SSC CHSL 2019 Official Paper 34(Held On: 26 Oct, 2020 Shift 1) (Previous Year Paper)

The correct answer is- Panacea.

Key Points

• Let's look at the meaning of the marked option:
• Panacea- a solution or remedy for all difficulties or diseases
• Let's look at the meanings of the other given options: 
• Nectar- a sugary fluid secreted by plants, especially within flowers to encourage pollination by insects and other animals
• Tablet- a flat slab of stone, clay, or wood, used especially for an inscription
• Syrup- a thick sweet liquid made by dissolving sugar in boiling water, often used for preserving fruit
• Hence, from the given meanings, we find that Panacea is the correct one-word substitute.

The correct answer is- Descend

Key Points

• Let's look at the meanings of the given word and marked option:
• Ascend- climb to the summit of (a mountain or hill) ((पहाड़ या पहाड़ी) के शिखर पर चढ़ना)
• Descend- move or fall downward (नीचे की ओर बढ़ना या गिरना)
• ​​Let's look at the meanings of the other given options: 
• Decent- conforming with generally accepted standards of respectable or moral behavior.
• Rise- move from a lower position to a higher one; come or go up (निम्न स्थिति से उच्चतर की ओर बढ़ना; ऊपर आना या जाना)
• Climb- go or come up (a slope, incline, or staircase), especially by using the feet and sometimes the hands; ascend (जाना या ऊपर आना (ढलान, झुकना, या सीढ़ी), विशेष रूप से पैरों और कभी-कभी हाथों का उपयोग करके)
• Hence from the given meanings, we find that Ascend and Descend are antonyms. ​​​​

Additional Information  

• Let's look at the antonyms for the given word:
• Antonyms-  nosedive, pitch, tumble, slump

The correct answer is- Articulate.

Key Points

• Let's look at the meanings of the given word and marked option:
• Enunciate- express (a proposition, theory, etc.) in clear or definite terms
  
• Articulate- (of a person or a person's words) having or showing the ability to speak fluently and coherently
  
• ​​Let's look at the meanings of the other given options: 
• Engage- occupy, attract, or involve (someone's interest or attention)
  
• Confine- keep or restrict someone or something within certain limits of (space, scope, quantity, or time)
• Create- bring (something) into existence
• Hence from the given meanings, we find that Enunciate and Articulate are synonyms.

The correct answer is - Profesional.

Key Points

• Let's look at the correct spelling and meaning of the marked option:
• Professional- relating to or belonging to a profession
  
• Example: 
• He isn't a professional artist but an amateur one.
• Let's look at the meanings of the other given options:
• Professor- a teacher of the highest rank in a college or university
  
• Profuse- (especially of something offered or discharged) exuberantly plentiful; abundant
• Protrude- extend beyond or above a surface

The correct answer is- grave.

Key Points

• ​An adjective is any member of a class of words that modify nouns and pronouns.
• ​Let's have a look at the meanings of the given adjectives:
• large- of considerable or relatively great size, extent, or capacity
• grave- giving cause for alarm; serious
• small- of a size that is less than normal or usual
• big- of considerable size, extent, or intensity
• As per the context of the sentence, deforestation can be prevented only if people are aware of its serious effects.
• Hence in the given blank part of the sentence, the correct choice will be the 2nd option i.e. grave.

The correct answer is- prohibiting​.

Key Points

• A gerund is a word ending in "-ing" that is made from a verb and used as a noun.
• Just as nouns sometimes function as objects in a sentence, so can gerund phrases.
• For example:
• ​Tim enjoys running with scissors.
• In the given sentence, we need the gerund form of the verb 'prohibit' i.e. prohibiting.
• The verb 'prohibit' means formally forbid (something) by law, rule, or other authority.
• Thus the 2nd option i.e. 'prohibiting' will be the correct choice.
  

​

 

• The 1st and the 4th option are completely wrong as the sentence is in the present tense.
• The 3rd option is incorrect as this verb is doesn't conform to the plural subject i.e. laws.

The correct answer is - with​.

Key Points​

• There are some verbs/nouns/adjectives which are followed by fixed preposition given below:
• ​Exonerate from, refrain from, suspicious of, cope with, aptitude for, inured to, accused of, predilection for, respite from, vexed at, etc.
• Example:
• ​After spending some time on the island, they became inured to the hardships.​
• ​Hence, according to the phrases given above, 'with' will be the correct choice.
• The given phrase 'cope with' means to deal with and attempt to overcome problems and difficulties​.
  

Additional Information

• There are some fixed prepositional phrases given below:
• ​by the dint of, out of jealousy, in danger, by car/bus/train, owing to, on a trip, for a change, etc.
• For example:
• ​I went on a trip to Goa last month.

The correct answer is- however.

Key Points

• An adverb is a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group, expressing a relation of place, time, circumstance, manner, etc.
• ​Let's have a look at the meanings of the given adverbs:
• however- used to introduce a statement that contrasts with or seems to contradict something that has been said previously
  
• whenever- at whatever time; on whatever occasion (emphasizing a lack of restriction)
• whoever- the person or people who; any person who
• wherever- in or to whatever place (emphasizing a lack of restriction)
• As per the context of the sentence, man has brought his own downfall despite all the help from trees in many ways.
• Hence in the given blank part of the sentence, the correct choice will be the 1st option i.e. however.

The correct answer is- which.

Key Points​​

• ​The pronouns 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, 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/whose' 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 'whom' if the noun/pronoun is the object of the verb in the dependent clause.
• Example: 
• The uncle whom we met at the family reunion is coming to visit. (The noun 'uncle' is the object of the verb met.)
• The person with whom I spoke was able to help me. (The noun 'person' is the object of the preposition with.)
• ​Since we are referring to **'**one of the ways' in this sentence, 'which' will be used in the blank part of the sentence.
  

 ​​​​

Additional Information  ​

• ​​We use 'which' in relative clauses to refer to animals and things.
• Example: 
• You need to tick the box which says Yes.

The correct answer is- criticizing.

Key Points

• ​Let's have a look at the meanings of the given words:
• applauding- show approval or praise by clapping
  
• appreciating- recognize the full worth of
• flaunting- display (something) ostentatiously, especially in order to provoke envy or admiration or to show defiance
• criticizing- indicate the faults of (someone or something) in a disapproving way
• The idiom 'burnt her boats' which is used in the former part of the sentence means to destroy all possible ways of going back to that situation.
• This idiom indicates that Janki did something which upset her previous supervisor.
• Hence in the given blank part of the sentence, the correct choice will be the 4th option i.e. criticizing.

The correct answer is- the situation had become unbearable.

Key Points

• Let's look at the meaning of the given idiom:
• The straw that broke the camel’s back/the last straw- the last in a series of bad things that happen to make someone very upset, angry, etc.
• Example: 
• It had been a difficult week, so when the car broke down, it was the straw that broke the camel's back.
  

​ ​​​​

Additional Information  

• Let's look at the origin of the idiom:
• According to Wikipedia, the straw that broke the camel's back is from an Arabic proverb about “how a camel is loaded beyond its capacity to move or stand”.
• It is a "reference to any process by which cataclysmic failure (a broken back) is achieved by a seemingly inconsequential addition, a single straw."

The correct answer is- blamed.

Key Points

• ​Let's have a look at the meanings of the given words:
• appreciated- recognize the full worth of
  
• praised- express warm approval or admiration of
• liked- find agreeable, enjoyable, or satisfactory
• blamed- used for emphasis, especially to express disapprobation or annoyance
• The word 'failure' used in the sentence indicates that the equation between the sales team and the engineers would not have been pleasant.
• Hence in the given blank part of the sentence, the correct choice will be the 4th option i.e. blamed.

The correct answer is- Autobiography.

Key Points

• Let's look at the meaning of the marked option:
• Autobiography- an account of a person's life written by that person
• Let's look at the meanings of the other given options: 
• Essay- a short piece of writing on a particular subject
• Biography- an account of someone's life written by someone else
• Travelogue- a movie, book, or illustrated lecture about the places visited and experiences encountered by a traveler
• Hence, from the given meanings, we find that Autobiography is the correct one-word substitute.

The correct answer is - By whom was Ravana killed?

Key Points

• The given sentence is in an active voice form, hence we need to convert it into a passive voice form.
• We need to follow these instructions while changing the voice of an interrogative sentence.
• The preposition 'by' will commence the sentence.
• The objective case of the pronoun 'who' will be used now. (whom)
• The given sentence is in the simple past tense.
• The passive verb form for the simple past interrogative sentence: was/were + subject + past participle form of the verb.
• So, 'killed Ravana' changes into 'was Ravana killed'.
• At last line up the remaining part.
  

Following these steps, we finally get- By whom was Ravana killed?

The correct answer is- Samurai Jack drawn​.

Key Points

• The simple past tense is used to talk about things that happened or existed before now.
• It shows that we are talking about something that has already happened.
• The structure is given below:
• Subject + V2 + object.
• Example:
• ​Wolfgang entered a hula hoop contest.
• In the given question, the act of taking the sword out has already taken place.
• Hence according to the rule and example given above, 'drew' will replace 'drawn' in the part given in the 4th option.
  

Correct Sentence: Samurai Jack drew his sword to exact revenge on his superiors.

Additional Information

• Some phrases are followed by past indefinite/simple tense as given below:

• ​It's high time, It's time, It's about time, etc.

• For example:

• It's high time I start preparing for my final exams*.*

• It's high time I started preparing for my final exams.

The correct answer is - DABC.

Key Points

• While arranging the parts of the passage, we should find some grammatical or contextual connections between them:
• Sentence D introduces us to the subject 'Mahesh'. It is the introductory sentence and will be put in the first place.
• Sentence A tells us about how the twins were going about learning to drive. It will be put in second place.
• Sentence B tells us about Mahesh's attitude towards the twins. It will be put in third place.
• The last sentence is C as it mentions the scenario after two months of learning.
  
• Thus, the correct order is - DABC

The correct answer is - Flevor.

Key Points

• Let's look at the correct spelling and meaning of the marked option:
• Flavour- the distinctive taste of a food or drink
  
• Example: 
• He didn't really like the flavour of the drink.
• Let's look at the meanings of the other given options:
• Floor- the lower surface of a room, on which one may walk
  
• Flour- a powder obtained by grinding grain, typically wheat, and used to make bread, cakes, and pastry
• Flower- the seed-bearing part of a plant, consisting of reproductive organs (stamens and carpels) that are typically surrounded by a brightly colored corolla (petals) and a green calyx (sepals)

The correct answer is- Doing something that fails someone’s plan.

Key Points

• Let's look at the meaning of the given idiom:
• Upset someone’s applecart- to cause trouble, especially by spoiling someone's plans
• Example: 
• She upset our applecart by canceling the plan at the eleventh hour.
  

​​​​​

Additional Information  

• Let's look at the origin of the idiom:
• This great idiom originated as "upset the cart" and it has been in use since Roman times which has a similar meaning: "mess up the whole thing".

​

Upset someone’s applecart: खेल बिगाड़ देना

The correct answer is- Gentle.

Key Points

• Let's look at the meanings of the given word and marked option:
• Harsh- unpleasantly rough or jarring to the senses
• Gentle- having or showing a mild, kind, or tender temperament or character
• ​​Let's look at the meanings of the other given options: 
• Bitter- having a sharp, pungent taste or smell; not sweet
• Tough- (of a substance or object) strong enough to withstand adverse conditions or rough or careless handling
• Grave- giving cause for alarm; serious
• Hence from the given meanings, we find that Harsh and Gentle are antonyms.
  

 ​​​​

Additional Information  

• Let's look at the antonyms for the given word:
• Antonyms- peaceable, pacific, placid, serene

The correct answer is- as well as​.

Key Points

• An adverb is a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group, expressing a relation of place, time, circumstance, manner, etc.
• As well is an adverb which means ‘also’, ‘too’ or ‘in addition’. We usually use 'as well' at the end of a clause.
• As well as is a multi-word preposition which means ‘in addition to’.
• Example:
• We look forward very much to seeing you again and to meeting your wife as well.
• When they go to Austria, they like walking as well as skiing.
• As per the structures given above, the adverb 'as' will replace 'also' in the 1st option.
  

Correct Sentence: The director wanted Aziz to play the role of the doctor as well as that of the apprentice.

 ​​​​

Additional Information  

• The adverb 'there' is used to begin some stories written in a traditional style.
• Example:
• There once lived a poor widow who had a beautiful daughter.

The correct answer is- Gary exclaimed that he had finally cleared his exams with distinction.

Key Points

• Let's look at the steps to change the sentence from direct to indirect speech:
• When the direct speech is in an exclamatory form, we follow the steps given below:
• Convert the sentence in the direct speech into assertive.
• The tense of reported speech is changed only when the reporting verb is in the past tense.
• The reporting verb said is converted into exclaimed.
• The pronoun 'I' is replaced by 'he' accordingly.
• Similarly 'my' will be replaced by 'his' in the latter part of the sentence.
• The helping verb is changed according to the tense, followed by the 3rd form of the verb.
• The present perfect tense i.e. have cleared will be changed to the past perfect tense i.e. had cleared.
• ​​At last line up the remaining part.
  

Following these steps, we finally get- Gary exclaimed that he had finally cleared his exams with distinction.

The correct answer is- Amass

Key Points

• Let's look at the meanings of the given word and marked option:
• Assemble- (of people) gather together in one place for a common purpose; Amass
• Amass- to collect or put together a large quantity of something
• ​Let's look at the meanings of the other given options: 
• Disband- (of an organized group) break up or cause to break up and stop functioning
• Detach- disengage (something or part of something) and remove it
• Address- the particulars of the place where someone lives or an organization is situated
• ​Hence from the given meanings, we find that Assemble and Amass are synonyms.

The correct answer is- on.

Key Points​

• ​There are some fixed prepositional phrases given below:
• ​by the dint of, out of jealousy, on strike, by the dozen, owing to, on a trip, for a change, etc.
• For example:
• ​I went on a trip to Goa last month.
• ​The phrase 'on strike' means (of employees) refuse to work as a form of organized protest, typically in an attempt to obtain a particular concession from their employer.
• Thus the preposition 'on' will be the correct choice.
  

Correct Sentence: All the employees of the nationalized banks are on strike.

Additional Information

• There are some verbs/nouns/adjectives which are followed by fixed preposition given below:
• ​Exonerate from, refrain from, suspicious of, interested in, inured to, accused of, predilection for, respite from, vexed at, etc.
• Example:
• ​After spending some time on the island they became inured to the hardships.

The correct answer is- marrying to Philip​.

Key Points

• Let's look at the points given below:
• Subject + marry/divorce (any verb form) + Object.
• Subject + get/be + married + to + Object.
• Subject + get/be + divorced + from + Object.
• ​Example:
• ​Lauren Bacall married her co-star, Humphrey Bogart.
• She got/is married to someone she met at college.
• She got/is divorced from her second husband.
• As per the structures given above, the verb 'married' will replace 'marrying' in the 1st option.
  

Correct Sentence: Queen Elizabeth got married to Philip, former Prince of Greece and Denmark.

The correct answer is - CABD.

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 'Akbar the great'. It is the introductory sentence and will be put in the first place.
• Sentence A tells us about Akbar's command to make Birbal leave the kingdom. It will be put in second place.
• Sentence B tells us about how Birbal lived his life after leaving the kingdom. It will be put in third place.
• The last sentence is D as it mentions how Akbar reacted after months of being without his favourite minister.
  
• Thus, the correct order is - CABD

When the paper is unfolded it will appear like :-

So, answer is the figure given below

Hence, the correct answer is "Option (4)".

The given figure in question is embedded in option (4).

Hence, the correct answer is "Option (4)".

Members : Deepali, Vijay, Sunita, Mohit

Family chart,

Drawing the family tree as per the given information :

From the family tree, we get

Deepali is the daughter of Vijay and Mohit is the husband of Deepali.

So, Mohit is son-in-law of Vijay.

Hence, the correct answer is "Son-in-law".

Udometer, Ombrometer and  Pluviometer are Rainfall measuring instruments.

While Decibelmeter is noise measuring instrument.

Thus, Decibelmeter is different from other options.

Hence, the correct answer is **"**Decibelmeter".

Additional Information

• A rain gauge (also known as an udometer, pluviometer, or an ombrometer) is an instrument used by meteorologists and hydrologists to gather and measure the amount of liquid precipitation over an area in a predefined period of time.

The central arrow is rotated 90° in clockwise direction and the arrow in the top left corner and the star in the bottom right corner are interchanging the positions.

Similarly,

The shape in the bottom left corner and the triangle in the top right corner are interchanging their places.

Hence, the correct answer is "Option (3)".

The pattern followed here is :- The first letter of each word is decreasing by 2 and the second letter of each word is increasing by 4.  

Hence, the correct answer is "OZ".

The logic follows here is:- Each term is increasing by 1 successively start from 15.

Hence, the correct answer is "553".

Venn diagram according to the given information :

Solar System, Earth, Jupiter

Earth and Jupiter both are the planet of Solar System they are two different kinds of planets.

There are no relation between Earth and Jupiter but both come under in the Solar System. 

Hence, the correct answer is "Option (3)".

Additional Information

1. Jupiter is a gas giant with no discernible solid surface, while Earth is a terrestrial planet. Jupiter's primary atmosphere consists of hydrogen and helium, while Earth's atmosphere is composed of a mix of oxygen and nitrogen and other chemicals.
2. There are eight planets in the solar system: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.

Given:

⇒ A's salary = Rs.45000

Calculation:

⇒ B's salary = 45000 × 2 = Rs.90000

⇒ C's salary = 90000 × 3/5 = Rs.54000

∴ Total salary of A, B and C = 90000 + 45000 + 54000 = Rs.1,89,000

The logic follows here is:- Each letter is increasing by 3 and getting the next letter.

Option 1) 

Option 2) 

Option 3) 

Option 4) 

Option 2, 3, and 4 are following this logic but option 1 is different from other options.

So, Option (1) is an odd one.

Hence, the correct answer is "CFIM".

Concept used :

Opposite faces don't show up together in a particular position of dice.

Considering dice position (1) :

a and d cannot be the opposite to s.

Considering dice position (3) :

f and g cannot be the opposite to s.

Thus, the remaining letter "e" will be opposite to "s".

Hence, the correct answer is "e".

The logic followed here is :

The first word is the product and the second is the ingredient/material used to make it.

Belt is made using Leather.

Similarly,

Bread is made using Flour.

Hence, the correct answer is "Flour".

The logic follows here is :

Column wise

First-term = {(Second term)² + (Third term)²} × 2.

First column → 116, 3, 7

(3² + 7²) × 2 = (9 + 49) × 2 = 58 × 2 = 116

Second column → 160, 8, 4

(82 + 42) × 2 = (64 + 16) × 2 = 80 × 2 = 160

Similarly,

Third column → ?, 13, 2

(132 + 22) × 2 = (169 + 4) × 2 = 173 × 2 = 346

? = 346

Hence, the correct answer is "346".

The logic follows here is :

Letters of given words are arranged in alphabetical order (A - Z) from left to right.

 

Therefore, SMART is rearranged as AMRST.

Similarly,

 

DESIGN will be rearranged as DEGINS.

Hence, the correct answer is "DEGINS".

Arranging alphabets in alphabetical order means that they are arranged in alphabetical order from A to Z. 

Example: A, B, C, D, E, F, ......., Z.

Given equation is :

4 × 3 + 10 - 2 ÷ 7 = 10

To balance the equation :

(I). 4 × 3 + 10 - 2 ÷ 7 = 10

Interchanging ( × and + ) and using BODMAS rule,

4 + 3 × 10 - 2 ÷ 7 = 10

4 + 3 × 10 - 0.28 = 10

4 + 30 - 0.28 = 10

34 - 0.28 = 10

33.72 ≠ 10.

LHS ≠ RHS.

(II). 4 × 3 + 10 - 2 ÷ 7 = 10

Interchanging ( ÷ and - ) and using BODMAS rule,

4 × 3 + 10 ÷ 2 - 7 = 10 

4 × 3 + 5 - 7 = 10 

12 + 5 - 7 = 10 

17 - 7 = 10 

10 = 10.

LHS = RHS.

(III). 4 × 3 + 10 - 2 ÷ 7 = 10

Interchanging ( + and - ) and using BODMAS rule,

4 × 3 - 10 + 2 ÷ 7 = 10

4 × 3 - 10 + 0.28 = 10

12 - 10 + 0.28 = 10

12.28 - 10 =10

2.28 ≠ 10.

LHS ≠ RHS.

(IV). 4 × 3 + 10 - 2 ÷ 7 = 10

Interchanging ( ÷ and × ) and using BODMAS rule,

4 ÷  3 + 10 - 2 × 7 = 10

1.33 + 10 - 2 × 7 = 10

1.33 + 10 - 14 = 10

11.33 - 14 = 10

-2.67 ≠ 10.

LHS ≠ RHS.

Hence, the correct answer is "÷ and -".

The logic follows here is :

(First number) × (First number - 1) = Second number.

For 7 : 42

7 × (7 - 1) = 7 × 6 = 42.

Similarly,

For 18 : ?

18 × (18 - 1) = 18 × 17 = 306.

Hence, the correct answer is "306".

The logic follows here is :

(I). 156 : 12

12² + 12 = 144 + 12 = 156

(II). 210 : 14

14² + 14 = 196 + 14 = 210

(III). 240 : 15

15² + 15 = 225 + 15 = 240

(IV). 276 : 16

16² + 16 = 256 + 16 = 272 ≠ 276

Thus, 276 : 16 is the odd one.

Hence, the correct answer is **"**276 : 16".

The logic follows here is :

(Sum of place values of alphabets) × 1.5 = Given number

For GOLF = 60

(7 + 15 + 12 + 6) × 1.5 = 40 × 1.5 = 60.

For START = 117

(19 + 20 + 1 + 18 + 20) × 1.5 = 78 × 1.5 = 117.

Similarly,

For NEST

(14 + 5 + 19 + 20) × 1.5 = 58 × 1.5 = 87.

Hence, the correct answer is "87".

The logic follows here is :

Hence, the correct answer is "I and Y".

The logic follows here is :

Row-wise

(First term × Second term) - {First term × (First term - 1)}

First row → 3, 30, 84

(3 × 30) - {3 × (3 - 1)} = 90 - (3 × 2) = 90 - 6 = 84.

Second row → 2, 10, 18

(2 × 10) - {2 × (2 - 1)} = 20 - (2 × 1) = 20 - 2 = 18.

Similarly,

Third row → 4, ?, 260

(4 × ?) - {4 × (4 - 1)} = 260

(4 × ?) - {4 × 3} = 260

(4 × ?) - 12 = 260

(4 × ?) = 260 + 12 = 272

? = 272 ÷ 4

? = 68

Hence, the correct answer is "68".

The mirror image formed when the mirror is placed on the right side of the figure:

Hence, the correct answer is "Option 4".

The logic followed here is:

1. Intact and Unflawed are synonyms meaning not damaged and perfect.

2. Entire and Partial are antonyms.

3. Bright and Luminous are synonyms.

4. Pure and Perfect are synonyms.

Both the words are synonyms in all the options except option 2, where the given words are antonyms.

Hence, the correct answer is "Entire : Partial".

The least possible Venn diagram for the given statements is:

Conclusions:

I. No printer is a scanner → False (There is no direct relation given so it can be possible but not definite, hence, false.)

II. Some printers are mouse → True (As some mouse are printers, some printers are mouse is true.)

III. No printer is a mouse → False (It is definitely false as some printers are mouse as shown in the diagram.)

IV. No scanner is a printer → False (There is no direct relation given so it can be possible but not definite, hence, false.)

Hence, the correct answer is "Only conclusion II follows".

The given words follow the order:

3. Junk Food : First, junk food is eaten.
4. Disease : The junk food leads to disease.
5. Medicine : Medicine is taken to cure the disease.
6. Healthy : After the medicine is taken, we become healthy.

So, the correct order is 3, 1, 2, 4.

Hence, the correct answer is "3, 1, 2, 4".

Given figure:

Triangles:

ABF, FBE, BED, BCD, BFD

GHI, KJL, XYZ

So, there are 8 triangles in total.

Hence, the correct answer is "8".

Given:

$2a + \frac{1}{{a;}} = 4$

Formula used:

(a + b)2 = a2 + b2 + 2ab

Calculation: 

$2a + \frac{1}{{a;}} = 4$      ----(1)

Divided by 2 in equation number (1)

$\Rightarrow \frac{1}{2};\times\left( {2a + \frac{1}{{a;}}} \right) = ;\frac{1}{2} \times 4$

$\Rightarrow a; + ;\frac{1}{{2a}} = 2$

Squaring both sides

$\Rightarrow {\left( {a + ;\frac{1}{{2a}}} \right)^2} = 4$

$\Rightarrow {a^2} + ;\frac{1}{{4{a^2}}} + 2 \times a \times \frac{1}{{2a}} = 4$

$\Rightarrow {a^2} + ;\frac{1}{{4{a^2}}} + 1 = 4$

$\Rightarrow {a^2} + \frac{1}{{4{a^2}}} = 3$

∴ The correct answer is 3.

Given:

A reduction of 20% in the price of sugar

Purchase to obtain 4 kg more for Rs.160

Calculation:

Let the original price per kg of sugar is Rs. x

Then the reduced price per kg = x × (80/100) = 4x/5

Quantity of sugar that can be bought for Rs.160 originally = Rs. 160/x

Quantity of sugar that can be bought for Rs.160 with reduced price = 160/(4x/5) = 800/4x

According to the question,

⇒ 800/4x = (160/x) + 4

⇒ (800/4x) – (160/x) = 4

⇒ (800 – 640)/4x = 4

⇒ 160 = 16x

⇒ x = 10

∴ The original price of sugar is 10 Rs. per kg

We have to follow the BODMAS rule

Calculation:

⇒ $2\frac{1}{{36}}; \div {\rm{;}}\frac{5}{9};of;\left( {5\frac{1}{{10}} + 2\frac{1}{5}} \right) + ;\frac{2}{5}; \div 3\frac{1}{5}$

⇒ $\frac{{73}}{{36}}; \div {\rm{;}}\frac{5}{9};of;\left( {\frac{{51}}{{10}} + \frac{{11}}{5}} \right) + ;\frac{2}{5}; \div {\rm{;}}\frac{{16}}{5}$

 ⇒ $\frac{{73}}{{36}}; \div \frac{5}{9};of;\left( {;\frac{{51 + 22}}{{10}}} \right) + \frac{2}{{16}}$

⇒ $\frac{{73}}{{36}}; \div ;\frac{5}{9}; \times ;\frac{{73}}{{10}}; + ;\frac{1}{8}$

⇒ $\frac{{73; \times ;9; \times ;10}}{{36; \times ;5; \times 73}}; + ;\frac{1}{8}$

⇒ $\frac{1}{2} + \frac{1}{8}$

⇒ $\frac{{4; + ;1}}{8}$

⇒ $\frac{5}{8}$

∴ The correct answer is 5/8

Given:

a² + b² + 2b + 4a + 5 = 0,

Formula used:

(a + b)²  = a² + b² + 2ab

Calculation:

a² + b² + 2b + 4a + 5 = 0,

⇒ a² + 4a + b² + 2b + 5 = 0

⇒ (a + 2)² = a² + 4a + 4

⇒ (b + 1)² = b² + 2b + 1

⇒ a² + 4a + 4 + b² + 2b + 1 = 0

⇒ (a + 2)² + (b + 1)² = 0

So, a + 2 = 0

⇒ a = -2

And, b + 1 = 0

⇒ b = -1

Then, $\frac{{2a - 3b}}{{2a + 3b}}$

Put the value of a and b in this equation

$\Rightarrow \frac{{2 \ \times\ \left( { - 2} \right)\ -\ 3\ \times\ \left( { - 1} \right)}}{{2 \ \times \ \left( { - 2} \right)\ + \ 3 \ \times\ \left( { - 1} \right)}}$

$\Rightarrow \frac{{ - 4 \ +\ 3}}{{ - 4\ -\ 3}}$

⇒ -1/-7 

⇒ 1/7

∴ The value of

$\frac{{2a - 3b}}{{2a + 3b}}$  is  1/7

Given:

A train takes 45 minutes to cover a certain distance at a speed of 80 km/h

His speed is increased by 125%

Then how long will it take the train to cover 8/5 of the same distance 

Formula used:

$velocity= distance/time$

Calculation:

Distance = velocity × time

Distance = 80 × (45 / 60)

⇒ 60 km

Speed is increased by 125%

⇒ 80 + 80 × (125/100)

⇒ 180 km/hour

The train to cover 8/5 of the same distance 

Distance = 60 × (8/5)

⇒ 96 km

So time is taken by train,

Time = distance/speed

⇒ (96/180) =  8 / 15 hr 

⇒ (8/15) hr = (8 / 15) × 60 = 32 minutes

⇒ 32 minutes

Therefore, covered the distance by train in 32 minutes

Given:

A = 80% more than C

B = 20% more than C

Calculation:

According to the problem

${\rm{A}} = \frac{{180}}{{100}}C = 1.8C;$      ---- (1)

${\rm{B}} = \frac{{120}}{{100}}C = 1.2C;$    ---- (2)

divide equation 1 by 2

⇒ $\frac{{\rm{A}}}{{\rm{B}}} = \frac{{1.8C}}{{1.2C}};$

⇒ $\frac{{\rm{A}}}{{\rm{B}}} = \frac{3}{2};$

∴ The ratio of A to B is 3 ∶ 2

Given:

A can-do work in 15 days

B can do work in 10 days 

Concept used:

A can do a work in n days 

So, A's one day work = 1/n

Calculation: 

A can-do a work in 15 days 

⇒ A's one-day work = 1/15

B can do a work in 10 days

⇒ B's  one day work = 1/10

A and B's one day work = 1/15 + 1/10

⇒ 5/30 = 1/6

Two days work of A and B will be 2/6 = 1/3

Remaining work after B left = 1- 1/3 = 2/3

A will finished remaining work in = (2/3) × 15 =  10 days

∴ Total number of days to complete work is 10 + 2 = 12 days  

Shortcut Trick

LCM of 15 and 10 is 30 

A = 15 × 2 = 30

B = 10 × 3 = 30

Total work = 30 unit

B does 3 unit work in one day

A does 2 unit work in one day

⇒ (A + B)'s one day's work is (3 + 2) unit = 5 unit

⇒ (A + B)'s two days' work is (5 × 2) unit = 10 unit

⇒ Remaining work = 30 - 10 = 20 unit 

A will complete remaining work in, 20/2 = 10 days 

Total number of days = (10 + 2) days = 12 days

∴ Total number of days to complete work is 12 days

Formula used:

Dividend = divisor × quotient + remainder

Calculation:

let the number be x

x = 899 × q + 63

x = (29 × 31 × q + 58) + 5

x = 29 × 33 × q + 5

∵ p = 33 × q

x = 29p + 5

when x is divided by 29, quotient = p

Remainder = 5

Shortcut Trick

Remainder 63 is divided by 29 then what Remainder will come it will be the final answer

⇒ 63/29 remainder is 5 

⇒ 63 = 29 × 2 + 5

∴ Remainder is 5

Given:

Old profit = 30%

New profit = 45%

Formula used:

$;Profit\% ; = ;\frac{{SP; - ;CP}}{{CP}}; \times 100$

Calculation:

Let the original cost price of the article be X.

Old selling price at 30% profit will be = $\frac{{130}}{{100}};x$

⇒ 1.3x

both cost price and selling price of the article are decreased by Rs.100

∴ New CP = x -100 and new SP = 1.3x - 100

$;Profit\% ; = ;\frac{{SP; - ;CP}}{{CP}}; \times 100$

 

$45; = ;\frac{{\left( {1.3x; - ;100} \right); - ;\left( {x; - ;100} \right)}}{{x; - ;100}}; \times ;100;$

⇒ 0.45x - 45 = 1.3x - 100 - x + 100

⇒ 0.45x - 0.3x = 45

⇒ 0.15x = 45

x = 300

The original cost price is 300

Calculation:

According to the problem

Total production of LCD in the year 2012 and 2014 =

14 + 9 = 23

Total production of TV in the years 2012 and 2014 =

8 + 12 = 20

∴ the required ratio 23: 20

Given:

cosec θ = 13/12

Forumula used:

H = hypotenuse, P = perpendicular, B = base

H² = P² + B²

cosecθ = H/P, sinθ = P/H, cosθ = B/P

Calculation:

⇒ cosec θ = 13/12 = H/P

⇒ H = 13, P = 12, B² = H² – P²

⇒ B² = 13² – 12² = 5²

⇒ B = 5

⇒ sinθ = 12/13, cosθ = 5/13, and cosec θ = 13/12

putting the value of sinθ and cosθ in $\frac{{2sin\theta - 3cos\theta }}{{4sin\theta - 9cos\theta }}$

⇒ $\frac{{2 \times \frac{{12}}{{13}} - 3 \times \frac{5}{{13}}}}{{4 \times \frac{{12}}{{13}} - 9 \times \frac{5}{{13}}}}$

⇒ 3

∴ The value of $\frac{{2sin\theta - 3cos\theta }}{{4sin\theta - 9cos\theta }}$ is 3.

Given:

tanθ + cotθ = 2

Calculation:

Put the value of θ = 45^o, tan45^o = 1, and cot45^o = 1

Then, tanθ + cotθ = 2

⇒ tan45^o + cot45^o = 2

⇒ 1 + 1 = 2

putting the value θ = 45 in tan100θ + cot100θ

⇒ tan¹⁰⁰45 + cot¹⁰⁰45 

⇒ 1¹⁰⁰ + 1¹⁰⁰

⇒ 2

∴ The value of tan100θ + cot100θ is 2.

Shortcut TrickIf x + 1/x = 2; it's only possible when x = 1.

So tan¹⁰⁰θ + cot¹⁰⁰θ  = 2

Given:

Pie-chart shows the monthly expenditure incurred by a family on various items, and their savings.

The expenditure on education is Rs. 2,700 more than that on housing

Formula used:

Expediture = (θ/360°) × given rupees

Calculation:

According to the pie-chart,

Education = 75°, Housing = 60°.

The expenditure on education is greater than housing = 75° – 60°.

⇒ 15°

According to the given,

⇒ 15° = 2700

⇒ 1° = 2700/15 

⇒ Rs. 180

The total expenditure on food and clothing = 125° + 18° 

⇒ 143°

Then, 1° = Rs. 180

⇒ 143° = 180× 143

⇒ Rs. 25,740

∴ The total expenditure on food and clothing is Rs. 25,740.

Given:

compound interest(C.I.) - Rs. 328

Rate - 5% p.a.

Time - 2 years

Formula used:

$compound;interest = principal\left( {{{\left( {1 + \frac{r}{{100}}} \right)}^t} - 1} \right)$

Calculation:

According to formula,

⇒ $compound;interest = principal\left( {{{\left( {1 + \frac{r}{{100}}} \right)}^t} - 1} \right)$

putting the value of C.I., rate, time in above formula

⇒ $328 = principal\left( {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right)$

⇒ $328 = \frac{{principal\left( {21 × 21 - 20 × 20} \right)}}{{20 × 20}}$

⇒ principal = $\left( {328 × 20 × 20} \right)/41$

⇒ principal = Rs. 3200

∴ The sum is Rs. 3200.

Ratio method:

Rate = 5%

⇒  5/100 = 1/20

⇒ 41 unit = 328

⇒ 1 unit = 328/41

⇒ 1 unit = 8

Then, sum is 400 unit

⇒ 400 unit = 400 × 8

⇒ Rs. 3200

∴ The sum is Rs. 3200.

Given:

The monthly incomes is Rs. 64,800

the monthly expenditure incurred by a family on various items, and their savings is 360° 

Formula used:

saving income = (saving angle (θ)/360°) × monthly income

Calculation:

<br>

According to the pie-chart,

⇒ Saving angle = 35°

For one month,

⇒ Saving income = (saving angle (θ)/360°) × monthly income

⇒ Saving income = (35°/360°) × 64800

⇒ Saving income = Rs.6300

⇒ Saving income in a whole year = Rs.6300 × 12 months

⇒ Rs.75600

∴ Yearly savings are Rs.75600.

Mistake Points Monthly income/saving is given and yearly saving is asked hence Saving will be more than Expenditure

Given:

List price of an article = Rs. 8500 and two discount offered first one is 12% and second one we have to find. Also the selling price = Rs. 6358

Calculation:

List price = Rs. 8,500 and Discount = 12% (12% = -3/25 = 22/25)

⇒ After first discount price came down by = (8500) × 22/25 = 85 × 88 = Rs. 7480

⇒ As given selling price = Rs. 6,358

⇒ Discount given = Rs. (7480 - 6358) = Rs. 1122

⇒ Discount is on the given List price = (1122/7480) × 100 = 15%.

Given:

As shown in above figure

Let us consider a triangle ABC were ∠A = 4x°, ∠B = 3x°, ∠C = 8x°

As The Largest angle is ∠C है, and the Smallest angle is ∠B

Calculation:

As we know the sum of all angle of triangle = 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ 4x° + 3x° + 8x° = 180°

⇒ 15x° = 180°

⇒ x° = 180°/15° = 12°

⇒ ∠A = 4 × 12° = 48°, ∠B = 3 × 12° = 36°, ∠C = 8 × 12° = 96°

∴ ∠C - ∠ B = 96° - 36° = 60°

Given:

Let Us consider our given Triangle a right angle triangle.

2∠ABC = 9∠ACB and 2∠BAC = 7∠ACB. If AB = 8 cm, AC = 17 cm,

Let us consider that ∠ABC = x°, ∠BAC = z°, ∠BCA = y°

Calculation:

⇒ 2∠ABC = 9∠ACB

⇒ 2 × x° = 9 × y°

⇒ x°/y° = 9/2 _____ (1)

⇒ 2 × z° = 7 × y°

⇒ z°/y° = 7/2 _____ (1)

Now, take the ratio of the angles

⇒  x° : y° : z°

⇒ 9 : 2 : 7

As the sum of all the angle of a triangle = 180°

⇒ 9 + 2 + 7 =  180°

⇒ 1 unit = 180°/18 = 10°

∴ x° : y° : z°

 (9 : 2 : 7) × 10° = 90°, 20°, 70 °

⇒ The given triangle is a right angle triangle

Now, By Pythagoras Theoram

 8²  + 15² = 17²

∴ BC = 15 cm

Given:

As Shown in the above figure. Let us assume this is the given cube having side = A cm. Total Surface Area of the cube = 2400 cm² _______ (1)

Formula used:

Total Surface Area of a given Cube = 6 ×a²

Where, a = Side of the cube

Volume of the Cube  = a³

Calculation:

⇒ As Total Surface area of a cube = 6 × A² = 2400

⇒ A² = (2400)/6 = 400

⇒ A²= √ 400 = 20 cm

Now, Volume of the cube = A³ = (20)³

∴ Volume of the cube = 8000 cm³

Given:

As we can see in the diagram that the production of LCD's in the year 2011, 2012, 2013 are as follows:

7000, 9000, 14000 units

The Production of TV's in the year 2011, 2012, 2013 are as follows: 6000, 8000, 13000 units

Calculation:

The Sum of the LCD's is

⇒ 7000 + 9000 + 14000 = 30,000 units

⇒ The average of LCD's = ( 30000)/3 = 10,000 units ______ ( 1 ) Now, The sum of the TV's = 6000 + 8000 + 13000 = 27,000 units ⇒ The Average of the TV's = 27,000/3 = 9000 units ______ ( 2 )

⇒ Subtract ( 1 ) & ( 2 )

⇒ 10,000 – 9,000 = 1000 units

Given :

∠BDS = 90° BC = 40 cm, BC = 40 cm, BP = 28 cm and CD = 25 cm

Concept: Line joining from centre of Circle to a tangent makes Right angle at Tangent

calculation:

Joint OR and OS from centre to tangential point R, S respectively

∠ORD = 90°

∠OSD = 90° 

∠DSO = 90°

⇒ DROS is square

⇒ DR = SO (SO is radius)

PB = 28 cm

⇒ QB = 28 (tangent from a same point)

⇒ QC = 12, DC = 25 

⇒ RC = 12 (tangent from a same point),

⇒ DR = 13 cm DS = 13 cm (DR = DS) (tangent from a same point) 

⇒ DR = 13 cm

Given : a3 + b3 + c3 - 3abc, when a = 225, b = 226, and c = 227 

Formula used :

$⇒ {a^3} + {b^3} + {c^3} - 3abc = \frac{1}{2}\left( {a + b + c} \right);\left[ {{{\left( {;a - b} \right)}^2} + {{\left( {b - c;} \right)}^2} + {{\left( {c - a} \right)}^2}} \right]$

${a^3} + {b^3} + {c^3} - 3abc = \frac{1}{2}\left( {225 + 226 + 227} \right);\left[ {{{\left( {;225 - 226} \right)}^2} + {{\left( {226 - 227} \right)}^2} + {{\left( {227 - 225} \right)}^2}} \right]$

⇒ ${a^3} + {b^3} + {c^3} - 3abc = \frac{1}{2}\left( {678} \right);\left[ {{1^2} + {1^2} + {2^2}} \right]$

${a^3} + {b^3} + {c^3} - 3abc = \left( {678} \right)(3)$ = 2034

Shortcut Trick

If cosec A + cot A = x, then cosec A − cot A = 1/x.

Given: cosec A + cot A = 3 ⇒ cosec A − cot A = 1/3.

Adding both: 2 cosec A = 3 + 1/3 = 10/3 ⇒ cosec A = 5/3.

Since sin A = 3/5, using Pythagorean triplet (3, 4, 5), the base is 4.

cos A = Base/Hypotenuse = 4/5.

∴ The correct answer is 4/5.

Alternate Method

Given: cot A + cosec A = 3

Formula Used: cosec²A − cot²A = 1

⇒ (cosec A − cot A)(cosec A + cot A) = 1

⇒ (cosec A − cot A) × 3 = 1

⇒ cosec A − cot A = 1/3 --- (Equation 1)

⇒ cosec A + cot A = 3 --- (Equation 2)

⇒ Adding (1) and (2): 2 cosec A = 3 + 1/3 = 10/3

⇒ cosec A = 5/3

⇒ Since sin A = 1/cosec A, sin A = 3/5

⇒ cos²A = 1 − sin²A

⇒ cos²A = 1 − (3/5)² = 1 − 9/25 = 16/25

⇒ cos A = √(16/25) = 4/5

∴ The correct answer is 4/5.

Additional Information

Trigonometric Identities

Fundamental identities include sin²A + cos²A = 1, 1 + tan²A = sec²A, and 1 + cot²A = cosec²A.

Pythagorean Triplets

Common triplets like (3, 4, 5), (5, 12, 13), and (8, 15, 17) help in solving right-angled triangle problems quickly without long square root calculations.

Reciprocal Relations

Remember that cosec A = 1/sin A, sec A = 1/cos A, and cot A = 1/tan A.

Given :

AB is a diameter of circle centre O,

 

Formula used : linear pair angle,  angle on straight line = 180°

∠AOP = 130 °

∠POB = ( 180 ° - 130 °) = 50°

∆ POB = ∠P = ∠B ( Isosceles  triangle )

⇒ ∠POB = 50° 

∆ POB = ∠POB + ∠ OBP + ∠ BPO = 180°

⇒180° = 50°+ 2×∠BPO

⇒130/2 = ∠BPO 

⇒65°  =  ∠BPO

Let there be n numbers in the original list and let their mean be y.

Then, sum of n numbers = ny

According to Question

 $⇒ (ny+40)/(n+1)=y+4 ……(1 )$

$⇒(ny+40+30)/(n+2 )=y+5 ……(2 )$

On solving Eq 1

ny + 4n +y+4 = ny + 40

4n + y = 36                  ……(3)

Similarly eq 2

5n + 2y = 60                ……(4)

On solving eq 3 and 4 by elimination

y =  20 , n = 4

The correct answer is Pench.

• Pench Tiger Reserve is located in Madhya Pradesh in Seoni and Chhindwara districts.
• Pench Tiger Reserve comprises the Indira Priyadarshini Pench National Park, the Pench Mowgli Sanctuary, and a buffer.
• The Reserve gets its name from the Pench River that flows through the reserve.​
• Recently in NEWS
• The death of a 10-year-old ailing male tiger, in the Pench Tiger Reserve (PTR) to a ‘respiratory illness’ has raised concerns that whether the tiger should be tested for the novel coronavirus disease.

Important Points

• ​Dandeli-Anshi, Bhadra, and Nagarhole Tiger reserves are located in Karnataka.
• The government of India launched Project Tiger in the year 1973.
• The project aims at ensuring a viable population of Tigers in their natural habitats, protecting them from extinction, and preserving areas of biological importance.

The correct answer is a humanoid built by the Indian Space Research Organization (ISRO).

• Vyommitra is a female humanoid - something that has an appearance resembling a human but is robotic - built by ISRO.
• A Humanoid is a Robot with a human-like appearance that can interact, and behave just like humans in different environments.
• She has been built for ISRO's first unmanned Gaganyaan mission.
• Vyommitra can monitor module parameters, alert astronauts and perform life support operations.
• Vyommitra can recognize faces through artificial intelligence and is trained to handle critical functions.

​

 

​Gaganyaan Mission:

• The Gaganyan mission, scheduled for December 2021, is ISRO's first human space mission.
• It will be for the first time that India will launch its manned mission to space, making the country fourth in line to have sent a human to space.
• The human spaceflight will take 16 minutes to reach orbit where it will stay for five to seven days.