SSC CHSL Previous Paper 21 (Held On: 15 Oct 2020 Shift 3) (Previous Year Paper)

The correct answer is "No improvement".

Key Points

• The given sentence is in the past continuous tense form of the active voice.
• The rule of making past continuous tense (active voice): Subject + was/were + verb (Ist form) + ing + object + (.).
• The adjective 'troubled' is acting as the object.
• Therefore, there is no need for any improvement in the underlined segment.
• Hence, the correct answer is option 4.

The correct answer is Neeta said that she wanted to see how Pragya performed in her preboard examinations.

• The given sentence is a direct speech.
• The basic rules for changing or converting direct speech into indirect speech:
• The commas and inverted commas are removed and 'that' is added.
• The first person 'me' will be changed into the third person 'she'.
• "Let me" becomes 'wanted'.
• The present simple tense format 'Subject + V1 (performs) + Object' will be changed into the past simple tense format 'Subject + V2 (performed) + Object'.
• From the following rules, we get the correct sentence as- option 2.**

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

The correct answer is "Mishap".

Key Points

• Let us explore the given options:
• Mishap means an unfortunate accident.
• Menace means a threat or danger.
• Magical means relating to, using, or resembling magic.
• Mystery means something that is difficult or impossible to understand or explain.
• Hence, the correct answer is option 1.

The correct answer is "Hamper".

Key Points

• Let us explore the given options:
• Deprive means to prevent from having or using something.
• Indulge means to become involved in an activity.
• Facilitate means to make an action or process easy or easier.
• Hamper means to hinder or impede the movement or progress of someone or something.
• Hence, the correct answer is option 4.

The correct answer is "recorded".

Key Points

• Let us explore the given options:
• 'Reaped' means received something, especially something beneficial as a consequence of one's own or another's actions.
• 'Recorded' means set down in writing or some other permanent form for later reference.
• 'Played' means engaged in an activity for enjoyment and recreation rather than a serious or practical purpose.
• 'Responded' means said something in reply.
• Hence, the correct answer is option 2.

The correct answer is "growth".

Key Points

• Let us explore the given options:
• 'Health' means a mental or physical condition.
• 'Wealth' means an abundance of valuable possessions or money.
• 'Growth' means the process of increasing in size.
• 'Slowdown' means an act of slowing down.
• Hence, the correct answer is option 3.

The correct answer is "rose".

Key Points

• The given sentence is in the simple past tense and will take a past tense form of the verb.
• Let us explore the given options:
• 'Had risen' is the past perfect form of the verb.
• 'Is rise' is the simple present form of the verb.
• 'Rises' is the third-person present form of the verb.
• 'Rose' is the past tense form of the verb.
• Hence, the correct answer is option 4.

The correct answer is "directly".

Key Points

• Let us explore the given options:
• 'Deftly' means in a clever way.
• 'Decently' means in a way that conforms with generally accepted standards of respectable or moral behaviour.
• 'Directly' means with nothing or no one in between.
• 'Dutily': This word doesn't have any meaning or existence.
• Hence, the correct answer is option 3.

The correct answer is "attractive".

Key Points

• Let us explore the given options:
• 'Unattractive' means not pleasing or appealing to look at.
• 'Impossible' means not able to occur, exist, or be done.
• 'Attractive' means relating to the attraction between physical objects.
• 'Possible' means able to be done or achieved.
• Hence, the correct answer is option 3.

The correct answer is "Implicatted".

Key Points    

• Let us explore the options:
• 'Pressurised' means an attempt to persuade or coerce someone into doing something.
• 'Suppression' means the action of forcibly put an end to something.
• 'Implicatted': There is no such word in English or we can say that there is some spelling mistake in this word.
• 'Coercion' means the practice of persuading someone to do something by using force or threats.
• Hence, the correct answer is option 3.
  

Additional Information

• If we remove the letter 't' between 't' and 'e' then it will become a meaningful word 'Implicated' which means to show someone to be involved in a crime.

The correct answer is "​The neighbourhood were getting disturbed".

Key Points

• In the given sentence, the plural form of the verb 'were' is incorrect.
• The subject of the sentence 'neighbourhood' is a singular form of the noun.
• But, the verb 'were' used with the singular subject is plural in form.
• We know that subjects and verbs must agree with one another in number (singular or plural).
• Thus, if a subject is singular, its verb must also be singular; if a subject is a plural, its verb must also be plural.
• Therefore, the singular past verb 'was' should be used in place of 'were'.
• Hence, the correct answer is option 1.
  

Correct Sentence: The neighbourhood was getting disturbed with the loud music that was playing at the wedding party in the big bungalow.

The correct answer is "Scattered".

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Key Points  

• The word 'Interspersed' means to scatter or set here and there among other things.
• The synonyms of the word 'Interspersed' are "scattered, mingled, mixed".
• From the synonym of the given word, we can say that the word 'Scattered' is the same in meaning.
• The word 'Scattered' means occurring or found at intervals or various locations rather than all together.

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

 

Additional Information

• The antonyms of the word 'Interspersed' are "extracted, withdrew, detached".
• Example of 'Interspersed' in a sentence:
• Tragic musical compositions were interspersed with moments of silence.

The correct answer is "​that you are going".

Key Points

• In the given sentence, the past form of the verb 'would' is incorrect.
• The given sentence is in the present continuous tense.
• The present continuous tense is used to show that an action is going to take place in the near future.
• The present continuous is formed using am/is/are + present participle (V+ing).
• Therefore, the second person singular present form of the verb 'are' should be used in place of 'would'.
• Hence, the correct answer is option 1.
  

Correct Sentence: "Did you tell your parents that you are going to a movie with me this evening?" My friend asked me.

The correct answer is "BADC".

​

Key Points

• The sentence 'B' is independent of any other sentences as it is giving general information about "North India". Hence, 'B' is the first part.
• The phrase "minimum temperature" in the sentence 'A' is linked with the 'harsh winter' mentioned in the sentence 'B'. Hence, 'A' follows 'B'.
• The phrase 'wind factor' mentioned in the sentence 'D' is linked with the 'winds' mentioned in the sentence 'A'. Hence, 'D' follows 'A'.
• The sentence 'C' is the concluding sentence. Hence, the sentence 'C' is the last sentence.
  

After rearranging the sentences: North India has been witnessing a harsh winter this year. The minimum temperature in the national capital dropped yesterday as cold northwesterly winds continued to blow in from the hills. A favourable outcome of the wind factor was that there was a slight decrease in air pollution levels due to the wind speeds. However, experts said the minimum temperatures would increase over the next few days due to a cloud cover.

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 "Irational".

Key Points    

• Let us explore the options:
• 'Escalation' means a rapid increase.
• 'Irritable' means having or showing a tendency to be easily annoyed.
• 'Irational': There is no such word in English or we can say that there is some spelling mistake in this word.
• 'Appreciation' means recognition and enjoyment of the good qualities of someone or something.
• Hence, the correct answer is option 3.
  

Additional Information

• If we add the letter 'r' between 'I' and 'r' then it will become a meaningful word 'Irrational' which means not logical or reasonable.

The correct answer is "delayed".

Key Points

• Let us explore the given options:
• 'Built' means constructed something by putting parts or material together.
• 'Delayed' means postponed or defer action.
• 'Broken' means having breaks or gaps in continuity.
• 'Repaired' means restored something damaged, faulty, or worn to a good condition.
• Hence, the correct answer is option 2.
  

Complete Sentence: The flyover was closed in October last year for repairs but its reopening has been delayed as it will be ready only in March this year.

The correct answer is 'Planned.'

Key Points

• Let us see the meaning of Impromptu:
• Impromptu: made or done without previous thought or preparation. (पिछले विचार या तैयारी के बिना बनाया या किया गया।)
• Example: The more you practice giving impromptu presentations, the more comfortable you become doing so.
• Let us see the meanings of the given options:
• Planned: decided on and made arrangements in advance. (निर्णय लिया और पहले से व्यवस्था की।)
• Fast: moving or capable of moving at high speed. (तेज गति से चलने में सक्षम।)
• Appropriate: suitable or proper in the circumstances. (परिस्थितियों में उपयुक्त या उचित।)
• Unplanned: not planned. (अनियोजित, योजनारहित।)
• From the meanings of the given words, we can say that the word 'Planned' is the most appropriate ANTONYM of the given word 'IMPROMPTU.'
• Hence, the correct answer is 'Planned.'

Additional Information

• Let us see the synonyms of the given options:

The correct answer is "Strong".

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Key Points  

• The word 'Fragile' means easily broken or damaged.
• The antonyms of the word 'Fragile' are "strong, sturdy, tough".
• From the antonym of the given word, we can say that the word 'Strong' is opposite in meaning.
• The word 'Strong' means able to withstand hardship, strain, or exposure.

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

 

Additional Information

• The synonyms of the word 'Fragile' are "breakable, delicate, frangible".
• Example of 'Fragile' in a sentence:
• The carbon fibre obtained was partially melted and was too fragile to handle.

The correct answer is "​Admit that you are wrong".

Key Points

• Given Idiom: Eat humble pie means to admit an error and become submissive and apologetic in doing so.
• For example, But, by making the critics eat humble pie, he's on the front foot.
• From the given options, the second option is the most appropriate meaning of the given idiom.

Hence**,** the correct answer is Admit that you are wrong.

Mistake Points

• We may think from the phrase "Eat humble pie" and the options that it is all about to eat a pie, but the correct answer is option 2. So be careful while dealing with such questions.
  

Additional Information

• The idiom/phrase originates from: In the United Kingdom, what is known as offal meat which is the liver, heart, entrails of an animal was known as numbles in the early 14th century. Speculation is that the pies made from numbles eventually come to know umbles through metanalysis (the process of change in the sound and the use of a word in the English language). Since 1330 the mention of umble pies is common. Samuel Pepys used it in his diary at least on two occasions.

The correct answer is "​so it was a bit scared".

Key Points

• In the given sentence, the adjective 'scared' used is incorrect.
• 'Scared' is an adjective used to describe a person or maybe an animal that is frightened or worried.
• 'Scary' is an adjective used to describe something or someone that causes fear or terror.
• Therefore, the adjective 'scary' should be used in place of 'scared'.
• Hence, the correct answer is option 3.
  

Correct Sentence: The park was well lighted at night but it was deserted, so it was a bit scary.

The correct answer is "​To be ignored".

Key Points

• Given Idiom: To fall on deaf ears means to be ignored or disregarded.
• For example, Criticisms of these practices used to fall on deaf ears.
• 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 "To fall on deaf ears" and the options that it is all about falling off something on deaf ears, but the correct answer is option 1. So be careful while dealing with such questions.
  

Additional Information

• The idiom/phrase originates from: The expression most often refers to something a person does not wish to hear, such as a reproach or advice, and therefore he or she reacts as though physically unable to hear it. The term dates from the fifteenth century and has been a cliche since the nineteenth century.

The correct answer is "CADB".

​

Key Points

• The sentence 'C' is independent of any other sentences as it is giving general information about "The state of Jharkhand". Hence, 'C' is the first part.
• The phrase "this state" in the sentence 'A' refers back to the 'state of Jharkhand' mentioned in the sentence 'C'. Hence, 'A' follows 'C'.
• The phrase "These forests" mentioned in the sentence 'D' refers back to the 'Saranda forests' mentioned in the sentence 'A'. Hence, 'D' follows 'A'.
• The sentence 'B' is the concluding sentence. Hence, the sentence 'B' is the last sentence.
  

After rearranging the sentences: The state of Jharkhand faces water scarcity every summer. Saranda forests, in Singhbum, are a huge catchment for rivers and streams in this state. These forests are India's largest contiguous Sal forests and the current plan says mining should not be allowed in the dense forest as rivers are drying up. If these forests are opened up for mining purposes the remaining rivers and streams will dry up.

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  'Acted.'  

Key Points

• The word 'Masqueraded' means as in played, acted.
• ​Example: A journalist masqueraded as a man in distress.
• Let's look at the meanings of the given options:
• Dropped- having fallen or been allowed to fall vertically. (गिरने या लंबवत गिरने की अनुमति दी गई।)
• Acted- behaved in the way specified. (निर्दिष्ट तरीके से व्यवहार किया।)
• Managed- capable of being easily apprehended or understood. (किसी पर या किसी चीज पर नियंत्रण बनाए रखना।)
• Disappeared- ceased to be visible  (दिखना बंद होना।)
• From the meanings of the given words, we can say that the word 'Acted' is the most appropriate synonym of the given word 'MASQUERADED.​'
• Hence, the correct answer is 'Acted.'

Additional Information

• Let us see the synonym of the given options:
  

The correct answer is "Diamonds can be bought but sympathy cannot be brought".

Key Points   ​

• The given sentence is made up of two parts:
• ​We can buy diamonds
• We cannot buy sympathy
• ​Both the sentence use a modal verb 'can'. The structures for active/passive voices for modal verbs are:
• Active: Subject + Modal verb + Verb (Ist form) + Object
• ​Passive: Object + Modal verb + be + Verb (IIIrd form) + by + Subject
• With the help of the above structures, we can convert the given sentences into passive voices:
• ​Diamonds can be bought
• Sympathy cannot be bought
• ​Now, if we combine these two sentences, the complete sentence would be:
• Diamonds can be bought but sympathy cannot be bought.
• ​Hence, the correct answer is option 2.

The correct answer is "audiences".

Key Points

• Let us explore the given options:
• 'Personalities' means the lively, engaging qualities.
• 'Politics' means the activities associated with the governance of a country or area.
• 'Accountants' means people whose job is to keep, inspect, and analyse financial accounts.
• 'Audiences' means the assembled spectators or listeners at a public event such as a play, film, concert, or meeting.
• Hence, the correct answer is option 4.
  

Complete Sentence: Today's audiences are only interested in watching movies with the stories they can relate to the cinema.

The pattern followed here is:

The shaded part shifts right side while the line in second row shifts left side.

Hence, the figure in option 4 is the correct answer.

The least possible Veen diagram for the given statement is :

I. Some jugs are bottles → True ( as, all bottle are jugs and some jugs are glasses)

II. Some glasses are jugs → True (Some jugs are glasses)

III. All glasses are bottles → False (It is possible but not definite)

Hence, only conclusion I and II follow.

The mirror image would be as follows :

Hence, the figure in option 4 is the correct answer.

The number of triangles in the given figure is :

So, there are 7 triangles in the given figure.

Hence, '7' is the correct answer.

The positions of the letters according to the English alphabet series :

The pattern followed here is :

Similarly,

Hence, 'VRKSJQL' is the correct answer.

Let, the age of Y is 'a'

The age of X is 'a + 5'

The total of the current age of X and Y is :

X + Y = 33

a + 5 + a = 33

2a = 33 - 5

2a = 28

a = 28 ÷ 2

a = 14

So, the present age of Y is 14.

After 7 year age is Y is 14 + 7 = 21

Hence, '21' is the correct answer.

1. Yuan is currency of China.

2. Dollar is currency of USA. 

3. Dinar is currency of Kuwait. 

4. Oslo is the capital of Norway.

Hence, 'Oslo' is odd among all.

The life stage of a person is first the newborn child is Infant then the childhood gets started after childhood the Adolescent start which is between 13 to 18 year and then Adulthood started then the final stage is old age.

1. Infant

2. childhood

3. Adolescent

4. Adult

5. Old age 

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

All postgraduate should be graduate first but sisters may be graduates or post-graduates.

So, the Venn diagram for the relation is :

 

Hence, the figure in option (3) is the correct answer.

Logic : The first number get multiply by their next prime number.

The pattern followed here is :

11 × 13 = 143

Similarly,

23 × 29 = 667

Hence, '667' is the correct answer.

The paper when unfolded looks like,

 

Hence, the figure in option 2 is the correct answer.

The positions of letters according to the English alphabet series :

The pattern followed here is :

Similarly, 

Hence, 'NTS' is the correct answer.

Basic material to make curtain is cloth.

Similarly

Basic material to make ornament is gold.

Hence, 'Gold' is the correct answer.

Checking the given options:

1)  LKUK/ LAAK/ LAUK/ LLUK (Does not follow any pattern)

2) LAUK/UAUK/ LAAK/ LLUK (Does not follow any pattern)

3) LAUK/ LAUK/ LAUK/ LAUK (Follow the pattern)

4) LLUK/ UAUK/ LAAK/ LLUK (Does not follow any pattern)

Hence, 'ALUUA' is the correct answer.

Preparing the family tree using the following symbols,

Vikas's wife's sister's mother is Sunita means Sunita is the mother of Vikas's wife

So, Sunita is the mother in law of Vikas.

Hence, 'Mother in law' is the correct answer.

Logic: The cube of the first number get increased by 3 to get the second number and the first number is multiplied by the next number according to number series.

The pattern followed here is:

4³ → 64 

64 + 3 = 67

4 × 5 = 20

Similarly,

3³→ 27

27 + 3 = 30

3 × 4 = 12

Hence, '(3, 30, 12)' is the correct answer.

The pattern followed here is :

Hence, '349' is the correct answer.

Given,

From the given figure, D is adjacent to  A, C, B and F.

So, D is opposite to E

Hence, 'E' is the correct answer.

Logic : In all option when second number is divide by first number gives 8 except option (2).

By checking the options:

1. 25 : 200

200 ÷ 25 = 8

2) 22 : 166 

166 ÷ 22 =7.54

3. 14 : 112

112 ÷ 14 = 8

4. 15 : 120

120 ÷ 15 = 8

Hence, '22 : 166' is odd among all.

The question figure is embedded in, 

Hence, the figure in option (4) is the correct answer.

Asia is a continent and China is a country in Asia continent.

Similarly,

Asia is continent and Malaysia is a country in Asia continent.

Hence, 'Asia: Malaysia' is the correct answer.

According to the English Alphabet series and its positional value;

The pattern followed here is;

Vowels are getting square

For example, E = 5, will be written as 25

Consonants are getting an opposite number of alphabet series:

For example, B = 2, will be written as 25(opposite)

VARIOUS is coded as

V = 22 (consonant) = 5

A = 1 (vowel) = 1

R = 18 (consonant) = 9

I = 9 (vowel) = 81

O = 15 (vowel) = 225

U = 21 (vowel) = 441

S = 19 (consonant) = 8

Code is = 519812254418

Similarly,

P = 16 (consonant) = 11

E = 5 (vowel) = 25

N = 14 (consonant) = 13

S = 19 (consonant) = 8

I = 9 (vowel) = 81

O = 15 (vowel) = 225

N = 14 (consonant) = 13

Hence, the code for PENSION will be 11251388122513

The pattern followed here is :

16, 88, 296

16 ÷ 4 = 4

88 ÷ 4 = 22

296 ÷ 4 = 74

Similarly in option (2)

12, 66, 222

12 ÷ 3 = 4

66 ÷ 3 = 22

222 ÷ 3 = 74

Hence, (12, 66, 222) is the correct answer.

The positions of letters according to the English alphabet series:

1) BDH

B × 2 (positional value of B) → D ; D + 4 → H

2. DPT

D × 4 (positional value of D) → P ; P + 4 → T

3. EYC

E × 5 (positional value of E) → Y ; Y + 4 → C

4)CUZ

C × 3 (positional value of C) → I $\neq$U; U + 5 → Z

Hence, 'CUZ' is odd among all.

Checking the given options :

1. 72 and 24 

Given equations :

7 + 24 × 3 – 72 ÷ 18 = 58

After interchange the positions of the numbers according to the options.

7 + 72 × 3 – 24 ÷ 18 = 58

7 + 72 × 3 – 1.33 = 58

7 + 216 – 1.33 = 58

223 - 1.33 = 58 

221.67 ≠ 58

2. 3 and 7

7 + 24 × 3 – 72 ÷ 18 = 58

After interchange the positions of the numbers according to the options.

3 + 24 × 7 – 72 ÷ 18 = 58

3 + 24 × 7 – 4 = 58

3 + 168 – 4 = 58

171 - 4 = 58

167 ≠ 58

3) 18 and 24 

7 + 24 × 3 – 72 ÷ 18 = 58

After interchange the positions of the numbers according to the options.

7 + 18 × 3 – 72 ÷ 24 = 58

7 + 18 × 3 – 3 = 58

7 + 54 – 3 = 58

61 - 3 = 58

58 = 58

4. 7 and 18

7 + 24 × 3 – 72 ÷ 18 = 58

After interchange the positions of the numbers according to the options.

18 + 24 × 3 – 72 ÷ 7 = 58

18 + 24 × 3 – 10.28 = 58

18 + 72 – 10.28 = 58

90 -10.28

79.72 ≠ 58

Hence, '18 and 24' is the correct answer.

Shortcut Trick

Use the direct algebraic identity: (2a + 3b)² = 4a² + 9b² + 12ab

Substitute the given values: 8² = (4a² + 9b²) + 12 × 5

64 = (4a² + 9b²) + 60

4a² + 9b² = 64 − 60 = 4

∴ The correct answer is 4.

Alternate Method

Given:

⇒ 2a + 3b = 8

⇒ ab = 5

Formula Used:

⇒ (x + y)² = x² + y² + 2xy

Calculations:

⇒ Taking the square on both sides of the equation 2a + 3b = 8:

⇒ (2a + 3b)² = 8²

⇒ (2a)² + (3b)² + 2 × (2a) × (3b) = 64

⇒ 4a² + 9b² + 12ab = 64

⇒ Now, substitute the value of ab = 5 into the equation:

⇒ 4a² + 9b² + 12 × 5 = 64

⇒ 4a² + 9b² + 60 = 64

⇒ 4a² + 9b² = 64 − 60

⇒ 4a² + 9b² = 4

∴ The correct answer is 4.

Additional Information

Square of a Sum

(x + y)² = x² + 2xy + y². This identity relates the sum of two terms to their individual squares and their product.

Square of a Difference

(x − y)² = x² − 2xy + y². Useful for finding the difference of squares when the product is known.

Difference of Squares

x² − y² = (x − y)(x + y). A fundamental identity used for factorizing algebraic expressions.

Relation between Identities

(x + y)² − (x − y)² = 4xy. This connects the sum and difference squares directly with the product of the variables.

Given:

Radius of semi-circle = 4 cm

Formula used:

Area of triangle = (1/2) × Base × Height

Calculations:

The largest triangle that can be inscribed in a semi-circle will have a base equal to the diameter and a height equal to the radius of the semi-circle.

Base = 2 × R = 8 cm

Height = R = 4 cm

Area of the triangle = (1/2) × 8 × 4

⇒ 4 × 4

⇒ 16 cm²

∴ The area of the largest triangle that can be inscribed in the semi-circle is 16 cm2

Given:

Speed of Rakesh = 8 km/h

Time taken by Rakesh to cross the bridge = 30 minutes = (1/2) hours

Formula used:

Speed = Distance/Time

Calculations:

Let the length of the bridge be l

⇒ 8 = l/(1/2)

⇒ l = 8 × (1/2)

⇒ l = 4 km

∴ The length of the bridge is 4 km

Given:

a = 355 

b = 356 

c = 357

Formula used:

a3 + b3 + c3 - 3abc = (1/2) × (a + b + c) × [(a – b)2 + (b – c)2 + (c – a)2]

Calculations:

a3 + b3 + c3 - 3abc = (1/2) × (355 + 356 + 357) × [(355 – 356)2 + (356 – 357)2 + (357 – 355)2]

⇒ (1/2) × (1068) × (1 + 1 + 4)

⇒ 534 × 6

⇒ 3204

∴ The value of a3 + b3 + c3 - 3abc is 3204

Given:

\(225 - \left[ {42 - \left{ {25 - \left( {18{\rm{;}}-{\rm{;}}\overline {18; + ;13} } \right)} \right}} \right]\)

Calculations:

Solving the given equation,

\(225 - \left[ {42 - \left{ {25 - \left( {18{\rm{;}}-{\rm{;}}\overline {18; + ;13} } \right)} \right}} \right]\)

⇒ 225 – [42 – {25 – (18 – 31)}]

⇒ 225 – [42 – {25 – (-13)}]

⇒ 225 – [42 – {25 + 13}]

⇒ 225 – [42 – (38)]

⇒ 225 – 4

⇒ 221

∴ The value of the given equation is 221

Given:

Sum = Rs. 5000

Simple interest = Rs. 2000

Rate of interest = 10%

Formula used:

$SI = \frac{{P × {\rm{R}} × {\rm{T}}}}{{100}}$

Calculations:

Let the sum be invested for T years

⇒ 2000 = (5000 × 10 × T)/100

⇒ 2000 = 500T

⇒ T = 20/5

⇒ T = 4 years

∴ The sum of Rs. 5000 earns a simple interest of Rs. 2000 in 4 years

Given:

The ratio of the areas of two squares = 16 ∶ 1

Formula used:

Area of square = (Side of the square)²

The perimeter of square = 4 × (Side of the square)

Calculations:

Let the side of the two squares be a and b respectively

The ratio of the areas of two squares

⇒ a² ∶ b²  =16 ∶ 1

⇒ a ∶ b = 4 ∶ 1

The ratio of the perimeter of two squares

⇒ 4a ∶ 4b = (4 × 4) ∶ (4 × 1)

⇒ 16 ∶ 4

⇒ 4 ∶ 1

∴ The ratio of the perimeter of two squares is 4 ∶ 1

Given :

Sec θ - tan θ = 3 

Formula used :

Sec² θ - tan² θ = 1 or (sec θ - tan θ) × (Sec θ + tan θ) = 1

Calculations :

(sec θ - tan θ) (sec θ + tan θ) = 1

sec θ + tan θ = 1/3      ....(1)

sec θ  - tan θ = 3      ....(2) (given)

Solving equ (1) and (2) 

⇒ Sec θ = 10/6 = 5/3

⇒ cos θ = 3/5 (cos θ = (1/sec θ) 

∴ Cos θ = 3/5

Shortcut Trick

Using the Tangent-Secant Theorem: ZT² = ZY × ZX

Given: ZT = 6, ZY = 4, and YX = x

6² = 4 × (4 + x)

36 = 4 × (4 + x) ⇒ 9 = 4 + x

x = 5

∴ The correct answer is 5.

Alternate Method

Given:

Length of tangent ZT = 6

Length of external secant part ZY = 4

Length of internal secant part YX = x

Formula Used:

According to the Tangent-Secant Theorem, if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant part.

ZT² = ZY × ZX

Calculations:

⇒ Total length of secant ZX = ZY + YX

⇒ ZX = 4 + x

⇒ Applying the theorem: ZT² = ZY × (ZY + YX)

⇒ 6² = 4 × (4 + x)

⇒ 36 = 16 + 4x

⇒ 4x = 36 − 16

⇒ 4x = 20

⇒ x = 20 ÷ 4

⇒ x = 5

∴ The correct answer is 5.

Additional Information

Tangent-Secant Theorem

For a tangent segment ZT and a secant segment ZXY, the relation is ZT² = ZY × ZX.

Intersecting Chords Theorem

If two chords AB and CD intersect at a point P inside a circle, then PA × PB = PC × PD.

Tangent-Radius Property

A tangent at any point of a circle is perpendicular to the radius through the point of contact (OT ⊥ ZT).

Given :

A bar graph with income and expenditure of the company 

Calculations :

Income of year 2001 = 30 lakhs

Expenditure of 2000 = 15 

Expenditure of 2001 = 20 

Expenditure of 2002 = 15

Expenditure of 2003 = 15

Expenditure of 2004 = 30

According to question, we need to find expenditure of which year equal to income of year 2001 

Expenditure of year 2004 = income of the year 2001 = 30 lakhs 

∴ Expenditure of 2004 is equal to the income of 2001

Given :

XL is the centroid of a triangle XYZ and G is the centroid of the median 

Concept used :

In a triangle ABC if a median AD is drawn from A to side C, then centroid G divides the AD  in the ratio 2 : 1

Calculations :

XL = XG + GL

XG: GL = 2: 1 (G is the centroid)

⇒ XG = (2/3) of XL 

⇒ XG = (2/3) × 18

⇒ XG = 12 

∴ XG is 12 cm.

Concept used :

If the sum of digits of a number is divisible by 3, then the number is also divisible by 3

Calculations :

Sum of digits 

1st option  = 8 + 7 + 0 + 3 + 5 + 4 + 1 = 28

2nd option = 8 + 7 + 0 + 3 + 5 + 9 + 3 = 35

3rd option = 8 + 7 + 0 + 3 + 5 + 7 + 2 = 32

4th option = 8 + 7 + 6 + 5 + 0 + 0 + 1 = 27 

We can check that only 27 is the multiple of 3 

∴ Option 4 is the only option divisible by 3

Formula used :

sin²θ + cos²θ = 1 

sin 30° = 1/2 and cos 30° = √3/2

Calculations :

Cos²30° - sin²30° = (√3/2)² - (1/2)² 

⇒ (3/4) - (1/4) = 1/2 

Sin²15° + cos²15° = 1 

⇒ (Cos²30° - sin²30°)/(sin²15° + cos²15°) = (1/2)/1 = 1/2 

∴ value of the asked equation is 1/2 

Additional Information

Given: 

tan²x - 3 sec²x + 3 = 0 

Formula used :

sec²x = 1 + tan²x 

Calculations :

tan²x - 3 sec²x + 3 = 0 

put sec²x = 1 + tan²x 

⇒ tan²x - 3 (1 + tan²x) + 3 = 0

⇒ tan²x - 3 - 3 tan²x + 3 = 0 

⇒ -2 tan²x = 0 

⇒ tan²x = 0 

⇒ tan x = 0  (tan x = 0, when x = 0°)

∴ x will be 0°

Given :

A man sold his furniture at 25% gain.

Had he sold at 15% loss he would have received Rs.800 less 

Concept used :

Profit = selling price - cost price = profit % on cost price 

Loss = cost price - selling price = loss % on cost price  

Calculations :

Let the cost price of the item be 100x 

Selling price at 25% profit = cost price + profit 

⇒ cost price + 25% of 100x 

⇒ 100x + 25x = 125x 

Selling price at 15% loss = cost price - loss

⇒ 100x - 15% of 100x 

According to the question 

125x - 85x = 800 

⇒ 40x = 800 

⇒ x = 20 

⇒ cost price = 100x 

⇒ 100 × 20 = 2000 rupees 

∴ Cost price of the furniture is 2000 rupees

Given:

Rita’s income is 15% less than Richa’s income

Calculation:

Let Richa’s income be 100

⇒ Rita's income is 85

⇒ Richa’s income is 15 more than Rita’s income.

⇒ Percent of Richa’s income more than Rita’s income = 100 × 15/85 = 17$11\over 17$%

Given:

Income in 2001, 2002 is 30, 25 lakhs respectively

Formula Used:

Percentage Difference = 100 × Difference/Initial amount

Calculation:

⇒ Decreased amount = 30 – 25 = 5 lakhs

∴ Percentage Difference = 100 × 5/30 = 16$2\over3$%

Given:

The birth rate of Country C = 20

The birth rate of country E = 33

Calculation:

Required percentage = (20/33) × 100

⇒ 60.61% ≈ 60%

∴ The birth rate of Country C is approximately 60% of the birth rate of Country E.

Shortcut Trick

For three numbers a, b, and c, the fourth proportional is given by (b × c) ÷ a.

Here, a = 10, b = 12, and c = 15.

Fourth proportional = (12 × 15) ÷ 10 = 180 ÷ 10 = 18.

∴ The correct answer is 18.

Alternate Method

Given: Three numbers are 10, 12, and 15.

Formula Used: If a, b, c, and d are in proportion, then a : b = c : d or a × d = b × c.

⇒ Let the fourth proportional be x.

⇒ 10 : 12 :: 15 : x

⇒ 10 ÷ 12 = 15 ÷ x

⇒ 10 × x = 12 × 15

⇒ 10 × x = 180

⇒ x = 180 ÷ 10

⇒ x = 18

∴ The correct answer is 18.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is defined as √(a × b).

Third Proportional

For two numbers a and b, the third proportional c is such that a : b :: b : c, calculated as c = b² ÷ a.

Rule of Proportion

In any proportion a : b :: c : d, the product of the extremes (a × d) is always equal to the product of the means (b × c).

Given:

15 men required 6 days to plough 10 acres of land

Formula Used:

M­₁D₁/W₁ = M­₂D₂/W₂

Calculation:

⇒ M­₁ = 15, D₁ = 6, W₁ = 10

⇒ M­₂ =? ,D2 = 10, W2= 50

⇒ 15 × 6/10 = M₂ × 10/50

⇒ M₂ = 45

∴ The total men required is 45

Formula Used:

Percentage decrease = (x₁ -  x₂)/x₁ × 100

x1 → Original number 

x2 → New number 

Calculation:

Expenditure in 2001 = 20 lakhs

Expenditure in 2002 = 15 lakhs

Decrement = 20 - 15 = 5 lakhs

∴ Required percentage = (5/20) × 100 = 25%

Given:

The mean of 5 numbers is 28

One number is excluded so mean decreased by 5 i.e. 23

Formula Used:

Sum of numbers = Mean × No. of numbers

Calculation:

⇒ Sum of the 5 numbers = 5 × 28 = 140

Mean of 4 numbers is 23

⇒ Sum of the remaining four numbers = 4 × 23 = 92

∴ Excluded number = 140 – 92 = 48

Given:

x + y = 15, xy = 14

Formula Used:

(x – y)² = (x + y)² – 4xy

Calculation:

⇒ (x – y)² = (15)² – 4 × 14 = 225 – 56 = 169

∴ x – y = 13

Given:

Selling price of blanket = Rs 680

Discount = 15% and 20%

Formula Used:

Printed price = Selling price × [100/(100 – discount%)]

Calculation:

Printed price = Selling price × [100/(100 – discount%)]

⇒ 680 × [100/(100 – 15)] × [100/(100 – 20)]

⇒ 680 × (100/85) × (100/80)

⇒ 1000

∴ The printed price of the blanket is Rs 1000

Given:

∠AGB = 150°

Concept:

The angle made by the chord at centre is double the angle made by it in a major segment of the circle.

Calculation:

∠AGB = 2 × ∠ACB

⇒ 150° = 2 × ∠ACB

⇒ ∠ACB = 75°

∴ The value of ∠ACB is 75°.

The correct answer is Khangchendzonga National Park.

Key Points

• The Khangchendzonga National Park is a biosphere reserve, national park and India’s first mixed World Heritage site located in Sikkim.
• The park gets its name from the mountain Kanchenjunga.
• Gir National Park is known for its Asiatic Lions.
• It is located in the Gujarat state of India.
• Nagarhole National Park is located in the Mysore and Kodagu districts of Karnataka.
• Kanha National Park is nestled in the Maikal range of Satpuras in Madhya Pradesh.
• Tigers, jackals and wild pigs can be spotted in Kanha.

Additional Information

• India has a total of 42 UNESCO World heritage sites that include 34 cultural, 7 natural, and 1 mixed heritage site.
• The list of 7 national Natural World Heritage sites of UNESCO are as follows:
• Kaziranga Wild Life Sanctuary, Assam.
• Sundarbans National Park, West Bengal.
• Great Himalayan National Park, Himachal Pradesh.
• Manas Wild Life Sanctuary, Assam.
• Keoladeo National Park, Bharatpur, Rajasthan.
• Nanda Devi and Valley of Flowers National Parks, Uttarakhand.
• The Western Ghats.

The correct answer is William G Kaelin Jr, Sir Peter J Ratcliffe and Gregg L Semenza.

• 2019 Nobel Prize:

The correct answer is 17.

Key Points

• Mahmud of Ghazni was a Turkish conqueror who attacked India 17 times between 1000 to 1027 AD.
• The biggest invasion of Mahmud of Ghazni was in 1025 AD wherein he invaded the Somnath temple in Gujarat.
• In all his 17 invasions, a number of dynasties were conquered by him.

Additional Information

• Al-Biruni was an Iranian scholar and polymath. He was from Khwarezm — a region that encompasses modern-day western Uzbekistan, and northern Turkmenistan.
• The scholar was entrusted by Sultan Mahmud of Ghazni to write an account of the subcontinent.
• Kitab al-Hind is a book written by Al-Beruni and is an important source of Historians.

The correct answer is Cherrapunji lies on the windward side of the Khasi hills and receives rainfall from the Bay of Bengal branch of monsoon, while Shillong lies on the leeward side of the Khasi hills, which forms the rain shadow area.

• The highest rainfall in India is at Cherrapunji(Present name Sohra) in Mawsynram village of Meghalaya state.
• The Average rainfall of Cherrapunji is 11,777 mm or 463.7 inches.
• Mawsynram is located in the East Khasi Hills district.
• It is on the windward side of the hills and is surrounded by hills on three sides.
• It receives rain from southwest monsoon winds (Bay of Bengal branch), as the winds cannot move further striking the hills and due to condensation receives heavy rainfall.
• Shillong lies on the northern leeward slopes of the Khasi Hills and therefore receives less rain.

The correct answer is Mridangam.

• Palghat Mani Iyer associated with the Mridangam.

The correct answer is Article 74(1).

• Article 74(1) provides that there shall be a Council of Ministers with the Prime Minister as its head.
• Article 74 deals with the Council of Ministers to aid & advise the president.
• Article 44 is the Uniform Civil Code for the citizens.
• Uniform Civil Code will replace personal laws based on the holy books and customs of each major religious community in India.
• Article 21A is added in the Indian Constitution in the 86th Constitutional Amendment Act 2002.
• It is Right to elementary education.
• Article 34 - Restriction on rights conferred by this Part while martial law is in force in any area.

The correct answer is RAM.

• RAM is the fastest to read from and write to than the other kinds of storage in a computer.
• It is Volatile or temporary memory.
• Data gets erased when the power supply is off.
• Faster memory than ROM.
• It is used in the normal operations of a computer after starting up and loading the operating system.
• CD-ROM for "Compact Disc Read-Only Memory".
• CD-ROM is a CD that can be read by a computer with an optical drive.
• Floppy Disk is a type of disk storage composed of a disk of the thin and flexible magnetic storage medium.
• It is used for backup purpose.
• It is a type of secondary storage.
• The storage capacity of a common floppy disk is 1.44 MB.
• The hard disk is the main device for storing data in the computer.
• It uses magnetic technology (nowadays optical technology for storing data).
• It has a strong coating above the magnetic metallic oxide in order to protect the major components.

The correct answer is India’s dairy industry.

Key Points:

• Operation Flood was launched in 1970.
• It was a project of India's National Dairy Development Board (NDDB).
• It was the world's biggest dairy development program.
• In 30 years, it doubled milk available per person, and made dairy farming India's largest self-sustainable rural employment generator.
• Verghese Kurien, the chairman and founder of Amul, was named the chairman of NDDB by the then Prime Minister of India Lal Bahadur Shastri.
• He was known as the father of Operation flood.

The correct answer is To measure income inequality.

• Gini Coefficient represent the Distribution of Income.
• It measures the degree of income inequality in the country's population.
• Gini coefficient is also one of the indicators of economic development in the country.
• The value of the Gini Coefficient varies from 0 to 1.
• 0 means perfect equality everyone has the same income, and 1 means perfect inequality all the income is received by a single individual.
• Graphical Representation of the Gini Index (Lorenz curve)

The correct answer is Justice HL Dattu.

• The chairperson of the National Human Rights Commission was Shri Justice H. L. Dattu.
• The President appoints the chairperson and members of the NHRC for five years or until he is 70 years old (whichever is earlier).
• The National Human Rights Commission's non-constitutional bodies.
• The NHRC is responsible for human rights and established in 1993 under an act of Parliament.
• The human right act of 1993 provides the National, the State Human Rights Commission, and human rights courts.
• 10 December observed World Human Rights Day.
• Headquarter: Delhi

Additional Information

The correct answer is 250.

Key Points

• Article 80 of the Constitution lays down the maximum strength of Rajya Sabha as 250, out of which 12 members are nominated by the President and 238 are representatives of the States and of the two Union Territories.
• The present strength of Rajya Sabha, however, is 245, out of which 233 are representatives of the States and Union territories of Delhi and Puducherry and 12 are nominated by the President.
• The members nominated by the President are persons having special knowledge or practical experience in respect of such matters as literature, science, art, and social service.

The correct answer is Fuse.

• Fuse is a piece of wire of a material with a very low melting point.
• When a high current flows through the circuit due to overloading or a short circuit, the wires get heated and melts.
• As a result, the circuit is broken and current stops flowing.
• The fuse is always connected in the live path because if the live wire gets short-circuited somewhere within the appliance and results in the high current then the fuse can blow and protect the appliance.

Additional Information

• A capacitor is a device that stores electrical energy in an electric field.
• It is a passive electronic component with two terminals.
• The effect of a capacitor is known as capacitance.
• A surge protector is an electrical device that is used to protect equipment against power surges and voltage spikes while blocking voltage over a safe threshold (approximately 120 V).
• A Protective Relay is a device that detects the fault and initiates the operation of the circuit breaker to isolate the defective element from the rest of the system.

The correct answer is MARSIS.

• In July 2018, a stable body of liquid water was found on Mars using a radar instrument on board the European Space Agency's Mars Express orbiter. The tool that was used for the discovery is called MARSIS.
• MARSIS (Mars Advanced Radar for Subsurface and Ionosphere Sounding) is a low frequency, pulse-limited radar.

The correct answer is Just Fontaine.

• Just Fontaine scored the most goals at a single tournament in the entire history of FIFA World Cup.

• The 2022 FIFA World Cup is scheduled to be the 22nd edition of the FIFA World Cup.

• It is scheduled to take place in Qatar from 21 November to 18 December 2022.

• This will be the first World Cup ever to be held in the Arab world and the first in a Muslim-majority country.

• Federation Internationale de Football Association (FIFA) is the international governing body of football association.

• FIFA was founded in 1904 to oversee international competition among the national associations of Belgium, Denmark, France, Germany, the Netherlands, Spain, Sweden, and Switzerland.

• FIFA is headquartered in Zurich, Switzerland.

• Its membership now comprises 211 national associations.

The correct answer is Ryan ten Doeschate.

Important Points

• Ryan ten Doeschate had the distinction of having the highest career batting average in One Day Internationals as of January 2020.
• Ryan ten Doeschate is a right-handed batsman who represents the Netherlands in International cricket.
• For the years 2008, 2010, and 2011, Ryan ten Doeschate has been named ICC Associate Player of the Year.

Additional Information

• In 2020, the ICC Men's Player of the Decade award has been given to Virat Kohli hat was conducted by DNA India.
• Sachin Tendulkar holds the record of making the most number of 100 centuries in International cricket with 49 in ODIs and 51 in test cricket.
• The 2023 ICC men's Cricket world cup will be hosted by India. It will be the 13th edition of the ICC Men's Cricket World Cup.

The correct answer is 26 December 2019.

Important Points

• On 26 December 2019, the 120th birth anniversary of Shaheed Udham Singh celebrated in India.
• Shaheed Udham Singh was an Indian freedom fighter belonging to Ghadar Party. He was born in 1899 in the Sangrur district of Punjab.
• Shaheed Udham Singh is known for his assassination of Michael O'Dwyer in London, on 13 March 1940. Michael O'Dwyer was responsible for the Jallianwala Bagh massacre in Amritsar in 1919. As revenge, he was killed by Udham Singh.
• Michael O'Dwyer was an Irish Indian Civil Service officer and during 1913 and 1919 he was the former lieutenant governor of Punjab in British India.

​

Additional Information 

• On 26 November 2020, we celebrated Constitution day.
• On 28 September 2020, we celebrated the 113th birth anniversary of birth Shaheed Bhagat Singh.

The correct answer is Assam.

Important Points

• Assam is the states/union territories that are more likely to find the natural habitat of the one-horned rhinoceros (Indian Rhino).
• Kaziranga National Park of Assam has the largest population with more than 90% of greater-one horned rhinos.
• Kaziranga National Park lies partly in Golaghat District and partly in Nagaon District of Assam. It is the oldest park in Assam covers an area of 430 sq km along the river Brahmaputra on the North and the Karbi Anglong hills on the South.
• Kaziranga National Park a world heritage site is famous for the Great Indian one-horned rhinoceros, the landscape of Kaziranga is of sheer forest, tall elephant grass, rugged reeds, marshes & shallow pools. It has been declared as National Park in 1974.

Additional Information

• Hemis National Park located in Ladakh is one of Asia's most famous natural habitats of the Snow Leopard.
• Dachigam National Park located in Jammu and Kashmir is famous for the hangul, or Kashmir stag.

The correct answer is Flash drive.

Important Points

• Flash drive is a small, portable flash memory card that plugs into a computer’s USB port and functions as a portable hard drive.
• A flash drive is a portable data storage device. Flash drives consist of a number of flash chips, they are the larger memory modules.
• The chips that are used to read the contents of a single cell and to write the entire block of the cell are flash chips.
• Flash memory was invented in the 1980s by a Japanese engineer Fujio Masuoka.

Additional Information

• CD-ROM stands for "Compact Disc Read-Only Memory." CD-ROM contains data that can be read by a computer with an optical drive.
• DVD-ROM stands for "Digital Versatile Disk-Read Only Memory". This device is used to store files permanently and that file cannot be changed or erased.