SSC CHSL Previous Paper 13 (Held On: 13 Oct 2020 Shift 1) (Previous Year Paper)

The correct answer is '3' i.e. 'Accumulate'

Key Points

• Let's see the meaning of the given words-
• ​Stimulate→ It is a verb that means 'apply or act as a stimulus to'
• Formulate→ It is a verb that means 'create or prepare methodically.'
• Accumulate→ It is a verb that means 'gather together'
• Simulate→ It is a verb that means 'imitate or reproduce the appearance'

Hence, according to the meaning of the verb 'Accumulate' it fits in the blank because debts are going to be accumulated by people.

The correct answer is 'A' i.e. 'Adverse'

Key Points

• Let's see the meanings of the given words-
• ​Adverse→ It is an adjective that means 'preventing success or development'
• Averse→ It is an adjective that means 'Strongly disliking something'
• Traverse→ It is a verb that means 'travel or extend across or through'
• Inverse→ It is an adjective that means 'opposite in position or direction'
• We need an adjective to qualify the noun 'weather conditions.' Hence, according to the meaning of the words 'Adverse' is the correct answer.

So the correct sentence is→ This winter Adverse weather conditions have led people to remain indoors.

The correct answer is '2' i.e. error lies in part 2 of the sentence

Key Points

In part 2 of the sentence the usage of 'was' is incorrect instead, use 'were'

• According to grammar, Whenever we have a plural subject we should always use a plural verb hence in the given sentence there are two subjects which are joined with the coordinating conjunction 'and' the subjects are 'A Royal Bengal tigress and her three cubs' So use a plural verb.

So the correct sentence→  A Royal Bengal tigress and her three cubs were poisoned and their carcasses left to rot in the Wildlife Sanctuary in Goa

The correct answer is 'Benign'

Key Points

• Let's see the meanings of the given words
• Malignant→ It is an adjective that means 'If you say that someone is malignant, you think they are cruel and like to cause harm.' (घातक)
• Hesitant→ It is an adjective that means 'If you are hesitant about doing something, you do not do it quickly or immediately'. (दुविधा में पड़ा हुआ)
• Benign→ It is an adjective that means 'You use benign to describe someone who is kind, gentle, and harmless.' (सौम्य)
• Indignant→ It is an adjective that means 'If you are indignant, you are shocked and angry because you think that something is unjust or unfair.' (क्रोधित)
• Fatal→ It is an adjective that means 'leading to failure or disaster'. (घातक)
• As we can see from the meanings of the words given in the options that except 'Benign' all the other words can be Synonyms of the given word. So the correct answer is Option 3.

The correct answer is 'Better'

Key Points

• In the given blank, we need to use 'Better' because 'Even better' is a phrase that means 'when talking about something that's more positive or exciting or a better option than that which preceded it.'
• We cannot use 'best' because it is a superlative degree of 'good' and we don't need a superlative degree.

So the correct sentence is→ Treks in wilderness areas are even better as children can then engage with all kinds of life-forms on their turf.

The correct answer is 'Sanctuaries'

Key Points

• In the given blank, we need to write a noun which is in plural form because before the blank the coordinate conjunctions 'and' is used and before 'and' the noun is in a plural form which is 'parks'.
• Hence, we need to follow the rule of parallelism.
• In the given options only option 3 is in plural form 'Sanctuaries' so this is the correct answer.

So the correct sentence is→ Regular visits to national parks and sanctuaries are another way to get children hooked.

The correct answer is 'Needs'

Key Points

• In the given blank, we need to write a verb for the subject 'a dog or cat as a pet' which acts as a singular subject because of the usage of coordinate conjunction 'or' hence use a singular verb for them.
• In the given options, 'Will', 'Can', 'Must' are all modal verbs that can not be used as a main verb hence the correct answer is 'needs' which acts as a main verb in the singular form.

So the correct sentence is→ Keeping a dog or cat as a pet needs to be made mandatory.

The correct answer is 'Environmentalist'

Key Points

• In the given blank we have to fill a noun that starts with a vowel sound because the indefinite article has been used before the blank. Also, this noun will work as a noun apposition.
• Let's us check out the meanings of the given words-
• Environmentalist- A person who is concerned about protecting the environment.
• Environmental- It is an adjective.
• Environs- The surrounding area or district.
• Environment- The surroundings or area in which the person lives.
• So in the given options only option 1 works as a noun apposition hence it is the correct answer.

So the correct sentence is→ In his weekly column ‘Down in Jungle land’ Ranjit Lal, an environmentalist offers some useful suggestions.

The correct answer is 'Nature'

Key Points

• Before the blank, the preposition has been mentioned which 'in' hence after this we have to write a noun which acts as a prepositional object.
• In the given options, 'Natural' has been eliminated because it is an adjective so we can't it as a prepositional object.
• If we look at the meanings of the other given options then the most appropriate is 'Nature'
• 'Naturalist' is also a noun which means 'an expert in something' if we think rationally then why the children would be interested in the 'naturalist' hence this word is contextually incorrect.

So the correct sentence is→ One complaint parents and teachers have about children these days is that they are simply not interested in nature.

The correct answer is '3' i.e. error lies in this part of the sentence.

Key Points

In option 3, the usage of 'Scientist have' is incorrect instead use 'Scientists have'

• According to grammar, whenever we have a plural subject always use a plural verb or vice-versa.
• In the given sentence, we haven't used 'Scientist has' because before 'Scientist' the speaker of the sentence hasn't used any article.
• If the 'Scientist' is singular then we have to use the indefinite article which is not used in the sentence hence we can't change the sentence contextually so make the subject of the sentence in a plural form.

So the correct sentence is→ Scientists have recently announced that a more effective antidote for snakebite venom has been made.

The correct answer is 'Knack'

Key Points

• Let's see the meanings of the given words-
• Knack→ An acquired or natural skill at performing a task.
• Stack→  A pile especially a neat one.
• Quack→ An unqualified person who dishonestly claims to have medical knowledge.
• Snack→ A small quantity of food or a light meal.

So according to the meaning of the given words*,** the most appropriate word is 'Knack'*

The correct answer is 'Luxurious'

Key Points

• Let's see the meanings of the given words-
• Opulent→ It is an adjective that means 'Ostentatiously rich and luxurious.'
• Shabby→ It is an adjective that means 'worn out or dilapidated.'
• Virulent→ It is an adjective that means 'extremely severe or harmful in its effect.'
• Distant→ It is an adjective that means 'Far away from space or time.'
• Hence, according to the meanings, the most appropriate synonyms is 'Luxurious' hence it is the correct answer.
• 'Shabby' is an antonym of the given word 'Opulent'

The correct answer is 'Meticulous'

Key Points

• Let's see the meanings of the given words-
• Meticulous→ Very careful and precise.
• Garrulous→ Excessively talkative.
• Tremulous→ Slightly or quivering slightly; timid or nervous.
• Tumultuous→ Very loud or uproarious, excited, confused or disorderly.
• So, according to the meanings of the given words 'Meticulous' is the correct answer.

The correct answer is 'Inattentive'

Key Points

• The meaning of the given idiom is→ If talking to someone is like talking to a brick wall, the person you are speaking to does not listen.
• Let's see an example-
• ​I've tried to discuss my feelings with her, but it's like talking to a brick wall.

Additional Information

• Mnemonic to remember the idiom→ See the image given below. In the image, the person is talking with a wall which is a nuisance because the wall will not listen to anything. Hence, remember this image in your mind.

The correct answer is: Identical.

Key Points

• The word "diverse" means showing a great deal of variety; very different. (विविध)
• Example: The city is known for its diverse culture and traditions.
• "Identical" refers to being exactly the same, or very similar. (समान)
• Example: The twins were so identical that even their parents had trouble telling them apart.
• Hence, we can infer that the opposite of 'diverse' is 'identical'.

Therefore, the correct answer is: Identical.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Parallel (समानांतर): Lines or planes that are side by side and having the same distance continuously between them.
• Example: The two roads run parallel to each other for miles.
• Practical (व्यावहारिक ): Concerned with the actual doing or use of something rather than with theory and ideas.
• Example: He has a very practical approach to solving problems.
• Farcical (हास्यास्पद): Relating to or resembling a farce, especially because of absurd or ridiculous aspects.
• Example: The entire situation turned into a farcical comedy of errors.

The correct answer is 'BACD'

Key Points

• Sentence B- is the independent sentence which is going to be the first sentence of the passage.
• Sentence A- Connects sentence B because it tells what happened after the '70s.
• Sentence C- Connects sentence A because it tells further that after not allowing people to reclaim what they are going to do next.
• Sentence D will be the last sentence because it tells what is the condition of people now.

So the correct sequence is 'BACD' which is given in option 4

The correct answer is 'Spoken in'

Key Points

• In the underlined part, 'For' preposition is incorrect because it is used for the following things:-
• To show reason or cause
• having as a destination
• representing something.
• Affecting or with regard to.
• Hence, none of the usages of 'for' connect with the other statement which is written after the preposition hence this needs to be improved.
• 'In' preposition is correct because it is used to show an enclosed space or a place that is surrounded by boundaries.
• In the given sentence, 'Villages' are the enclosed spaces 2-dimensional spaces hence with 2-D objects always use the preposition 'in'
• Let's see an example-
• The dog is in the garden. (Garden is the 2-D space.)

So the correct sentence is→ Sele, is a near-extinct language, spoken in just five villages in Nepal, which lie close to Tibet.

The correct answer is: Option 3.

Key Points

• The word "Decieve" is incorrectly spelt. The correct spelling is "Deceive".
• "Decieve" is not a valid English word. (गलत अंग्रेजी शब्द)
• Example: The word "decieve" is often a common misspelling.
• The correct word is "Deceive", which means to make someone believe something that is not true. (धोखा देना)
• Example: He tried to deceive his friends with a false story.

Therefore, the correct answer is: Option 3.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Business (व्यवसाय): The practice of making one's living by engaging in commerce.
• Example: She started her own business at a very young age.
• Fattening (मोटा करने वाला): Likely to make you fat.
• Example: Eating too many sweets can be very fattening.
• Dessert (मिठाई): A sweet course typically eaten at the end of a meal.
• Example: We had ice cream for dessert.

The correct answer is '2' i.e. 'Ravi asked Ritu how many sets of class 12 practice papers she had finished.'

Key Points

• According to the rule of Direct-Indirect speech, Whenever the tense in the reported speech is the present perfect tense convert this tense into the past perfect tense.
• In the given Options there is only one option which is given in the past perfect tense which is option 2.
• Option 1→ is incorrect because it is written in the past perfect continuous tense which is incorrect.

Additional Information

Reporting Verb →The first verb part of the sentence that comes before the quotation marks are called the Reporting verb. 

Reported Speech→ The statement (words) spoken by the speaker and which is written in quotation marks (“ ”) is called the Reported speech.

• Present tense changed into→ a Past tense
• If the Reported speech is a universal truth or a general fact, then its ‘tense’ does not change irrespective of the Reporting verb.
• Present continuous tense changed into→past continuous tense.
• Present Perfect Changes into→ Past Perfect
• Present Perfect Continuous Changes into→ Past Perfect Continuous

The correct answer is: Option 4.

Key Points

• The word "Accomodate" is incorrectly spelt. The correct spelling is "Accommodate" which means to provide lodging or sufficient space for someone or something. (समायोजित करना)
• Example: The hotel can accommodate up to 500 guests.
• "Accommodate" means to fit in with the wishes or needs of. (समायोजित करना)
• Example: They were kind enough to accommodate our late arrival.

Therefore, the correct answer is: Option 4.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Quizzes (प्रश्नोत्तरी): Short tests or assessments.
• Example: The teacher gave us pop quizzes to test our understanding of the material.
• Acceptable (स्वीकार्य): Something that is satisfactory or allowable.
• Example: The proposal was found to be acceptable by the board members.
• Beginning (शुरुआत): The point in time or space at which something starts.
• Example: The beginning of the movie was very captivating.

The correct answer is '4' i.e. ​To take on more than one can deal with

Key Points

• 'Bite off more than one can chew' means 'take on a commitment one cannot fulfill.'
• Let's see an example:-
• ​We bit off more than we could chew in our original reform proposals.

Additional Information

• Mnemonic to remember the idiom→ As we can see in the image a baby is eating a fruit which is impossible to eat by him. Remember this image for this idiom.

The correct answer is 'Infuriate'

Key Points

• Let's see the meanings of the given words-
• Enrage→ make very angry. (बहुत गुस्सा करना।)
• Infuriate→ make irritated or angry. (चिढ़ या क्रोधित करना)
• Alleviate→ make less severe. (कम गंभीर बनाओ।)
• Placate→ To pacify, calm or appease. (शांत करना, प्रसन्न करना।)

So according to the meaning of the words, the most appropriate is 'Infuriate' the rest of the words are antonyms of the given words.

The correct answer is '2' i.e. ​'Delhi was lashed by rains and the temperature was brought down by a few degrees'

Key Points

• While changing Active to passive remember the following points-
• First, look at the tense of the sentence. Because tense doesn't change while changing the active to passive.
• Second, find out the subject and the object of the sentence. Be cautious about the prepositional phrase and infinitive.
• In the given sentence, The subject is 'Rains' and the verb is 'lashed' which is written in the past tense hence the tense will not be changed.
• The tense hasn't changed in option 2 only. Hence, it is the correct.

Additional Information

• We use 'Being' when the tense is in continuous tense.

The correct answer is '3' i.e. 'are located'

Key Points

In the given sentence, the underlined phrase to be replaced with 'are located'

• In the given sentence, 'as' is a conjunction and it makes the clause the subject of this clause is 'ports' hence the verb is used in the plural form and the verb V₃ 'located' should be used instead of 'locating' because 'be + located' means 'be situated in a particular place'
• Let's see an example-
• ​These factories should not be located in the center of the city.

So the correct sentence is→ The Arabian Sea region is very important for India as several major ports are located there.

Additional Information

• The forms of 'be' are 'is, am, are, was, were' all are linking verbs which are used to connect the subject and its complement.

The correct answer is 'CDAB'

Key Points

• Sentence C- will be the opening sentence for the passage because it starts with the pronoun 'We' also, it is an independent sentence.
• Sentence D- will be the second sentence because 'but' conjunction is used to show the contrast or this sentence is opposing sentence C also, it tells what happens after constructing the clinics.
• Sentence A- will be the third sentence because it gives the example of the 'roadblocks' or what are the obstructions while making the clinics.
• Sentence B- will be the last sentence of the passage because 'however' is used to show the contrast and it shows the contrasts to sentence A.

So the correct sequence is- 'CDAB'

Given,

Weight : Kilogram

Here we see the unit of weight is Kilogram.

Similarly,

The unit of Resistance is Ohm.

All other options do not share the same relationship.

Hence, the correct answer is Resistance : Ohm.

Given,

3 : 27

12 : 1757

7 : 343

11 : 1331

The pattern followed here is

3 = 3³ = 27

12 = 123 ≠ 1757 (12³ = 1728)

7 = 73 = 343

11 = 113 = 1331

Hence, the correct answer is 12 : 1757.

Given,

Interchanges:

Sign ÷ and -

Numbers: 15 and 5

We have to interchange "÷" with "-" and 15 with 5

1) 4 × 30 - 5 ÷ 15 + 14 = 21

After interchanges

4 × 30 ÷ 15 - 5 + 14

4 × 2 - 5 + 14

17 ≠ 21

2) 4 × 30 - 15 ÷ 5 + 12 = 27

After interchanges

4 × 30 ÷ 5 - 15 + 12 

4 × 6 - 15 + 12

= 24 - 15 + 12

21 ≠ 27

3) 4 × 30 - 15 ÷ 5 + 12 = 21

After interchanges

4 × 30 ÷ 5 - 15 + 12 

4 ×  6 - 15 + 12

24 - 15 + 12 = 21 = RHS

4) 12 × 30 - 15 ÷ 5 + 4 = 37

After interchanges

12 × 30 ÷ 5 - 15 + 4

12 × 6 - 15 + 4

72 - 15 + 4

61 ≠ 37

Hence, the correct answer is 4 × 30 - 15 ÷ 5 + 12 = 21.

Given,

A × B means 'A is the wife of B',

A ÷ B means 'A is the father of B'.

1) S ÷ U × J ÷ R

2) R ÷ J ÷ S × U

3) S × U × R ÷ J

4) J × S ÷ R × U

Here, the expression in option 2 means R is the paternal grandfather of S.

Hence, the correct answer is R ÷ J ÷ S × U.

Given,

88 : 308 : : 126 : ?

The pattern followed here is,

${88\over 2}$× 7 = 308

Similarly,

${126 \over 2}$× 7 = 441

Hence, 441 is the correct answer.

Concept Used:

 $Triangles = n× {{n + 1} \over2}×H$

Where, 

n= number of small triangles

H = number of ‘end to end’ horizontal lines

→ In, ∆ABC:

n= number of small triangles = 2

H = number of ‘end to end’ horizontal lines = 4 (BC, HI, FG, and DE)

$Triangles = 2× {{2 + 1} \over2}×4 = 12$

Hence, Total triangles in ∆ABC = 12

→ Now, the remaining Triangles: 1(∆AJK)

→ Now Adding all the ∆s:

Total ∆s = 12 + 1 = 13

Hence, the correct answer is 13.

Given,

1. Mankind
2. Manner
3. Manuscript
4. Management
5. Making

According to English alphabetical order, the words must be in the following order,

5. Making
6. Management
7. Mankind
8. Manner
9. Manuscript

Hence, the correct answer is 5, 4, 1, 2, 3.

Given,

When the cube is formed after folding the sheet the following numbers will be opposite to each other as shown below,

Hence, the correct answer is 1.

Given,

Mammals, Reptile, Non-chordates, Amphibian

These are the class in animal classification. According to this Snake is a reptile.

Hence, the correct answer is Reptile.

Given,

EQM, GRL, ISK, KTJ, ?

The pattern followed here is,

Hence, the correct answer is MUI.

Given,

Statements:

1. Some computers are phones.
2. All phones are televisions.

The least possible Venn diagram for the given statements is as follows.

Conclusions:

I. Some phones are computers → True (From Venn diagram we see some phones are computers)

II. Some televisions are computers → True (From Venn diagram we see some Televisions are computers)

III. No television is a computer → False (From Venn diagram we see some Televisions are computers)

Hence, the correct answer is Only conclusions I and II follow.

Given,

Here we see in 1^st and 2^nd figure is mirror image of each other.

Similarly,

In option 4, this is the mirror image of 3^rd figure.

 

Hence, option 4 is the correct answer.

The pattern followed here is;

Given,

TENDER - 185414520

The pattern followed here is,

Similarly,

Hence, the correct answer is 45201952117518.

Given,

In the mirror image, the changes take place in the left and right part of the image and top and bottom part of the image remains the same.

Therefore, we get  

Hence, the correct answer is

Given,

(15, 49, 201)

The pattern followed here is

15 × 3 + 4 = 49 × 4 + 5 = 201

The same pattern is followed by

29 × 3 + 4 = 91 × 4 + 5 = 369

Hence, the correct answer is (29, 91, 369).

Given,

(15, 556, 331)

The pattern followed here is,

15² = 225; 556 − 331 = 225

Similarly,

9² = 81; 159 − 78 = 81

Hence, the correct answer is (9, 159, 78).

The pattern followed here is;

Given,

SECTION → PHZQLRK

Similarly,

Hence, the correct answer is ERPQHOP.

Given,

When folded at the dotted line we get,

Hence, the correct answer is

The pattern followed here is;

Given,

LZ : OA : : UR : ?

From the above table, we see L is related O and Z is related to A

Similarly, U is related to F and R is related to I

Therefore, FI is related to third letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster.

Hence, the correct answer is FI.

Given,

 

Here, we see 

this figure is embedded in figure X.

Hence, the correct answer is

Given,

In the above Venn diagram, we see there must be some part where all three circles must show common characteristics.  

Hence, the correct answer is Mothers, Sisters, Daughters.

Given,

Amount = 504

Ratio = 7 : 8 : 9

7x + 8x + 9x = 504

24x = 504

x = 21

Amount received by B and C,

8 × 21 + 9 × 21 = 168 + 189 = 357

Hence, the correct answer is Rs. 357.

Given,

88, 95, 106, 119, 136, 155, 178, ?

The pattern followed here is,

Addition of prime numbers in numbers, (7, 11, 13, 17, 19, 23)

88 + 7 = 95 

95 + 11 = 106

106 + 13 = 119

119 + 17 = 136

136 + 19 = 155

155 + 23 = 178

178 + 29 = 207

Here, we see addition of consecutive prime number in each term.

Hence, the correct answer is 207.

The pattern followed here is;

Given,

PUZ, BGL, AFK, NSW

The pattern followed here is,

P + 5 = U + 5 = Z

B + 5 = G + 5 = L

A + 5 = F + 5 = K

N + 5 = S + 4 = W

Hence, the correct answer is NSW.

Given,

Malaria, Depression, Dengue, Typhoid

All the above are infectious diseases except depression.

Hence, the correct answer is Depression.

Given:

A person purchases 40 items at Rs. 10 each.

He sells a part of them profit of = 25%

He sells remaining at loss of = 10%

Net profit earned by him = 4%

Formula:

Profit = SP – CP

Profit % = Profit/CP × 100

Loss = CP – SP

Loss % = Loss/CP × 100 

Mixture and Allegation method:

a           b

      c

p          q

Where a > c > b

(a - c)/(c - b) = p/q

Calculation:

25%       (-10%)

         4%

14       :      21

Ratio of times sell at 25% to that of 10% loss = 14 : 21 = 2 : 3

According to the question

2 + 3 = 5 unit

5 unit = 40 items

1 unit = 40/5 = 8 unit

Number of items sells at 10% loss = 8 × 3 = 24 items.

Given:

1/(9 - 4√5)² + 1/(9 + 4√5)²

Formula:

(a + b)² = (a² + b² + 2ab)

(a - b)² = (a² + b² - 2ab)

(a² - b²) = (a + b) (a - b)

Calculation:

1/(9 - 4√5)2 + 1/(9 + 4√5)2

⇒ [(9 + 4√5)2 + (9 - 4√5)2]/[(9 - 4√5)2 (9 + 4√5)2]

⇒ (81 + 80 + 72√5 + 81 + 80 - 72√5)/(81 - 80)

⇒ 322

Formula:

(a + b)2 = (a2 + b2 + 2ab)

(a - b)2 = (a2 + b2 - 2ab)

(a + b)² + (a – b)² = 2(a² + b²) 

(a + 1/a)² = a² + 1/a² + 2

Calculations:

$\frac{1}{(9-4√5)^2} + \frac{1}{(9 + 4√5)^2 }$

a = (9 – 4√5)     ...1)

⇒ 1/a = 1/(9 – 4√5)

⇒ 1/a = {1/(9 – 4√5)} × {(9 + 4√5)/(9 + 4√5)}

⇒ 1/a = (9 + 4√5)/{(9)² – (4√5)²}

⇒ 1/a = 9 + 4/√5     ...2)

So, $\frac{1}{(9-4√5)^2} + \frac{1}{(9 + 4√5)^2 }$

From eq.(1) and (2)

⇒ (1/a²) + 1/(1/a)² 

⇒ a² + 1/a² 

⇒ a² + 1/a² + 2 – 2

⇒ (a + 1/a)² – 2

⇒ {9 – 4√5 + (9 + 4/√5)}² – 2 

⇒ (9 – 4√5 + 9 – 4√5)² – 2 

⇒ 324 – 2 = 322

∴ The correct answer is 322

Given:

Radius of cylindrical vessel R = 6 cm

Height of cylindrical vessel H = 5 cm

Diameter of spherical metal each ball = 2 cm

Formula:

Volume of cylinder = πr²h

Volume of sphere = (4/3) πr³

Calculation:

Radius of each ball r = 2/2 = 1 cm

Let number of balls be x 

According to the question

x × (4/3) × π × 1³ = π × 6² × 5

⇒ x = 180 × (3/4)

⇒ x = 135

∴ Number of balls are 135.

Shortcut Trick

When 10 numbers are dropped from the start and 10 next numbers are added, the average increases by the number of terms shifted.

Shift = 10 terms ⇒ M − N = 10.

Given M² − N² = 600 ⇒ (M − N)(M + N) = 600.

10 × (M + N) = 600 ⇒ M + N = 60.

Solving: M = 35, N = 25.

Average of 3M and 5N = (3 × 35 + 5 × 25) ÷ 2 = (105 + 125) ÷ 2 = 115.

∴ The correct answer is 115.

Alternate Method

Given: Average of 35 consecutive natural numbers = N.

Formula: Average of consecutive numbers = (First + Last) ÷ 2.

⇒ Let the first number be a. Then N = (a + a + 34) ÷ 2 = a + 17.

⇒ New set starts from a + 10. Then M = (a + 10 + a + 10 + 34) ÷ 2 = a + 27.

⇒ Difference M − N = (a + 27) − (a + 17) = 10.

⇒ M² − N² = 600 ⇒ (M − N)(M + N) = 600.

⇒ 10(M + N) = 600 ⇒ M + N = 60.

⇒ Adding (M − N) and (M + N): 2M = 70 ⇒ M = 35.

⇒ Subtracting: 2N = 50 ⇒ N = 25.

⇒ Required Average = (3M + 5N) ÷ 2 = (3 × 35 + 5 × 25) ÷ 2.

⇒ Required Average = (105 + 125) ÷ 2 = 230 ÷ 2 = 115.

∴ The correct answer is 115.

Additional Information

Consecutive Numbers Average

For n consecutive numbers, if the first term is a, the average is a + (n − 1)/2.

Average Shift Property

If the first k terms are replaced by the next k terms in a consecutive series, the average increases by exactly k.

Algebraic Identity

The identity a² − b² = (a − b)(a + b) is frequently used to solve difference of squares in average problems.

Given:

A = 2 (sin6 θ + cos6 θ) - 3 (sin4 θ + cos4 θ)

Formula:

(sin6 θ + cos6 θ) = (1 - 3 sin² θ cos² θ)

Proof:

(sin6 θ + cos6 θ) = (sin² θ + cos² θ) (sin⁴ θ + cos⁴ - sin² θ cos² θ)

⇒ (sin6 θ + cos6 θ) = 1 [(sin² θ + cos²)² - 3 sin² θ cos² θ]

⇒ (sin6 θ + cos6 θ) = (1 - 3 sin² θ cos² θ)

(sin4 θ + cos4 θ) = (1 - 2 sin2 θ cos2 θ)

Proof: 

⇒ (sin4 θ + cos4 θ) = [(sin2 θ + cos2)2 - 2 sin2 θ cos2 θ]

⇒ (sin4 θ + cos4 θ) = (1 - 2 sin2 θ cos2 θ)

Calculation:

A = 2 (sin6 θ + cos6 θ) - 3 (sin4 θ + cos4 θ)

⇒ A = 2 (1 - 3 sin² θ cos² θ) - 3 (1 - 2 sin2 θ cos2 θ) 

⇒ A = 2 - 6 sin² θ cos² θ - 3 + 6 sin² θ cos² θ

⇒ A = 2 - 3

⇒ A = - 1

Now,

cos α = √[(3 + A)/(5 + A)]

⇒ cos α = √[(3 - 1)/(5 - 1)]

⇒ cos α = √(2/4)

⇒ cos α = 1/√2

⇒ cos α = cos 45°

⇒ α = 45°

Now

3α

⇒ 3 × 45°

⇒ 135°

Shortcut Trick

Let θ = 90° 

A = 2(1 - 0) - 3(1 + 0)

⇒ A = -1 

So cos α = √2/4 = 1/√2

⇒ α = 45° 

∴ 3α = 135°

Given:

2x+y-2z = 88z-5-y

54y-6z = 25y+z

34x-3z = 9x+z

Formula:

a^m × aⁿ = a^{{m + n}}

Calculation:

2x+y-2z = 88z-5-y

⇒ 2x+y-2z = 23(8z-5-y)

Comparing on power

⇒ x + y - 2z = 24z - 15 - 3y

⇒ x + 4y - 26z = -15     ----(1)

54y-6z = 25y+z

⇒ 54y - 6z = 52 (y + z)

Comparing on power

⇒ 4y - 6z = 2 (y + z)

⇒ 4y - 6z = 2y + 2z

⇒ 2y = 8z

⇒ y = 4z     ----(2)

34x-3z = 9x+z

⇒ 34x-3z = 32(x + z)

Comparing on power

⇒ 4x - 3z = 2x + 2z

⇒ 4x - 2x = 2z + 3z

⇒ 2x = 5z

⇒ x = 2.5z     ----(3)

From equation (1), equation (2) and equation (3)

⇒ x + 4y - 26z = -15

⇒ 2.5z + 4 (4z) - 26z = - 15

⇒ 2.5z + 16z - 26z = - 15

⇒ - 7.5z = - 15

⇒ z = 2

From equation (2)

y = 4 × 2

⇒ y = 8

From equation (3)

x = 2.5 × 2

⇒ x = 5

Now, 

2x + 3y + 5z

⇒ 2 × 5 + 3 × 8 + 5 × 2

⇒ 10 + 24 + 10

⇒ 44

Given:

AC and DE are parallel 

∠CAB = 38

∠ABC = b

∠CBD = a

Calculation:

∠CAB = 2a

⇒ 2a = 38

⇒ a = 38/2

⇒ a = 19

∴  ∠CBD = 19

∠CAB + ∠ABD = 180 (∵ AC and BD are parallel) 

⇒ 2a + b + a = 180

⇒ 38 + b + 19 = 180

⇒ b = 180 - 57

⇒ b = 123

∴ ∠ABC = 123

Now,

∠ABC + 5 ∠CBD

⇒ 123 + 5 × 19

⇒ 123 + 95

⇒ 218

Calculation:

The production ratio of S1 = 765/415 = 1.84

The production ratio of S2 = 856/390 = 2.19 

The production ratio of S3 = 729/356 = 2.04

The production ratio of S4 = 964/550 = 1.75

The production ratio of S5 = 580/280 = 2.07

The production ratio of S6 = 865/440 = 1.96

Now we can say

The production ratio (production to land) of S2 and S4 is highest and lowest respectively.

Given;

117 Cos2 A + 129 Sin2 A = 120  and 170 Cos2 B + 158 Sin2 B = 161

Formula:

sin² A + cos² A = 1

cosec A = 1/sin A

sec A = 1/cos A

Calculation:

117 Cos2 A + 129 Sin2 A = 120 

⇒ 117 Cos2 A + 117 Sin2 A + 12 sin² A = 120

⇒ 117 + 12 sin² A = 120

⇒ 12 sin² A = 120 - 117

⇒ sin² A = 3/12

⇒ sin² A = 1/4

∴ cosec² A = 4

170 Cos2 B + 158 Sin2 B = 161

⇒ 12 cos² B + 158 Cos2 B + 158 Sin2 B = 161

⇒ 12 cos² B + 158 = 161

⇒ 12 cos² B = 161 - 158

⇒ cos² B = 3/12

⇒ cos² B = 1/4

∴ sec² B = 4

Now,

cosec² A sec² B

⇒ 4 × 4

⇒ 16

Calculations:

Follow BODMAS rule to solve this question, as per the order given below,

A = $[\frac{3}{7} ; of; 4\frac{1}{5} ÷ \frac{18}{25} + \frac{17}{24}] ; of; [\frac{289}{16} ÷ (\frac{3}{4} + \frac{2}{3})^2]$

A = $[\frac{3}{7} ; of ; \frac{21}{5} ÷ \frac{18}{25} + \frac{17}{24}] ; of ; [\frac{289}{16} ÷ (\frac{3}{4} + \frac{2}{3})^2]$

A = [3/7 × 21/5 × 25/18 + 17/24] × [289/16 ÷ (17/12)²]

A = [3/7 × 21/5 × 25/18 + 17/24] × [289/16 ×  (12/17)2]

A = [3 × 3 × 5/18 + 17/24] × [144/16 ]

A = [ 5/2 + 17/24] × [9]

A = [ 60/24 + 17/24] × [9]

A = [ 77/24] × [9]

A = [ 77/8] × [3]

∴ 8A = 8 × [ 77/8] × [3]

∴ 8A = 231

∴ The value of 8A is 231

From option 1

C scored in Math = 67

C scored in Physics = 87

C scored in Chemistry = 72

In the regarding C we can say, Math is the most difficult and Physics is the easiest.

So, option 1 is wrong.

From option 2.

D scored in Math = 84

D scored in Physics = 76

D scored in Chemistry = 80

In the regarding D we can say, Physics is the most difficult and Math is the easiest.

So, option 2 is wrong.

From option 3

B scored in Physics = 65

C scored in Physics = 87

E scored in Physics = 69

Now we can say Physics is easier for C than for B and E.

So option 3 is correct.

Formula:

CP = SP × [100/(100 + Profit)]

Calculation:

Cost price of the item for B = 1,32,000 × (100/110) = Rs. 1,20,000

Cost price of the items for A = 1,20,000 × (100/120) = Rs. 1,00,000

If C had purchased the items for A instead of B, then cost price for C = 1,32,000 × (95/100) = Rs. 1,25,400

∴ Profit of A = 1,25,400 - 1,00,000 = Rs. 25,400

Shortcut Trick

Let the time taken by the passenger train be T hours.

Speed of passenger train = 1176 / T

Speed of express train = 1176 / (T − 5)

Difference in speed: [1176 / (T − 5)] − [1176 / T] = 70

Testing option (3): If T = 12, then speed = 1176 / 12 = 98 km/h. Express speed = 1176 / 7 = 168 km/h.

Difference = 168 − 98 = 70 km/h. Condition satisfied.

∴ The correct answer is 12 hr.

Alternate Method

Given: Distance = 1176 km, Time difference = 5 hours, Speed difference = 70 km/h.

Formula Used: Speed = Distance ÷ Time

⇒ Let time taken by passenger train = T

⇒ Speed of passenger train (S_p) = 1176 / T

⇒ Speed of express train (S_e) = 1176 / (T − 5)

⇒ S_e − S_p = 70

⇒ [1176 / (T − 5)] − [1176 / T] = 70

⇒ 1176 [ (T − (T − 5)) / (T(T − 5)) ] = 70

⇒ 1176 × 5 / (T² − 5T) = 70

⇒ 5880 = 70(T² − 5T)

⇒ 84 = T² − 5T

⇒ T² − 12T + 7T − 84 = 0

⇒ T(T − 12) + 7(T − 12) = 0

⇒ T = 12 (Time cannot be negative)

∴ The correct answer is 12 hr.

Additional Information

Speed-Time Relation

For a constant distance, speed is inversely proportional to time (S₁ / S₂ = T₂ / T₁).

Average Speed formula

When a distance is covered at different speeds, Average Speed = Total Distance ÷ Total Time.

Distance Formula for Speed Difference

Distance = [ (S₁ × S₂) / (S₁ − S₂) ] × Time Difference.

Given:

2145 : x :: 3003 : 42

Formula:

If a : b :: c : d ,then

a/b = c/d

Calculation:

2145 : x :: 3003 : 42

⇒ 2145/x = 3003/42

⇒ x = 2145 × (42/3003)

∴ x = 30

Now,

x : 2508 :: y : 11704

⇒ 30 : 2508 :: y : 11704

⇒ 30/2508 = y/11704

⇒ y = (30/2508) × 11704

∴ y = 140

Given:

Number of customers of operator P = 3.6 lakhs

Number of customers of operator Q = 4.2 lakhs

Percentage in city C who are customer of operators P = 15%

Percentage in city C who are customer of operators Q = 23%

Formula:

x% of a number = Actual number × (x/100)

Calculation:

Number of people in city C who are customer of operator P = 3,60,000 × (15/100) = 54,000

Number of people in city C who are customer of operator Q = 4,20,000 × (23/100) = 96,600

∴ Required difference = 96,600 - 54,000 = 42,600

Given:

∠ACB + ∠BAC = 80∘

∠BDE = 35∘

∠BCE = 45∘

Concept used:

The sum of two interior opposite angles is equal to exterior angle of a triangle.

i.e. ∠ACD = ∠ABC + ∠BAC

Calculation:

From the following figure join E to P, then

∠DBC = ∠ACB + ∠BAC (According to Theorem)

∴ ∠DBC = 80^∘

∠DBC + ∠BCE = ∠CPD (According to Theorem)

∠CPD = 80^∘ + 45^∘

∴ ∠CPD = 125^∘

∠CED = ∠CPD + ∠BDE (According to Theorem)

∠CED = 125^∘ + 35^∘

∴ ∠CED = 160^∘

Formula:

If a number is divisible by 2 and 3, then we can say the number also divisible by 6.

Divisibility Law of 2: A number divisible by 2 if its unit digit is 2, 4, 6, 8 or 0.

Divisibility Las of 3: A number divisible by 3 if sum of its digit is divisible by 3.

Calculation:

Check option 1.

3,49,722 is divisible by 2 because unit digit of the number is 2.

3 + 4 + 9 + 7 + 2 + 2

27

3,49,722 is divisible by 3 because sum of digit of the number is divisible by 3.

∴ 3,49,722 is divisible by 6.

Given:

∠ABC = 95° and ∠FED = 115°

Formula:

The sum of the opposite angle of cycle quadrilateral is 180°.

Calculation:

Join A to F

In quadrilateral ABCF

∠ABC + ∠AFC = 180

⇒ 95 + ∠AFC = 180

⇒ ∠AFC = 180 - 95

⇒ ∠AFC = 85

In quadrilateral AFED

∠FAD + ∠FED = 180

⇒ ∠FAD + 115 = 180

⇒ ∠FAD = 180 - 115

⇒ ∠FAD = 65

In ΔAFP

⇒ ∠AFP + ∠FAP + ∠FPA = 180

⇒ 85 + 65 + ∠FPA = 180

⇒ ∠FPA = 180 - 150

⇒ ∠FPA = 30

∠APC + ∠FPA = 180 (linear pair)

⇒ ∠APC + 30 = 180

⇒ ∠APC = 180 - 30

∴ ∠APC = 150

Given:

Expenditure in 2016-2017 = 720

Expenditure in 2017-2018 = 820

Expenditure in 2018-2019 = 845

Formula:

Average = Sum of all observations/Total number of all observations

Calculation:

Average expenditure of all three years = (720 + 820 + 845)/3 = 2385/3 = 795

∴ Expenditure in 2019-2020 = 795 × (130/100) = 1033.5

Given:

A man purchased a car for price = Rs. 12 lakh

Car was insured at  = 80% of the cost of the car

Car was sold at the loss of = 15%

The percentage of the insured amount paid by the insurance company = 90%

Formula:

x% of a number = Actual number × (x/100)

Given:

SP = 12,00,000 × (85/100) = 10,20,000

Amount paid by the insurance company = 12,00,000 × (80/100) × (90/100) = 8,64,000

∴ Required difference = 10,20,000 - 8,64,000 = 1,56,000 or 1.56 lakhs

Given:

Case-1

Principal = 12,000

Rate = r%

Time = 4 month

Case-2

Principal = (12,000 + 6,000) = 18,000

Rate = 2r%

Time = 8 months

Total SI = Rs. 2800

Formula:

SI = Prt/100

Calculation:

According to the formula

2800 = [(12,000 × r × 4/12)/100] + [(18,000 × 2r × 8/12)/100]

⇒ 2800 = 40r + 240r

⇒ 280r = 2800

⇒ r = 2800/280

⇒ r = 10%

∴ The initial rate of interest was 10%.

Given:

AD is bisector of angle ∠CAB.

BD is bisector of angle ∠CBF.

∠ACB = 34°

Formula:

If AD is bisector of angle ∠CAB and BD is bisector of angle ∠CBF, then

∠ADB = (1/2) ∠ACB

Calculation:

According to the question

∠ADB = (1/2) × 34°

∴ ∠ADB = 17°

Given:

$[\frac{\sqrt{3} + 2SinP}{1-2CosP}]^3 + [\frac{1 + 2CosP}{\sqrt{3} - 2SinP}]^3$

Calculation:

$[\frac{√{3} + 2SinP}{1-2CosP}]^3 + [\frac{1 + 2CosP}{√{3} - 2SinP}]^3$

Put P = 30° 

⇒  $[\frac{√{3} + 2Sin30}{1-2Cos30}]^3 + [\frac{1 + 2Cos30}{√{3} - 2Sin30}]^3$

⇒ $[\frac{√{3} + 2(1/2)}{1-2(\sqrt3/2 )}]^3 + [\frac{1 + 2(\sqrt3/2)}{√{3} - 2(1/2)}]^3$

⇒ $[\frac{√{3} + 1}{1-\sqrt3}]^3 + [\frac{1 + \sqrt3}{√{3} - 1}]^3$

⇒ $[\frac{√{3} + 1}{1-\sqrt3}]^3 - [\frac{1 + \sqrt3}{1-√{3}}]^3$

⇒ 0

The value of $[\frac{\sqrt{3} + 2SinP}{1-2CosP}]^3 + [\frac{1 + 2CosP}{\sqrt{3} - 2SinP}]^3$ is 0.

Given:

$(a^{\frac{2}{3}} + 2a^\frac{1}{2} + 3a^\frac{1}{3} + 2a^\frac{1}{6} + 1)(a^\frac{1}{3} - 2a^\frac{1}{6}+1) -a^\frac{1}{2}(a^\frac{1}{2} - 2)$

Calculation:

Put a^1/6 = k, then

⇒ (k⁴ + 2k³ + 3k² + 2k + 1) (k² - 2k + 1) - k³ (k³ - 2)

⇒ k⁶ + 2k⁵ + 3k⁴ + 2k³ + k² - 2k5 - 4k4 - 6k3 - 4k2 - 2k + k4 + 2k3 + 3k2 + 2k + 1 - k⁶ + 2k³

⇒ 1

Given:

5 men and 8 women can complete a task = 34 days

4 men and 18 women can complete the same task = 28 days

Formula:

Total work = Efficiency × Time

Calculation:

Let efficiency of 1 man and 1 woman be x and y respectively, then

(5x + 8y) × 34 = (4x + 18y) × 28

⇒ (5x + 8y) × 17 = (4x + 18y) 14

⇒ 85x + 136y = 56x + 252y

⇒ 85x - 56x = 252y - 136y

⇒ 29x = 116y

⇒ x/y = 116/29

⇒ x : y = 4 : 1

Total work = (5 × 4 + 8 × 1) × 34

Total work = (20 + 8) × 34

Total work = 28 × 34

Efficiency of 3 men and 5 women in 1 day = (3 × 4 + 5 × 1) = 12 + 5 = 17

∴ Time taken by 3 men and 5 women to complete the whole work = (28 × 34)/17 = 56 days

The correct answer is Programmable read-only memory

Key Points

• PROM stands for Programmable Read-Only Memory.
• Read-only memory (ROM) is a type of memory that is used in electronics and computers.
• It is a non-volatile memory, that is, information stored in such memory is permanent and cannot be changed.
• The other two types of ROM are
• Electrically Erasable Programmable ROM (EEPROM)
• Erasable Programmable ROM (EPROM)

Additional Information

• Primary memory can be divided into RAM (Random Access Memory) and ROM (Read Only Memory)

The correct answer is Tamanna.

• CBSE and NCERT have launched an online aptitude test called Tamanna’.
• Tamanna stands for Try And Measure Aptitude And Natural Abilities.
• Tamanna is an aptitude test that aims to help students of Class 9 and 10 to make a better choice of subjects, eventually helping them in making an informed decision while choosing subjects in Class 11 and 12.

The correct answer is Odisha.

Key Points

• Chhau means shadow its a form of mask dance.
• There are 3 main styles of Chhau dance
• Jharkhand - Saraikella Chhau
• Odisha - Mayurbhanj Chhau- In this type of Chhau, the artists don't wear a mask.
• West Bengal - Purulia Chhau

Additional Information

The correct answer is Bhitarkanika Wildlife Sanctuary, Odisha.

• Bhitarkanika Mangroves is a part of Bhitarkanika Wildlife Sanctuary.
• It is located in Odisha.
• It covers an area of 650 square kilometres.
• The core area of the sanctuary was declared Bhitarkanika National Park.
• It is famous for its Saltwater crocodiles and Olive ridley sea turtle.
• It was designated a Ramsar Wetland of International Importance in 2002.
• Bhitarkanika Wildlife Sanctuary includes Gahirmatha Marine Wildlife Sanctuary.

The correct answer is Meghalaya.

• The Garo Khasi And Jayantia Hills were formed in the same age as of the Malwa Plateau.
• The Garo, Khasi, And Jayantia Hills are located in Meghalaya.
• The hills are named after the tribes found particularly in that region.
• Meghalaya is also known as the Scotland of the East.

The correct answer is Erode Venkatappa Ramasamy.

Key Points

• E.V. Ramaswami Naicker started the Self Respect Movement.
• He is also known as Periyar.
• The objective of the movement was to end Bramhanical domination in society.
• He felt that it was the prime instrument of exploitation of the lower caste.
• One of the methods he employed was to organise marriage without Brahmins.
• He was a pioneer of social justice and fought against untouchability.
• He said Manu’s law as unhuman and Puranas as fairy tales.
• He opposed the imposition of Hindi upon Dravidians.
• He tore caste name hoards on hotels, cut off the holy thread of Brahmins, broke the idols and beat up the deities with a chappal.

Additional Information

• C. Rajagopalachari was the first and last Governor-General of independent India.
• He was the first governor of West Bengal (15 August 1947 to 21 June 1948).
• Apart from this, he was also Minister for Home Affairs of the Indian Union and Chief Minister of Madras state.
• He was the first recipient of India's highest civilian award, the "Bharat Ratna".
• ​C. N. Annadurai was the first Chief Minister of Tamil Nadu.
• He was an Indian politician who served as Tamil Nadu's 1st chief minister for 20 days in 1969 and as Madras state's fifth and last chief minister from 1967 to 1969 when Madras state name was changed to Tamil Nadu.

The correct answer is Batukeshwar Dutt.

• Batukeshwar Dutta along with Bhagat Singh was the main accused in Assembly Bomb Case.
• They were members of the Hindustan Socialist Republican Association.
• In 1929, they threw bombs at the Central Legislative Assembly.
• They did not want to injure anyone but wanted to make a statement that they would not bear the colonial rule of Britishers.
• It was against the Public Safety Bill and the Trade Dispute Bill.
• Dutta also initiated a historic hunger strike along with Bhagat Singh to protest against the abusive treatment of Indian political prisoners.
• Ram Prasad Bismil participated in the Mainpuri conspiracy of 1918, and the Kakori conspiracy of 1925.
• He also resisted the British rule in India.
• Ashafaqulla was also a revolutionary like Bhagat Singh and stood against the atrocities of Britishers.
• Surya Sen was best known for leading the 1930 Chittagong armoury raid.

Additional Information

• The Forward Bloc of the Indian National Congress was formed on June 22,  1939,  by Netaji Subhas Chandra Bose,  who had resigned from the presidency of the Indian National Congress on 29 April after being outmanoeuvred by Mohandas K. Gandhi.
• Subhas Chandra Bose was elected as the President of the Indian National Congress (INC) in 1939 against Dr Pattabhi Sitaramayya.
• Subhash Chandra Bose and Sardul Singh Kavishar were the party's first president and vice-president respectively.
• Bhagat Singh, Rajguru and Sukhdev were sentenced to death in the Lahore conspiracy case and ordered to be hanged on 23 March 1931.
• Chandra Shekhar Azad was born in Jhabua, Madhya Pradesh on 23 July 1906, he died on 27 February 1931 in Allahabad.
• He was an Indian revolutionary who reorganised the Hindustan Republican Association under its new name of Hindustan Socialist Republican Association (HSRA) after the death of its founder, Ram Prasad Bismil, and three other prominent party leaders, Roshan Singh, Rajendra Nath Lahiri and Ashfaqulla Khan.
• https://economictimes.indiatimes.com/news/politics-and-nation/remembering-bhagat-singh-on-his-110^th-birth-anniversary/bombing-of-the-assembly/slideshow/60868938.cms#:~:text=On%20April%208%2C%201929%2C%20Bhagat,protest%20against%20an%20unfavourable%20Bill.

The correct answer is Arunachal Pradesh Legislative Assembly.

• The Arunachal Pradesh Legislative Assembly (APLA) adopted a new logo, reflecting the distinct identity and culture of the state.
• The new logo consists of the national emblem and foxtail orchid (Rhynchostylis Retusa), the state flower.
• The national emblem in the logo signifies the federal system of the Indian Constitution.
• The flower foxtail orchid represents the state, its people and culture of the state.
• The blue color of the logo denotes the autonomy of the assembly secretariat.

Note: State’s Legislative Assemblies of Tripura, Meghalaya, and Mizoram uses the National Emblem of India.