SSC CHSL Previous Paper 3 (Held On: 17 March 2020 Shift 3) (Previous Year Paper)

The correct answer is Lair.

Key Points

• Let's look at the meaning of the marked option:
• Lair- the habitation of wild animals (जंगली जानवरों का आवास)
• Let's look at the meanings of the other given options: 
• Cage- an enclosure made of wire or metal bars in which birds or animals can be kept (एक बाड़े या तार या धातु की छड़ें जिसमें पक्षियों या जानवरों को रखा जा सकता है)
• Kennel- outbuilding that serves as a shelter for a dog (आउटबिल्डिंग जो कुत्ते के लिए आश्रय के रूप में कार्य करता है)
• Hutch- a cage (usually made of wood and wire mesh) for small animals (छोटे जानवरों के लिए एक पिंजरा (आमतौर पर लकड़ी और तार की जाली से बना)
• Hence, from the given meanings, we find that Lair is the correct one-word substitute.

The correct answer is Panacea.

Key Points 

• Let's look at the meanings of the other given options: 
• Panacea- something that will solve all problems or cure all illnesses(सर्वरोगहारी, रामबाण दवा)
• Medicine- the branches of medical science that deal with nonsurgical techniques(दवा, औषधि)
• Treatment- care provided to improve a situation especially medical procedures or applications that are intended to relieve illness or injury(इलाज, चिकित्सा)
• Therapy- (medicine) the act of caring for someone as by medication or remedial training etc.(उपचार, चिकित्सा)
• Hence, from the given meanings, we find that Panacea is the correct one-word substitute.

The correct answer is No improvement.

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:

• No- quantifier; used with either mass nouns or plural count nouns for indicating a complete or almost complete lack or zero quantity of

• Any- used to refer to one or some of a thing or number of things, no matter how much or how many

• ​The adjective 'no' is used with **singular/**plural countable nouns, whereas 'any' is used with singular countable nouns.

• Both of the adjectives are used in a negative sense and hence can't be used together.

• Since the required structure has already been followed in the given sentence, the 3^rd option i.e. No improvement will be the correct choice.

Correct Sentence: There was no sign of recognition on his face when they met after ten years.

The correct answer is at the work​​.

Key Points​

• ​There are some fixed prepositional phrases given below:

• ​by the dint of, at work/home, come in contact with something, by the dozen, owing to, on a trip, for a change, etc.

• For example:

• If he’s not at home, he must still be at work.

• ​The phrase 'at work' means at the place where one works​. In this phrase, A/an is not used.

• Thus the 2^nd option is the correct choice.

Correct Sentence: We were busy at work and went for lunch only at 2.30 pm.

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, a predilection for, a respite from, vexed at, etc.
• Example:
• ​After spending some time on the island they became inured to the hardships.

The correct answer is This​.

Key Points​​

• ​The pronouns that connect a clause or phrase to a noun or a pronoun, is called a relative pronoun.
• The demonstrative pronouns are used instead of a noun phrase to indicate distance in time or space in relation to the speaker.
• They also indicate grammatical number – singular or plural.

• Examples:
• Would you like to share some of this pizza with me?
• I’d like you to put these things away before we go.​
• ​As the noun given after the 1^st blank i.e. 'area' is singular and near to the speaker, the 3^rd option i.e. This will be used in the 1^st blank.

The correct answer is to​.

Key Points​

• ​There are some fixed prepositional phrases given below:
• ​by the dint of, out of jealousy, be home to someone/anyone, by the dozen, owing to, on a trip, for a change, etc.
• For example:
• His courtyard was home to a lot of birds.
• ​The phrase 'be home to someone/anyone' means to be the place where that thing is located or, in the case of living things, where they live​.
• Thus the 2^nd option i.e. to is the correct choice in the 2^nd blank.

The correct answer is found​.

Key Points​​

• ​The pronoun that connects a clause or phrase to a noun or a pronoun, is called a relative pronoun.
• The most common relative pronouns are:
• who, whom, what, 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.
• ​Since no relative pronoun has been used after the noun 'birds', the 3^rd option i.e. found (the past participle form of the verb used as an adjective) will be used in the 3^rd blank.

The correct answer is high.

Key Points

• Let's look at the meanings of the given options:- 
• high- at a great altitude
• flight- a formation of aircraft in flight
• far- located at a great distance in time or space or degree
• soaring- the act of rising upward into the air
• ​As per the possible context of the sentence, the above-mentioned park contains various species of birds (Himalayan monal pheasant for instance) that fly at great altitudes.
• Hence, from the given meanings, we find that the 1^st option i.e. high is the correct choice in the 4^th blank.

The correct answer is landscape.

Key Points

• Let's look at the meanings of the given options:- 
• shore- the land along the edge of a body of water
• scene- the place where some action occurs
• movement- a change of position that does not entail a change of location
• landscape- an expanse of scenery that can be seen in a single view
• ​As per the possible context of the sentence, the scenery of the Valley of Flowers National Park is accompanied by the Nanda Devi National Park.
• Hence, from the given meanings, we find that the 4^th option i.e. landscape is the correct choice in the 5^th blank.

The correct answer is Resume duty.

Key Points

• Let's look at the meaning of the given idiom:

• Back in the saddle- doing something that you stopped doing for a period of time

• Example: 

• I needed to take a break for a bit, but now, I'm back in the saddle.

• ​Thus from the explanation given above, we find that the 1^st option is the correct choice.

 ​​​​

Additional Information  

• Let's look at the origin of the idiom:
• The expression 'get back in the saddle' came into use in the 1800s. The image is of someone, such as a jockey or cowboy, who has fallen off a horse and must get back in the saddle to resume riding the horse. Common wisdom dictates that someone who falls off a horse must immediately return to the saddle in order to conquer the horse’s temperament and one’s fears.

The correct answer is BDAC.

Key Points

• While arranging the parts of the passage, we should find some grammatical or contextual connections between them:
• Sentence B introduces us to the subject 'the king getting captured by a tribe'. It is the introductory sentence and will be put in the first place.
• Sentence D tells us about the next step taken by the tribal priest. It will be put in second place.
• Sentence A tells us about the instance when the priest noticed that the king's finger was missing. It will be put in third place.
• The last sentence is C as it tells us the consequences of the above-mentioned instance.

Thus, the correct order is- Once while traveling across a forest, the king was captured by a powerful tribe. The tribal priest decided to sacrifice the king to their God. Just before the sacrifice, however, he noticed that one of the king’s fingers was missing. Since it was not acceptable to sacrifice an incomplete person to God, the king was released.

The correct answer is assets.

Key Points

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

• funding- a reserve of money set aside for some purpose

• reports- a written document describing the findings of some individual or group

• policies- a plan of action adopted by an individual or social group

• assets- a resource with economic value that an individual, corporation, or country owns or controls with the expectation that it will provide a future benefit

• As per the context of the sentence, there is a possibility of doubling the resources of the life insurance sector by ramping up digitisation and leveraging next-generation technologies.

• Hence, from the given meanings, we find that the 4^th option i.e. assets is the correct choice.

​Correct Sentence: By accelerating digitisation and leveraging next-generation technologies, the life insurance sector can double its assets to Rupees 70 lakh crores, a study said.

The correct answer is Dishevelled.

Key Points

Let's look at the meanings of the given word and marked option:

• Prim- affectedly dainty or refined
• Dishevelled- in disarray; extremely disorderly

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

• Principle- a basic generalization that is accepted as true and that can be used as a basis for reasoning or conduct
• Intellectual- of or associated with or requiring the use of the mind
• Mature- fully considered and perfected

Hence from the given meanings, we find that Prim and Dishevelled are antonyms.

The correct answer is Inhale.

Key Points

• Let's look at the meanings of the given word and marked option:
• Exhale- to expel air
• Inhale- to draw deep into the lungs by breathing
• ​​Let's look at the meanings of the other given options: 
• Expel- to force to leave or move out
• Inspire- to heighten or intensify
• Respite- a (temporary) relief from harm or discomfort
• Hence from the given meanings, we find that Exhale and Inhale are antonyms.

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 'Vitamin deficiency​'. It is the introductory sentence and will be put in the first place.
• Sentence A tells us about the primary cause of vitamin deficiency. It will be put in second place.
• Sentence B tells us about the consequences one has to face who suffers from vitamin deficiency. It will be put in third place.
• The last sentence is C as it tells us the importance of the absorption of various nutrients through a sound digestive system.

Thus, the correct order is- Vitamin deficiency is not just caused by a lack of vitamins in the diet. Problems in the absorption of vitamins are the main cause of vitamin deficiency. This is the reason why people with metabolic disorders such as obesity, often suffer from vitamin deficiency. Hence, digestion and the absorption mechanism in the body are very important.

The correct answer is Systemetic.

Key Points

• Let's look at the correct spelling and meaning of the marked option:
• Systematic- according to an agreed set of methods or organized plan (विधियों या संगठित योजना के एक सहमत सेट के अनुसार)
• Example: 
• We've got to be more systematic in the way that we approach this task.

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

• Denounce- to speak out against (के खिलाफ बोलना)
• Ascertain- to establish after a calculation, investigation, experiment, survey, or study (गणना, जांच, प्रयोग, सर्वेक्षण, या अध्ययन के बाद स्थापित करने के लिए)
• Combination- a collection of things that have been combined; an assemblage of separate parts or qualities (चीजों का एक संग्रह जो संयुक्त हो गया है; अलग-अलग हिस्सों या गुणों का एक संयोजन)

The correct answer is Supple.

Key Points

• Let's look at the meanings of the given word and marked option:

• Resilient- able to recoil or spring back into shape after bending, stretching, or being compressed

• Supple- moving and bending with ease

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

• Furious- marked by the extreme and violent energy

• Lazy- moving slowly and gently

• Baseless- without a basis in reason or fact

• Hence from the given meanings, we find that Resilient and Supple are synonyms.

The correct answer is were airdropped for animals starving​.

Key Points

• The simple past tense is used when we talk about things that happened or existed before now.
• The structure is given below:
• Subject + V2 + object. (Active Voice)
• Object + was/were + V3 + by + subject. (Passive Voice)
• Example:
• ​He won the car race. (active voice)
• The car race was won by him. (passive voice)
• Since the sentence follows the passive voice structure and takes place in the past tense, the 3^rd form of the verb i.e. airdropped will be used instead of 'airdrop' in the underlined part.

Correct Sentence: Carrots and sweet potatoes were airdropped for animals starving during the tragic bushfires in Australia.

The correct answer is Solve the problem​.

Key Points

• Let's look at the meaning of the given idiom:
• Cross that bridge when one comes to it​- deal with a problem when and if it arises
• Example: 
• I don't know how we'll pay the bills if you quit your job, but we'll cross that bridge when we come to it.
• ​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:
• Don't cross the bridge until you come to it is an English language idiom cliché. Though the history of where the phrase came from is unclear, it is believed to have originated from a proverb by Henry Wadsworth Longfellow.

The correct answer is what that​.

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, what, 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.
• ​Two relative pronouns can't be put together, hence 'that' will be removed from the part given in the 2^nd option.

​Correct Sentence: No matter what the mother did the baby didn’t stop crying.

​​​

Additional Information  ​​

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

The correct answer is Experts said, “Several steps are being taken to promote foreign trade as it constitutes 45% of the country’s economy”.

Key Points​​

The indirect speech is in the assertive form, let's look at the steps to change the sentence from indirect to direct speech:

• The reporting verb said will remain the same as no object has been mentioned after it.
• The connector 'that' is replaced by a comma and inverted commas.
• The tense of indirect/reported speech is changed only when the reporting verb is in the past tense.
• The verb (passive voice) in the past continuous tense will be changed to the present continuous tense in direct speech resulting in the following changes:
• were being taken - are being taken.
• constituted - constitutes. (past simple into present simple)

​​​At last, line up the remaining part, following these steps, we finally get - Experts said, “Several steps are being taken to promote foreign trade as it constitutes 45% of the country’s economy”.

The correct answer is Happen.

Key Points

• Let's look at the meanings of the given word and marked option:

• Occur- take place

• Happen- to exist or begin to exist because of an action, situation, or event

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

• Hasten- to act or move at high speed

• Hinder- to be a hindrance or obstacle to

• Hamper- to prevent the progress or free movement of

• Hence from the given meanings, we find that Occur and Happen are synonyms.

The correct answer is The research paper was written by Jiya with the help of her tutor.

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 (Jiya) and object (the research paper) 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, 'wrote' changes to 'was written'.
• At last line up the remaining part.

​

Following these steps, we get - The research paper was written by Jiya with the help of her tutor.

The correct answer is up.

Key Points​​

• ​Let's look at the meanings of the following phrasal verbs:
• bring in- move something indoors
• bring out- elicit, evoke, or emphasize a particular quality
• bring up- to raise a child
• bring over- to take someone or something from one place to the place where someone else is, especially their home
• As per the context of the sentence, Madhuri took care of her sister's daughter after her parents passed away.
• The phrasal verb 'bring up' will be the correct choice in the blank part of the sentence.

​Correct Sentence: Madhuri is bringing up her sister’s daughter after the death of the child’s parents.

The correct answer is Capricious.

Key Points

• Let's look at the meaning of the marked option:

• Capricious- changing mood or behaviour suddenly and unexpectedly

• Example: 

• He was a cruel and capricious tyrant.

Let's look at the correct spelling and meaning of the other given options:

• Avalanche- a slide of large masses of snow and ice and mud down a mountain

• Ecstasy- a state of being carried away by overwhelming emotion

• Complaisant- showing a cheerful willingness to do favors for others

The logic is:

3² + 1 = 9 + 1 = 10

52 + 1 = 25 + 1 = 26

72 + 1 = 49 + 1 = 50

92 + 1 = 81 + 1 = 82

112 + 1 = 121 + 1 = 122

Hence, '122' is the correct answer.

The total number of triangles in the given figure is shown below:

Hence, ‘26’ is the correct answer.

When the mirror is placed on line PQ in the question figure, the answer figure that is the correct mirror image of the question figure is shown below:

Hence, ‘option 4’ is the correct answer.

1. yyrsx

Given: rtx_sx_z_txy_ _ yz

After filling the blanks with the letters in the option given above, we get:

rtxysxyz / rtxysxyz

A particular pattern is repeating itself when the sequence is divided into two equal parts.

2. yyrxs

Given: rtx_sx_z_txy_ _ yz

After filling the blanks with the letters in the option given above, we get:

rtxysxyz / rtxyxsyz

No particular pattern is repeating itself when the sequence is divided into two equal parts.

3. sysyx

Given: rtx_sx_z_txy_ _ yz

After filling the blanks with the letters in the option given above, we get:

rtxssxyz / stxyyxyz

No particular pattern is repeating itself when the sequence is divided into two equal parts.

4. yxyrs

Given: rtx_sx_z_txy_ _ yz

After filling the blanks with the letters in the option given above, we get:

rtxysxxzytxyrsyz

No particular pattern is repeating itself when the sequence is divided into two equal parts.

Hence, ‘yyrsx’ is the correct answer.

The answer figure that when placed in the blank space of the question figure will complete the pattern is shown below:

Hence, ‘option 2’ is the correct answer.

1. • and –

Given equation: (72 ÷ 18) + 30 × 8 − 4 = 20

After interchanging the signs, we get:

L.H.S. = (72 ÷ 18) - 30 × 8 + 4

= 4 – 240 + 4

= 8 – 240

= -232 ≠ R.H.S

2. • and × 

Given equation: (72 ÷ 18) + 30 × 8 − 4 = 20

After interchanging the signs, we get:

L.H.S. = (72 ÷ 18) × 30 + 8 − 4

= 4 × 30 + 8 – 4

= 120 + 8 – 4

= 128 – 4

= 124 ≠ R.H.S

3. × and ÷ 

Given equation: (72 ÷ 18) + 30 × 8 − 4 = 20

After interchanging the signs, we get:

L.H.S. = (72 × 18) + 30 ÷ 8 − 4

= 1296 + 3.75 – 4

= 1299.75 – 4

= 1295.75 ≠ R.H.S

4) + and ÷ 

Given equation: (72 ÷ 18) + 30 × 8 − 4 = 20

After interchanging the signs, we get:

L.H.S. = (72 + 18) ÷ 30 × 8 − 4

= 90 ÷ 30 × 8 – 4

= 3 × 8 – 4

= 24 – 4

= 20 = R.H.S.

Hence, ‘+ and ÷’ is the correct answer.

The figure in which the question figure is embedded when Rotation is not allowed is shown below:

Hence, ‘option 2’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘R38T’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘G’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Instead of 'NM', it should be 'MN' in the series.

Hence, ‘NM’ is the correct answer.

The logic is:

Butter : Milk → Butter is obtained from milk.

Similarly,

Oil : ? → Oil is obtained from oil seeds (endosperm) of some plants.

Hence, ‘seed’ is the correct answer.

The logic is:

First diagram: 13 + 108 = 11² 

⇒ 121 = 11²

Second diagram: 

26 + 55 = 92 

⇒ 81 = 92

Similarly,

Third diagram: ? + 157 = 142 

⇒ ? + 157 = 196

⇒ ? = 196 - 157

⇒ ? = 39

Hence, '39' is the correct answer.

All numbers except '52477' are even numbers, while '52477' is an odd number.

Hence, '52477' is the odd one out.

The logic is:

Ship : Sailor → Sailor is a person who works on a ship or a person who sails a boat.

Similarly,

Laboratory : Scientist → Scientist is a person who works in a Laboratory.

Hence, ‘Laboratory : Scientist’ is the correct answer.

The total number of triangles in the given figure is shown below:

Hence, ‘9’ is the correct answer.

The logic is:

Hence, ‘40’ is the correct answer.

The sum of the ages of a mother, daughter and son is 96 years.

Mother + Daughter + Son = 96

Sum of their ages after 5 years = 96 + 5 × 3

= 96 + 15

= 111

Hence, ‘111’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘JMWHTHCKF’ is the correct answer.

The logic is:

Similarly,

Hence, ‘CHARCH’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘HIH’ is the correct answer.

The logic is:

19 : 23 → 19 + 4 = 23

Similarly,

97 : ? → 97 + 4 = 101

Hence, ‘101’ is the correct answer.

The person who likes all the given eating materials is shown below:

C likes meat, and the shaded area shows that C likes both milk and bread.

Therefore, only C is the person who likes all the eating materials.

Hence, ‘Only C’ is the correct answer.

The paper when unfolded will appear as shown below:

Hence, ‘option 1’ is the correct answer.

The least possible Venn diagram is:

(I) Some dogs are cats. → True (As, Some cats are dogs)

(II) Some cats are trees. → False (As, there is no definite relation between cats and trees. Hence, false)

Hence, only conclusion I follows.

The logic is:

First diagram: 9 × 13 + 13 = 130

Second diagram: 14 × 9 + 9 = 135

Similarly,

Let the missing number is x.

Third diagram: 7 × x + x = 168

⇒ 8x = 168

⇒ x = 168 ÷ 8

⇒ x = 21

Hence, ‘21’ is the correct answer.

Given:

sinθ = 4/5 

Formula Used:

sin3θ = 3sinθ - 4sin³θ  

Calculation:

sin3θ = 3sinθ - 4sin3θ  

⇒ sin3θ = 3(4/5) - 4(4/5)³

⇒ sin3θ = 12/5 - 256/125

⇒ sin3θ = 44/125  

∴ The answer is 44/125.

From the Graph, 

The number of student passed in class 4 = 45 + 12 = 57 

The number of student passed in class 5 = 38 + 15 = 53 

The number of student passed in class 6 = 42 + 10 = 52

The number of student passed in class 7 = 30 + 25 = 55 

57 > 55 > 53 > 52

∴ the highest number of student passed in class 4

Given:

The difference between a number and one-third of that number is 228.

Calculation:

Let number be x 

According to Question,

x - (1/3)x = 228 

⇒ 2x/3 = 228

⇒ x = 228 × 3/2 = 342 

 20% of the number = (20/100) × 342 = 68.4 

∴ 20% of the number is 68.4.

Given 

2in2x - 1 = 0

Formula Used 

Radian = (π/180) × angle in degree 

Calculation 

⇒ 2sin2x - 1 = 0

⇒ 2sin²x = 1 

⇒ sinx = 1/√2 

⇒ x = 45° 

⇒ x (In radian) = (π/180) × 45° = π/4  

∴ the value of x is π/4

Given:

The side of the triangle is 5, 6 and 7 cm 

Formula Used:

Area of triangle = √[s(s - a)(s - b)(s-c)],     where s = semiperimeter of the triangle 

Semiperimeter (S) = (1/2) × Sum of sides of the triangle

Calculation:

Semiperimeter (s) = (a + b + c)/2 = (5 + 6 + 7)/2 = 9

⇒ Area of the triangle = √[s(s - a)(s - b)(s-c)]

⇒ √[9(9 - 5)(9 - 6)(9 - 7)] = √(9 × 4 × 3 × 2) = 14.69 cm² 

∴ the area of the triangle is 14.69 cm2

Calculation 

According to question, 

(1/5) of (3/8) of (1/3) of 11760

⇒ (1/5) × (3/8) × (1/3) × 11760 = 294 

∴ Required answer is 294.

Given:

cotθ = 80/39

Formula Used:

cosec²θ - cot²θ  = 1 

Calculation:

cosec²θ - (80/39)² = 1

⇒  cosecθ = √(1 + (80/39)² = 89/39 

∴ The required value of cosecθ is 89/39

Given:

Smith can do the work in 12 days 

Ajit can do the same work in 18 days 

Formula used:

Work = Time × Efficiency 

Calculation: 

Take the LCM (12, 18) = 36 

⇒ let the total work be 36 units

Efficiency of Smith = 36/12 = 3 units/day

Efficiency of Ajit = 36/18 = 2 units/day 

Work completed by them in 4 days = (3 + 2) × 4 = 20 units

⇒ Remaining Work = 36 - 20 = 16  units

⇒ Fraction of remaining work of the total work = 16/36 = 4/9 

∴ Fraction of remaining work of the total work is 4/9.

Given:

Height of the equilateral triangle = 12 cm 

Formula Used:

Height of triangle = (√3/2) × side of an equilateral triangle 

Area of an equilateral triangle = (√3/4) × side²

Calculation:

Side of the triangle = (2/√3) × 12 = 8√3 

Area of the triangle = (√3/4) × (8√3)² 

⇒ (√3/4) × 64 × 3 = √3 × 16 × 3 = 48√3 cm²

∴ The area of equilateral triangle is 48√3 cm²     

Traditional Method

Height = 12 cm

Height = √3/2 × Side

12 = √3/2 × Side

Side = 24/√3 cm

Area of Eq Triangle = √3/4 × Side2

Area of Eq Triangle = (√3/4) × (24/√3) × (24/√3)

⇒ 6 × 24/√3 

Now 6 can be written as 2 × √3 × √3

⇒ 2 × √3 × √3 × 24/√3 = 48√3 cm2

Shortcut Trick

Discount Percentage = (Discount ÷ MRP) × 100

Discount = 978 − 925 = 53

Discount % = (53 ÷ 978) × 100 ≈ 5.4%

∴ The correct answer is 5.4%.

Alternate Method

Given:

MRP (Marked Price) = ₹978

SP (Selling Price) = ₹925

Formula Used:

Discount = MRP − Selling Price

Discount % = (Discount / MRP) × 100

Calculations:

⇒ Discount Amount = 978 − 925 = 53

⇒ Discount % = (53 ÷ 978) × 100

⇒ Discount % = 5300 ÷ 978

⇒ Discount % ≈ 5.419%

∴ The correct answer is 5.4%.

Additional Information

Marked Price (MRP)

The price printed on the product label, also known as the List Price or Tag Price. Discounts are always calculated on this value.

Successive Discounts

When two discounts d₁% and d₂% are given, the Effective Discount = (d₁ + d₂ − (d₁ × d₂)/100)%.

Profit/Loss Base

While Discount is calculated on Marked Price, Profit or Loss is always calculated on the Cost Price (CP).

Given:

x = 1 + √2

Concept Used:

a² + b² = (a + b)² - 2ab

Calculation:

x = 1 + √2

⇒ 1/x = 1/(1 + √2)

⇒ 1/x = (√2 - 1)/(√2 + 1) × (√2 - 1)

⇒ 1/x = (√2 - 1)

Now,

x + 1/x = √2 + 1 + √2 - 1

⇒ (√x + 1/√x)² - 2 = 2√2

⇒ (√x + 1/√x)² = 2 + 2√2

⇒ (√x + 1/√x) = √4.8284                 [√2 = 1.414]

⇒ (√x + 1/√x) = 2.1973

∴ (√x + 1/√x) = 2.1973

Concept used: 

divisibility rule of 9 : If Sum of all digit is divisible by 9 , then the number will be divisible by 9

Calculation: 

⇒ From options 

⇒ We consider option (1) , number = 734895 

⇒ sum of digit = 7 + 3 + 4 + 8 + 9 + 5 = 36 

⇒ 36 is divisible by 9, so number is also divisible by 9 

∴ 734895 is divisible by 9

From the Graph 

Total Number of student of class 6 = 42 + 10 + 8 = 60 

Number of student who pass of class 6 = 42 + 10 = 52 

⇒ Pass percentage of class 6 = (52/60) × 100 = 86.66% 

∴ the pass percentage of class 6 is 86.66%

Given: 

Speed of 1^st car = 72 km/hr 

speed of 2^nd car = 54 km/hr

Formula Used: 

x km/hr = x × (5/18) m/s 

Distance = time × speed

Calculation:

The speed of the 1^st car = 72 km/hr = 72 × 5/18 = 20 m/s 

⇒ The distance "AB" travelled by car in 20 seconds is = 20 × 20 = 400 m

The speed of the 2^nd car = 54 km/hr = 54 × 5/18 = 15 m/s

⇒ The distance "BC" travelled by car in 20 seconds is = 15 × 20 = 300 m

Since two cars are moving at right angles to each other, so we will apply the Pythagoras theorem to find the distance between them.

The distance "AC" between them after 20 seconds is, √(AB² + BC²) 

⇒√(400² + 300²) 

⇒ √25000 

⇒ 500 m 

∴ After 20 seconds the distance between them will be 500 m.

Given: 

The difference between 2 numbers = 6 

Formula Used:

a² - b² = (a - b)(a + b) 

Calculation: 

Let two number be a and b respectively [Where a > b]

Accordingly, 

a - b = 6      ----(1)

And,

a2 - b² = 60

⇒ 60 = (a + b)(a - b)

⇒ 60 = 6(a + b) 

⇒ (a + b) = 10      ----(2)

From (1) and (2) get,

a = 8, b = 2 

Sum of their cube = a³ + b³ = 8³ + 2³ = 512 + 8 = 520 

∴ The sum of their cube is 520.

Given: 

Radius of circle = 6 cm

Formula Used: 

Equation : (x - x₁)² + (y - y₁)² = c² 

Where (x₁, y₁) is the center of the circle and c is the radius of the circle

Calculation: 

The center is at the origin

So here, x₁ = 0, y₁ = 0

Radius of the circle (c) = 6 cm

Equation of circle is

(x - 0)2 + (y - 0)2 = 62  

⇒ x² + y² - 36 = 0 

∴ The required equation of the circle is x2 + y2 - 36 = 0.

Shortcut Trick

Sum of ratio parts = 7 + 9 = 16 units

Total items given = 560

1 unit = 560 ÷ 16 = 35

Number of chairs (9 units) = 9 × 35 = 315

∴ The correct answer is 315 chairs.

Alternate Method

Given: Ratio of tables to chairs = 7 : 9. Total tables and chairs = 560.

Formula Used: Value of a part = (Ratio of part ÷ Sum of ratios) × Total Value

⇒ Let the number of tables be 7x and chairs be 9x.

⇒ 7x + 9x = 560

⇒ 16x = 560

⇒ x = 560 ÷ 16 = 35

⇒ Number of chairs = 9 × 35 = 315

∴ The correct answer is 315 chairs.

Additional Information

Ratio and Proportion

If a total quantity Q is divided in ratio a:b, then the first part is (a/(a+b)) × Q and the second part is (b/(a+b)) × Q.

Compound Ratio

For two ratios a:b and c:d, the compound ratio is (a × c) : (b × d).

Given: 

Length of the chord = 24 cm 

Formula Used: 

If a perpendicular is drawn from the center of a triangle to any chord of the circle then the perpendicular will bisect the chord into two equal part.

(Hypotnuese)² = (perpendicular)² + base²

Area of circle = πR² 

Calculation:

In ΔOAC, OA = radius of triangle 

AC = 1/2(AB) [we know that, chord is divide in equal part by perpendicular from center to the chord]

⇒ OA² = (AC)² + (OC)² 

⇒ OA = √(12² + 5²) = 13

Area of circle = πR²

⇒ (22/7) × 13²

⇒ 531.14 cm²

∴ The area of the circle is 531.14 cm²

Given 

Perimeter of Rectangle = 730 cm 

Formula Used 

Perimeter of rectangle = 2(L + B) , 

Area of rectangle = L × B , where L = length and B = Breadth

Calculation 

⇒ let the length and breadth be 3x and 2x respectively 

⇒ Perimeter = 730 cm

⇒ 2(5x) = 730 

⇒ x = 73 

so , length = 3x = 3 × 73 = 219 cm 

Breadth = 2x = 2 × 73 = 146 cm 

Area of rectangle = 219 × 146 = 31974 cm²

∴ The area of rectangle is 31974 cm²

Given:

Concept used:

Total number of student in class 4 = 45 + 12 + 3 = 60 

Number of student who passed in class 4 = 45 + 12 = 57 

Pass percentage of class 4 = (57/60) × 100 = 95% 

∴ The pass percentage of class 4 is 95%

Given:

Calculation:

⇒ The number of student passed in class 4 = 45 + 12 = 57 

⇒ The number of student passed in class 5 = 38 + 15 = 53 

⇒ The number of student passed in class 6 = 42 + 10 = 52

⇒ The number of student passed in class 7 = 30 + 25 = 55 

∴ The least number of student passed in class 6

Shortcut Trick

The sum of squares of two numbers is given by the formula: (Sum)² − 2 × (Product).

⇒ Sum of squares = 59² − (2 × 840)

⇒ Sum of squares = 3481 − 1680

⇒ Sum of squares = 1801

∴ The correct answer is 1801.

Alternate Method

Given:

Sum of two numbers (x + y) = 59

Product of the numbers (xy) = 840

Formula Used:

We use the algebraic identity: (x + y)² = x² + y² + 2xy

Calculations:

⇒ (59)² = x² + y² + 2 × 840

⇒ 3481 = x² + y² + 1680

⇒ x² + y² = 3481 − 1680

⇒ x² + y² = 1801

∴ The correct answer is 1801.

Additional Information

Square of a Difference

The identity for the square of a difference is (a − b)² = a² + b² − 2ab. It can be related to the sum of squares as a² + b² = (a − b)² + 2ab.

Relationship between Identities

The two identities are linked by: (a + b)² − (a − b)² = 4ab. This is useful for finding the difference between numbers when the sum and product are known.

Difference of Two Squares

The formula a² − b² = (a + b)(a − b) is another fundamental identity used to factorize the difference of two quadratic terms.

Given 

Principal = Rs 8000 

Rate of interest = 6.5% per month

Formula Used 

Amount = principal(1 + R/100)^t

Calculation

⇒ Amount = 8000[1 + 6.5/(12 × 100)]¹⁸

⇒ Amount = 8000(1.0054)¹⁸

⇒ Amount = 8000(1.1021) = 8816.97 

∴ The amount he will get at the end of 18 months is Rs 8816.97

We know that, by Binomial thorem, 

 (1 + r)ⁿ ≈ 1 + nr + n(n - 1)/2 × r² + ...

Monthly interest rate, r = (6.5/12)%

Now, we can calculate the amount = 8000 × {1 + 18 × (6.5/12)% + (18 × 17)/2 × [(6.5/12)%]²}

Amount ≈  8000 × {1 + 0.097 + 0.003} 

Amount ≈  8000 × 1.1 ≈ 8800

So, from the options, we can conclude that Rs 8816.97 will be the correct solution.

Important Points

Note that, in doing the second method, we only need to know, the binomial theorem, a basic two-power calculation to get the solution that is nearest to our required actual solution.

Given 

The average age of 16 student = 20 

the average age of 5 student = 20 

Formula used 

Average = Sum of observation/No. of observation

Calculation 

Total age of 16 student = 16 × 20 = 320 

⇒ Total age of 5 student = 5 × 20 = 100 

⇒ Total age of 10 student = 10 × 20.4 = 204 

⇒ Let the age of 16^th student be x 

⇒ 320 = 100 + 204 + x 

⇒ x = 16 

∴ The age of 16^th college student is 16.

Given 

Selling price of an article at 20% profit = Rs 600 

Formula Used 

Cost price = selling price/(100 + profit%) × 100 

Selling price = cost price/100 × (100 - loss%)

Calculation 

Cost price = (600/120) × 100 = Rs 500 

Selling price = (500/100) × 80 = Rs 400

∴ The selling price of an article at 20% loss is Rs 400

The correct answer is Telangana.

• Nizam Sagar Dam is situated in Telangana.

Key Points

• Nizam Sagar Dam:
• The dam is located in Telangana.
• It is situated on the Manjira River.
• It was built in 1923 by Mir Osman Ali Khan, the then ruler of Hyderabad.
• Manjira river is a tributary of the Godavari.
• The Godavari originates from Trimbakeshwar in Nashik.
• It is also known as Dakshin Ganga
• Other tributaries of Godavari: Penganga, Wardha, Indravati, Sabri.

Additional Information

• Tungabhadra Project is on the river Tungabhadra in Karnataka.
• Nagarjuna Sagar Project is on Krishna in Andhra Pradesh.
• The main dam of the Mayurakshi Project, known as the Massanjore Dam (or Canada Dam), is indeed located in Dumka, Jharkhand.

The correct answer is groundwater.

• Atal Bhujal Yojana (ABY) is related to groundwater.

Key Points

• Atal Bhujal Yojana (ABY):
• Atal Bhujal Yojana (ATAL JAL) is a Central Sector Scheme of the Ministry of Jal Shakti.
• The scheme was launched on  25^th December 2019 on the special occasion of the 95^th birth anniversary of former PM Atal Bihari Vajpayee.
• The aim of the scheme is to improve groundwater management through community participation.
• The States included in the Atal Bhujal Yojana are Gujarat, Haryana, Karnataka, Madhya Pradesh, Maharashtra, Rajasthan and Uttar Pradesh.

The correct answer is Karnataka.

• Bankapura Peacock Sanctuary is situated in Karnataka.

Key Points

• Bankapura Peacock Sanctuary:
• The sanctuary is famous for peacocks is situated in Karnataka.
• The sanctuary is located inside the Bankapura Fort.
• The sanctuary has more than 1000 peacocks.
• Other national parks and sanctuaries in Karnataka are Bandipur National Park, Nagarhole National Park, Dandeli Wildlife Sanctuary, Bhadra Wildlife Sanctuary, Ranganathittu Bird Sanctuary, Bannerghatta National Park and Kabini.

Additional Information

The correct answer is 1930.

• The first Commonwealth Games were held in 1930.

Key Points

• The 1^st Commonwealth Games were held in 1930 at Hamilton, Canada.
• After Olympics, Commonwealth Games is the second-largest sports festival in the world.
• The Games are held once in four years but only in between the Olympic years.
• The 1^st Commonwealth Games were held in 1930 at Hamilton, Canada.
• India participated for the first time in the second Commonwealth games held in London in 1934.

Additional Information

• The Commonwealth Games is a festival of sports of the Commonwealth countries.
• Since 1930, the games have been conducted every four years except for 1942 and 1946.
• The 2018 Commonwealth Games were held in Goldcoast, Australia.
• The 2022 Commonwealth Games will be held in Birmingham, England.

The correct answer is 1975.

• The first Regional Rural Bank was established in India in the year 1975.

Key Points

• Regional Rural Banks:
• The Regional Rural Banks (RRBs) are the newest form of banks that came into existence since the middle of the 1970s.
• It was sponsored by individual nationalised commercial banks with the objective of developing the rural economy by providing crediting and depositing facilities for agriculture and other productive activities of all kinds in rural areas.
• Regional Rural Banks (RRBs) were set up under the terms of the 26 September 1975 ordinance and the RRB Act of 1976.
• First Regional Rural Bank was established on 2 October 1975.
• The Prathama Bank of Moradabad, Uttar Pradesh was the first RRB.
• Currently, there are 43 RRBs in India.

Additional Information

• Oudh Commercial Bank was the first complete Commercial Bank of India.
• ​The Imperial Bank was established in the year 1921 by merging three main Presidency Banks.
• It was later rechristened as State Bank of India in 1955.
• Nationalisation of Banks was done in 1969.

The correct answer is LIGO.

• LIGO was used to detect gravitational waves for the very first time.

Key Points

• LIGO is Laser Interferometer Gravitational-Wave Observatory.
• It is located in Richland, Washington.
• In 2015, scientists detected gravitational waves for the very first time.
• A gravitational wave is an invisible ripple in space.
• These first gravitational waves occurred when two black holes crashed into one another.
• The collision took place 1.3 billion years ago. But, the ripples didn’t make it to Earth until 2015.
• Causes of a gravitational wave are:
• When a star explodes asymmetrically.
• When two big stars orbit each other.
• When two black holes orbit each other and merge.

The correct answer is 1906.

• The Muslim League was founded in 1906.

Key Points

• Formation of the Muslim League:
• It was set up in 1906 AD, under the leadership of Aga Khan, Nawab Salimullah of Dhaka and Nawab Mohsin-ul-Mulk.
• Aga Khan was the first president of the Muslim League.
• It supported the partition of Bengal, opposed the Swadeshi Movement, and demanded special safeguards for its community and a separate electorate for the Muslims.
• Muhammad Ali Jinnah joined the Muslim league in 1913.
• In 1930, Iqbal suggested the union of the Frontier Province–Baluchistan, Sindh and Kashmir–as a Muslim state within the federation.
• Chaudhry Rehmat Ali invented the term ‘Pakstan’ (later ‘Pakistan’) in 1935 AD.
• The Lahore Session of the Muslim League was held in March 1940 AD.
• Pakistan Resolution was passed and the Federal scheme was rejected as envisaged in the Government of India Act, 1935 AD.

The correct answer is 14,500 km.

• The approximate length of the navigable inland waterways of India is 14,500 km.

Key Points

• As per the National Waterways Act, 2016 a total of 111 have been declared as National Waterways (NW).
• The waterway from Haldia to Allahabad was made a National Waterway in 1986.
• The Inland Waterways Authority of India (IWAI) came into existence on 27 October 1986.

Additional Information

• Inland Waterways:
• Rivers, lakes, canals, backwaters and reservoirs primarily constitute the source for inland waterways.
• A stretch of water, not part of the sea, over which craft of a carrying capacity not less than 50 tonnes can navigate when normally loaded is called a navigable inland waterway.

The correct answer is high-level language.

• Python is a high-level language.

Key Points

• Python
• It is a high-level language.
• It allows programming in Object-Oriented and Procedural paradigms.
• The language was created by Guido van Rossum.
• It was first released in 1991.
• It is used for web development (server-side), software development, mathematic, and system scripting.
• It can work on platforms like Windows, Mac, Linux, Raspberry Pi, etc

Additional Information

• Machine language and Assembly language are an example of a low-level language.
• Machine language is a low-level language that is comprised of binary digits i.e. ones and zeros.
• An assembly language is a language designed for a specific type of processor.

The correct answer is 953.

• There are 953 windows on the outside walls of Hawa Mahal of Jaipur.

Key Points

• Hawa Mahal was built by Maharaja Sawai Pratap Singh in 1799.
• Red and pink sandstone was used for constructing this marvellous monument.
• The construction was done in the shape of the crown because Sawai Pratap Singh was believed to be a great devotee of Lord Krishna and wanted to look it like Krishna’s crown.
• The Hawa Mahal was made to allow royal ladies to watch the daily drama in the street below, without being noticed.
• It reflects a fusion of Islamic Mughal and Hindu Rajput architecture.

The correct answer is 1517.

• Ibrahim Lodhi becomes the sultan of Delhi in 1517.

Key Points

• Ibrahim Lodhi:
• He was the last king of the Lodi dynasty and the last sultan of Delhi.
• He was the son of Sikandar Lodi.
• Daulat Khan Lodi, the Governor of Punjab, invited Bahur to overthrow Ibrahim.
• He captured Gwalior and was defeated by Rana Sanga of Mewar.
• Ibrahim Lodi was defeated and killed at the hands of Babur in the First Battle of Panipat in 1526 AD.

Additional Information

• Administration:
• The head of the military department was called Ariz-i-Mamalik.
• Diwan-i-Risalat dealt with the religious matter. The Qazi dispensed civil law based on Muslim law (Sharia).
• Diwan-i-Insha headed by Dahir-i-Mumalik managed the royal correspondence.
• The rulers posted intelligence agents called Barids in different parts of the empire.

The correct answer is 2015.

• Motor Vehicles Agreement (MVA) for the Regulation of Passenger, Personal and Cargo Vehicular Traffic signed between sub-grouping of four SAARC nations, Bangladesh, Bhutan, India and Nepal (BBIN) was passed in 2015.

Key Points

• Motor Vehicles Agreement:
• India, Nepal, Bhutan and Bangladesh signed a Motor Vehicles Agreement (MVA) for the Regulation of Passenger, Personal and Cargo Vehicular Traffic among the four South Asian neighbours in Thimpu, Bhutan.
• The act will facilitate a way for a seamless movement of people and goods across their borders for the benefit and integration of the region and its economic development.
• The MVA Agreement was signed by the Union Minister of Road Transport & Highways and Shipping Mr Nitin Gadkari with Mr Obaidul Quader, Minister of Road Transport and Bridges of Bangladesh, Mr Lyonpo D. N. Dhungyel, Minister of Information and Communications, Bhutan, and Mr Bimalendra Nidhi, Minister of Physical Infrastructure and Transport, Nepal.

Additional Information

• South Asian Association for Regional Cooperation (SAARC):
• SAARC was established in Dhaka on 8 December 1985 with the signing of the SAARC Charter.
• The Headquarters and Secretariat of the SAARC are at Kathmandu, Nepal.
• It consists of countries like Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, Sri Lanka.
• Afghanistan became the newest member at the 13^th annual summit of SAARC in 2005.
• There are nine Observers to SAARC they are Australia, China, the European Union, Iran, Japan, the Republic of Korea,  Mauritius, Myanmar and the United States of America.

The correct answer is Khashaba Dadasaheb Jadhav.

• Khashaba Dadasaheb Jadhav is associated with wrestling.

Key Points

• The First Indian to Win an Olympic Bronze is Khashaba Jadhav.
• Khashaba Dadasaheb Jadhav is associated with wrestling.
• The word associated with Wrestling is Freestyle, Hal Nelson, Point, Heave, etc.
• The famous person associated with wrestling is as follows: Sakshi Malik, Sushil Kumar Solanki, Udey Chand, Jatindra Charan Goho, Khashaba Dadasaheb Jadhav (K D Jadhav), Yogeshwar Dutt.

Additional Information

The correct answer is Atal Bihari Vajpayee.

• Rohtang Pass in Himachal Pradesh after former prime minister Atal Bihari Vajpayee in a tribute to him on his 95^th birth anniversary.

Key Points

• Rohtang Tunnel connects Manali to Lahaul-Spiti valley.
• The tunnel is 9.02 km long.
• It is built in the Pir Panjal Range of the Himalayas at an altitude of 3000 metres from the Mean Sea Level (MSL).
• The tunnel is also known as the World’s longest highway tunnel.
• It was built by Border Roads Organisation (BRO).

The correct answer is Peter Handke.

• Peter Handke won the Nobel prize 2019 in literature.

Key Points

• Peter Handke was awarded the 2019 Nobel prize in literature for an influential work that with linguistic ingenuity has explored the periphery and the specificity of human experience.
• The first man to win Nobel Prize for Literature was Sully Prudhomme.
• Nobel Prize:
• The Nobel Prizes are given under the will of Alfred Bernhard Nobel, who died in 1896.
• Nobel Prizes are given each year in the six fields.
• The Nobel Prizes for Peace, Physics, Chemistry, Medicine, and Literature were started in 1901.
• The Nobel Prize for Economics was started in 1968.
• The prize-awarding bodies are the Swedish Academy of literature awards the Prize in Literature.
• The Royal Swedish Academy of Sciences awards the prize in Physics and Chemistry.
• The Nobel Assembly of Karolinska Chirurgical (Sweden) awards the prize in Medicine (Physiology).
• The Bank of Sweden awards the Prize in Economics.
• The Committee of the Norwegian Parliament awards the prize for Peace.

Additional Information

• In 2018, Olga Tokarczuk won the Man Booker International Prize for her novel Flights.
• The 2016 Nobel Prize in Literature was awarded to Bob Dylan.
• Kazuo Ishiguro won the 2017 Nobel Prize for Literature.