SSC CHSL Tier-1 2021: Official Paper (Held On : 3 June 2022 Shift 1) (Previous Year Paper)

The correct answer is: allowed

Key Points

• Allow (verb) means to give permission for somebody/something to do something or for something to happen.
• We use "have/has + v3" in the present perfect tense when an action that started in the past and is directly related to the present, such as actions that are still continuing or that indicate a change over time.
• The given sentence talks about the period of 1920.
• So, the sentence must be written in the simple past tense, when the action started and finished in the past.
• The structure should be Subject + V2+ object.

Therefore, option 1 is the correct answer that can substitute the underlined segment in the given sentence.

Corrected sentence: In the 1920s, new technology allowed filmmakers to attach to each film a soundtrack of speech.

The correct answer is: Spacios 

Key Points 

• Spacios = Spacious means having a lot of space; large in size. (बहुत जगह होना; आकार में बड़ा)
• Example - The hotel rooms are spacious and comfortable.

Therefore, except for option 1, the rest of the options are correctly spelt.

Additional Information 

• Lyre means an ancient musical instrument consisting of a U-shaped frame with strings attached to it. (एक प्राचीन वाद्य यंत्र जिसमें एक यू-आकार का फ्रेम होता है, जिसमें तार लगे होते हैं)
• Irrespective means regardless or in spite, and it is almost always followed by the word "of." (परवाह किए बिना या बावजूद)
• Soluble means that will dissolve in liquid. (तरल पदार्थ में घुल जाने वाला; घुलनशील, विलेय)

The correct answer is: To leave

Key Points 

• The idiom "Get away" means to leave or escape from a person or place. (किसी व्यक्ति या स्थान से दूर जाना या बचना)
• Example - We walked to the next beach to get away from the crowds.
• So, it is clear that the most appropriate meaning of the given idiom "Get away" is "To leave"

Hence, the correct answer is option 4.

The correct answer is Do not oppress the disabled.

Key Points

• Given sentence "The disabled should not be oppressed" is in Simple Present Tense and in Passive voice.
• The rule for changing a simple Present Indefinite tense form into an Active voice is as follows:
• ​Interchange the subject with the object and vice-versa.
• While converting the negative sentences with should into an active voice, the subject starts with Do not.
• Convert the verb "Disable" into a past participle or 3^rd form of the verb.
• "Should not" will change into "Do not."
• Structure: Subject + first form of verb + Object.
• Example: The car should not be moved. (Active Voice)

                           Do not move the car. (Passive Voice)

Additional Information

• The Active voice is used when the subject of the sentence does the action.
• The Passive voice is used when we focus on the object of the sentence.

The correct answer is Repel.

Key Points

• Attract refers to drawing something or someone toward them by virtue of their traits, particularly positive ones.
• Example: Flowers attract butterflies.
• Repel refers to making something or someone stops approaching you or attacking you.
• Example: The smell of the place repelled tourists.
• ​Attract and Repel have different meanings.

Therefore, the correct option is Repel. 

Additional Information

• Flex refers to expressing extreme joy or pride about an accomplishment or possession, typically in a way that irritates others.
• Rash refers to numerous little red dots on the skin.
• Destroy refers to seriously harming something such that it cannot be utilised.

The correct answer is Between two dangers. 

Key Points

• The most appropriate meaning of the given idiom "Between Scylla and Charybdis" is "Between two dangers."
• Between Scylla and Charybdis refers to being forced to choose between two unappealing options.
• ​Example: Mike does not see that his actions will bring him between Scylla and Charybdis.
• ​Therefore, as per the points mentioned above, we find that the correct answer is Between two dangers.

Additional Information

• Meaning and examples of some idioms of the play "Between."

The correct answer is Over.

Key Points

• In the given options the correct option to be filled in the blank is Over.
• The word "over" is used to describe a movement or position that is superior to another.
• It can also be used while referring to movement across a surface. 
• Example: A bird flew over my home.
• Thus, the correct option is Over.

 The correct sentence is: We love to swing from the branches over the pond.

Additional Information

• We use the word "on" when referring to a place on a surface.
• We use the preposition "in" when describing a location in relation to a bigger area.
• We use the word "under" when referring to something that is beneath or beneath another.

The correct answer is Does he remember.

Key Points

• "Is he remembering" is grammatically incorrect in this sentence.
• The correct usage is "Does he remember" instead of "Is he remembering."
• The tense used in this sentence is Interrogative Simple Present Tense.
• Structure of Interrogative Simple Present Tense: “Do or Does” + Subject + first form of a verb + Object.
• Example: Does she read the novels she bought?

The correct sentence is: Does he remember our help?

The incorrectly spelt word is "Audasious." 

Key Points

• In the given options "Audasious" is incorrectly spelt. Its correct spelling is "Audacious."
• Let's look at its meaning.
• Audacious: Demonstrating a readiness to take chances or offend people.
• ​Example: He described the speech as audacious.
• ​Therefore, as per the points mentioned above, we find that the correct answer is Audacious.

Additional Information Let's look at the meaning of other options also: 

The incorrectly spelt word is "Guarmet." 

Key Points

• In the given options "Guarmet" is incorrectly spelt. Its correct spelling is "Gourmet."
• Let's look at its meaning.
• Gourmet: A person with a passion for and extensive knowledge of food**.**
• ​Example: She is a chef and a gourmet.
• ​Therefore, as per the points mentioned above, we find that the correct answer is "Gourmet."

Additional Information

Let's look at the meaning of other options also: 

The correct answer is To have nothing to do.

Key Points

• The most appropriate meaning of the given idiom "Be at a loose end " is "To have nothing to do."
• Be at a loose end refers to a state of being idle.
• ​Example: If you find yourself at a loose end, you could always read the novel.
• Therefore, as per the points mentioned above, we find that the correct answer is To have nothing to do.

Additional Information

• Let's look at the meaning and examples of some idioms of the play "Loose."

The correct answer is "Ephemeral."

Key Points

• The appropriate answer is "Ephemeral" which means "Lasting for a very short period of time."
• Ephemeral: Lasting merely a short period of time.
• Example: Fame in the industry is Ephemeral.
• ​Therefore, the correct option is Ephemeral.

​

Additional Information

• Permanent refers to something that lasts forever.
• Ceaseless refers to something having no end or appearing to have no end.
• Pungent refers to strong and harsh flavours or aromas.

The correct answer is "Vocabulary raises the standard of the English language." 

Key Points

• In "He incorporates daily vocablary in his gestures" the incorrect spelling is vocablary.
• In "Reading stories developed her vocabluary" the incorrect spelling is vocabluary.
• In "She has her own vockbulary words from English and Hindi" the incorrect spelling is vockbulary.
• The correct spelling is Vocabulary.
• Vocabulary: All the words that a specific person is familiar with and uses.
• Example: Reading increases your vocabulary.

The correct answer is Ate that lobster.

Key Points

• "Ate that lobster" is grammatically incorrect in this sentence.
• The correct usage is "Eaten that lobster" instead of "Ate that lobster."
• The tense used in this sentence is Past Perfect tense.
• Structure of Past Perfect tense: Subject + had +V3 form + Object.
• Example: *She had already left the party when I reached there.*​

The correct sentence is: After he had eaten that lobster, he began to feel sick.

The correct answer is Absurd.

Key Points

• Illogical means not prudent, smart, or rational, typically because they are motivated by their emotions rather than critical consideration. 
• Example: Her statements are totally illogical.
• Absurd refers to things which are either foolish and unreasonable or amusingly silly.
• Example: The answers that she gave in the test were totally absurd.
• "Illogical" and "Absurd" are similar in meaning.

Therefore, the correct option is Absurd**.**

Additional Information

• Unfavourable refers to not offering you a competitive edge or a high likelihood of success.
• Biased refers to showing an excessive affinity for or aversion to a person depending on one's own preferences.
• Factual refers to utilising or containing facts.

The correct answer is 'She did not hire me'.

Key Points

• The given sentence is in Simple Past Tense and in Passive voice.
• Rules to change a Passive voice to an Active voice :
• The subject and object are interchanged i.e. the subject become the object and the object becomes the subject.
• Passive pronouns (her) change to active pronouns (she).
• Active pronouns (I) change to passive pronouns (me).
• 'By' is removed.
• The structure :
• Object + was/were+ not +V3+ by Subject (Passive voice)
• Subject +did+ not+v1+ object (Active voice)
• Example- She was not taken by him. (Passive voice)
• He did not take her. (Active voice)

Additional Information

• In passive voice, a sentence emphasizes the object performing an action.
• In active voice, a sentence emphasizes the subject performing an action.

The correct answer is 'prolong'.

Key Points

• To Protract means to make something last for a long time or last longer than necessary.
• Example- He has certainly taken his time, even protracting the process.
• To Prolong means to extend the duration of something to make it longer.
• Example- An idea that prolonged the life of the engine by years.
• It is clear that 'Prolong' is the most appropriate meaning for the underlined word 'protract'.

Additional Information

• Control means the power to influence something.
• Example- The whole project is under the control of the project manager.
• Accept means consent to receive or undertake something. 
• Example- He accepted the position as the new CEO of the company.
• Cease means to come or bring to an end.
• Example- The hostilities ceased and normal life was resumed.

The correct answer is 'shall have completed'.

Key Points

• The sentence is in Future perfect tense.
• The structure for future perfect tense : Subject + (auxiliary verb + have) + V3
• So the right sentence would be:
• She shall have completed her graduation by 2023.

Additional Information

• The future perfect tense refers to a completed action in the future.
• When we use this tense, we project ourselves forward into the future and look back at an action that will be completed sometime later than now.
• It is often used with a time expression.
• Example- Won't they have arrived by 5 pm?

The correct answer is 'commisarate'.

Key Points

• In the given options, 'commisarate' is an incorrectly spelt word.
• The right spelling would be 'commiserate'.
• Commiserate means to express or feel sympathy or pity.
• Example-She went over to commiserate with Rose on her unfortunate circumstances.

Additional Information

• Decennial means recurring every 10 years.
• Example- It is time for the decennial census.
• Nausea means a feeling of sickness with an inclination to vomit.
• Example- A wave of nausea engulfed him as soon as he saw the rotting dead body.
• Curriculum means the subjects comprising a course of study in a school or college.
• Example- I was in charge of developing the curriculum​ and its course components for this academic year.

The correct answer is 'CDAB'.

Key Points

• Sentence C comes first as it gives an introduction and definition regarding the subject matter i.e online education.
• Sentence D comes second as it carries the definition to the advantages point.
• Sentence A comes next as it continues the advantages part.
• Sentence B comes last as it concludes the whole discussion about online education.
• Hence, the right order is CDAB.

The correct answer is 'so'.

Key Points

• Here 'so' has a similar meaning to that of 'very'.
• In sentences like this, 'so' is used to add emphasis and to make the meaning stronger.
• Example- He is so proud of his son.
• Hence it is the most appropriate option to fill in the blank.

The correct answer is 'to'.

Key Points

• Here the word 'stomach' is used as a verb.
• Stomach as a verb means to bear without overt reaction or resentment.
• Example- She couldn't stomach the ongoing office politics.
• There is already a verb present in the same sentence (find), so there is a need for a to-infinitive to include the other verb in the sentence.
• Among the given options, 'to' is the most appropriate one because it makes the verb a to-infinitive form.

The correct answer is 'fact'.

Key Points

• Fact means a thing that is known or proven to be true.
• Example- He blatantly ignored some historical facts​ while writing that book.
• Since the point being tried to be made is a statement that is supposedly true, 'fact' is the most appropriate option to fill in the blank.

Additional Information

• A Story means an account of real or imaginary people told for entertainment.
• Example- Jumanji is a story of adventure and thrill.
• The term means a word or phrase used to describe a thing or to express a concept, especially in a particular branch or field of study.
• Example- The scientific term for human beings is Homosapiens.
• Myth means a traditional story concerning the early history of people or explaining a natural phenomenon involving supernatural beings or events.
• Example- He found the ancient Celtic myths too fascinating.

The correct answer is Allowed.

Key Points

• The word allowed is a past form of the word allow which means to let (someone) have or do something.(अनुमति देना)
• Example: My mother allowed me to go for a picnic.

Additional Information

• The word cared means to feel concerned or interested; attach importance to something. (परवाह)

Example: They don't care about human life.

• The word thrown means to send something through the air with force, especially by a sudden movement of the arm. (फ़ेकना)

Example: The coat was thrown over the back of the chair.

• The word transited means pass across or through (an area). (गुज़रना)

Example: The new large ships will be too big to transit the Panama Canal.

The correct answer is Interpret.

Key Points

• The verb is a term that serves as the major component of the predicate of a sentence and is used to describe an action, state, or event, such as hear, become, or happen.
• The word Interpret is a verb which means to give a definition of (information or actions).
• Example: I am sorry, I interpret something wrong.

Additional Information

• The word deny means a state that one refuses to admit the truth or existence of.​
• Example: You can't deny that you don't like Jim.
• The word accept means agreement to receive or perform (something offered).​
• Example: I accept I broke the vase.
• The word malign means wicked in character or outcome.​
• Example: She had a strong and malign influence.

Logic : (First number - 2) × 3 = Second number

1. 27 : 75 

⇒ (27 - 2) × 3 

⇒ 25 × 3 ⇒ 75

2. 39 : 111 

⇒ (39 - 2) × 3 

⇒ 37 × 3 ⇒ 111

Similarly, 

3. 45 : ?

⇒ (45 - 2) × 3 

⇒ 43 × 3 ⇒ 129

Hence, '129' is the correct answer.

The positional values of English alphabet is as follows:

The pattern followed here is: Opposite letters 

'ELBOW' is written as 'DLYOV' 

‘ANKLE' is written as 'VOPMZ'

Similarly,

'WRIST' will be written as:

Hence, "GHRID" is the correct answer.

The paper when unfolded will appear as shown below:

Hence, 'option 1' is the correct answer.

Given : 15 July 2002 is a Monday

• Total number of days in a normal year = 365
• Number of odd days in a normal year = 365 ÷ 7 = 1
• Total number of days in a leap year = 366
• Number of odd days in a leap year = 366 ÷ 7 = 2
• 15 July 2002 (Monday) + 1 odd day (2003) + 2 odd days (2004) + 1 odd day (2005) = 15 July 2005 (Friday)
• Total number of days from 15 July 2005 to 16 October 2005 = 16 (July) + 31 (August) + 30 (September) + 16 (October) = 93
• Total number of odd days from 15 July 2005 to 16 October 2005 = 93 ÷ 7 = 2
• Now starting from 15 July 2005, every 7^th day will be a Friday.
• Therefore, Friday + 2 = 16 October 2005 i.e., Sunday

Hence, 'option 1' is the correct answer.

The correct mirror image of the given figure when the mirror is placed at MN:

Hence, "Option 3" is the correct answer.

Given : B E _ K P C _ H K P _ E H K P_ E H K P

Lets check each option:

1) F, E, Q, H ⇒ B,E,F,K,P - C,E,H,K,P - Q,E,H,K,P - H,E,H,K,P

No pattern is followed.

2. F,D,Q,H ⇒ B,E,F,K,P - C,D,H,K,P - Q,E,H,K,P - H,E,H,K,P

No pattern is followed.

3. H,D,Q,E ⇒ B,E,H,K,P - C,D,H,K,P - Q,E,H,K,P - E,E,H,K,P

No pattern is followed.

4. H,E,D,E ⇒ B,E,H,K,P - C,E,H,K,P - D,E,H,K,P - E,E,H,K,P

In this series, pattern is followed.

Hence, 'option 4' is the correct answer.

The paper when unfolded will be as shown below:

Hence, 'option 3' is the correct answer.

Logic : Square root of first number + 10 = second number

1. 64 : 18

⇒ √64 + 10 

⇒ 8 + 10 = 18

And,

2. 196 : 24 

⇒ √196 + 10 

⇒ 14 + 10 = 24

Similarly,

3. 529 : ?

⇒ **√**529 + 10

⇒ 23 + 10 = 33

Hence, the correct answer is "33".

The correct mirror image of the given figure when the mirror is placed at MN.

Hence, "Option 3" is the correct answer.

The positional values of English alphabet is as follows:

The pattern followed here is:

UNCLEAR is written as CNULRAE

And,

PRIVACY is written as IRPVYCA

Similarly,

NUCLEAR is written as:

Hence, 'CUNLRAE' is the correct answer.

Family Chart:

Given : 

• A is the brother of C
• B is the only sister of D who is the maternal uncle of C.
• E is the father of C.

Hence, the correct answer is "Son".

The least possible Venn diagram:

Conclusions:

I. Some biscuits are cakes → False (As no sweet is a biscuit and all cakes are sweets. So some biscuits are cakes is not true)

II. Some chocolates are sweets → False (As no sweet is a biscuit and some chocolates are biscuits. So some chocolates sweets is not true)

III. No cake is a chocolate → False (There is no direct relation between cake and chocolate. So, it may or may not be true. Hence, this is considered false).

Hence, the correct answer is "None of the conclusions follow".

Logic : (First number ÷ Second number) + 7 = Third number

1. (45, 9, 12)

⇒ (45 ÷ 9) + 7 

⇒ 5 + 7 = 12

And,

2. (21, 3, 14)

⇒ (21 ÷ 3) + 7 

⇒ 7 + 7 = 14

Lets check each option:

1) (55, 5, 11) 

⇒ (55 ÷ 5) + 7 

⇒ 11 + 7 = 18 ≠ 11

2) (66, 6, 17)

⇒ (66 ÷ 6) + 7 

⇒ 11 + 7 = 18 ≠ 17

3) (80, 10, 15)

⇒ (80 ÷ 10) + 7

⇒ 8 + 7 = 15 

4) (70, 5, 13)

⇒ (70 ÷ 5) + 7 

⇒ 14 + 7 = 21 ≠ 13

Hence, 'option 3' is the correct answer.

The positional values of English alphabet is as follows:

The pattern followed here is: 

Twice the value of consonant whereas vowel is written as it is.

 'RESET' is written as '36538540'

And

'START' is written as '384013640'

Similarly, 

'STOP' will be written as:

Hence, '38401532' is the correct answer.

Logic : (First number + 1)²  = Second number

Lets check each option:

1) 3 : 16

⇒ (3 + 1)²  ⇒ (4)²  ⇒ 16

2) 6 : 49

⇒ (6 + 1)²  ⇒ (7)² ⇒ 49

3) 12 : 169

⇒ (12 + 1)² ⇒ (13)² ⇒ 169

4) 9 : 64

⇒ (9 + 1)² ⇒ (10)² ⇒ 100 ≠ 64

So, 9 : 64 is the odd one out.

Hence, 'option 4' is the correct answer.

BODMAS Rule:

Explanation :

If we apply BODMAS rule on the given equation

⇒ (84 D 14) A 17 C 13 B (75 D 15) A 9 B 7

⇒ (84 ÷ 14) + 17 - 13 ×( 75 ÷ 15 ) + 9 × 7

⇒ 6 + 17 - 13 × 5 + 9 × 7

⇒ 6 + 17 - 65 + 63

⇒ 86 - 65

⇒ 21

Hence, 21 is the correct answer.

Table of English alphabet positional value

According to given coding language

IS

  9 × 19 = 171 - 2 = 169

AM 

1 × 13 = 13 - 2 = 11

Similarly,

IN

9 × 14 = 126 - 2 = 124

Hence, 124 is the correct answer.

The logic followed here is:

Logic: (First number)³ - 4 = Second number

Hence, the correct answer is "13"

Given : 

Explanation :

The two dices with one face common in the figures

Then write it in a clockwise order starting from the common face then the positional value become the opposite face.

Here 2 is the common face in both the dices. The opposite faces are

6 → 1

3 → 4

2 → 5

Hence, 5 is the correct answer.

Explanation : The pattern followed here is : 

Logic: First number = (second no)² ×( second no. +1)

Option 1 : 25: 5

⇒  25 ≠ 5² × 6

Option 2 : 80 : 4

⇒ 80 = 4² × 5

Option 3 : 36 : 3

⇒ 36 = 3² ×4

Option 4 : 2 : 12

⇒ 12 = 2² × 3

Hence, 25 : 5 is the correct answer.

Explanation :

Let's take common number in both the dices

12 and 13 both are common in both the dices. Now move clockwise direction in both dice.

13-12-14 first dice

13-11-12 second dice

13 is opposite to 12 and 12 is opposite to 13

so, 14 is opposite to 11 as shown below

Hence, 11 is the correct answer.

The pattern followed here is:

Hence, the correct answer is "546".

Explanation : 

Logic: Second number completely divide by.

1. 576 is divisible by 16

And

2. 80 is also divisible by 8 .

Among the options(we have to select the option that will be divisible by 22)

3) 1452 is divisible by 22 .

Hence, 1452 is the correct answer.

The table of English alphabet positional value

According to positional value

Note: G(7) = 7 + 26 = 33, 33 - 15 = 18(R) As alphabet series end with 26, We take 26 as 0 or starting point.  

C(3) = 26 + 3 = 29, 29 - 15 = 14(N),As alphabet series end with 26, We take 26 as 0 or starting point.  

Hence, "ISCN" is the correct answer.

The pattern followed here is:

Hence, "657" is the correct answer.

Given:

The 9 - digit number 5p42978n6 is divisible by 72.

Calculations:

Number should be divisible by 72. then, number should be divisible by 8 and 9 both.

Largest possible value of n to be divisible by 8 is = 9

And second largest possible value of n to be divisible by 8 = 5

⇒ 856/8 = 107

For n = 5 , then

Number should be divisible by 9 -

= (5 + p + 4 + 2 + 9 + 7 + 8 + 5 + 6) 

= 46 + p

Therefore, (46 + p) should be divisible by 9 then for p = 8 this condition will satisfy.

So, possible value of p = 8

Then, 2p - 1 

= 2(8) - 1

= 16 - 1

= 15

∴ The value of (2p - 1) is 15.

Calculations:

The sum of imports-exports in year 2006-07 = 1036 + 818 = 1854

The sum of imports-exports in year 2007-08 = 954 + 988 = 1942

The sum of imports-exports in year 2008-09 = 618 + 878 = 1496

The sum of imports-exports in year 2009-10 = 432 + 216 = 648

The sum of imports-exports in year 2010-11 = 685 + 930 = 1615

Here, 648 < 1496 < 1615 < 1854 < 1942

$\therefore$  The imports-exports is minimum in year 2009-10.

Given:

Length of diagonal of Cube = 6√3 cm

Concept used:

Diagonal of a cube of side a = a√3

Calculations:

Let the side of the cube be ''a".

According to question,

Diagonal = 6√3 

⇒ a√3 = 6√3

⇒ a = 6 cm

Hence, The side is 6 cm

$\therefore$ Length of side of the cube is 6 cm.

Given:

The diameter of base of a right circular cone = 16 cm.

The height of the right circular cone = 6 cm.

Formula used:

The volume of a cone = (1/3)πr2h

(l)2 = (r)2 + (h)2

where, r = Base radius of a cone, h = Height of a cone and l = Slant height of a cone

Calculation:

The diameter of the base = 16 cm,

Radius = 16/2 = 8 cm

The volume of the cone = (1/3)πr2h

⇒ (1/3) × π × 82 × 6

⇒ 128π cm3

∴ The volume of the cone is 128π cm3.

Given: 

Cost of first variety = Rs. 45/kg

Cost of second variety = Rs. 48/kg

Selling price of mixture = Rs. 46/kg

Formula used:

Rule of alligation:

(Quantity of cheaper/Quantity of dearer) = [(Cost price of dearer) – (Mean price)]/[(Mean price) – (Cost price of cheaper)]

Calculations:

According to question, the mean price of the mixture is Rs. 46/kg.

Let the ratio of the two varieties be R.

Using the rule of alligation,

⇒ R = (48 - 46)/(46 – 45)

⇒ R = 2/1

⇒ R = 2 : 1

∴ The ratio in which the two varieties must be mixed to sell the mixture for Rs. 46/kg is 2 ∶ 1.

cosec θ + cot θ = 5

Formula used:

$1+cosθ=2cos^2 (θ/2)$

$sinθ=2sin (θ/2)cos (θ/2)$

sinθ = p/h and cosθ = b/h

where p → perpendicularh → hypotenuse

b → base

Calculation:

⇒ $\frac{ 1}{ sinθ }+\frac{ cosθ}{ sinθ}=\frac{ 1+cosθ}{ sinθ}=5$

⇒ $\frac{ 2cos^2 (θ/2)}{ 2sin (θ/2)cos (θ/2)}=5$

⇒ $\frac{ cos (θ/2)}{ sin (θ/2)}=cot(θ/2)=5$

Now, 

$sin (θ/2)=\frac{1}{\sqrt{26}}$ and $cos (θ/2)=\frac{5}{\sqrt{26}}$

$cosecθ=\frac{1}{ sin θ}=\frac{1}{2 sin (θ/2) cos (θ/2)}$

substituting,  we get 

$cosecθ=\frac{1}{2× \frac{1}{\sqrt{26}}× \frac{5}{\sqrt{26}}}$ $=\frac{26}{10}=\frac{1}{2}(5+\frac{1}{5})$

Alternate MethodAs we know that,

cosec²θ - cot²θ = 1

⇒ (cosecθ + cotθ)(cosecθ - cotθ) = 1

⇒ 5 × (cosecθ - cotθ) = 1

⇒ cosecθ - cotθ = 1/5      ----(1) 

and cosec θ + cot θ = 5     ----(2)

Adding equation(1) and equation(2)

⇒ 2cosecθ = 5 + 1/5

⇒ cosecθ = ​1/2( 5 + 1/5)

Formula used

Two successive discounts x and y 

The total discount =  $-x-y+\frac{x\times y}{100}$

Calculation:

Case 1: two successive discounts of 15%

Total discount = 27.75%

Case 2: two successive discounts of 12% and 18%

Total discount=27.84%

Case 3: buying 7 articles and get 3 free

let cost price of an article = Rs 1

He got 10 articles with price of seven

Discount=$\frac{10-7}{10}\times 100= 30\%$%

so the most discount is offered in case 3

Given

average of 16 numbers=23

average of 7 numbers=21

average of 8numbers=24

Calculation

sum of 16 numbers = average × number 

⇒ 23 × 16 = 368

sum of the first 7 numbers = 21 × 7 =147

sum of the last 8 numbers = 24$×$8=192

sum of 16 numbers

⇒ sum of first 7 numbers + 8^thnumber+sum of last 8 numbers

⇒ 368 = 147 + 8thnumber + 192

⇒ 8thnumber = 29

The 8thnumber is 29

Given:

solid cuboid dimension = 49 cm × 33 cm × 24 cm

Formula used:

The volume of a cuboid = a × b × c, where a,b, c are dimensions

The volume of a sphere = $\frac{4}{3}~$× π × r³, where r is the radius

Calculation:

For remolding volume of sphere is equal to volume of cuboid 

⇒  $\frac{4}{3}~$× π × r³  = 49 × 33 × 24

⇒ r³ = 9261

⇒ r = ³√9261 = 21

solving this we get r=21cm

∴ The radius of the sphere is 21 cm​​​.

The ratio of distance 4:7

If Ravina traveled 4 km then Suhel travels 7 km

So if Suhel travel 63 km that is 9 × 7

So Ravina travelled 9 ×  4 = 36 km

Ravina travels 36km

Given

percentage of girls 64%

girls chosen soccer 81.25%

number of girls chosen soccer  is 143

Calculation

Total percentage of the class=100%

let total number of students in class is T

girls chosen soccer is 81.25% of the 64% of T

So $\frac{64}{100}\times \frac{81.25}{100}$(\times\) T=143

⇒ T = 275

The total number of students in the class is 275

Given

Taking last three years

in year 2018 =  10 lakh loss

in year 2019 =  5 lakh loss

Combining those two, total 15 lakh loss

Then in the year 2020 = 35 lakh profit

So,  35 - 15 = 20 lakh profit

So for last three years there is a profit of 20 lakhs

450 + 752 - 125 x $\frac{3}{100}$ of 1000 - {650 $\div$ (16 - 3)}

applying BODMAS rule 

⇒ 450 + 752 - 125 x $\frac{3}{100}$ of 1000 - {650 $\div$ (13)}

⇒ 450 + 752 - 125 x $\frac{3}{100}$ of 1000 - 50

⇒ 450 + 752 - 125 x 30- 50

⇒ 450 + 752 - 3750 - 50

⇒ 1202 - 3750 - 50 = - 2598

Given

selling price of earphone= 2000Rs

profit percentage = numerical value of cost price

Formula used

profit percentage=$\frac{Sp-Cp}{Cp}× 100$

Sp = selling price= 2000Rs

Cp = cost price

Calculation

from the question, 

= Profit percentage,= $\frac{Sp-Cp}{Cp}× 100$

⇒ CP = (2000 - CP)/(CP) × 100

Let CP be x, 

⇒ x = (2000 - x)/x  × 100

⇒ x² = (2000 - x) × 100

⇒ x² + 100x - 2,00,00

⇒ x² + 500x - 400x - 2,00,000 = 0

⇒ x(x + 500) - 400(x + 500)

⇒ (x - 400) (x + 500) = 0

⇒ x = 400 as CP can not be negative

The cost price of the earphone is Rs. 400

Shortcut Trick

Growth factor for 1 year = Amount₃ ÷ Amount₂ = 4913 ÷ 4624 = 17/16.

Since the time gap from 0 to 2 years is two 1-year intervals:

Principal (P) = Amount₂ ÷ (Growth factor)²

P = 4624 ÷ (17/16)² = 4624 × (256 ÷ 289)

P = 16 × 256 = 4096.

∴ The correct answer is ₹4,096.

Alternate Method

Given:

Amount after 2 years (A₂) = ₹4,624

Amount after 3 years (A₃) = ₹4,913

Formula Used:

A = P(1 + r/100)ⁿ

Calculations:

⇒ (1 + r/100) = A₃ ÷ A₂

⇒ (1 + r/100) = 4913 ÷ 4624

⇒ Dividing by 289: (1 + r/100) = 17/16

⇒ P(1 + r/100)² = 4624

⇒ P × (17/16)² = 4624

⇒ P × (289/256) = 4624

⇒ P = (4624 × 256) ÷ 289

⇒ P = 16 × 256

⇒ P = 4096

∴ The correct answer is ₹4,096.

Additional Information

Compound Interest Concept

In Compound Interest, the interest earned in each period is added to the principal to calculate the interest for the next period. The amounts in successive years form a Geometric Progression (GP).

Rate of Interest Shortcut

If amounts for two consecutive years are given, Rate (r) = [(A_n+1 − A_n) ÷ A_n] × 100.

SI vs CI for 2 Years

The difference between Compound Interest and Simple Interest for 2 years is given by the formula: Difference = P(r/100)².

GIVEN:

$x +\frac{1}{x}$ = 10

CALCULATION:

As, we have $x +\frac{1}{x}$ = 10 

⇒ $x^2 + 1 = 10 x$ 

⇒   $x^2 = 10 x - 1$

Now , on putting  the value of $x^2$ in the equation $7x\over x^2 +1 -8x$  we get,

⇒    $7x\over ( 10x -1) +1 -8x$  = $7x\over2x$ = 7/2 or 3.5

Hence, the value is 3.5.

GIVEN:

Marked price = Rs50,000

FORMULA USED:

Discount = Marked price × Discount Rate

Selling price = ( 1-d1/100) × ( 1-d2/100) × M.P.              Where M.P. → Marked price,

d1 and d2 → Successive discount rates respectively.

Selling price = Marked price - Discount

CALCULATION:

On considering  1^st condition  we have,

Discount = Rs10,000 and M.P. = Rs50,000

⇒ Selling price = ( M.P.- Discount)

⇒ 50,000 - 10,000

⇒ Rs40,000

On considering 2^nd condition we have,

Discount Rate = 25% , M.P. = Rs50,000, 

⇒ Discount = M.P. × Discount Rate   

⇒ 50,000 × 25/100 = Rs12,500

Hence,

⇒ Selling price = ( M.P.- Discount)

⇒ 50,000 - 12,500 = Rs37,500

On considering 3^rd condition we have,

d1 = 10% d2 = 10% , M.P. = Rs50,000

Selling price = ( 1-d1/100) × ( 1-d2/100) × M.P. 

⇒ (1 - 10/100) × (1 - 10/100) × 50,000     

⇒ 9/10× 9/10 × 50,000 = Rs40,500

On considering 4^th condition we have,

d1 = 15% , d2 = 10 % , M.P. = Rs50,000

⇒ Selling price = ( 1-15/100) × ( 1-10/100)  × 50,000

⇒ 17/20 × 9/10 × 50,000 = Rs38,250

Since, on condition 2^nd i.e. on discount of flat 25% we have lowest selling price . Hence, it is more beneficial to the customers.

Hence, condition 2^nd i.e.(ii), is in option no.3 .So, it is the required answer .

Given:

four runners to complete 1 round takes 400 sec, 600 sec, 720 sec, and 900 sec  respectively

Concept used:

Lowest Common Multiple ( L.C.M )

Calculation:

When the four runners will meet at the starting point, they would have completed different numbers of rounds

Hence, the time at which they will meet will be the L.C.M of the individual time taken by them

⇒ L.C.M. of 400, 600, 720, and 900  =  3600 sec.

Hence, they will meet after 3600 seconds.

GIVEN:

Votes by which the successful candidate won the election = 6120

CALCULATION:

Let the  initial votes be x 

15% of the voters did not cast their votes and 10% of the votes were declared invalid

Hence, Total valid votes = x × ( 85/100) × ( 90/100)

Successful candidate received 55% of valid votes

⇒ non -successful candidate received  45% of valid votes

⇒ Difference = ( 55 -45) = 10%

Votes by which successful candidate won the election = 6120

⇒ x × ( 85/100) × ( 90/100) × ( 10/100) = 6120

⇒ x = 80,000.

Hence, the number of voters enrolled on the voter list were 80,000.

GIVEN:

x-2y = 3

2xy = 5

FORMULA USED:

(a + b)² = a² + b² + 2ab               

(a - b)2 = a2 + b2 - 2ab    

CALCULATION:

Now, (x - 2y) = 3 ,

on squaring both sides we get,

⇒ (x - 2y)² = 3²         

⇒ x² + 4y² - 2 ×  x × 2y = 9 

⇒ x² + 4y² = 9 + 4xy      ----(1)

Also , it is given 2xy = 5 

⇒ xy = 5/2      ----( 2)

Now, (x + 2y)² = x² + 4y² + 4xy     

put the value of x² + 4y² from equation (1) and the value of xy from equation (2),

⇒ (x + 2y)2 = (9 + 4xy) + 4× 5/2   

⇒( 9+ 4 × 5/2 ) + 10

⇒ (19 +10) = 29.

Hence, the value is 29.

GIVEN:

$a^2 + b^2 + \frac{1}{a^2} + \frac{1}{b^2} = 4$

FORMULA USED:

(a - b)² = a² + b² - 2ab                   

where a = 1^st term, b = 2^nd term

CALCULATION:

The given equation  is $a^2 + b^2 + \frac{1}{a^2} + \frac{1}{b^2} = 4$ 

the equation can be rearranged as,

⇒ $(a^2 + \frac{1}{a^2} -2 )+( b^2 + \frac{1}{b^2} -2) = 0.$ 

⇒ $(a^2 + \frac{1}{a^2} - 2.a^2.\frac{1}{a^2}) + (b^2 +\frac{1}{b^2} -2.b^2.\frac{1}{b^2})$ = 0.   Now, this is in the form of $a^2 - b^2 -2.a.b.$  

⇒ $( a- \frac{1}{a})^2 + (b -\frac{1}{b})^2 = 0.$ 

Hence,  $( a - \frac{1}{a})^2 = 0.$  and $( b -\frac{1}{b})^2 = 0.$         

(as they are in the square form, hence, both individuals have to be zero, to satisfy the equation).

Now, $( a - \frac{1}{a})^2 = 0.$

⇒ a = 1/a 

⇒ a² = 1 so, a⁴ = 1  

$( b -\frac{1}{b})^2 = 0.$

⇒ $b^2 =1$  so, b⁴ = 1

Now, $( a^4 + b^4)$ = (1+ 1) = 2.

Hence, the value is 2.

GIVEN:

die is thrown = 1000 times

CONCEPT USED:

Frequency = no. of times  a particular outcome appears

CALCULATION:

Number appearing on the dice greater than or equal to five i.e. N( 5 and  6)

⇒ ( frequency of outcome 5 + frequency of outcome 6)

⇒  (175 +190) =  365.

Hence, 365 times the number which is equal to 5 or greater than 5 appears.

GIVEN:

 Average of  age of 36 students   = 14 years

Average of teacher  and students = 15 years

FORMULA USED:

Average = sum of values/ number of values

CALCULATION:

⇒ Sum of students / 36 = 14 

⇒ sum of age of students = ( 36 × 14 ) = 504.

⇒ ( sum of students + teacher) /37 = 15

⇒ sum of age of students and teacher = ( 37× 15) = 555

⇒ Age of teacher = ( sum of age of students and teacher) - sum of age of student  = (555- 504) = 51 years.

Hence, the teacher is 51 year old.

GIVEN:

In triangle ABC, DE// BC

AD/.DB = 9/8 

CONCEPT USED:

Basic Proportionality Theorem (BPT) = If line DE is parallel to side BC of triangle ABC that intersects the other sides into two points, line DE divides AB and AC in proportion.

AD/AB = AE/AC = DE/BC

CALCULATION:

In triangle ABC, AD/DB = 9/8

⇒ AD/AB = DE/BC 

⇒ 9/(9+8) = DE/BC 

⇒ 9/17 = DE/BC

Hence, DE :BC = 9:17.

GIVEN:

Manoj fetches 5 litres of water in = 4 minutes

Swathi fetches 4 litres of water in = 5 minutes 

FORMULA USED:

Efficiency = Total work / Time taken to do work

CALCULATION:

Efficiency of Manoj = Total unit / time taken = 5/4 litres/min

Efficiency of Swathi = Total unit/ time taken = 4/5 =  litres/min

⇒ Efficiency of Manoj and Swathi  together

⇒  ( 5/4 +4/5) litres/min

⇒ 41/20 litres/min

Total unit =  205 litres

⇒ Time taken =  Total unit/Total efficiency

⇒ = 205÷( 41/20)

⇒  205 × $20\over 41$  = 100 minutes.

Hence, time taken together is 100 minutes.

The correct answer is Ilaiyaraaja.

Key Points

• R. Gnanathesikan, known as Ilaiyaraaja, has been conferred the prestigious title of ‘Maestro’ by London’s Royal Philharmonic Orchestra, with whom he had been the only Asian to have composed a full symphony as on 6^th March 2022.
• He is an Indian film composer, conductor-arranger, singer, and lyricist who works in the Indian film industry, predominantly in Tamil cinema in addition to Telugu cinema.
• He is a nominated Member of Parliament in the Rajya Sabha since July 2022.
• Music legend Ilaiyaraaja stands out with his phenomenal achievements bringing in structural changes within the Tamil film world.

Additional Information

• Allah Rakha Rahman is an Indian film composer, record producer, singer, and songwriter who works predominantly in Indian cinema and occasionally international cinema. In 2010, the Indian government awarded him the Padma Bhushan, the nation's third-highest civilian award.
• Devi Sri Prasad is an Indian film composer, lyricist, singer-songwriter, and performer. Popularly known by his initials DSP, he is best known for his work in Telugu films. He also worked in a few Tamil films.
• Gopi Sundar C. S. is an Indian music director, programmer, playback singer, songwriter, actor, and performer who works prominently in Malayalam, Telugu, and Tamil film industries.

The correct answer is Reserve Bank of India.

Key Points

• Cash Reserve Ratio (CRR) is the share of a bank’s total deposit that is mandated by the Reserve Bank of India (RBI) to be maintained with the latter as reserves in the form of liquid cash.
• The current cash reserve ratio is at 4%, this will be changed to 4.5% from May 21^st.
• Objectives of Cash Reserve Ratio:
• Cash Reserve Ratio ensures that a part of the bank’s deposit is with the Central Bank and is hence, secure.
• Another objective of CRR is to keep inflation under control. During high inflation in the economy, RBI raises the CRR to reduce the amount of money left with banks to sanction loans. It squeezes the money flow in the economy, reducing investments and bringing down inflation.

Additional Information

• The statutory Liquidity Ratio (SLR) is the proportion of liquid assets to time and demand liabilities.
• The rate of SLR is 18.00%.

The correct answer is Tokyo. 

Key Points

• The Paralympic Games or Paralympics, also known as the Games of the Paralympiad, is a periodic series of international multi-sport events involving athletes with a range of physical disabilities, including impaired muscle power, impaired passive range of movement, limb deficiency, leg length difference, short stature, hypertonia, ataxia, athetosis, vision impairment and intellectual impairment.
• There are Winter and Summer Paralympic Games, which since the 1988 Summer Olympics in Seoul, South Korea, are held almost immediately following the respective Olympic Games.
• The Paralympics has grown from a small gathering of British World War II veterans in 1948 to become one of the largest international sporting events by the early 21^st century.
• The Paralympics has grown from 400 athletes with a disability from 23 countries in Rome in 1960, where they were proposed by doctor Antonio Maglio, to 4520 athletes from 163 National Paralympic Committees at the 2020 Summer Paralympics.

Additional Information

• International Paralympic Committee (including Paralympic athletics, Paralympic swimming, Paralympic shooting, Paralympic powerlifting, Para-alpine skiing, Paralympic biathlon, Paralympic cross-country skiing, Para ice hockey, Para snowboarding).

The correct answer is RK Laxman.

Key Points

• Rasipuram Krishnaswami Laxman was an Indian cartoonist, illustrator, and humorist.
• He is best known for his creation "The Common Man" and for his daily cartoon strip, You Said It in The Times of India, which started in 1951. R. K.
• He was born on 24 October 1921, in Mysuru.
• He died on 26 January 2015, at Deenanath Mangeshkar Hospital and Research Center, Pune.
• He wrote You Said it, Maalgudi Ki Kahaniyan, The best of Laxman, and more books.

Additional Information

• Ajit Ninan is an Indian political cartoonist, best known for drawing the Centrestage series of cartoons in India, Today magazine and Ninan's World in the Times of India. Ninan lives in New Delhi, where he works for the Times of India.
• Ottupulackal Velukkuty Vijayan, commonly known as O. V. Vijayan, was an Indian author and cartoonist, who was an important figure in modern Malayalam language literature.
• Mario Miranda popularly known as Mario de Miranda was an Indian cartoonist and painter based in Loutolim in the Indian state of Goa.

The correct answer is Bhubaneswar.

Key Points

• In January 2022, in Bhubaneswar an initiative - Deaddiction, Reformation and Entrepreneurial Assistance for Making a Safe Society (Dreams) was launched to rehabilitate drug addicts.
• Drug addicts, who were involved in snatching, theft, or other property-related offence in the city, may soon get a fresh lease of life.
• The commission police have decided to facilitate their treatment in deaddiction centres, bring them to the mainstream and provide them livelihood support.
• They will initially help 50 drug addicts under their new incentives.
• Police will launch awareness campaigns in slums and educational institutes to make them free from drugs.

Additional Information

• It is to be noted here that the city police launched the DREAMS project in February this year with an aim to help the drug addicts, who were involved in snatching, theft, or other property-related offences in the city, to return to normal life.
• They were engaged in different activities like yoga, dance, and playing chess. Proper food and other facilities were provided at the deaddiction centers which helped the drug addicts to return to normalcy now.