SSC CHSL Previous Paper 5 (Held On: 18 March 2020 Shift 2) (Previous Year Paper)

The correct answer is- since June 2017​.

Key Points

• The present perfect continuous is a verb tense that shows an action or state that either occurred at an indefinite time in the past or began in the past and continued to the present time.
• The structure is given below:
• Subject + has/have + been + V1 + -ing + since/for + object.
• Since is used for a point of time (1982, last month, etc.) whereas for is used for any duration (4 days, 6 months, etc.).
• Example:
• ​The factory has been working well since 1945.
• As a point of time i.e. 1917 has been given in the question, 'since' will replace 'from' in the underlined part.
• In this way, we are left with the only correct choice as the 4th option.
  

Correct Sentence: Priya has been working in this school since June 2017.

The correct answer is- Equipment.

Key Points

• Let's look at the meanings of the given word and marked option:
• Kit- a set of articles or equipment needed for a specific purpose
  
• Equipment- the necessary items for a particular purpose
• ​​​Let's look at the meanings of the other given options: 
• Information- facts provided or learned about something or someone
  
• Particle- a minute portion of matter
• Element- a part or aspect of something abstract, especially one that is essential or characteristic
• Hence from the given meanings, we find that Kit and Equipment are synonyms.

The correct answer is- Inflexible.

Key Points

• Let's look at the meanings of the given word and marked option:
• Versatile- able to adapt or be adapted to many different functions or activities
• Inflexible- unwilling to change or compromise
• ​​Let's look at the meanings of the other given options: 
• Truthful- (of a person or statement) telling or expressing the truth; Honest
• Insincere- not expressing genuine feelings
• ​Hence from the given meanings, we find that Versatile and Inflexible are antonyms.

The correct answer is- Include everything​.

Key Points

• Let's look at the meaning of the given idiom:
• Touch/cover all bases- to include, make reference to, or take action on every desired or required element or aspect (of something)
• Example: 
• We need to make sure that we are covering all the bases in our campaign.
  

​ ​​​​

Additional Information  

• Let's look at the origin of the idiom:
• In baseball, batters have to touch the first, second, and third bases to score a run.

The correct answer is- by.

Key Points

• The given sentence is in the simple past tense. The passive verb form for simple past is: 
• was/were + past participle form of the verb + by + subject.
• The given sentence is in a passive voice form (was commissioned) as evident from the usage of the above-mentioned structure.
• Thus, we are left with the only correct choice as the 1st option i.e. by.

The correct answer is- was.

Key Points

• The simple past tense is used when we talk about things that happened or existed before now.
• The structure is given below:
• Subject + V2 + object. (Active Voice)
• Object + was/were + V3 + by + subject. (Passive Voice)
• Example:
• ​He won the car race. (active voice)
• The car race was won by him. (passive voice)
• Since the given sentence is in active voice form, 'was' will be used in the 2nd blank.
  

Additional Information

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

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

• For example:

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

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

The correct answer is - over.

Key Points

• Let's look at the meanings of the given words:
• over- above so as to cover or protect
• about- on the subject of; concerning
• into- indicating the direction toward which someone or something is turned when confronting something else
• aside- to one side; out of the way
• As per the context of the given sentence, the chhatri (a parasol or umbrella-like complex) was erected with an intention to provide respect and shelter to the remains of Buddha.
• The structure was built exactly above the relics of the Buddha in order to protect them.
• In the current scenario, the 1st option i.e. over is the correct choice in the 3rd blank.

The correct answer is - structure.

Key Points

• Let's look at the meanings of the given words:
• structure- the arrangement of and relations between the parts or elements of something complex
• wall- a continuous vertical brick or stone structure that encloses or divides an area of land
• conduit- a channel for conveying water or other fluid
• bridge- a structure carrying a road, path, railroad, or canal across a river, ravine, road, railroad, or other obstacles
• As per the context of the given sentence, the chhatri (a parasol or umbrella-like complex) was erected with an intention to provide respect and shelter to the remains of Buddha.
• In the current scenario, the 1st option i.e. structure is the correct choice in the 4th blank.

The correct answer is - intended.

Key Points

• Let's look at the meanings of the given words:
• outlined- draw, trace, or define the outer edge or shape of (something)
• intended- have (a course of action) as one's purpose or objective
• informed- give (someone) facts or information; tell
• predicted- stated or estimated as likely to happen in the future; forecast
• As per the context of the given sentence, the chhatri was erected with an intention to provide respect and shelter to the remains of Buddha.
• In the current scenario, the 2nd option i.e. intended is the correct choice in the 5th blank.

The correct answer is- main leaders​.

Key Points

• Let's look at the meaning of the given idiom:
• Big fish- an important, successful, or influential person
• Example: 
• Meeting a big fish like the company's CEO can be quite an intimidating experience for an intern.

​ ​​​​

Additional Information  

• Let's look at similar idioms which have the same meaning:
• A big cheese, a big gun, a big wheel, etc.

The correct answer is - CBDA.

Key Points

• While arranging the parts of the passage, we should find some grammatical or contextual connections between them:
• Sentence C introduces us to the subject 'Shahid Afridi'. It is the introductory sentence and will be put in the first place.
• Sentence B tells us about the event of Waqar Younis giving his bat to Shahid Afridi. It will be put in second place.
• Sentence D tells us about the actual owner (Sachin Tendulkar) of the bat gifted by Waqar Younis. It will be put in third place.
• The last sentence is A as it mentions the act of Shahid Afridi hitting the fastest ODI century.
  
• Thus, the correct order is - CBDA.

The correct answer is- Kirti asked me, “Did you watch the movie on television last night ?” 

Key Points​

• Let's look at the steps to change the sentence from indirect to direct speech:
• The tense of direct speech is changed only when the reporting verb is in the past tense.
• When the indirect speech is in an assertive form, we follow the steps given below:
• Connectors 'whether/why' or 'if' are replaced by the comma and inverted commas.
• The tense of reported speech is changed only when the reporting verb is in the past tense.
• Change the reported speech from assertive to interrogative.
• The personal pronouns will be changed according to the subject and object of the reporting verb.
• ​Here the 1st person 'I' will change into the 2nd person 'you' as per the object.
• Past perfect tense (had watched) in indirect speech changes to Past simple in direct speech (Did you watch).
• Words showing time and place are changed accordingly. (the previous night-last night)
• ​At last line up the remaining part.
  

 Following these steps, we finally get- Kirti asked me, “Did you watch the movie on television last night ?”

The correct answer is- Cynosure.

Key Points

• Let's look at the meaning of the marked option:
• Cynosure- a person or thing that is the center of attention or admiration
• Let's look at the meanings of the other given options: 
• Organizer- a person who organizes
• Leader- the person who leads or commands a group, organization, or country
• Politician- a person who is professionally involved in politics, especially as a holder of or a candidate for an elected office
• Hence, from the given meanings, we find that Cynosure is the correct one-word substitute.

The correct answer is - Medetative.

Key Points

• Let's look at the correct spelling and meaning of the marked option:
• Meditative- relating to or absorbed in meditation or considered thought
• Example: 
• She closed her eyes and went into a meditative trance.
• Let's look at the meanings of the other given options:
• Appended- add (something) as an attachment or supplement
• Pensive- engaged in, involving, or reflecting deep or serious thought
• Apprehensive- anxious or fearful that something bad or unpleasant will happen

The correct answer is- Clear.

Key Points

• Let's look at the meanings of the given word and marked option:
• Nebulous- in the form of a cloud or haze; hazy
• Clear- easy to perceive, understand or interpret
• ​​Let's look at the meanings of the other given options: 
• Familiar- well known from long or close association
• Common- occurring, found, or done often; prevalent
• Mutual- (of a feeling or action) experienced or done by each of two or more parties toward the other or others
• Hence from the given meanings, we find that Nebulous and Clear are antonyms.

The correct answer is- resemble to each other.

Key Points​

• ​There are some verbs that are not followed by a preposition. Some of them are given below:
• ​​consider, discuss, influence, emphasize, resemble, inform, return, etc.
• Example:
• ​We can discuss about the opportunity for a promotion. (incorrect)
• We can discuss the opportunity for a promotion. (correct)
• Hence the part given in the 3rd option, the verb 'resemble' won't be followed by the preposition 'to'.
  

Correct Sentence: It is difficult to make out that they are twins because they do not resemble each other. 

Additional Information

• Some verbs can be both prepositional and not prepositional, depending on the context or the verb tense.
• In the simple present tense, comprise is never prepositional.
• When comprised follows is or was, it functions as an adjective and requires the preposition of.
• Example:
• ​Five people comprise the committee. (active voice)
• The committee is comprised of five people. (passive voice)

The correct answer is - ADBC.

Key Points

• While arranging the parts of the passage, we should find some grammatical or contextual connections between them:
• Sentence A introduces us to the subject 'Mulla Nasruddin'. It is the introductory sentence and will be put in the first place.
• Sentence D tells us about the first day of the salon which the subject had opened. It will be put in second place.
• Sentence B tells us about a particular customer talking to the subject. It will be put in third place.
• The last sentence is C as it mentions the type of haircut the customer wanted for his beard.
  
• Thus, the correct order is - ADBC.

The correct answer is: **Option 3**.

**Key Points**

- The word **"anodyne"** means something that relieves pain or is not likely to cause offense; often used to describe something that is soothing or harmless. (दर्द निवारक, निरापद)
- **Example:** The doctor's anodyne words helped to calm the anxious patient.
- **"Benign"** refers to something that is gentle, kind, and not harmful. (सौम्य)
- **Example:** The benign tumor was easily removed and did not pose any further health risks.

Therefore, the correct answer is: **Option 3**.

**Additional Information**

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

- **Hostile** (शत्रुतापूर्ण): Unfriendly and antagonistic.
- **Example:** The hostile crowd made it difficult for the speaker to continue.
- **Gigantic** (विशाल): Extremely large.
- **Example:** The gigantic statue stood tall in the center of the park.
- **Harmful** (हानिकारक): Causing or likely to cause harm.
- **Example:** Smoking is harmful to your health.

This format provides a clear explanation of the correct answer and additional information about the other options, making it easy to understand and learn from.

The correct answer is- in one of the channel​.

Key Points

• ​​'One of/only one of' is always followed by a noun/pronoun in the plural form and verb in the singular form.

• For example:

• One of my friends are a dancer.

• One of my friends is a dancer.

• As per the rule and example given above, 'channels' will be used instead of 'channel' in the part given in the 1st option.
  

Correct Sentence: Oh dear! The audio in one of the channels on television is not clear at all. 

• ​If a subject and a verb are joined by a relative pronoun, the verb will agree with the antecedent to the relative pronoun.
• Example:
• He is one of those men who trust everybody whom he socializes with.

The correct answer is - The ball had been hit towards the boundary by the batsman. 

Key Points

• The given sentence is in the active voice, hence we need to convert it into the passive voice.
• Find the subject (The batsman) and object (the ball) of the sentence and exchange their places.
• The given sentence is in the past perfect tense. The passive verb form for the past perfect is: 
• Had + been + past participle form of the verb.
• So, 'had hit' changes to 'had been hit'.
• At last line up the remaining part.
  

Following these steps, we finally get - The ball had been hit towards the boundary by the batsman.

The correct answer is - challenges.

Key Points

• Let's look at the meanings of the given words:
• challenges- a task or situation that tests someone's abilities
  
• crashes- cause (a moving object) to collide with an obstacle or another vehicle
• contests- an event in which people compete for supremacy in a sport, activity, or particular quality
• crunches- crush (a hard or brittle foodstuff) with the teeth, making a loud but muffled grinding sound
• As per the context of the given sentence, the woman politician is enquired about the obstacles she had to go through in her profession.
• In the current scenario, the 1st option i.e. challenges is the correct choice in the given sentence.
  

Correct Sentence: The reporter asked the politician, “As a woman leader, what are some of the major challenges that you face?”

The correct answer is - revealed.

Key Points

• Let's look at the meanings of the given words:
• retracted- withdraw (a statement or accusation) as untrue or unjustified
  
• resumed- begin to do or pursue (something) again after a pause or interruption
• revealed- make (previously unknown or secret information) known to others
• redirected- direct (something) to a new or different place or purpose
• As per the context of the given sentence, the inspection divulged the event of two ancient buildings withstanding a strong tremor of the earthquake.
• In the current scenario, the 3rd option i.e. revealed is the correct choice in the given sentence.
  

Correct Sentence: Earthquake inspection revealed that the two ancient buildings that remained intact after the Hiroshima bombing in Tokyo would not withstand a strong tremor.

The correct answer is- Scullery.

Key Points

• Let's look at the meaning of the marked option:
• Scullery- a small kitchen or room at the back of a house used for washing dishes and other dirty household work
• Let's look at the meanings of the other given options: 
• Pantry- a small room or closet in which food, dishes, and utensils are kept
• Ante-room- an antechamber, typically serving as a waiting room
• Larder- a room or large cupboard for storing food
• Hence, from the given meanings, we find that Scullery is the correct one-word substitute.

The correct answer is- No improvement​.

Key Points

• Let's look at the structures given below in active and passive forms:
• Active- Subject + modal verb + V1 + Object.
• Passive- Object + modal verb + be + V3 + by + Subject.
• Example:
• She might her task. (active)
• Her task might be finished by her. (passive)
• ​The former part of the sentence given in the question conforms to the passive voice structure.
  

Following the passive voice form, we finally get- The struggle for climate change must be prioritised given that our population is increasing and not decreasing.

Additional Information  ​​​​

• There is a difference between 'must' and 'have to' given below:
• Must expresses obligation or compulsion imposed by the speaker.
• Whereas 'have to' expresses external obligations.
• Example: 
• ​We must fasten our seat belts. (the speaker thinks so)
• They have to help the needy. (others think this and not the speaker)

The correct answer is - Impeccable.

Key Points

• Let's look at the meaning of the marked option:
• Impeccable- (of behavior, performance, or appearance) in accordance with the highest standards of propriety; faultless
  
• Example: 
• Even in her own lands, the matriarch's rank had to be absolutely impeccable to allow her to speak.
• Let's look at the correct spelling and meaning of the other given options:
• Susceptible- likely or liable to be influenced or harmed by a particular thing
  
• Propensity- an inclination or natural tendency to behave in a particular way
• Impressionable- easily influenced because of a lack of critical ability

The paper when unfolded will appear as shown below:

Hence, ‘option 1’ is the correct answer.

The option in which the given figure is embedded when rotation is not allowed is shown below:

Hence, ‘option 2’ is the correct answer.

The logic is:

23 ∶ 120 → 23 : (23 + 1) × 5

Similarly,

1) 54 ∶ 250 → 54 : (54 + 1) × 5 ≠ 250

2) 45 ∶ 230 → 45 : (45 + 1) × 5 = 230

3) 18 ∶ 90 → 18 : (18 + 1) × 5 ≠ 100

4) 63 ∶ 316 → 63 : (63 + 1) × 5 ≠ 316

Hence, ‘45 ∶ 230’ is the correct answer.

The logic is:

Similarly,

Hence, ‘CXYEIF’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Note: The logic is → Place value of letters – (No. of letters in the word – 1)

Hence, ‘33’ is the correct answer.

I. Apple is not a book. → True (As, No cup is a book and Apple is a cup)

II. Apple may or may not be a book. → False (It cannot be concluded from the given statements)

Hence, only conclusion I follows.

The pattern followed here is,

1568, 2628, and 1432 are divisible by 4.

2514 is not divisible by 4.

hence, 2514 is the different one.

The figures in the series is rotating in clockwise direction.

So, the next figure in the series will be option 3 as shown below:

Hence, ‘option 3’ is the correct answer.

The option which is the exact mirror image of the given alphanumeric figure when the mirror is held at the right side is shown below:

Hence, ‘option 3’ is the correct answer.

The logic is:

Gradual : Abrupt → Gradual is antonym of Abrupt.

Similarly,

Factual : ? → Factual is antonym of Fictional.

Hence, ‘Fictional’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘RZVP’ is the correct answer.

1) dffgccef

ccdeffgc / ccdeffgc / ccdeffgc

Here we see that the same pattern is repeated when the series is divided into three equal parts.

2) eececfce

cceeecgc / ccdeffec / fcdcefgc

No pattern is repeated when the series is divided into three equal parts.

3) cffeccef

ccceffgc / ccdeffec / ccdeffgc

No pattern is repeated when the series is divided into three equal parts.

4) ffceefde

ccfefcgc / ccdeffee / fcddefgc

No pattern is repeated when the series is divided into three equal parts.

Hence, ‘dffgccef’ is the correct answer.

According to given conditions,

K is the mother of A.

Hence, ‘Mother’ is the correct answer.

The number of squares in the figure is shown below:

Hence, ‘33’ is the correct answer.

If are 3 rows and 3 columns in the above figure. So let n = 3.

Here, we using formulas for finding the number of squares in an n × n grid as follows.

Formula :-

n² + (n - 1)² + (n - 2)² + - - - - - - - - - - + (n - n)²

Now substitute n = 3 in the above formula,

3² + (3 - 1)² + (3 - 2)² + (3 - 3)²

9 + 2² + 12 + 0 = 9 + 4 + 1 = 14

If are 2 rows and 2 columns in the above figure. So let n = 2.

Now substitute n = 2 in the above formula,

2² + (2 - 1)² = 4 + 1 = 5

Now,

Till now, total squares = 14 + 5 + 8 = 27

6 squares are given in detail (square no. 26, 28, 30, 31, 32, 33)

So, total number of squares = 27 + 6 = 33.

The logic is:

$\frac{{5; \times ;6}}{2}$ = 15

$\frac{{4; \times ;9}}{2}$ = 18

Similarly,

$\frac{{6; \times 7}}{2}$ = ?

=>  $\frac{{42}}{2}$= ?

=> 21 = ?

Hence, ‘21’ is the correct answer.

1) ÷, ×, =, -

Given expression: 18 Y 2 Y 3 Y 3 Y 9

After replacing Y’s, we get:

18 ÷ 2 × 3 = 3 – 9

=> 9 × 3 = -6

=> 27 ≠ -6

2) ×, =, -, ÷

Given expression: 18 Y 2 Y 3 Y 3 Y 9

After replacing Y’s, we get:

18 × 2 = 3 – 3 ÷ 9

=> 36 = 3 – 0.34

=> 36 ≠ 2.67

3) ×, ÷, +, =

Given expression: 18 Y 2 Y 3 Y 3 Y 9

After replacing Y’s, we get:

18 × 2 ÷ 3 + 3 = 9

=> 12 + 3 = 9

=> 15 ≠ 9

4) ÷, ×, =, × 

Given expression: 18 Y 2 Y 3 Y 3 Y 9

After replacing Y’s, we get:

18 ÷ 2 × 3 = 3 × 9

=> 9 × 3 = 27

=> 27 = 27

Hence, ‘÷, ×, =, × ’ is the correct answer.

The logic is:

(36, 10, 16) → (6², 6 + 4, 4²)

Similarly,

1) (81, 11, 4) → (9², 9 + 2, 2²)

Hence, ‘(81, 11, 4)’ is the correct answer.

One pound is approximately equal to 0.453 kg.

1 pound = 0.453 kg

Jennifer bought 4.409 pounds of custard apple.

4.409 pounds = (4.409 × 0.453) kg

= 1.997277 kg

 2 kg

Hence, ‘2’ is the correct answer.

The logic is:

Hence, ‘83’ is the correct answer.

In 1^st and 2^nd dice, ‘3’ is the common face on both the dice, so the faces opposite to each other is shown below:

So, ‘5’ will be on the face opposite to the face showing the number '1'.

Hence, ‘5’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

1) CDJK → C + 1 = D; D + 6 = J; J + 1 = K

2) OPTU → O + 1 = P; P + 4 = T; T + 1 = U

3) LMST → L + 1 = M; M + 6 = S; S + 1 = T

4) ABHI → A + 1 = B; B + 6 = H; H + 1 = I

Hence, ‘OPTU’ is the odd one out.

The pattern followed here is:

According to the alphabetical positions of the letters,

Note: The place values of the reverse letters when moved three steps backward, the code for the word is obtained.

Similarly,

Hence, ‘20-19-10-4-15-5-4’ is the correct answer.

The logic is - 

1. Calf → Young one of a cow is called a calf.

2. Nest → Home of birds is called nest.

3. Shed → Home of cows is called cow shed.

4. Hive → Home of bees is called bee hive.

So, all options except ‘calf’ represents name of home of different animals, while ‘calf’ is the name of the young one of an animal.

Hence, ‘Calf’ is the odd one out.

The logic is:

Exercise : Gymnasium → Gymnasium is a room or building equipped for gymnastics, games, and other physical exercise.

Similarly,

Boxing : ? → A boxing ring, often referred to simply as a ring or euphemistically the squared circle, is the space in which a boxing match occurs.

Hence, ‘Ring’ is the correct answer.

The Venn diagram that best represents the relationship between Tortoise, Mammal, and Amphibian is shown below:

Tortoise is a reptile.

There is a difference between tortoises and turtles.

Tortoises dwell on land, while turtles live in the water.

An animal of the type that gives birth to live babies, not eggs, and feeds its young on milk from its own body are called mammals.

Amphibians are small vertebrates that need water, or a moist environment, to survive. The species in this group include frogs, toads, salamanders, and newts.

Hence, ‘option 1’ is the correct answer.

Given:

(p) + (1/p) = 2

Concept Used:

If (a) + (1/a) = 2, then a will always be equal to 1

Calculation:

Using concept,

We get value of p = 1

Then, 

p × p × p = (p)³

⇒ (p)³ = (1)³

∴ The value of p × p × p is 1

Given:

The area of the rectangle is 288 cm²

The perimeter and breadth of a rectangle are in the ratio 6 ∶ 1

Formula used:

Area if rectangle = length × breadth

Perimeter = 2(length + breadth)

Calculation:

Length = l, breadth = b

According to question,

2(l + b)/b = 6/1

⇒ 2l + 2b = 6b

⇒ 4b = 2l

⇒ l/b = 2/1

So, length = 2X, breadth = X  

Area of rectangle = 288

⇒ (2X × X) = 288

⇒ 2X² = 288

⇒ X² = 144

⇒ X = 12

∴ Length of rectangle is 24 cm.

Given:

A person covers 700 m distance in 6 minutes

Formula used:

Speed = Distance/time

Calculation:

Speed = v, Distance = 700 meter, time = 6 minutes

v = 700/6 (m/minute)

Here,

1 m = 1/1000 km

1 minute= 1/60 hour

⇒ v = (700/1000)/(6/60)

⇒ v = (700 × 60)/(6 × 1000)

⇒ v = 7km/hr

∴ His speed in km/h is 7km/hr.

Shortcut Trick

Any speed change from m/minute to km/hr so multiply by 3/50

And speed change from km/hr to m/minute so multiply by 50/3

Here,

v = (700/6) × (3/50)

⇒ v = 70/10 km/hr

⇒ v = 7 km/hr

Given:

The sides of the right-angled triangle are 5 cm and 12 cm.

Concept Used:

Perimeter = Sum of all sides of the triangle

Calculation:

The sides of the right-angled triangle are 5 cm and 12 cm.

Then, Base = 5 cm

Height = 12 cm

Hypotenuse = √(5)² + (12)² = √ 25 + 144 = √ 169 = 13 cm

Then, Perimeter = 5 + 12 +13 = 30 cm

∴ The perimeter of a right-angle triangle is 30 cm.

Given:

30% of 400 + x% of 70 = 25% of 536.

Calculation:

30% of 400 + x% of 70 = 25% of 536.

⇒ 30/100 × 400 + x/100 × 70 = 25/100 × 536

⇒ 120 + 7x/10 = 134

⇒ 7x/10 = 14

⇒ x = 20

∴ The value of x is 20.

Given:

$\sin θ - \cos θ = \frac{1}{{29}}$

Formula used:

Sin²θ + Cos²θ = 1

Calculation:

Sinθ – Cosθ = 1/29

⇒ (Sinθ – Cosθ)² = (1/29)²

⇒ Sin2θ + Cos2θ – 2SinθCosθ = 1/841

⇒ 1 – 2SinθCosθ = 1/841

⇒ 1 – 1/841 = 2SinθCosθ

⇒ 840/841 = 2SinθCosθ

(Sinθ + Cosθ)²

⇒ Sin2θ + Cos2θ + 2SinθCosθ

⇒ 1 + 840/841

⇒ {(841 + 840)/841}

⇒ 1681/841

⇒ 41/29

∴  The value of sinθ + cosθ is 41/29

Shortcut TrickIf (a)sinθ - (b)cosθ = c

then (a)cosθ + (b)sinθ = d

Then a² + b² = c² + d²

So now from the equation;

⇒ 1 + 1 = 1/841 + d²

d² = 2 - 1/841

d = 41/29

Given:

Number of girls who got marks (> = 75%) = 7

Number of girls who got marks (60% - 74%) = 53

Number of girls who got marks (<60%) = 5

Calculation:

Total number of girls = 7 + 53 + 5 = 65

7 girls got distinction

So, % of girl who got distinction

⇒ (7/65) × 100

⇒ 700/65

⇒ 10.76

⇒ Percentage = 10.76%

∴ 10.76% of girls got distinction

Given:

Number of boys whose marks range >= 75% = 12

Number of boys whose marks range 60% - 74% = 45

Number of boys whose marks range <60% = 8

Number of girls whose marks range >= 75% = 7

Number of girls whose marks range 60% - 74% = 53

Number of girls whose marks range <60% = 5

Concept used:

Using the concept of percentage.

Calculation:

Total number of boys = 12 + 45 + 8 = 65

Total number of girls = 7 + 53 + 5 = 65

Percentages of boys who got marks from 60% to 74% = (45/65) × 100

⇒ The required percentage = 69.23%

Percentages of girls who got marks from 60% to 74% = (53/65) × 100

⇒ The required percentage = 81.53%

So, The ratio of percentages of boys and girls who got marks from 60% to 74% = (69.23%)/(81.53%) = 69.23 ∶  81.53

∴ The ratio of percentages of boys and girls who got marks from 60% to 74% is 69.23 ∶  81.53.

Given:

The average of four consecutive even numbers is 27.

28 adding on each number.

Formula used:

Average = (Sum of total observations)/(Total Number of observation)

Calculation:

Let the four numbers be a, a + 2, a + 4, a + 6.

Let 'x' be added to the number then new average is 28.

(Sum of total observations) = (Total Number of observation) × Average

a + a + 2 + a + 4 + a + 6 = 27 × 4

⇒ 4a + 12 = 108 

⇒ 4a = 96

⇒ a = 24

(Sum of total observations) = (Total Number of observation) × Average

⇒ (a) + (a + 2) + (a + 4) + (a + 6) + x = 28 × 5

⇒ 4a + 12 + x = 140

⇒ 108 + x = 140 

⇒ x = 32

∴ The number added to 32 to numbers then new average is 32.

Given:

If a certain principal amounts to Rs 87750 with 8% per annum in four years.

Formula Used:

Simple interest (S.I) = (P × R × T)/100 (where P is the principal, R is the rate of interest, T is the time period)

Amount = P + S.I = P + (P × R × T)/100 = P (1 + R × T/100)

Calculation:

Let P be the principal amount at 8% p.a for 4 years.

Now by using the above-mentioned formula the Simple interest will be

⇒ S.I = (P × 8 × 4)/100

And the amount will be = S.I + P

⇒ Amount = (P × 8 × 4)/100 + P = P(132/100)

Now as given Amount is Rs 87750

⇒ 87750 = P(132/100)

⇒ P = Rs 66477.2

∴ The principal is Rs 66477.2

Shortcut Trick Amount  = S.I + P

⇒ Amount = (P × 8 × 4)/100 + P ⇒ 87750 = P(132/100) ⇒ P = 66,477.2

Formula Used:

Sin(A +B) = SinACosB + CosASinB

Cos(A – B) = CosACosB + SinASinB

Calculation:

⇒ Sin(60 + θ) = Sin60×Cosθ + Cos60×Sinθ

⇒ Sin(60 + θ) = (√3/2)Cosθ + (1/2)Sinθ       ----(1)

⇒ Cos(30 – θ) = Cos30×Cosθ + Sin30×Sinθ

⇒ Cos(30 – θ) = (√3/2)Cosθ + (1/2)Sinθ      ----(2)

⇒ Now the value of Sin(60 + θ) – Cos(30 – θ) from (1) & (2)

⇒ (√3/2)Cosθ + (1/2)Sinθ – (√3/2)Cosθ - (1/2)Sinθ = 0

∴ The answer is 0 

Short Trick:

Put θ = 0°, we get 

⇒ Sin60 - Cos30 = 0

∴ From both we get 0

Given:

Efficiency of P = 3 × Efficiency of Q

Q can complete the work in 24 days

Formula used:

Total work = efficiency × Time period

Calculation:

Let the efficiency of P be 3x

Let the efficiency of Q be x

Total work = 24 × x

P and Q can complete the (24 × x) work in {(24 × x)/(3x + x)} days

⇒ 24/4 = 6

∴ P and Q together finish the same task in 6 days.

Given:

Income ratio of P and Q = 5 : 6

Individual savings of P and Q = ₹ 200

Expenditure ratio = 3 : 4

Formula used:

Profit = Investment × Time period

Calculation:

Let income of P be 5x

Let income of Q be 6x

(5x – 200)/(6x – 200) = 3/4

⇒ 20x – 800 = 18x – 600

⇒ 20x – 18x = 800 – 600

⇒ 2x = 200

⇒ x = 100

Income of P = 100 × 5 = 500

Income of Q = 100 × 6 = 600

∴ The income of Q is 600.

Given:

If a + b + c + d = 2.

Calculation:

If a + b + c + d = 2

For maximum value a = b = c = d

⇒ 4a = 2

⇒ a = 2/4

⇒ a = 1/2

Putting the value of a in (1 + a)(1 + b)(1 + c)(1 + d)

⇒ (1 + 1/2)(1 + 1/2)(1 + 1/2)(1 + 1/2)

⇒ (3/2)(3/2)(3/2)(3/2)

⇒ 81/16

∴ The maximum value of (1 + a) (1 + b) (1 + c) (1 + d) is 81/16.

Given:

A dozen pairs of gloves worth Rs.600 are available at a discount of 10%.

Formula used:

Selling price = Marked price (100 – D%)/100

Calculation:

Marked price of 12 pair of gloves = Rs. 600

Selling price of 12 pairs of gloves after discount

⇒ 600(100 – 10)/100

⇒ Rs. 540

If cost price of of 12 pair is Rs. 540 = (12 × 270)/540

⇒ 6 pairs

∴ 6 pair of gloves can be bought for Rs. 270.

Given:

Diameter if wheel,D = 210 cm = 2.1 m

Speed of car, v = 120 km/hour

Formula used:

V = (πDN)/60

V → speed, D → diameter, N → number of revolution

Calculatioon:

V = (πDN)/60

⇒ 120 × 5/18 = (π × 2.1 × N)/60

1 km/hour = 5/18 m/s

⇒ N = (120 × 5 × 60)/(18 × 2.1 × π)

⇒ N = 303.03

∴ Revolution of wheel in a minute is 303.03

Given:

Total number of students = 100

Calculation:

Number of male students = x

So, number of female students = 100 – x

According to question

⇒ 100 – x = x/100 × 100

⇒ 100 – x = x

⇒ 2x = 100

⇒ x = 50

∴ Number of male students are 50

Given:

The selling price of a book, including the sales tax, is Rs.956.34

The rate of sales tax is 10%.

The shopkeeper made a profit of 15%.

Calculation:

Let the actual selling price be x

⇒ x + 10% x = 956.34

⇒ x + 10(x)/100 = 956.34

⇒ x + x/10 = 956.34

⇒ 11x/10 = 956.34

⇒ x = (956.34 × 10)/11

⇒ x = 869.4

Now let CP be 100

⇒ Profit % = 15%

⇒ SP = 100 × 115/100

⇒ SP = 115

⇒ 115 = 869.4

⇒ 1 = 869.4/115

⇒ CP = 100 × 869.4/115

⇒ CP = 756

∴ The cost price of a book is Rs.756.

Shortcut TrickCP = $\frac{SP}{(1 \space + \space Sales \space tax) \space (1 \space + \space Profit)}$

CP = $\frac{956.34}{(1 \space + \space .10) \space (1 \space + \space .15)}$

CP = 756

Given: 

n is a positive integer

n is divided by 7, remainder is 2

Calculation:

Let k is any integer.

⇒ n = 7k + 2

By trial and error method

Option 1,

⇒ n + 2 = 7k + 2 + 2

⇒ n + 2 = 7k + 4

⇒ When n + 2 is divided by 7, the remainder is 4.

Option 2,

⇒ n + 1 = 7k + 2 + 1

⇒ n + 1 = 7k + 3

⇒ When n + 1 is divided by 7, the remainder is 3.

Option 3,

⇒ n + 3 = 7k + 2 + 3

⇒ n + 3 = 7k + 5

⇒ When n + 3 is divided by 7, the remainder is 5

Option 4,

⇒ n + 5 = 7k + 2 + 5

⇒ n + 5 = 7k + 7

⇒ When n + 5 is divided by 7, the remainder is 0.

∴ The n + 5 yields the remainder 0.

Let k is any integer.

⇒ n = 7k + 2

Put k = 1

⇒ n = 7(1) + 2

⇒ n = 9

⇒ The multiple of 7 nearest to 9 is 14

⇒ 14 – 9 = 5

⇒ 5 should be added to n

∴ The n + 5 yields the remainder 0.

Given:

Two circles touch each other externally,

Distance between their centres = 8 cm

Radius of 1^st circle = 3 cm

Formula used:

When two circles touch each other externally then the distance between their centres is given by the sum of their radii

Distance between centres = Radius of 1^st circle + Radius of 2^nd circle

Calculation: 

Let ‘r’ be the radius of 2^nd circle

According to the question,

⇒ 8 = 3 + r

⇒ r = 8 – 3 = 5 cm

∴ The radius of other circle is 5 cm.

Given: 

$\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...,,...,,...,,...,,...,,.,\infty } } } }$ 

Calculation: 

Let 'a' be the value of $\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...,,...,,...,,...,,...,,.,\infty } } } }$

⇒ a = $\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...,,...,,...,,...,,...,,.,\infty } } } }$

Squaring both sides, we get 

⇒ a² = 30 + $\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...,,...,,...,,...,,...,,.,\infty } } } }$

⇒ a² = 30 + a 

⇒ a² - a - 30 = 0 

⇒ a² - 6a + 5a - 30 = 0 

⇒ (a - 6)(a + 5) = 0 

⇒ a = 6, -5 

a = - 5 is not possible

∴ The value of $\sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30 + ...,,...,,...,,...,,...,,.,\infty } } } }$ is 6.

Given:

The perimeter of an isosceles triangle = 125 cm

And the base = 33 cm

Concept used:

An isosceles triangle is a that has two sides of equal length.

Formula used:

P = (2a + b)

Where,

P = Perimeter, a = Two equal sides, b = Base

Calculation:

Let the length of the each sides be x cm

P = (2a + b)

⇒ 125 = (2x + 33)

⇒ (125 – 33) = 2x

⇒ 2x = 92

⇒ x = 92/2 = 46

∴ The length of the equal sides is 46 cm.

Given:

Number of boys = 12

Calculation:

Total Boys = (45 + 12 + 8) = 65

According to the question,

The percent of boys who got distinction = (12/65) × 100

⇒ 240/13 = 18.46%

∴ The percent of boys who got distinction is 18.46%.

Given

Sin x = - 1/2

Concept used

If Sin x is negative then sin lies in 3rd quadrant or 4th quadrant, according to the following details:

Calculation

Sin x = - sin (1/2)

⇒ Sin x = - sin (π/6)

⇒ Sin x = sin (2π - π/6)

⇒ Sin x = sin (12π - π)/6

⇒ Sin x = sin (11π/6)

∴ x is 11π/6

Important Points

It is important for a candidate to remember the basic relation of conversion from degree to radian:

180° = π radians

Given

Calculation

Total strength of the class = 65 + 65 = 130

The correct answer is 2014.

Key Points

• Telangana became the 29th State of India with Hyderabad as its capital on 2 June 2014.
• Chandrasekhar Rao, the chief of Telangana Rashtra Samiti (TRS) was sworn-in as the first Chief Minister of Telangana.
• The state of Telangana was formed according to the Andhra Pradesh Reorganisation Bill 2014.
• Telangana is surrounded by Maharashtra and Chhattisgarh in the North, Karnataka in the West, and Andhra Pradesh in the South and East directions.
• ESL Narasimhan was the governor at the time of the formation of the new state of Telangana.

The correct answer is Uttar Pradesh.

Key Points

• The maximum strength of the Lok Sabha House is 550 members - 530 members to represent the States and 20 members to represent the Union Territories.
• The current strength of the Lok Sabha is 543 seats.
• Uttar Pradesh has the highest number of Lok Sabha seats i.e 80.
• Tamil Nadu has 39 Lok Sabha seats.
• Andhra Pradesh and Rajasthan have 25 Lok Sabha seats each.

Important Points

• Lok Sabha:
• Lok Sabha is the lower house of the parliament.
• Rajya Sabha is a permanent house and is not subject to dissolution while the Lok Sabha has a five-year term, and is subject to dissolution at the end of its term.
• The Lower House can be dissolved earlier by the President on the advice of the Prime Minister.
• It can also be dissolved if the President feels that no feasible government can be formed after the resignation or fall of a regime.
• The maximum strength of the House is 552 members.
• To become a member of Parliament, one should not be less than 30 years of age in the case of Rajya Sabha and not less than 25 years of age in the case of Lok Sabha
• To become a member of Lok Sabha, a candidate should have the following eligibility criteria:
• The candidate should be a citizen of India.
• The candidate should have at least 25 years of age.
• The candidate should not hold an office of profit under the Indian government or the government of any other state.
• The candidate should not be an unstable mind.

Important Points

• 104th Amendment Act, 2020 -
• Extended the deadline for the cessation of seats for SCs and STs in the Lok Sabha and states assemblies from Seventy years to Eighty.
• Removed the reserved seats for the Anglo-Indian community in the Lok Sabha and state assemblies.

The correct answer is New Zealand.

Key Points

• 2019 ICC World Cup was hosted by England.
• New Zealand defeated India in the semi-final of the ICC ODI Cricket World Cup 2019 by 18 runs.
• 2019 Cricket World Cup was won by England and it was their first winning title.
• Rohit Sharma emerged as the leading run-scorer in the 2019 ICC ODI World Cup.
• Australian bowler Mitchell Starc ended up as the leading wicket-taker in the 2019 ICC ODI World Cup.

The correct answer is Anup Kumar Singh.

• Anup Kumar Singh is the current Director General (DG) of the National Security Guard (NSG) as of February 2021.
• Anup Kumar Singh, a 1985-batch Indian Police Service officer of the Gujarat cadre, was appointed the NSG Director General in October last year.
• He was retired from this post on September 30,2020.

Key Points

• National Security Guard (NSG) is an Indian counter-terrorism unit under the Ministry of Home Affairs.
• NSG was formed on September 22, 1986, following Operation Blue Star, the Golden Temple attack, and the assassination of Indian Prime Minister Indira Gandhi, "for combating terrorist activities and protect states against internal disturbances".
• NSG motto is "Sarvatra Sarvottam Suraksha".

The correct answer is Light pen.

Key Points

• Light pen:
• Itis a pointing device that is used to select a displayed menu item or draw pictures on the monitor screen.
• It is an input device that utilizes a light-sensitive detector to select objects on a display screen.
• It allows the user to point to displayed objects or draw on the display screen in a similar way to a touchscreen.
• Use of Light pen::
• It can be used as input coordinate positions by providing necessary arrangements.
• If background color or intensity, a light pen can be used as a locator.
• It is used as a standard pick device with many graphics systems.
• It can be used as valuators

Additional Information

• Optical mark recognition (OMR):
• it is an electronic method of entering human-handled data into the system by identifying certain markings on a document.
• MICR (magnetic ink character recognition):
• It is a character-recognition technology that makes use of special magnetized ink to verify the legitimacy or originality of paper documents.
• Bar code reader:
• It is an electronic device that scanner the printed barcodes and decodes the data contained in the barcode.

The correct answer is Sikkim.

Key Points

The correct answer is Aravalli Hills.

Key Points

• Aravallis:
• They are one of the oldest fold mountains of the world.
• Aravallis are aligned in north-east to the south-west direction and stretches through the states of Delhi, Haryana, Rajasthan and Gujarat.
• Aravalli is 700 kilometers-long mountain range that starts from India's western state of Gujarat.
• The Aravalli Range is an eroded stub of ancient mountains.
• The highest peak is Guru Shikhar which is elevated at 1,722 metres.

Important Points

• Fold mountains are formed when two of Earth's tectonic plates are pushed together within the earth's upper crust.
• There are two types of fold mountains: young fold mountains and Old fold mountains e.g. of the USA.
• Young Fold mountains:
• They are of recent origin.
• They are higher than the old fold mountains.
• Examples include the Rocky Mountains, Andes and Himalayas.
• Old fold mountains:
• They have formed years ago.
• They are lower than the young fold mountains.
• These have gentle slopes.
• The Ural Mountains, Aravali ranges and  Appalachians are examples of old fold mountains.
• The three parallel ranges of the Himalayas longitudinal extent are: 
• Himadri (Great or Inner Himalayas):
• The northernmost range is called the Himadri and extends for about 2400 km.
• Mt. Everest and Mt. Kanchenjunga are a part of these ranges.
• Himachal (Lesser Himalayas):
• It lies to the south of Himadri.
• Some famous ranges are the Pir Panjal range, Dhaula Dhar and Mahabharat ranges.
• It has some famous valleys like Kullu, Kangra and Kashmir.
• Shivalik (Outer Himalayas):
• This is the outermost range of the Himalayas.
• Shivaliks are known by different names in different areas such as Dafla, Miri, Abor and Mishmi Hills in Arunachal Pradesh.

Additional Information

• Western Ghats:
• Western Ghats range extends from river Tapti in Maharashtra in the north to Kanyakumari in the south.
• The Western Ghats are known as Sahyadri in northern Maharashtra, Sahya Parvatham in Kerala and Nilagiri Malai in Tamil Nadu.
• The Western Ghats runs through six states i.e Gujarat, Maharashtra, Goa, Karnataka, Tamil Nadu, Kerala and two Union Territories i.e Dadra & Nagar Haveli and Pondicherry.
• Anamudi in Kerala is the highest peak in the Western Ghats and is located on the Anaimalai hills.
• The Western Ghats and the Eastern Ghats are connected at Biligirirangan Hills in Karnataka.
• The meeting point of the Eastern Ghats and the Western Ghats is the Nilgiri plateau.
• The Eastern Ghats are a discontinuous range of mountains along India's eastern coast.
• The Eastern Ghats spread over the states of Odisha, Andhra Pradesh, Telangana, Karnataka and Tamil Nadu.

The correct answer is Clement Attlee.

Key Points

• Clement Attlee was the Prime Minister of Britain/UK when British Parliament passed an independence bill for India in July 1947.
• The Indian Independence Act was passed in 1947.
• The act created two new independent dominions; India and Pakistan.
• Pakistan was split into Pakistan and East Pakistan which is now Bangladesh. The Bengal and Punjab provinces were partitioned between the two new countries.
• Lord Mountbatten was the last viceroy of British India and the first Governor-General of independent India.
• Jawaharlal Nehru became India's first Prime Minister and Muhammad Ali Jinnah became Pakistan's first Governor-General and Liaquat Ali Khan its Prime Minster.

Additional Information

• Winston Churchill was the British PM who appointed the cripps mission in march 1942 to resolve the Indian political crisis in order to get the support of India for their efforts in World War II.
• Cripps Mission:
• In order to get the support of India in world war II, Cripps Mission was sent to India in 1942.
• Few proposals of this mission are:
• Dominion status to India after the war.
• Constitution-making body after the war.
• Constitution so framed would be acceptable by the British Government only if certain province desires to stay away from the Union of India.
• Any province which wouldn't accept the new constitution would have the right to sign a separate agreement with British
• Gandhi called Cripps Mission as 'A post-dated cheque drawn on a failing bank' due to the Cripps offer of Dominion Status after the war.
• The communal award was announced by Ramsay Macdonald, the British PM.
• Important features of this award are:
• The separate electorate for the Muslims, Sikhs, Anglo Indians, Indian Christians, as well as the depressed classes.
• 3 percent of seats were reserved for women.
• 71 seats in total were reserved for the depressed classes in the provincial legislature.
• Gandhi rejected it and then started fast unto death in Yervada Jail against this award.

The correct answer is Serbia.

Key Points

• ATP Cup tennis tournament was held at three venues in the Australian cities of Brisbane, Perth, and Sydney in January 2020.
• Serbia won the tournament by defeating Spain with 2–1 in the final.
• Russia was defeated by Serbia in the semi-finals with 0-3.
• Australia was defeated by Russia in the semi-finals with 0-3.

Additional Information

• ATP Cup is a men's Tennis tournament, featuring teams from 20 countries.
• The 2021 ATP Cup will be played from 2-6 February.
• The five-day tournament will take place at Melbourne Park in Rod Laver Arena and in John Cain Arena.
• The winning team gets total prize money of AU$22 million or the US$ 15 million.
• A player that remains undefeated throughout the tournament will earn 750 ATP ranking points while a doubles would win a maximum of 250 points.

The correct answer is Eritrea.

Key Points

The correct answer is Jammu and Kashmir.

Key Points

• Dumhal folk dance:
• It is the popular folk dance of the Union Territory of Jammu and Kashmir.
• This dance is only performed by the men of the Wattal tribe of the region.
• This dance is performed on the beats of Drum and other instruments.

Important Points

The correct answer is Iran.

• Iran admits to 'unintentionally' shooting down a Ukrainian airliner, Boeing 737-800 passenger aircraft in January 2020.
• The Iranian government admitted that the airline was shot down having mistaken it for a cruise missile.
• The Boeing 737-800 airliner, flight PS752, crashed five minutes after takeoff from Tehran’s Imam Khomeini airport on Jan. 8, just hours after Iran fired a barrage of missiles at U.S. targets in Iraq.
• Iran’s President Hassan Rouhani took to Twitter to call the crash a “great tragedy” and “unforgivable mistake.”
• The Iranian statement stressed that the “human error” occurred during very high tensions with the U.S.

Additional Information

Facts:

• Iran:
• Tehran is the capital of Iran.
• Hassan Rouhani is the current president of Iran.
• It is bordered by Turkey, Iraq, Turkmenistan, Azerbaijan, Armenia, Afghanistan, and Pakistan.
• Syria:
• Damascus is the capital of Syria:
• It is bordered by Lebanon to the southwest, the Mediterranean Sea to the west, Turkey to the north, Iraq to the east, Jordan to the south, and Israel to the southwest.
• Bashar al-Assad is the current president of Syria.
• Saudi Arabia:
• It is bordered by Iraq, Jordan, Kuwait, Oman, Qatar, United Arab Emirates, and Yemen.
• Riyadh is the capital city of Saudi Arabia.
• Mohammed bin Salman Al Saud is the Crown Prince of Saudi Arabia.
• Iraq:
• Iraq is bordered by Turkey, Iran, Syria, Jordan, Kuwait, and Saudi Arabia.
• Baghdad is the capital of Iraq.
• Barham Salih is the current president of Iraq.

The correct answer is India.

Key Points

• India finished the year 2019 as the top shooting nation in the world as per the International Shooting Sport Federation’s (ISSF) overall rankings for 2019.
• While India leads the standings with 30 medals overall (21 gold, 6 silver, and 3 bronze), China is second with 11 gold, 15 silver, and 18 bronze medals.
• The USA is placed third with 15 medals (six gold, six silver, and three bronze).
• Russia is placed fourth with five gold, six silver and five bronze medals.

Additional Information

• The International Shooting Sport Federation(ISSF) was founded in 1907.
• It is the governing body of the Olympic Shooting events in rifle, pistol and shotgun disciplines.
• The president of ISSF is Vladimir Lisin(as of Feb 2021).
• Headquarters: Munich, Germany.