestigious award for his contribution to sand art.
• Representing India at the International Scorrano Sand Nativity event held in Lecce from November 13 to 17.
• Mr. Pattnaik created a 10-foot high sand sculpture of Mahatma Gandhi along with Russian artist Pavel Minilkov.

Additional Information

• Sudarsan Pattnaik has also won the People's Choice Award at a prestigious sand sculpting festival in the U.S.
• Sudarsan Pattnaik won Padma Shree award.
• He also won the gold medal for the People's Choice Award at the 3^rd Moscow World Sand Sculpture Championship.

The correct answer is Satya Nadella.

Key Points

• Microsoft's India-born Chief Executive Officer Satya Nadella has occupied the top spot in Fortune's Businessperson of the Year 2019 list.
• It is an annual compilation that also includes Mastercard CEO Ajay Banga and Arista head Jayshree Ullal.
• Banga is ranked 8^th, while Ullal comes in at the 18^th spot in the list for which Fortune looked at 10 financial factors ranging from a total return to shareholders to return on capital.
• Both Banga and Ullal are of Indian-origin.

Additional Information

Some Indian-origin CEOs of top MNCs:

• Google - Sundar Pichai
• Rajeev Suri - Nokia
• Shantanu Narayen - Adobe System
• Arvind Krishna - IBM
• Satya Nadella - Microsoft

The correct answer is Bihar.

Key Points

• National Highway 18 (a combination of old NH 32, NH 33, and NH 5) is a National Highway in India.
• It originates from Gobindpur, Dhanbad, and terminates at Balasore, Odisha.
• It passes through Dhanbad city, Mahuda, Chas, Purulia, Balarampur, Jamshedpur, Ghatshila, Baharagora, Baripada, and Balasore.
• It was earlier NH32 but it got changed in 2012.
• The total length of NH 18 is 361 Kms.

Important Points

• Longest highway of India- NH 44
• Shortest highway of India - NH 47(A)
• Highest highway of India - NH 1(A)
• National Highway Authority of India (NHAI) is responsible for constructing National Highways in India.
• NHAI formed in 1988.
• State Highways are maximum in Maharashtra.

The correct answer is State Bank of India*.*

Key Points

• On January 14, 2020, the South Central Railway (SCR) Zone of Indian Railways has signed an MoU (memorandum of understanding ) with the State Bank of India (SBI) for 'doorstep banking'.
• Under which the bank will collect earnings generated from all 585 stations of the zone.
• The key benefit of this MoU is that real-time information will be available about the cash being deposit at various stations, which will facilitate accountability.

Additional Information

About Indian Railways:

• Founded - 16 April 1853.
• Headquarters - New Delhi
• Minister - Piyush Goyal
• CEO of Railways board - VK Tripathi

About State Bank of India:

• Founded - 1 July 1955
• Headquarters - Mumbai
• Chairman - Dinesh Kumar Khara