SSC CHSL 2019 Official Paper 10 (Held On: 12 Oct, 2020 Shift 1) (Previous Year Paper)

The correct answer is "Declaration".

Key Points

• The word 'Assertion' means a solemn and often public declaration of the truth or existence of something.
• The synonyms of the word 'Assertion' are "declaration, affirmation, claim".
• From the synonym of the given word, we can say that the word 'Declaration' is the same in meaning.
• The word 'Declaration' means a formal or explicit statement or announcement.

Hence, the correct answer is option 3. 

Let's see the meaning of other given options-

Additional Information

• The antonyms of the word 'Assertion' are "disavowal, contradiction, denial, negation".
• Example of 'Assertion' in a sentence:
• At the moment, not even Williams can make that assertion.

The correct answer is: Option 4.

Key Points

• The word "Faithfuly" is incorrectly spelt; the correct spelling should be "Faithfully". (वफादारी से)
• Example: She served her employer faithfully for many years.
• "Faithfully" means in a loyal manner. (वफादारी से)
• Example: He has faithfully followed the traditions of his ancestors.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Awfully (बहुत): Very; extremely.
• Example: The weather was awfully cold last night.
• Unduly (अनावश्यक रूप से): To an unwarranted degree; excessively.
• Example: She was unduly worried about her exams.
• Unruly (अविनीत): Disorderly and disruptive.
• Example: The teacher found it difficult to manage the unruly class.

The correct answer is "A number of protestors were beaten by the police last night".

Key Points  

• In Active Voice, a sentence emphasizes the subject, performing an action.
• In Passive Voice, a sentence emphasizes the action or the object of the sentence.
• The given sentence is in the active voice and 'The police' is the subject and 'a number of protestors' is the object.
• When we convert this sentence into passive voice, the subject 'The police' of the active voice becomes the object, the object 'a number of protestors' becomes the subject.
• The passive format "were + V3" should be used.
• This is the active and passive voice rule for the past simple tense.
• Hence, the correct answer is option 4.

Additional Information

• Verbs of passive format have a different set of tenses (*V3 - Past participle or Third form of the Verb) as given below in the table:

 

The correct answer is "​Angry about something".

Key Points

• Given Idiom: Up in arms means angry and complaining about something.
• Example: The arts community will be up in arms with this line of questioning.
• From the given options, the first option is the most appropriate meaning of the given idiom.
• Hence, the correct answer is option 1.

Mistake Points

• We may think from the phrase "Up in arms" and the options that it is all about to give up fighting and surrender or throw up arms in joy, but the correct answer is option 1. So be careful while dealing with such questions.

Additional Information

• The idiom/phrase originates from: The literal meaning of the phrase dates back to the 1500s. It is related to the fact that weapons and armour are also called arms. One of the first examples of the phrase can be found in King Richard III, by William Shakespeare. The play was written in the late 1500s.

The correct answer is "excessive".

Key Points

• In the given sentence, an adjective should be used to describe the noun 'usage'.
• Let us explore the given options:
• Exceeding will act as a gerund means be better than; surpass.
• Excessive will act as an adjective means more than is necessary, normal, or desirable; immoderate.
• Exceed will act as the base form of the verb means be better than; surpass.
• Exceedingly will act as an adverb means extremely.
• Hence, the correct answer is option 2.

The correct answer is "seriously".

Key Points

• In the given sentence, an adverb should be used to modify the verb 'think'.
• Let us explore the given options:
• Serious will act as an adjective means solemn or thoughtful in character or manner.
• Seriousness will act as a noun means the quality or state of being serious.
• Series will act as a noun means a number of events, objects, or people of a similar or related kind coming one after another.
• Seriously will act as an adverb means to a degree that is significant or worrying.
• Hence, the correct answer is option 4.

The correct answer is "the".

Key Points

• Let us explore the given options:
• The determiner 'many' means a large number of.
• The determiner 'the' is used for denoting one or more people or things already mentioned or assumed to be common knowledge.
• The determiner 'any' is used to refer to one or some of a thing or a number of things, no matter how much or how many.
• The determiner 'a' is used when referring to someone or something for the first time in a text or conversation.
• Hence, the correct answer is option 2.

The correct answer is "to take".

Key Points

• Let us explore the given options:
• To taking is incorrect as infinitives are never conjugated with -ed or -ing at the end because they are not used as verbs in a sentence.
• Takes is incorrect as the verb 'takes' is a third-person singular present verb.
• To take is correct as the infinitive verb "to take" will act as an object of the sentence.
• Taken is incorrect as it is the past participle form of the verb and the given sentence is in the present tense.
• Hence, the correct answer is option 3.

The correct answer is "switch off".

Key Points

• The noun 'switch' means a device for making and breaking the connection in an electric circuit.
• Let us explore the given options:
• The preposition 'in' is used for expressing inclusion or involvement.
• The preposition 'over' means above so as to cover or protect.
• The preposition 'up' means from a lower to a higher point of (something).
• The preposition 'off' is used when a machine or piece of electrical equipment that is off is not switched on or is not being used.
• Hence, the correct answer is option 4.

The correct answer is "Deceit".

Key Points 

• The word 'Guile' means the inclination or practice of misleading others through lies or trickery.
• The synonyms of the word 'Guile' are "deceit, artifice, cheating".
• From the synonym of the given word, we can say that the word 'Deceit' is the same in meaning.
• The word 'Deceit' means the action or practice of deceiving someone by concealing or misrepresenting the truth.

Hence, the correct answer is option 4. Let's see the meaning of other given options-

 

Additional Information

• The antonyms of the word 'Guile' are "honesty, probity, sincerity".
• Example of 'Guile' in a sentence:
• Wann advised me to use whatever kind of guile I can come up with to make my son a Mets fan.

The correct answer is "​to be as durable as".

Key Points

• In the given underlined segment, the use of "so durable as" is incorrect as "so...as" can only be used with negative like 'not'.
• We use not + so + adjective/adverb + as to make comparisons, meaning not to the same degree.
• In the first option, 'most' is used which is not a comparative adjective but a superlative adjective.
• In the third option, 'very' is not generally comparable. We can use 'very' before superlative adjectives that end in -est.
• But we use as + adjective/adverb + as to make comparisons when the things we are comparing are equal in some way.
• Hence, the correct answer is option 4.

Correct Sentence: Lenovo has launched ThinkPad XI Fold, the world’s first foldable laptop which is claimed to be as durable as its other devices.

Additional Information

• We can use "as...as" for both negative and positive, "so...as" can only be used with negative.

The correct answer is "unaware".

Key Points

• Let us explore the given options:
• Recognised means acknowledged the existence, validity, or legality of someone or something.
• Unconfirmed means not confirmed as to truth or validity.
• Unaware means having no knowledge of a situation or fact.
• Renowned means a known or talked about by many people; famous.
• Hence, the correct answer is option 3.

Complete Sentence: If the video clip of the murder had not been shared on social media, the world would likely have remained unaware of the tragedy.

The correct answer is - Construct.

Key Points  

• The word 'Demolish' means to destroy (as a building) completely by knocking down or breaking to pieces. ('demolish' शब्द का अर्थ है  पूरी तरह से नष्ट करना या टुकड़े-टुकड़े करना।)
• Example: Some wanted to demolish the building and construct a new one on its site.
• The word 'Construct' means to build or make (something, typically a building, road, or machine). ('construct' शब्द का अर्थ है निर्माण करना या बनाना (आमतौर पर एक इमारत, सड़क या मशीन))
• From the above information, we can say that the word 'construct' is the opposite word for 'demolish.'

Hence, the correct answer is option 3.

Additional Information

• The synonyms of the word 'Demolish' are 'level, pull down, unbuild.'
• The antonyms of the word 'Demolish' are 'construct,​ build, erect, put up, raise.'
• Let's see the meaning and mnemonics of other given options:

The correct answer is: Option 3.

Key Points

• The word "Sincearly" is incorrectly spelt. The correct spelling is "Sincerely" which means in a genuine and honest manner. (ईमानदारी से)
• Example: She spoke sincerely about her experiences.
• "Sincerely" refers to expressing true feelings without any pretense. (ईमानदारी से)
• Example: He sincerely apologized for the mistake.
• Hence, the correctly spelt word is 'Sincerely'.

Therefore, the correct answer is: Option 3.

Additional Information

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

• Popularly (लोकप्रिय रूप से): In a way that is liked or admired by many people.
• Example: The artist is popularly known for his unique style.
• Beggarly (भिखारी जैसा): In a manner that is very poor or inadequate.
• Example: They lived in beggarly conditions after losing their home.
• Jocularly (हास्यपूर्वक): In a joking or humorous way.
• Example: He spoke jocularly to lighten the mood.

The correct answer is "Provoke trouble".

Key Points

• Given Idiom: Stir up a hornet’s nest means to create, provoke, or trigger a dangerous, troublesome, or complicated situation.
• Example: According to my brother Paul, this Lonnie Norton was asking a lot of questions and stirring up a hornet's nest around town.
• From the given options, the first option is the most appropriate meaning of the given idiom.
• Hence, the correct answer is option 1.

Additional Information

• The idiom/phrase originates from: The phrase dates back from the 1700s and relates to the anger that hornets show as a metaphor for causing a commotion.

The correct answer is He asked me if I attend the film festival at Goa every year.

Key Points

• The given sentence is a direct speech.
• The basic rules for changing or converting direct speech into indirect speech:
• The question mark (?) is removed and a full stop (.) is used at the end of a sentence.
• The given example is an interrogative sentence starting with a helping verb, therefore, 'do' will be replaced with 'if/whether'.
• The second person 'you' will be changed into 'I'.
• The interrogative statement is changed into an assertive statement (helping verb will come after the subject).
• If reported speed in past/present routine action(here every year shows the routine action) then, there is no change in tense of reported speech.
• From the following rules, we get the correct sentence as- option 3*.*

Additional Information

• The following table will enable us to know how tense changes into Indirect speech:

 

The correct answer is "DACB".

​

Key Points

• The sentence 'D' is independent of any other sentences as it is giving general information about "The Regional Transport Offices of Delhi". Hence, 'D' is the first part.
• The phrase "This test" in the sentence 'A' refers back to the 'new driving test' mentioned in the sentence 'D'. Hence, 'A' follows 'D'.
• The pronoun 'It' in the sentence 'C' refers back to the 'Driving Test Track' mentioned in the sentence 'A'. Hence, 'C' follows 'A'.
• The phrase "these specific skills" in the sentence 'B' refers back to the 'specific driving skills' mentioned in the sentence 'C'. Hence, 'B' follows 'C'.

After rearranging the sentences: The Regional Transport Offices of Delhi have recently introduced a new driving test. This test is conducted on the fully automated Driving Test Track designed by Maruti Suzuki. It is a fully-automated track having six segments to test specific driving skills. Each of these specific skills is to be tested and need to be completed successfully in under seven minutes by the candidate.

Important Points

• Important Rules to Solve the Para Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentence and eliminate the irrelevant options.
• Try to identify the opening (independent sentence) and closing sentences (concluding sentence).
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.

The correct answer is "BCDA".

​

Key Points

• The sentence 'B' is independent of any other sentences as it is giving general information about the film "The Secret Life of Frogs". Hence, 'B' is the first part.
• The phrase "The film" in the sentence 'C' refers back to 'The Secret Life of Frogs' mentioned in the sentence 'B'. Hence, 'C' follows 'B'.
• The pronoun 'It' in the sentence 'D' refers back to 'The film' mentioned in the sentence 'C'. Hence, 'D' follows 'C'.
• The pronoun 'them' in the sentence 'A' refers back to 'unique species of frogs' mentioned in the sentence 'D'. Hence, 'A' follows 'D'.

After rearranging the sentences: The Secret Life of Frogs is the first-ever film on the Amphibians of India. The film has been shot extensively in the Western Ghats. It showcases unique species of frogs that are critically endangered. The most well-known among them is the Purple Frog needing immediate protection.

Important Points

• Important Rules to Solve the Para Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentence and eliminate the irrelevant options.
• Try to identify the opening (independent sentence) and closing sentences (concluding sentence).
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.

The correct answer is "one of a pioneers of Indian art".

Key Points

• In the given sentence, the use of the article 'a' before the specific noun 'pioneers' is incorrect.
• 'A' is an indefinite article, which means that it refers to, or introduce, an unspecified noun. In other words, we use an indefinite article in front of a noun when we're not referring to a particular person, place, thing or idea, but we want to convey that we're talking about any person, place, thing or idea.
• We use 'a' before a consonant sound (here surprising).
• In the given sentence, the noun 'pioneers' is specific or particular.
• The definite article 'the' is used before singular and plural nouns when the noun is specific or particular.
• Hence, the correct answer is option 4.

Correct Sentence: When I met Akbar Padamsee, one of the pioneers of Indian art, he was 87 but still alert and active.

Additional Information

• There are three articles: a, an, and the. Articles are used before nouns or noun equivalents and are a type of adjective.

 

The correct answer is "Redundant".

Key Points

• Let us explore the given options:
• Redundant means not or no longer needed or useful; superfluous.
• Dominant means having power and influence over others.
• Abundant means existing or available in large quantities; plentiful.
• Reluctant means unwilling and hesitant; disinclined.
• Hence, the correct answer is option 1.

The correct answer is "India witnesses the death".

Key Points

• In the given sentence, the present participle form of the verb 'witnessing' used is incorrect.
• The verb third-person singular present should be used with the noun 'India'.
• Therefore, the third-person singular verb 'witnesses' should be used instead of the present participle form of the verb 'witnessing'.
• Hence, the correct answer is option 2.

Correct Sentence: It is reported that everyday India witnesses the death of over 2000 babies aged less than one year.

The correct answer is "Your skill lie".

Key Points

• In the given sentence, the base form of the verb 'lie' used is incorrect.
• The verb third-person singular present should be used in the simple present tense with the pronoun 'Your'.
• In the present tense, regular verbs are conjugated by adding an 's' in the third person singular.
• Therefore, the third-person singular verb 'lies' should be used instead of the base form of the verb 'lie'.
• Hence, the correct answer is option 1.

Correct Sentence: Your skill lies in cheering up people who are stressed out, wounded up or generally just annoyed.

Additional Information

Lay and lie are the two most difficult irregular verbs because when we speak, we frequently misuse them. As a result, our ears are used to hearing incorrect forms. When we encounter a wrong form while we are proofreading, it sounds right.

Definition of Lay

Lay means to put something (or someone) down. Because lay is a transitive verb, a direct object will follow. A direct object receives the action of the verb.

Read this example:

• Before returning to the Godzilla marathon on late night TV, Quentin laid his sleeping son Jeremy on the bed and covered him with a quilt.

Quentin laid whom on the bed? Jeremy.

Definition of Lie

Lie, on the other hand, means to rest or recline. Lie is an intransitive verb, so no direct object will follow.

• The center of Diane's bed always smells like dog because Reliable, her beagle, lies there every chance he gets.

What is Reliable doing in the middle of the bed? Resting.

The correct answer is "Neglect".

Key Points

• The word 'Surveillance' means close observation, especially of a suspected spy or criminal.
• The antonyms of the word 'Surveillance' are "neglect, carelessness, ignorance".
• From the antonym of the given word, we can say that the word 'Neglect' is opposite in meaning.
• The word 'Neglect' means not to pay proper attention to; disregard.

Hence, the correct answer is option 2. Let's see the meaning of other given options-

Additional Information

• The synonyms of the word 'Surveillance' are "care, guidance, supervision".
• Example of 'Surveillance' in a sentence:
• US Department of Justice reports have never identified a single terror attack prevented by mass surveillance.

The correct answer is "visionary".

Key Points

• Let us explore the given options:
• Voluntary means done, given, or acting of one's own free will.
• Literary is the one concerned with literature as a profession.
• An opponent is one's adversary in a contest, conflict, or dispute.
• A visionary is a person with original ideas about what the future will or could be like.
• Hence, the correct answer is option 4.

Complete Sentence: Padamse worked like a mathematician and was a true visionary who experimented with numerous mediums. 

Let us look at the meanings in Hindi- 

• Voluntary- स्वैच्छिक
• Literary- साहित्यिक
• Adversary- वैरी
• Visionary- काल्पनिक

The correct answer is "Authentic".

Key Points

• Let us explore the given options:
• Unreal means imaginary or illusory.
• Academic means relating to education and scholarship.
• Authentic means of undisputed origin and not a copy; genuine.
• Majestic means having or showing impressive beauty or scale.
• Hence, the correct answer is option 3.

Room comes first in the order.

It is followed by Flat.

Flat is followed by Apartment.

Apartment is followed by Street.

Street is followed by Town.

The correct order is,

Room (3) → Flat (1) → Apartment (4) → Street (2) → Town (5)

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

The pattern followed is,

All follow the same pattern, except ‘TVW’.

Hence, “TVW” is the odd one.

Given,

N is coded as 30 and COT is coded as 78

The pattern followed is,

For COT,

 

Similarly,

For PET,

 

Hence, “84” is the correct answer.

The paper when unfolded will look like,

Hence, option 1 is the correct answer.

Concept:

1. We have to check the conclusions are 100% match with the statement. If the conclusion is 100% match with the given statement then the conclusion is true. If there is a 1% chance of not following the statement then the conclusion is considered to be false.

2. The possibility case can be considered to be "false" in "definite case".

3. In Possibility case, either "can" or "possible" word must be present.

The least possible Venn diagram is,

Conclusion I: Some beans are breads → False (This is possible but not definite)

Conclusion II: Some breads are beans → False (This is possible but not definite)

Hence, neither conclusion I nor II follows

Note: 

Conditions of Either-or case:

1. The elements should be the same in both the statements.
2. Individually both the conclusions should be false.
3. One conclusion should be positive and one conclusion should be negative (Complementary pair)

The two complementary pairs are:

1. All + Some not

2. No + Some

Additional Information

(Square of first number + square of third number) × 2 = Middle Number

(3, 68, 5) → ( 3²  + 5²) × 2= (9  + 25) × 2 = 34 × 2 = 68

1) (2, 10, 1) → ( 2²  + 1²) × 2= (4  + 1) × 2 = 5 × 2 = 1

2. (2, 72, 10) → ( 2²  + 10²) × 2= (4  + 100) × 2 = 104 × 2 = 208 ≠ 72

3. (5, 72, 8) → ( 5²  + 18²) × 2= (64  + 25) × 2 = 89 × 2 = 178 ≠ 72

4. (4, 64, 5) → ( 4²  + 5²) × 2= (16  + 25) × 2 = 41 × 2 = 82 ≠ 64

Hence, “(2, 10, 1)” is the correct answer.

Given,

John used to buy petrol at the rate of Rs. 80 per liter till last month.

Now he buys it at the rate of Rs. 85 per liter.

Increase in percentage = (85 – 80)/ 80 × 100

= 5/ 80 × 100

= 0. 0625 × 100 = 6.25

Hence, “6.25 %” is the correct answer.

The number of triangles in the given figure is,

 

Hence, “20” is the correct answer.

Alternate Method

 

Triangles:

BCF, CEF, EFG, CDE, GHE,

HEK, JHK, AIG, BCE, CGE,

CDG, CEF, EJK, CGK, GIK,

ACG, CIK, AIC, AIK, ACK 

So, there are 20 triangles in the given figure.

Hence, the correct answer is "20".

The correct mirror image of the given figure is,

Hence, option 1 is the correct answer.

The pattern followed is,

Similarly,

Hence, “QTCV” is the correct answer

The pattern followed is,

The set of letters ‘ababccd’ are repeated.

solving the given alternatives.

1. abacccd/ ababccd/ababccd  (Does not follow any pattern)

2. ababccd/ ababccd/ababccd (Follow the pattern)

3) abaaccd/ abbbdcd/ababccd (Does not follow any pattern)

4) ababccd/ ababcad/ababccd (Does not follow any pattern)

Hence, “bacccd” is the correct answer.

Milk is obtained from a cow.

Similarly,

Eggs are obtained from hens.

Hence, “hen: egg” is the correct answer.

The pattern followed is,

All follow the same pattern, except ‘TUGD’.

Hence, “TUGD” is the odd letter cluster.

T

he pattern followed is,

Similarly,

Hence, “OCINCOC” is the correct answer.

Lizard is a reptile, and,

Mammals are represented separately.

The correct Venn diagram is,

Hence, option 3 is the correct answer.

The pattern followed is,

The number of sides in the figures keeps on increasing. In the first figure there are three sides, in the second figure there are four sides, in the third there are five sides, in the fourth there are six sides and in the answer figure there must be seven sides.

And,

The number of lines surrounding the figure keeps on decreasing by one.

The figure which will come next in the series is,

Hence, option 1 is the correct answer

The pattern followed is,

8: 49 → 8 – 1 = 7, 7² = 49

So,

8: 49

Similarly,

Option 1 → 9: 87 → 9 – 1 = 8, 8² = 64, not 87

Option 2 → 12: 121 → 12 – 1 = 11, 11² = 121

Option 3 → 13: 170 → 13 – 1 = 12, 12² = 144, not 170

Option 4 → 15: 210 → 15 – 1 = 14, 14² = 196, not 211

’12: 121’ share the same relationship as that shared by the given number-pair.

Hence, “12: 121” is the correct answer.

Replacing the following signs and solving the equation,

Option 1 → ×, =, -, ÷ 

Replacing the signs

26 × 2 = 3 - 3 ÷ 13

Using BODMAS rule,

26 × 2 = 3 – 0.23

52 is not equal to 2.77

Option 2 → ÷, ×, =, -

Replacing the signs

26 ÷ 2 × 3 = 3 - 13

Using BODMAS rule,

13 × 3 = 3 – 13

39 is not equal to – 10

Option 3 → ×, ÷, +, =

Replacing the signs

26 × 2 ÷ 3 + 3 = 13

Using BODMAS rule,

26 × 0.66 + 3 = 13

17. 16 + 3 = 13

20.16 is not equal to 13

Option 4 → ÷, ×, =, × 

Replacing the signs

26 ÷ 2 × 3 = 3 × 13

Using BODMAS rule,

13 × 3 = 3 × 13

39 = 39

Hence, option 4 is the correct answer.

Joule is the unit of work.

Similarly,

Hectare is the unit of area.

‘Hectare’ is related to the third word in the same way as the second word is related to the first word.

Hence, “hectare” is the correct answer

The pattern followed is,

All numbers are divisible by 4, except ‘255’

268 ÷ 4 = 67

124 ÷ 4 = 31

212 ÷ 4 = 53

255 ÷ 4 = not divisible.

Hence, “255” is different from the rest.

The given figure is embedded in,

Hence, option 4 is the correct answer.

Chirp, Neigh and Bleat are sounds made by different animals and birds.

Whereas,

Frisk refers to searching of hidden items.

Hence, “frisk” is the odd one.

LOGIC:

First Number,

Second number = (First Number × 2) + 1,

Third Number = (Second Number × 2) + 1

The pattern followed here is:

(7, 15, 31) →

First Number = 7,

Second number = (7 × 2) + 1 = 15

Third Number = (15 × 2) + 1 = 31

Similarly when we go through option we find only one such combination. 

(3, 7, 15) →

First Number = 3,

Second number = (3 × 2) + 1 = 7

Third Number = (7 × 2) + 1 = 15

Hence, the correct answer is (3, 7, 15) .

Given,

Disha’s salary = 17x

Pratima’s Salary = 15x

17x – 15x = 3000

2x = 3000

X = 1500

So pratima’s salary = 15 × 1500 = 22500 Rs

Hence, “Rs. 22,500” is the correct answer.

By comparing fig. (1) and fig. (3)

‘2’ is opposite to ‘4’.

‘3’ is opposite to ‘5’.

And,

‘1’ is opposite to ‘6’.

Hence, “6” is the correct answer.

Given:

SP of the motorcycle = Rs. 70000

Profit % = 25%

Formula:

SP = CP × (100 + Profit%)/100

Calculation:

CP of the motorcycle = 70000 × (100/125)

New SP of the motor cycle to gain 30% = 70000 × (100/125) × (130/100)

= Rs. 72,800

Given:

O is centre of the circle, BC is a chord and CD is a tangent through the point C.

∠AOC = 118°

Concept:

The angle subtended by an arc of a circle at its center is twice the angle it subtends on any point of the circle's circumference.

For any circle, the angle between a tangent and a chord through the point of contact of the tangent is equal to the alternate segment.

Calculation:

According to the formula

∠AOC = 2∠ABC 

⇒ 118° = 2∠ABC

⇒ ∠ABC = 118°/2 

⇒ ∠ABC = 59°

Also, ∠ABC = ∠ACD 

⇒ ∠ACD = 59° 

∴ ∠ACD is 59°.

Given:

Average age of 25 men = 28 years

Formula Used:

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

Calculation:

Sum of age of 25 men = 28 × 25 = 700

If 5 men of average age of 25 years joined them,

Sum of age of 5 men = 25 × 5 = 125 years

Now,

Sum of age of 30 men = 700 + 125 = 825 years

⇒ Average age of 30 men = 825/30 = 27.5 years

∴ The average age of all the men together is 27.5 years.

Given:

8 cosec2θ + 25 sin2 θ

Formula:

The minimum value of "a cosec2θ + b sin2 θ" is given by $2\sqrt{ab}$

Calculation:

Minimum Value of 8 cosec2θ + 25 sin2 θ = $2\sqrt{(8 × 25) }$

⇒ $2\sqrt{200}$

⇒ $2\sqrt{(100 × 2)}$

⇒ 2 × 10√2 

⇒ 20√2

Given:

Richa travels from A to B at the speed = 15 km/hr

Richa travels from B to C at the speed = 20 km/hr

Richa travels from C to D at the speed = 30 km/hr

AB = BC = CD

Formula:

Average speed = Total distance/Total time

Calculation:

Let AB = BC = CD = 60 km (LCM of 15, 20 and 30)

Total distance = 3 × 60 = 180 km

Time taken by Richa to travels from A to B = 60/15 = 4 hrs.

Time taken by Richa to travels from B to C = 60/20 = 3 hrs.

Time taken by Richa to travels from C to D = 60/30 = 2 hrs.

Total time taken by Richa to travels from A to D = 4 + 3 + 2 = 9 hrs.

∴ Average speed = 180/9 = 20 km/hr.

In ΔABC

 

AM = BM = CM = 15 (circumradius)

ML is perpendicular to BC, then

ML will divide the BC in two equal parts so,

BL = LC = 24/2 = 12 cm

In right angled ΔMLC,

(MC)² = (ML)² + (LC)²

⇒ 15² = ML² + 12²

⇒ ML² = 225 - 144 

⇒ ML = √81

∴ ML = 9 cm

Given:

In ΔXYZ, L and M are the middle points of the sides XY and XZ, respectively. 

LR : RM = 1 : 2 and

LR = 3 cm

Formula:

If ΔABC ∼ ΔPQR, then

AB/PQ= BC/QR = AC/PR

Calculation:

LR : RM = x : 2x

LR = 3 cm, then

x = 3 cm

Hence, 2x = 3 × 2 = 6 cm

LM = LR + RM

⇒ LM = 3 + 6 = 9 cm

In ΔXYZ and in ΔXLM

∠X = ∠X [common]

∠XYZ = ∠XLM

∠XZY = ∠XML

∴ ΔXYZ ∼ ΔXLM

Now,

LM/YZ = XL/XY

⇒ 9/YZ = XL/2XL  [∵ L is mid point of XY]

⇒ 9/YZ = 1/2

⇒ YZ = 9 × 2 

∴ YZ = 18 cm

Given:

Diagonal of rectangle = 15 cm

Length of the rectangle = 12 cm

Formula:

Diagonal² = Length² + Breadth²

Area of the rectangle = Length × Breadth 

Calculation:

 According to the formula

15² = 12² + Breadth²

⇒ Breadth² = 225 – 144 

⇒ Breadth = √81

⇒ Breadth = 9

∴ Area of the rectangle = 9 × 12 = 108 cm²

Given:

Expenditure of the company during the year 1996 = Rs. 30 lakhs

Profit of the company during the year 1996 = 45 lakh

Formula:

$profit\ =\ {Income - Expenditure}$

Calculation:

According to the given formula

45 = Income - 30

⇒ Income  = 45 + 30

∴ Income = 75 lakhs.

Shortcut Trick

From 1/a + 1/b + 1/c = 0, we get ab + bc + ca = 0.

From ac = 4/b, we get abc = 4.

Use formula: a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − (ab + bc + ca)).

28 − 3(4) = 2 × (a² + b² + c² − 0).

16 = 2 × (a² + b² + c²) ⇒ a² + b² + c² = 8.

∴ The correct answer is 8.

Alternate Method

Given:

a + b + c = 2

1/a + 1/b + 1/c = 0

ac = 4/b ⇒ abc = 4

a³ + b³ + c³ = 28

Formula Used:

a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)

a³ + b³ + c³ 28

−

3abc 3 × 4 = 12

=

Difference 16

16 = (a + b + c) × (a² + b² + c² − 0) 16 = 2 × (a² + b² + c²)

Calculations:

⇒ 1/a + 1/b + 1/c = 0

⇒ (bc + ac + ab) / abc = 0

⇒ ab + bc + ca = 0

⇒ From formula: 28 − 3(4) = (2)(a² + b² + c² − 0)

⇒ 28 − 12 = 2(a² + b² + c²)

⇒ 16 = 2(a² + b² + c²)

⇒ a² + b² + c² = 16 / 2

⇒ a² + b² + c² = 8

∴ The correct answer is 8.

Additional Information

Sum of Squares Identity

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca). This connects the sum, squares, and product pairs.

Cubic Identity Condition

If a + b + c = 0, then a³ + b³ + c³ = 3abc. This is a very common shortcut in competitive exams.

Reciprocal Relation

Whenever 1/a + 1/b + 1/c = 0 is given, it directly implies that the sum of the products taken two at a time (ab + bc + ca) is zero.

Given:

Total amount which is divided among A, B and C = Rs. 6,300

X : Y = 7 : 5 and Y : Z = 4 : 3

Calculation:

X : Y = 7 : 5     ----(1)

Y : Z = 4 : 3     ----(2)

Multiply by 4 in equation (1) and multiply by 5 in equation (2)

X : Y : Z = 28 : 20 : 15

Ratio of X : Y : Z = 28x : 20x : 15x

According to the question

28x + 20x + 15x = 6,300

⇒ 63x = 6,300

⇒ x = 6,300/63

⇒ x = 100

∴ Share of Y = 20 × 100 = Rs. 2,000

Given:

15 men can complete a task in 10 days.

Formula:

M₁ × D₁ = M₂ × D₂

Calculation:

M₁ = 15, D₁ = 10 and M₂ = 20 

According to the formual

15 × 10 = 20 × D₂

⇒ D₂ = 150/20

⇒ D₂ = 7.5 days

∴ 20 men can complete the same task in 7.5 days.

Calculation:

Profit of company in 1996 = 45 lakh

Profit of company in 1997 = 55 lakh

Profit of company in 1998 = 50 lakh

Profit of company in 1999 = 65 lakh

Profit of company in 2000 = 75 lakh

Profit of company in 2001 = 65 lakh

Profit percentage of company in 1997 increased by = [(55 - 45)/45] × 100 = 22.23%  

Profit percentage of company in 1998 decreased by = [(50 - 55)/55] × 100 = -9.09%

Profit percentage of company in 1999 increased by = [(65 - 50)/50] × 100 = 30%

Profit percentage of company in 2000 increased by = [(65 - 75)/65] × 100 = 15.39%

Profit percentage of company in 2001 decreased by = [(65 - 75)/75] × 100 = -13.34%

∴ In 1998-1999 the company increased fastest.

Given:

PL = 9 cm, LQ = 4 cm and LS = 6 cm

Formula:

If two chord PQ and RS intersect each other at L inside the circle, then

PL × LQ = RL × LS

Calculation:

According to the question

9 × 4 = RL × 6

⇒ RL = 36/6

∴ RL = 6 cm

Given:

Kachita's attendance in her school for academic session 2018- 2019 was 216 days.

Kachita's attendance % = 90%

Formula:

x as a percentage of y = (x/y) × 100 

Calculation:

Let total working days of the school were x days, then

x × (90/100) = 216

⇒ x = 216 × (100/90)

⇒ x = 240 days.

∴ Total working days of the school were 240 days.

Shortcut Trick

Divisibility rule for 11: |(Sum of odd position digits) − (Sum of even position digits)| = 0 or 11, 22, ...

Testing Option B (963391):

Sum of digits at odd places (9, 3, 9) = 21.

Sum of digits at even places (6, 3, 1) = 10.

Difference = 21 − 10 = 11 (which is divisible by 11).

∴ The correct answer is 963391.

Alternate Method

Given:

Options: A. 809781, B. 963391, C. 107611, D. 116571.

Formula Used:

A number is divisible by 11 if the difference between the sum of the digits at odd positions and the sum of the digits at even positions is 0 or a multiple of 11.

9 6 3 3 9 1 Odd Pos (Blue): 9+3+9 = 21 Even Pos (Orange): 6+3+1 = 10 Result: |21 − 10| = 11 (Divisible by 11)

Calculations:

⇒ Option A: 809781 → (8+9+8) − (0+7+1) = 25 − 8 = 17 (Not divisible by 11)

⇒ Option B: 963391 → (9+3+9) − (6+3+1) = 21 − 10 = 11 (Divisible by 11)

⇒ Option C: 107611 → (1+7+1) − (0+6+1) = 9 − 7 = 2 (Not divisible by 11)

⇒ Option D: 116571 → (1+6+7) − (1+5+1) = 14 − 7 = 7 (Not divisible by 11)

∴ The correct answer is 963391.

Additional Information

Divisibility by 3 and 9

A number is divisible by 3 (or 9) if the sum of its digits is divisible by 3 (or 9).

Divisibility by 4 and 8

A number is divisible by 4 if its last two digits are divisible by 4, and by 8 if its last three digits are divisible by 8.

Combined Divisibility Rule for 7, 11, and 13

Subtract the sum of digits in blocks of three from right to left in alternating signs; the result must be divisible by 7, 11, or 13 respectively.

Mr. Joshi's students who have shown improvement = 92 - 85 = 7%

Dr. Kalra's students who have shown improvement = 97 - 85 = 12%

Mrs.Taneja's students who have shown improvement = 100 - 98 = 2%

Mr. Saxena's students who have shown improvement = 87 - 78 = 9%

Hence,

Dr. Kalra's students have shown maximum improvement.

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

-15 + 90 ÷ [89 - { 9 × 8 + (33 - 3 × 7)}]

⇒ -15 + 90 ÷ [89 - {72 + (33 - 21)}]

⇒ -15 + 90 ÷ [89 - {72 + 12}]

⇒ -15 + 90 ÷ [89 - 84]

⇒ -15 + 90 ÷ 5

⇒ -15 + 18

⇒ 3

Given:

cos (x - y) = √3/2

sin (x + y) = 1/2

Formula:

cos30° = √3/2

sin30° = 1/2

Calculation:

cos(x - y) = √3/2

⇒ cos(x - y) = cos30°

(x - y) = 30°     ---- (1)

sin(x + y) = 1/2

⇒ sin(x + y) = sin30°

(x + y) = 30    ---- (2)

Add equation (1) and equation (2), we get

2x = 60°

∴ x = 30°

Given:

cot A = k

Formula:

cot A = Base/Perpendicular

sin A = Perpendicular/Hypotenuse 

(Hypotenuse)² = (Base)² + (Perpendicular)²

Calculation:

cot A = k/1

⇒ Base/Perpendicular = k/1

⇒ Base = k and Perpendicular = 1

(Hypotenuse)2 = (Base)2 + (Perpendicular)2

⇒ (Hypotenuse)2 = k2 + 12

⇒ Hypotenuse = √(1 + K²)

Now, sin A = 1/√(1 + k²)

Profit earned by the company in 1996 = 45 lakh

Profit earned by the company in 1997 = 55 lakh

Profit earned by the company in 1998 = 50 lakh

Profit earned by the company in 1999 = 65 lakh

Profit earned by the company in 2000 = 75 lakh

Profit earned by the company in 2001 = 65 lakh

∴ The profit earned by the company is maximum in the year 2000.

Given:

(cos θ + sin θ)/(cos θ - sin θ) = 8

Formula:

If x/y = a/b, then

Dividendo and Componendo rule

(x + y)/(x - y) = (a + b)/(a - b)

Calculation:

(cos θ + sin θ)/(cos θ - sin θ) = 8/1

Dividendo and Componendo rule

⇒ cos θ/sin θ = (8 + 1)/(8 - 1)

⇒ cot θ = 9/7

Given:

List price of the a bike is more than it's cost price = 15%

Discount % = 20%

Formula:

If a number is increase by x%, then

Increased number = Actual number × (100 + x)/100

SP = MP × (100 - Discount%)/100

Loss = CP – SP

Loss % = (Loss/CP) × 100 

Calculation:

Let cost price of bike be Rs. 100, then

List price of the bike = 100 × (115/100) = Rs. 115

SP of the bike = 115 × (80/100) = Rs. 92

Loss = Rs. 100 - Rs. 92 = Rs. 8 

∴ Loss% = (8/100) × 100 = 8%

Given:

x - 2y = 3 and xy = 5

Formula:

(x - y)² = x² + y² - 2xy 

Calculation:

(x - 2y)² = x² + 4y² - 2 × x × 2y

⇒ 3² = x² + 4y² - 4 × 5

⇒ x² + 4y² = 9 + 20 

⇒ x² + 4y² = 29     ...1)

(x² + 4y²)² = x⁴ + 16y⁴ + 2 × x² × 4y²

⇒ 29² = x4 + 16y4 + 8 × 25

⇒ x4 + 16y4 = 841 - 200 

⇒ x4 + 16y4 = 641     ...2)

(x² - 4y²)² = x4 + 16y4 - 2 × x2 × 4y2

⇒ (x2 - 4y2)2 = 641 - 8 × 25 

⇒ (x2 - 4y2)2 = 441

⇒ x2 - 4y2 = √441

∴ x2 - 4y2 = 21

By using substitution method 

if xy = 5 then the possibilities

 (x,y) = (1,5) (5,1)

 substitute the values x and y in the equation and check

 x - 2y = 5 - 2(1) = 3

x = 5, y = 1 satisfies 

substitute the values in this equaltion

 x2 - 4y2 = 5² - 4(1)² = 21

∴ x2 - 4y2 is 21

Given:

Principal = Rs. 3500

Amount = Rs. 4500

Rate of interest = 10% p.a

Formula:

SI = Prt/100

Calculation:

SI = Rs. 4500 - Rs. 3500

SI = Rs. 1000

According to the formula:

1000 = (3500 × 10 × t)/100

⇒ t = 1000/350

⇒ t = $2\frac {6}{7}$ years

∴ In $2\frac {6}{7}$ years Rs. 3,500 invested at the rate of 10% simple interest per annum, shall amount to Rs. 4,500.

The correct answer is  22.

Key Points

 Pankaj Advani -

• Pankaj Advani was born on 24^th July 1985 in Pune.
• He has been awarded -

1. Arjuna award for billiards and snooker
2. Rajiv Gandhi Khel Ratna award
3. Padma Bhushan
4. Padma Shri
5. The hero India's sports award.

Additional Information

 IBSF World Billiards Championship - 

• This tournament was earlier known as the "World Amateur Billiards Championship".
• Billiard sports are also known as " Cue sports".
• The highest governing body of this sports is the "World confederation of Billiards sports".

​

Hint

Note: 23 times Pankaj Advani wins the ‘IBSF World Billiards Championship. (as of now April 2021)

The correct answer is the Central Processing Unit ( CPU ).

Key Points

• CPU stands for the central processing unit.
• CPU is also known as the central processor or main processor.
• It performs arithmetic, logic, controlling, and Input / Output operations.
• CPU is a part of the hardware that is responsible to carry out functions of the computer program.
• The six main components of the CPU are -

1. Control unit
2. Arithmetic Logic Unit
3. Register
4. Cache
5. Buses
6. Clock

 

Important Points

• Hard Disk is a data storage device that is used to store digital data.
• RAM stands for Random access memory that is used to store working data and machine code.
• The keyboard is a kind of typewriter consisting of buttons and keys.

The correct answer is 26 November.

Key Points

Constitution Day - 

• Constitution day is also called " Samvidhan Diwas" or " National Law Day".
• The Government of India declared 26 November as Constitution Day on 19 November 2015 by a gazette notification.
• This day signifies the adoption of the Indian constitution in 1950.
• On this day constitution-related activities take place in schools, demand for equality, and the special parliamentary session takes place.
• The constitution was adopted on 26 November 1949 and it came into effect on **26 January 1950.**​

 ​

Important Points

• The day also marks the thoughts and ideas of Dr. B.R Ambedkar.
• He is also known as " Father of Indian Constitution".
• He was an economist, jurist, and social reformer and has a great contribution to Indian society.

The correct answer is 2010.

Key Points

   Kalibelia - 

• The Kalbelia folk dance and song belong to the state of Rajasthan.
• The costume of the Kalbelia dance is Lehenga, Odhani, or Angarkha.
• This dance is performed by both Men and Women.
• The Kalbelia songs are taken from mythology.
• The Kalbelia folk songs and dances of Rajasthan in the Representative List of the Intangible Cultural Heritage of Humanity.
• Kalbelia folk songs and dances of Rajasthan” were recognized by UNESCO as an intangible cultural heritage.

Important Points

  UNESCO -

• UNESCO stands for United Nations's Educational, Scientific, and Cultural Organizations.
• It was founded on 16^th November 1945.
• Its headquarter is in Paris, France.
• Its parent organization is the "United  Nations Economic Social Council".

The correct answer is 93.

Key Points

   Lok Sabha - 

• Lok Sabha is the lower house of India's bicameral parliament.
• Lok Sabha is a temporary house and can be dissolved earlier by the President on the advice of the Council of Ministers.
• The maximum strength of the House envisaged by the Constitution is 550, which is made up by the election of up to 530 members to represent the States, up to 20 members to represent the Union Territories.
• It is also known as the " House of people".
• Lok Sabha was founded on 17^th April 1952.
• The term limit of this house is 5 years.

​ 

Important Points

  Speaker and Deputy Speaker -

• He is the presiding officer of Lok Sabha.
• He is elected in the first meeting of Lok Sabha following the process of general elections.
• The current Lok Sabha speaker is Om Birla.
• The Deputy Speaker is the second highest authority in Lok Sabha.
• They act as presiding officers in the absence of a speaker.

The correct answer is Sikkim.

 

Key Points

 Sava Dawa -

• This festival is celebrated to mark the birth, enlightenment, and the attainment of Nirvana of Gautam Buddha.
• Gautam Buddha -

1. His full name is Gautama Buddha.
2. He was born in Lumbini, Nepal.
3. He is the founder of the " Buddhism religion".
4. He is also known as " Shakyamuni" or " Sage of the Skhaukya ".

​

Important Points

• The festival is celebrated on the full moon day of the fourth month of the Buddhist calendar.
• It is mostly celebrated across the street of Gangtok and commence their parade from Tsuk La Khang Monastery.
• The festival has been celebrated since 1950.

The correct answer is Pedology - Phytogeography.

 

Important Points

• Both are related to studies of Population.
• Demography is the study of human populations – their size, composition, and distribution across space – and the process through which populations change.
• ​Population geography is a study that deals with the spatial variation and analysis of the demographic components of change: migration, fertility, and mortality.
• Both related to Water
• Hydrology is the science that deals with the study of water.
• Oceanology is the study of the ocean.
• Both deal with humans and their culture.
• Anthropology is “the science of humanity”.
• It is the studies of human beings in aspects ranging from the biology and evolutionary history of Homo sapiens to the features of society and culture that decisively distinguish humans from other animal species.
• Cultural geography deals with making sense of people and the places they occupy through analyses of cultural processes, cultural landscapes, and cultural identities.

Key Points

• Here one is related to soil and the other is related to plants. 
• Phytogeography is the study of the distribution of plants or taxonomic groups of plants and its focus is to explain the ranges of plants in terms of their origin, dispersal, and evolution.
• Pedology researches the origins of soil as well as the morphology of soils and then classifies them.
• The term pedology is derived from "pedon" meaning "soil" and "logos" which means "study".
• Pedology is the study of soil formation, evolution, and the body of soil.

​

Additional Information

• Nowadays pedologist focuses on the pedogenesis process such as the evolution and functioning of the soil.
• "Vasily Vasil'evich Dukochaev" is considered as the father of the soil.

The correct answer is " Lord Dalhousie".

Key Points

• Lord Dalhousie served as Governor-General of India from 1848 to 1856.
• He introduced the passenger trains in railways in 1853, the electric telegraph in 1852, and uniform postage in 1854.
• He described all three as " Three great engines of social improvement".
• He has started engineering college in Roorkee.
• He made his summer capital Shimla.
• He is the founder of the " Public Works Department" or " PWD" in India.
• He has also served as " Governor General of Canada" or " Commander- in - chief" in India.

​

Important Points

• Lord Wellesley introduced Subsidiary Alliance by virtue of which the Indian kingdoms lost their sovereignty to the English during 1798.
• Fourth Anglo Mysore was fought during the governor-generalship of Lord Wellesley.
• During this war, Tipu Sultan died in the battle of Seringapatam in 1799.
• Fort William College was started by Lord Wellesley in the year 1800.
• Lord Canning served as Governor-General of India from 1856 to 1862.
• He also served as the first Viceroy of India.
• The Mutiny of 1857, which he was able to suppress successfully,
• Passing of Indian Councils Act, 1861 which introduced a portfolio system in India.
• Withdrawal of the “Doctrine of Lapse” was one of the main reasons for the mutiny of 1858.
• Introduction of the Code of Criminal Procedure.
• The Vernacular Press Act was passed in 1878 by Viceroy Lord Lytton (1876-1880).

Additional Information

• The doctrine of lapse was an annexation policy.
• The policy was applied by the British East India Company until 1859.
• Under this Doctrine, when the ruler of a protected state died without a natural heir, his state was not to pass to an adopted heir as sanctioned by the age-old tradition of the country.
• It was to be annexed to the British dominions unless the adoption had been clearly approved earlier by the British authorities.