SSC CHSL Tier-1 2021: Official Paper (Held On : 25 May 2022 Shift 2) (Previous Year Paper)

The erroneous spelling is "Informassional"

Key Points

• Let's look at the correct spelling and meaning of the word.
• Informational: 

relating to or characterized by facts about something; providing information.

• Example: I found the seminar on mental health and wellness by the clinical psychologist to be very informational.

​Hence, the correct answer is option 1.

Additional Information

• Let's look at the meaning of other words:
• Personnel: 

people employed in an organization or engaged in an organized undertaking such as military service.

• Informal: 

having a relaxed, friendly, or unofficial style, manner, or nature.

• Personal: 

belonging to or affecting a particular person rather than anyone else.

The correct answer is "carried me"

Key Points

• Let's look at the meaning of given phrasal verbs.
• carried me: to sustain or aid someone, especially during a challenging time.
• flew me: to soar or glide over someone or something
• ran me: To proceed through something very quickly or summarily.
• lift me: To pick or raise someone or something up (from some lower place or position) ​
• As per the meaning of the given words, "carried me" is the appropriate word choice for the blank.
• The implied meaning of the given sentence is that both the qualities of the speaker such as sincerity and patience sustained them through a challenging time.

The correct sentence is: My sincerity and patience carried me through all odds and problems of life.

Hence, the correct answer is option 1.

The correct answer is "narrow margin"

Key Points

• The meaning of the given idiom 'hair's breadth' is "

a very small amount or margin." (बहुत कम राशि या मार्जिन)

• We use the given idiom in a situation where we want to convey that somebody avoided or achieved something by a small margin. (हम दिए गए मुहावरे का उपयोग उस स्थिति में करते हैं जहाँ हम यह बताना चाहते हैं कि किसी ने छोटे अंतर से कुछ टाला या हासिल किया)​
• Example: My maths teacher told me that I had passed by a hair's breadth.

​Hence, the correct answer is option 3.

The correct answer is "a zealot".

Key Points:

• Let's look at the meaning of the given words:
• janissary: a devoted follower or supporter.(एक समर्पित अनुयायी या समर्थक)
• zionist: a supporter of Zionism; a person who believes in the development and protection of a Jewish nation in what is now Israel.(एक व्यक्ति जो एक यहूदी राष्ट्र के विकास और सुरक्षा में विश्वास करता है)
• zealot:  a person who has very strong opinions about something, and tries to make other people have them too(कट्टरपंथी, अति उत्साही, समर्थक)
• healer: 

a person who seeks to cure diseases or heal injuries by means other than conventional medical treatment.(घाव भरने वाला)

• As per the meaning of the given words, "a zealot​" can be the substitute for the underlined words in the given sentence.

​Hence, the correct answer is option 3.

The erroneous spelling is "Acomplishment"

Key Points

• Let's look at the correct spelling and meaning of the given word.
• Accomplishment: 

the successful achievement of a task.

• Example: The biggest accomplishment of my career as a teacher is that I was able to make a difference in the life of so many students.

​Hence, the correct answer is option 2.

Additional Information

• Let's look at the meaning of the other words:
• ​Enthusiasm: 

intense and eager enjoyment, interest, or approval.

• Convenience: 

the state of being able to proceed with something without difficulty.

• Auxiliary: 

providing supplementary or additional help and support.

• ​All the other words are spelled correctly.

The correct answer is "illegible".

Key Points

• Let's look at the correct spelling and meaning of the word.
• Illegible: 

not clear enough to be read.

• Example: His signature was illegible so the bank refused to encash the cheque.
• ​Hence, the correct answer is option 3.

The correct sentence is: Her writing is very illegible and so she loses marks in her exam.

The correct answer is "has been doing"

Key Points

• The given sentence should be in the present perfect Continuous tense.
• We need to use "has been" in the given sentence to make it the present perfect continuous tense.
• "Has" is an auxiliary verb used with the third person present tense and "been" is the past participle of "be".
• We use "has been" to describe actions that started in the past but continue to the present time.

The correct sentence is: My uncle has been doing business in Hyderabad for the last 10 years.

Hence, the correct answer is option 1.

The correct answer is "loathed".

Key Points

• Let's look at the meaning of the given words.
• loathed: feel intense dislike or disgust for. (नफरत करना)
• enhanced: intensify, increase, or further improve the quality, value, or extent of. (बढ़ा हुआ, ज़्यादा किया हुआ)
• revered: 

feel deep respect or admiration for (something)

. (परम पूजनीय)

• embraced: 

hold (someone) closely in one's arms, especially as a sign of affection. (गले से लगाना, संमिलित करना)

• As per the meaning of the given words, "loathed" is the appropriate synonym for the word mentioned in the bracket.
• Hence, the correct answer is option 1.

The complete sentence is: The party was so amazing that everyone loathed leaving it.

The correct answer is "treacherous"

Key Points

• Let's look at the meaning of the given word:
• ​Perilous: 

exposed to imminent risk of disaster or ruin.

• Let's look at the meaning of the given words:
• reliable: 

consistently good in quality or performance; able to be trusted.

• worthless: 

(of a person) having no good qualities; deserving contempt.

• adventurous: 

willing to take risks or to try out new methods, ideas, or experiences.

• treacherous: 

(of ground, water, conditions, etc.) presenting hidden or unpredictable dangers.

• As per the meaning of the given words, "treacherous**"** appropriate synonym of the word given in the brackets to fill in the blank.
• ​Example: Rajat warned the tourists, "The path ahead is treacherous, we must tread carefully".

The correct sentence is: Doing adventure sports is banned for athletes as it can be treacherous.

 

Hence, the correct answer is option 4.

The correct answer is "They renovated the library building in 2020."

Key Points

• There are a few things to keep in mind when changing a sentence from passive to active voice.
• In active voice, the subject or doer of the action is highlighted.
• In the given sentence, we will begin the sentence with the subject pronoun "they".
• The subject in passive voice becomes the object in active voice.
• In the given sentence, the "library building" becomes the object in the active voice.
• The given sentence is in the simple past tense. So we see that the past tense of "to be" which is "was" is used in the passive voice.
• We can avoid the usage of "to be" construction in the form of "was" for the active voice.
• The tense of the given sentence will still be in the simple past tense in active voice.

Hence, the correct answer is option 3.

The correct answer is "Have you uploaded the assignment?"

Key Points

• There are a few things to keep in mind when changing a sentence from passive to active voice:
• The subject is highlighted in the active voice and it comes at the beginning of the sentence.
• In the given sentence, the subject pronoun "you" will come to the beginning of the sentence.
• We usually use the helping verb "have" with the subject pronoun "you" in a sentence.
• We omit the use of "to be" constructions such as "been" which is the past participle of 'be' in active voice sentences.

Hence, the correct answer is option 2.

The correct answer is "I sip coffee."

Key Points

• There are a few things to keep in mind when changing a sentence from passive to active voice:
• Active voice highlights the subject of the sentence. The object in the passive voice becomes the subject of the active voice.
• The subject pronoun "me" at the end of the passive voice will change to "I" at the beginning of the active voice sentence.
• The subject in passive voice becomes the object in active voice.
• In the given sentence, "Coffee" is the object of the sentence in active voice.
• The past participle form of the verb "sipped"(V₃) in the passive voice will change to the base form of the verb "sip"(V₁).
• We don't need to use the preposition "by" in the active voice. It is used to denote the agent in the passive voice sentence.
• We also don't need the helping verb "is" in the given sentence when changing to active voice.
• The tense of the given sentence is in the simple past tense.

Hence, the correct answer is option 2.

The erroneous spelling is "Priviledge"

Key Points

• Let's look at the correct spelling and meaning of the word.
• Privilege: 

a special right, advantage, or immunity granted or available only to a particular person or group.

• Example: There are certain privileges that public servants enjoy but it also comes with a set of responsibilities.

​Hence, the correct answer is option 3.

Additional Information

• Let's look at the meaning of other words.
• ​Occurrence: 

an incident or event.

• Accommodation: 

a convenient arrangement; a settlement or compromise.

• Erroneous: 

wrong; incorrect.

• All the other words are spelled correctly.

The correct answer is "conservative".

Key Points

• Let's look at the meaning of the given word:
• Liberal: respecting and allowing many different types of beliefs or behaviour. 
• For example: Her parents were far more liberal than mine.
• Conservative: 

averse to change or innovation and holding traditional values.

• For example:  Old people are usually more conservative than young people.
• As per the meaning of the given words, "conservative" is the antonym of the highlighted word

Hence, the correct answer is "Option 2". 

Additional Information

• • Central: 

at the point or in the area that is in the middle of something.

• Hysterical: affected by or deriving from wildly uncontrolled emotion.
• Ineffectual: 

not producing any significant or desired effect.

The correct answer is "indulged, monetary"

Key Points

• Let's look at the meaning of the given words:
• honoured: 

regarded with great respect.

• professional: 

engaged in a specified activity as one's main paid occupation rather than as a pastime.

• Indulged: 

become involved in (an activity, typically one that is undesirable or disapproved of).

• monetary: 

relating to money or currency.

• regulated: 

control (something, especially a business activity) by means of rules and regulations.

• personal: 

belonging to or affecting a particular person rather than anyone else.

• thrived: 

prosper; flourish.

• devotional:

 used in religious worship.

• As per the meaning of the given words, "indulged" and "monetary" is the appropriate word choice for the respective blanks.
• The meaning of the given sentence is that manpower exporters and overseas recruiters engaged in illegal business for financial gains.

Hence, the correct answer is option 2.

The correct answer is "Bribe someone"

 Key Points

• ​The meaning of the given idiom is "give** someone money in exchange for a favor".** (किसी को रिश्वत देना)
• We use the given idiom in a situation where someone is offering a bribe to get things done in their favor. (हम दिए गए मुहावरे का उपयोग उस स्थिति में करते हैं जब कोई व्यक्ति अपने पक्ष में काम करवाने के लिए रिश्वत की पेशकश कर रहा हो)
• Example: Randhir said, "I want to win the title of prom king desperately, I am ready to grease someone's palm to win that title."
• ​Hence, the correct answer is option 3.

The erroneous spelling is "Embberassment"

Key Points

• Let's look at the correct spelling and meaning of the word.
• Embarrassment: a feeling of self-consciousness, shame, or awkwardness.
• Example: Her daughter's tantrums at the party caused her a lot of embarrassment in front of the guests.

Hence, the correct answer is option 4.

Additional Information

• Let's look at the meaning of the other words.
• ​Consciousness: 

the state of being aware of and responsive to one's surroundings.

• E.g.- The medication caused her to enter an altered state of consciousness.
• Encyclopedia: 

a book or set of books giving information on many subjects or on many aspects of one subject, and typically arranged alphabetically.

• E.g.- Meg liked his quiet manners and considered him a walking encyclopedia of useful knowledge.
• Euphemism: 

a mild or indirect word or expression substituted for one considered to be too harsh or blunt when referring to something unpleasant or embarrassing.

• E.g. The term 'early retirement' is nearly always a euphemism for redundancy nowadays.
• All the other words are spelled correctly.

The correct answer is "more educated".

Key Points

• In the given sentence we need to use the "more" in the comparative form to make the sentence grammatically correct.
• We need to use the comparative form as we are comparing the subject's education to her sister and saying that subject is more educated.
• We use the comparative form "more" with an adjective.
• In the given sentence, we use the comparative form more with the adjective "educated" in the given sentence.

The correct sentence is: She is more educated than her sister.

Hence, the correct answer is option 2.

The correct answer is "BDAC"

Key Points

• Let's look at the correct sequence of the given passage:
• Statement B is the opening sentence of the given passage as it begins by recalling an event from the author's past. The author mentions that he was fifteen at the time when he entered Morehouse College. He also mentions his ancestors studied in the same college. So Morehouse has had three generations of Kings.
• Statement D is the second sentence of the passage, as the author begins by describing his experience when he entered college. He states though he had been one of the top students in high school, he was still reading at only an eighth-grade level.
• Statement A is the third sentence of the passage as the author continues the story and adds more details from that time. He mentions that he was a young fellow at Morehouse.
• Statement C is the last sentence of the passage as he talks about the professors at the college. He states that the professors were not caught up in the clutches of state funds and could teach what they wanted with academic freedom and encouraged us in a positive quest for a solution to racial ills.

Hence, the correct sequence is BDAC.

The correct sentence is "how lucky I am to have".

Key Points

• In the given sentence, the position of the adjective "lucky" in the given sentence is incorrect.
• In order to make a coherent meaning, we need to use the adjective "lucky" before "I am" in the given sentence.
• The adjective "lucky" is modifying the meaning of the sentence.
• The implied meaning of the sentence is that the speaker is expressing his/her luck in having such wonderful sisters.

Hence, the correct answer is option 1.

The correct answer is "alone".

Key Points

• Let's look at the meaning of the given words:
• rather:  used as an adverb to indicate that something is true to a fairly great extent.
• change: 

make (someone or something) different; alter or modify.

• apart: (of two or more people or things) separated by a specified distance in time or space.
• alone: can be used as both adjective or adverb. It is used after a noun or pronoun to show that the person or thing mentioned is the only one.
• ​As per the meaning of the given words, "alone" is the appropriate word choice for the blank.
• The implied meaning of the given sentence is that people do yoga not just for fitness reasons but for union soul and body as well.

​Hence, the correct answer is option 1.

The complete passage is: Yoga is a personal journey for everyone as now most people are turning to it, not for fitness (1) alone, but for the union of both, body and soul. Yoga is an ancient practice that (2) originated in India. It involves movement, meditation and breathing (3) techniques to promote mental and physical well-being. There are many styles of yoga. A person should (4) choose a style based on their goals and fitness level. If yoga and pranayam are complemented with other forms of spiritual practice to purify the mental body and other bodies, then a person can achieve rapid spiritual progress in his lifetime. Thus a person can make progress to achieve the purpose of life which is to (5) merge with God.

The correct answer is "originated"

Key Points

• Let's look at the meaning of the given words.
• settled: 

resolve or reach an agreement about (an argument or problem).

• came: 

arrive at a specified place. Past tense of come.

• originated: 

have a specified beginning.

• involved: 

be or become occupied or engrossed in something.

• As per the meaning of the given words, "originated" is the appropriate word choice for the blank.
• The implied meaning of the given sentence is that the ancient practice of yoga started in India.

Hence, the correct answer is option 3.

The complete passage is: Yoga is a personal journey for everyone as now most people are turning to it, not for fitness (1) alone, but for the union of both, body and soul. Yoga is an ancient practice that (2) originated in India. It involves movement, meditation and breathing (3) techniques to promote mental and physical well-being. There are many styles of yoga. A person should (4) choose a style based on their goals and fitness level. If yoga and pranayam are complemented with other forms of spiritual practice to purify the mental body and other bodies, then a person can achieve rapid spiritual progress in his lifetime. Thus a person can make progress to achieve the purpose of life which is to (5) merge with God.

The correct answer is "techniques".

Key Points

• Let's look at the meaning of the given words:
• senses: 

a faculty by which the body perceives an external stimulus; one of the faculties of sight, smell, hearing, taste, and touch.

• techniques: 

a skillful or efficient way of doing or achieving something.

• phases: 

a distinct period or stage in a series of events or a process of change or development.

• pursuit: 

the action of pursuing someone or something.

• As per the meaning of the given words, "techniques" is the appropriate word choice for the blank.
• The implied meaning of the given sentence is that yoga involves skillful way of movement, meditation, and breathing to promote mental and physical well-being.

Hence, the correct answer is option 2.

The complete passage is: Yoga is a personal journey for everyone as now most people are turning to it, not for fitness (1) alone, but for the union of both, body and soul. Yoga is an ancient practice that (2) originated in India. It involves movement, meditation and breathing (3) techniques to promote mental and physical well-being. There are many styles of yoga. A person should (4) choose a style based on their goals and fitness level. If yoga and pranayam are complemented with other forms of spiritual practice to purify the mental body and other bodies, then a person can achieve rapid spiritual progress in his lifetime. Thus a person can make progress to achieve the purpose of life which is to (5) merge with God.

The correct answer is "choose".

Key Points

• Let's look at the meaning of the given words:
• choose: 

pick out (someone or something) as the best or most appropriate of two or more alternatives.

• familiarise: 

give (someone) knowledge or understanding of something.

• make: 

form (something) by putting parts together or combining substances; create.

• strike: 

hit forcibly and deliberately with one's hand or a weapon or other implement.

• As per the meaning of the given words, "choose" is the appropriate word choice for the blank.
• The implied meaning is that people should take up yoga based on their goals and fitness levels.

Hence, the correct answer is option 1.

The complete passage is: Yoga is a personal journey for everyone as now most people are turning to it, not for fitness (1) alone, but for the union of both, body and soul. Yoga is an ancient practice that (2) originated in India. It involves movement, meditation and breathing (3) techniques to promote mental and physical well-being. There are many styles of yoga. A person should (4) choose a style based on their goals and fitness level. If yoga and pranayam are complemented with other forms of spiritual practice to purify the mental body and other bodies, then a person can achieve rapid spiritual progress in his lifetime. Thus a person can make progress to achieve the purpose of life which is to (5) merge with God.

The correct answer is "merge".

Key Points

• Let's look at the meaning of the given words:
• Compete: 

strive to gain or win something by defeating or establishing superiority over others.

• Progress: 

forward or onward movement towards a destination.

• Merge: 

combine or cause to combine to form a single entity.

• Mark: a

 line, figure, or symbol made as an indication or record of something.

• As per the meaning of the given words, "merge" is the appropriate word choice for the blank.
• The implied meaning of the given sentence is that when yoga and pranayam are complemented with other forms of spiritual practice to purify the mental body and other bodies. Thus, this will enable them to fulfill the purpose of life which is to be one with god.

​Hence, the correct answer is option 3.

The complete passage is: Yoga is a personal journey for everyone as now most people are turning to it, not for fitness (1) alone, but for the union of both, body and soul. Yoga is an ancient practice that (2) originated in India. It involves movement, meditation and breathing (3) techniques to promote mental and physical well-being. There are many styles of yoga. A person should (4) choose a style based on their goals and fitness level. If yoga and pranayam are complemented with other forms of spiritual practice to purify the mental body and other bodies, then a person can achieve rapid spiritual progress in his lifetime. Thus a person can make progress to achieve the purpose of life which is to (5) merge with God.

The logic followed here is:

According to BODMAS Rule

 

Given equation:  41 * 2 * 36 * 6 * 57 * 7 * 4 * 3

Option 1 : Using the combination  +, −, =, ×, −, ÷, −

By BODMAS rule

41 + 2 - 36 = 6 × 57 - 7 ÷ 4 - 3

41 + 2 - 36 = 6 × 57 - 1.75 - 3

41 + 2 - 36 = 342 - 1.75 - 3

43 - 36 = 342 - 1.75 - 3

7 ≠ 337.2 ( LHS ≠ RHS )

Option 2 : Using the combination −, =, +, ×, −, +, ×

41 - 2 = 36 + 6 × 57 - 7 + 4 × 3

41 - 2= 36 + 342 - 7 + 12

41 - 2 = 390 - 7

39 ≠ 383 ( LHS ≠ RHS )

Option 3: Using the combination ×, +, ÷, −, =, ×, +

41 × 2 + 36 ÷ 6 - 57 = 7 × 4 + 3

41 × 2 + 6 - 57 = 7 × 4 + 3

82 + 6 - 57 = 28 + 3

88 - 57 = 31

31 = 31 ( LHS = RHS )

Option 4: Using the combination −, +, ×, −, =, +, ×

41 - 2 + 36 × 6 - 57 = 7 + 4 × 3

41 - 2 + 216 - 57 = 7 + 12

257 - 2 - 57 = 19

257 - 59 = 19

198 ≠ 19 ( LHS ≠ RHS )

Hence, ×, +, ÷, −, =, ×, + is the correct answer.

The logic followed here is-

According to BODMAS rule:

 

Given equation 78 * 3 * 14 * 80 * 2

Option 1: Using combination by BODMAS rule  +, ÷, =, ×

78 + 3 ÷ 14 = 80 × 2

78 + 0.2 = 80 × 2

78 + 0.2 = 160

78.2 ≠ 160 ( LHS ≠ RHS )

Option 2 : Using combination by BODMAS rule  +, ×, =, ÷

78 + 3 × 14 = 80 ÷ 2

78 + 3 × 14 = 40

78 + 42 = 40

120 ≠ 40 ( LHS ≠ RHS )

Option 3 : Using combination by BODMAS rule  ÷, +, =, ÷

78 ÷ 3 + 14 = 80 ÷ 2

26 + 14 = 40

40 = 40 ( LHS = RHS )

Option 4 : Using combination by BODMAS rule  −, =, +, ×

78 - 3 = 14 + 80 × 2

78 - 3 = 14 + 160

78 - 3 = 174

75 ≠ 174 ( LHS ≠ RHS )

Hence,  ÷, +, =, ÷  is the correct answer.

Given :

Bat and Ant are common in both dices. So, remaining two will be opposite face.

From the both dices :

 

Thus, Dog opposite to Fog

Hence, Fog is the correct answer.

Explanation:

The family tree diagram is shown below :

According to question

The blood relation diagram as follows

It is clear from above that lady is the Sister’s daughter of Vijay.

Hence, Sister’s daughter is the correct answer.

The logic followed here is:

Hence, 43 is the correct answer.

The logic followed here is**:**

In a mirror image left changes to right and the right changes to left vice-versa

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

Hence,

is the correct answer.

The logic followed here is:

According to BODMAS rule

 

Given equation: 25 * 5 * 10 * 2 * 8 * 11

Option 1: ÷, ×, +, –, =

Using the combination by BODMAS rule

25 ÷ 5 × 10 + 2 - 8 = 11

5 × 10 + 2 - 8 = 11

50 + 2 - 8 = 11

52 - 8 = 11

44 ≠ 11 ( LHS ≠ RHS)

Option 2: ×, ÷, –, +, =

using the combination by BODMAS rule

25 × 5 ÷ 10 - 2 + 8 = 11

25 × 0.5 - 2 + 8 = 11

12.5 - 2 + 8 = 11

20.5 - 2 =11

18.5 ≠ 11 ( LHS ≠ RHS )

Option 3 : –, +, ÷, ×, =

Using the combination by BODMAS rule

25 - 5 + 10 ÷ 2 × 8 = 11 

25 - 5 + 5 × 8 = 11 

25 - 5  + 40 = 11

65 - 5 = 11

60 ≠ 11 ( LHS ≠ RHS )

Option 4 : ÷, –, +, ×, =

using the combination by BODMAS rule

25 ÷ 5 - 10 + 2 × 8 = 11

5 - 10 + 2 × 8 = 11

5 - 10 + 16 = 11

21 - 10 = 11

11 = 11 ( LHS = RHS )

Hence, ÷, –, +, ×, = is the correct answer.

The logic followed here is:

3 march 2020 was Tuesday

First of all we will check is 2020 is a leap year 2020/4

so, 2020 is a leap year therefore February has 29 days.

Now, we will check days between 4 Feb 2020 - 3 march 2020

i.e. 26 + 3 odd days

   = 29/7( because week has 7 days )

remainder is 1 by dividing it

so we will -1 in Tuesday i.e. Monday

therefore 3 Feb 2020 is Monday

but, we have to find 3 Feb 2019

then we will do -1 in Monday

so, on 3 February 2019 is Sunday

Hence, Sunday is the correct answer.

The logic followed here is

The pattern followed is

Hence, ORLM is the correct answer.

The paper when unfolded will be shown as below:

Hence,

'option 2' is the correct answer.

Given:

Explanation: If two dice have the same face value in the given image then their clockwise or anti-clockwise numbers are known as opposite numbers in dice.

In first and second dice Bat and Cat are common in both dices.

*Thus, Egg is the opposite of Fog

Hence, Egg is the correct answer.

The logic followed here is:

The positional value table is as follows:

'HISTORY' is written as ‘SRHGLIB’ 

'RECORD’ is written as ’IVXLIW’

ARCHIEVE is written as ZIXSREV 

Hence, ZIXSREV is the correct answer.

The correct answer is option 1) CAZ.

SOLUTION:

The pattern followed here is :

Hence the answer is CAZ.

The logic followed here is:

The difference between the numbers is the multiple of 12 such that the difference between first two digit is 12 and the difference between last two digits is 48.

Therefore the difference between 2^nd and 3^rd digit should be 24 and the 3^rd and 4^th should be 36.

Which makes the missing number 92.

Hence the correct answer is 92.

The logic followed here is;

Here MN is the mirror.

The image on the right is the mirror image.

Now comparing the image with the options we get, option 4. 

Hence option 4) in correct.

The pattern in the given set is :

Quotient of (First term/second term) + second term = Third term 

Quotient of (75/25) + 25 = 28

 3 + 25 = 28

Quotient of (136/34) + 34 = 38

4 + 34 = 38

Similarly,

Let's apply and check in option 1 (27, 9, 15) ;

Quotient of (27/9) + 9 = 15

3 + 9 = 15

12 = 15 -- Incorrect 

Let's apply and check in option 2 (45, 9, 12) ;

Quotient of (45/9) + 9 = 12

5 + 9 = 12

14 = 12 -- Incorrect 

Let's apply and check in option 3 (55, 5, 11) ;

Quotient of (55/5) + 5 = 11

11 + 5 = 11 

16 = 11 -- Incorrect 

Let's apply and check in option 4 (105, 35, 38) ;

Quotient of (105/35) + 35​ = 38 

3 + 35 = 38 

38 = 38 -- Correct  

Hence the correct answer is (105, 35, 38).

The positional value table is as follows:

The pattern followed here is:

  AND

Now the given word can be coded as,

Hence the answer is RMYCT.

The logic followed here is:

Let's try each option and solve the equations we get,

Option 1) +, ×, =, ÷

96 + 6 - 24 = 49 ÷ 25

96 + 6 - 24 = 1.96

102 - 24 = 1.96

78 ≠ 1.96

78 not equals to 1.96 therefore this option is incorrect.

Option 2) ÷, −, =, +

96 ÷ 6 - 24 = 49 + 25

16 - 24 = 49 + 25

16 - 24 = 74 

-8 ≠ 74

-8 not equals to 74 therefore this option is incorrect.

Option 3) −, +, ×, =

96 - 6 + 24 × 49 = 25

96 - 6 + 1176 = 25

96 - 1182 = 25

-1086 ≠ 25 

-1086 not equals to 25 therefore this option is incorrect.

Option 4) ×, ÷, =, −

96 × 6 ÷ 24 = 49 - 25

96 × 0.25  = 49 - 25 

24 = 49 - 25 

24 = 24

24 is equal to 24 therefore this option is correct.

Hence the correct is ×, ÷, =, −

The logic followed here is:

Let's try each option and solve the equations we get,

Option 1) +, ÷,–,×, =

57 + 35 ÷ 7 - 14 × 2 = 34 

57 + 5 - 14  × 2  = 34

57 + 5 - 28 = 34

62 - 28 = 34 

34 = 34

34 is equal to 34 therefore this option is correct.

Option 2) ×, +, ÷,–, =

57 × 35 + 7 ÷ 14 - 2 = 34 

57 × 35 + 0.5 - 2 = 34

1995 + 0.5 - 2 = 34

1995.5 - 2 = 34

1993.5 ≠ 34 

1993.5 not equals to 34 therefore this option is incorrect.

Option 3) –,÷,+,×, =

57 - 35 ÷ 7 + 14 × 2 = 34 

57 - 5 + 14 × 2 = 34

57 - 5 + 28 = 34

85 - 5 = 34 

80 ≠ 34

80 not equals to 34 therefore this option is incorrect.

Option 4) +,–, ×,÷, =

57 + 35 - 7 × 14 ÷ 2 = 34 

57 + 35 - 7 × 7 = 34 

57 + 35 - 49 = 34

92 - 49 = 34 

43 ≠ 34

43 is not equal to 34 therefore this option is incorrect.

Hence the correct is option 1) +, ÷,–,×, =

The pattern in the given set is :

(First term × 7) - 3 = Second term

(Second term × 3) + 7 = Third term 

Let's apply and check in the given sets ;

First row- 6,39, 124

(First term × 7) - 3 = Second term                  (Second term × 3) + 7 = Third term

(6 × 7) – 3 = 39                                                  (39 × 3) + 7 = 124

(42) – 3 = 39                                                       117 + 7 = 124

39 = 39                                                                124 = 124

Third row- 11, 74, 229

(First term × 7) - 3 = Second term                  (Second term × 3) + 7 = Third term

(11 × 7) – 3 = 74                                                 (74 × 3) + 7 = 229

(77) – 3 = 74                                                        222 + 7 = 229

74 = 74                                                                 229 = 229

Now applying the pattern in second row- 8 , 53, ?

(First term × 7) - 3 = Second term                   (Second term × 3) + 7 = Third term

(8 × 7) – 3 = 53                                                    (53 × 3) + 7 = Third term

(56) – 3 = 53                                                         159 + 7 = Third term

53 = 53                                                                   166 = Third term

Hence the correct answer is 166.

The pattern is :

(first digit × second digit × 5) = Third digit 

Let's apply and check in the first row,

3 × 2 × 5 = 30

6 × 5 = 30

30 = 30 

Let's apply and check in the second row,

7 × 5 × 5 = 175

35 × 5 = 175

175 = 175 

Let's apply and check in the first row,

4 × 6 × 5 = Third digit 

24 × 5 = Third digit 

120 = Third digit 

Hence the correct answer is 120.

The pattern in the code is :

First term and second term,

Third term and fourth term,

Fifth term and sixth term, 

Hence the correct answer is VOAFLR.

The logic followed here is:

The relation between 1^st and 2^nd term is that its first and last characters are interchanged,

The relation between 3^rd and 4^th term is that its first and last characters are interchanged,

Therefore the relation between 3^rd and 4^th term is that its first and last characters are interchanged, and we get 

Hence the correct answer is BAT.

Let's understand the relationship between the classes;

King, father, queen 

• Some kings can be fathers.
• A queen is a female.

Combining both the facts we get, 

This diagram is same as the option 2).

Hence the correct answer is option 2).

In order to get the complete unfolded pattern we have to unfold the paper one by one in the order it was folded,

Here we get the completely unfolded paper and the pattern on it and the pattern matches with option 3.

Hence the correct answer is option 3).

Given:

Ratio of students playing cricket to those playing football is 27 : 13 and

Ratio of students playing football to those playing hockey is 26 : 14.

Total no. of students is 470

Calculations:

Ratio of students playing cricket, football and hockey respectively is 27 × 26 : 26 × 13 : 13 × 14 

⇒ 702 : 338: 182

⇒ 351: 169 : 91

⇒ 27 : 13 : 7

Now, according to the question, 

(27 + 13 + 7)k = 470

⇒ 47 × k = 470

⇒ k = 10

Now , no. of students playing cricket = 27k = 27 × 10 = 270

Percentage required = 270/470 × 100 = 57.45% 

∴ The percentage reduired = 57.45%

Given:

Calculations:

Students scored at least 30 marks but less than 40 marks on the test

⇒ Students scored less than 40 - Students scored less than 30

⇒ 8 - 6 = 2

∴ Students scored at least 30 marks, but less than 40 marks on the test is 2.

Shortcut Trick

Given: 14 = sec θ − cos θ

Substitute 14 in the second equation: x = (sec θ − cos θ) × sec θ

⇒ x = sec² θ − (cos θ × sec θ)

⇒ x = sec² θ − 1 = tan² θ

∴ The correct answer is tan² θ.

Alternate Method

Given: sec θ − cos θ = 14 and 14 sec θ = x

Formula Used: sec θ × cos θ = 1; sec² θ − 1 = tan² θ

⇒ From the first equation, we have 14 = sec θ − cos θ

⇒ Substitute the value of 14 in the second equation: x = (sec θ − cos θ) × sec θ

⇒ x = sec² θ − (cos θ × sec θ)

⇒ Since cos θ × sec θ = 1, we get x = sec² θ − 1

⇒ Using identity sec² θ − tan² θ = 1, x = tan² θ

∴ The correct answer is tan² θ.

Additional Information

Trigonometric Identities

Fundamental square relations: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Reciprocal Relations

The product of a trigonometric ratio and its reciprocal is always 1: sinθ × cosecθ = 1, cosθ × secθ = 1, and tanθ × cotθ = 1.

Given:

x + $\frac{1}{x}$ = - 13

Formula used:

a² + b² = (a + b)² - 2ab

Calculation:

x² + $\frac{1}{x^2}$ = (x + $\frac{1}{x}$)² - 2 × x × $\frac{1}{x}$

⇒ x² + $\frac{1}{x^2}$ = 13² - 2

⇒ x2 + $\frac{1}{x^2}$ = 167

Now,

x⁴ + $\frac{1}{x^4}$ = (x2 + $\frac{1}{x^2}$)² - 2

⇒ (167)² -2

⇒ 27889 - 2 = 27887

⇒ x⁴ + $\frac{1}{x^4}$ = 27887

∴ The value of x4 + $\frac{1}{x^4}$ = 27887**.**

Shortcut TrickIf  x + $\frac{1}{x}$ = p,

then x2 + $\frac{1}{x^2}$ = p² - 2

⇒ x + $\frac{1}{x}$ = - 13

⇒ x2 + $\frac{1}{x^2}$ = (-13)2 - 2 = 167 = k(Let)

If x2 + $\frac{1}{x^2}$ = k, 

then x⁴ + $\frac{1}{x^4}$ = k² - 2

⇒ x2 + $\frac{1}{x^2}$ = 167

⇒ x4 + $\frac{1}{x^4}$ = (167)2 - 2 

⇒ 27887

Given:

$x+\frac{1}{x}=7.5$

Formula used:

a³ + b³ = (a + b)³ - 3ab(a + b)

Calculation:

$x³+\frac{1}{x^3} =(x+\frac{1}{x})³-3×x×\frac{1}{x}(x+\frac{1}{x})$

⇒ $x³+\frac{1}{x³} = (7.5)³-3×(7.5)$

⇒ $x³+\frac{1}{x³} =421.875 -22.5 =399.37$

⇒ $x³+\frac{1}{x³} =399.37$ 

∴ option (\()1) is correct.

Given:

Previous Population(P) = 2 crores

Rate = 10%

Time = 2021 - 2018 = 3 years

Formula used:

New Population = $P(1+\frac{R}{100})$^T

Calculation:

New Population = $P(1+\frac{R}{100})$T

⇒ $20,000,000(1+\frac{10}{100})³$

⇒ $20,000,000(\frac{11}{10})³$

⇒ $20,000,000×\frac{1331}{1000}$

⇒ New Population = 26,620,000

∴ The population in 2021 is 2.662 crores.

Given: 

The successive discount are 20%, 40% and 75%.

Formula:

Successive discount = X + Y $-\frac{XY}{100}$

Where,

X = First discount

Y = Second discount

Calculation:

Successive discount = $X+Y-\frac{XY}{100}$

$20+40-\frac{(20×40)}{100}$ = 52%

Now, again

Successive discount = $X+Y-\frac{XY}{100}$

⇒ X = 52%, Y = 75%

⇒ $52+75-\frac{(52×75)}{100}$

⇒ $127-39$

⇒ $88$

∴ The single equivalent discount is 88%.

Given:

Graph representing sales of three companies in each year.

Calculations:

According to question, 

Half of the sum of sales of companies 2 and 3 together = sales of company 1

Now , in year 2015, we have

⇒ $\frac{(50+40)}{2} = 45$

Which is not equal to 30 i.e., sales of company 1 in that year.

Similarly, In the year 2016, we have

⇒ $\frac{(60+40)}{2}$ = 50

Which is exactly equal to 50 i.e., sales of company 1 in that particular year.

$\therefore$ The year in which half of the sales of 2^nd and 3^rd company is equal to sales of first company is 2016.

Shortcut Trick

Ratio of Officers : Workers = 35% : 65% = 7 : 13.

Deviation of Officer's salary from the combined average = +₹39,000.

Applying the net deviation rule: Sum of deviations = 0.

7 × (+39,000) + 13 × (Worker's deviation) = 0.

Worker's deviation = −(7 × 39,000) ÷ 13 = −₹21,000.

Total difference = Officer's surplus + Worker's deficit = 39,000 + 21,000 = ₹60,000.

∴ The correct answer is ₹60,000.

Alternate Method

Given:

Percentage of Officers = 35%

Percentage of Workers = 100% − 35% = 65%

Avg_Officer − Avg_Total = ₹39,000

Formula Used:

Weighted Average: n₁(A₁ − A_avg) = n₂(A_avg − A₂)

Calculations:

⇒ Ratio of Officers (n_O) to Workers (n_W) = 35 : 65 = 7 : 13

⇒ Let Avg_Total be A, then Avg_Officer = A + 39,000

⇒ Let Avg_Worker be A_W

⇒ 7 × (Avg_Officer − A) = 13 × (A − Avg_Worker)

⇒ 7 × (39,000) = 13 × (A − Avg_Worker)

⇒ A − Avg_Worker = (7 × 39,000) ÷ 13

⇒ A − Avg_Worker = 7 × 3,000 = 21,000

⇒ Difference = Avg_Officer − Avg_Worker

⇒ Difference = (Avg_Officer − A) + (A − Avg_Worker)

⇒ Difference = 39,000 + 21,000 = 60,000

∴ The correct answer is ₹60,000.

Additional Information

Alligation Rule for Averages

The ratio of the quantities of two groups is the inverse ratio of the differences of their individual averages from the combined average: n₁/n₂ = (A₂ − A_avg) / (A_avg − A₁).

Net Deviation Method

In any distribution, the sum of the products of the frequency and the deviation of each value from the mean is always zero: ∑ f_i(x_i − x̄) = 0.

Weighted Average Formula

The combined average of two groups is given by A_avg = (n₁A₁ + n₂A₂) / (n₁ + n₂), where n represents the number of items and A represents the average.

Given:

[7$\frac{1}{2}$ ÷ {1$\frac{1}{4}$ - $\frac{1}{2}$ (2$\frac{1}{2}$ - $\overline {\frac{1}{4} - \frac{1}{6}}$)}] ÷ ($\frac{1}{2}$ of 8$\frac{1}{3}$)

Concept used:

VBODMAS

Calculations:

 [7$\frac{1}{2}$ ÷ {1$\frac{1}{4}$ - $\frac{1}{2}$ (2$\frac{1}{2}$ - $\overline {\frac{1}{4} - \frac{1}{6}}$)}] ÷ ($\frac{1}{2}$ of 8$\frac{1}{3}$)

⇒  $[7\frac{1}{2}÷[1\frac{1}{4}-\frac{1}{2}(2\frac{1}{2}-\frac{1}{12})]÷(\frac{1}{2}of8\frac{1}{3})$

⇒ $[\frac{15}{2}÷[\frac{5}{4}-\frac{1}{2}(\frac{5}{2}-\frac{1}{12})]]÷(\frac{1}{2}×\frac{25}{3})$

⇒ $[\frac{15}{2}÷[\frac{5}{4}-\frac{1}{2}(\frac{29}{12})]]÷(\frac{1}{2}×\frac{25}{3})$

⇒ $[\frac{15}{2}÷[\frac{5}{4}-\frac{29}{24})]]÷(\frac{25}{6})$

⇒ $[\frac{15}{2}÷[\frac{1}{24}]]÷(\frac{25}{6})$

⇒ $[\frac{15}{2}\times[\frac{24}{1}]]÷(\frac{25}{6})$

⇒ $[15\times[\frac{12}{1}]]÷(\frac{25}{6})$

⇒ $180÷(\frac{25}{6})$

⇒ $180×\frac{6}{25}$ = 43.2

$\therefore$The value required is 43.2.

Shortcut Trick

Apply the Unitary Method logic: Consumption is directly proportional to Days.

Ratio of days = 18 ÷ 24 = 3/4

Consumption for 18 days = 6 kg × (3/4)

⇒ 18 ÷ 4 = 4.5 kg

∴ The correct answer is 4.5 kg.

Alternate Method

Given:

Sugar consumption for 24 days = 6 kg

Formula Used:

Consumption per day = Total Consumption ÷ Total Days

Calculations:

⇒ Consumption for 1 day = 6 ÷ 24 kg

⇒ Consumption for 1 day = 0.25 kg

⇒ Consumption for 18 days = 18 × 0.25 kg

⇒ Consumption for 18 days = 4.5 kg

∴ The correct answer is 4.5 kg.

Additional Information

Direct Proportion

When one quantity increases, the other also increases at a constant rate. Formula: x₁/y₁ = x₂/y₂.

Inverse Proportion

When one quantity increases, the other decreases. Formula: x₁ × y₁ = x₂ × y₂ (e.g., Men and Days in Time & Work).

Given:

Length = 50 m

Breadth = 35 m

Width = 2.5 m

Concept:

Volume of cuboid = length × breadth × height

Calculations:

Volume of pond =$50×35×2.5$

⇒ Volume= 4375 m³

∴ Capacity of the Pond is 4375 m³.

Given:

16 men can paint 15 walls in 45 days.

Calculations:

To paint 15 walls, 16 men take = 45 days

To paint 1 wall, 16 men will take = $\frac{45}{15}$ = 3 days

To paint 1 wall, 1 man will take = $16×3$ = 48 days

To paint 1 wall, 20 men will take = $\frac{1}{20}×48$ = $\frac{12}{5}$ days

To paint 20 walls, 20 men will take = $20×\frac{12}{5}$ = 48 days

∴ 20 men will take 48 days to paint 20 walls.

Shortcut Trick

M1 = 16, D1 = 45, W1 = 15, M2 = 20, W2 = 20

(M1 × D1)/W1 = (M2 × D2)/W2

⇒ $\frac{16 × 45}{15}$ = $\frac{20 × D2}{20}$ ⇒ 48 = D2

Given:

Cost price = Rs.6, 450

Profit = 16%

Concept:

Selling price = $\frac{(100+profit)}{100}×Cost \space price$

Calculation:

Selling price = $\frac{(100+16)}{100}×6, 450$

⇒ (116/100) × 6450

⇒ 58 ×129

∴ The Selling price is Rs. 7482​.

Given:

Winner got the votes equal to the sum of rest two candidates

Rest candidates got equal amount of votes .

Calculations:

Let the loosing candidates got x votes each 

Then, winner got 2x votes.

Now, according to question, 

2x + x + x = 1500

⇒ x = 375

⇒ Winner got 2x = 2 × 375

∴  Winner got 2x = 750 votes.

Given:

Product Price = Rs 2,700

Successive Discounts = 10% and 15%

Single Discount = 25%

Concept Used:

Discount = % of Discount × Product Price

Price After Discount = Product Price – Discount

Calculations:

For first successive discount of 10%,

⇒ Product Price $=2,700-10\% \times2,700$

⇒ Product Price $=2,700-\frac{10}{100}\times2,700$

⇒ Product Price $=2700-270$

⇒ Product Price = Rs 2,430

For second successive discount of 15%,

⇒ Product Price $=2430-15\%\times2430$

⇒ Product Price $=2430-\frac{15}{100}\times2430$

⇒ Product Price $=2430-364.50$

⇒ Product Price = Rs 2065.50

Price after single discount of 25%,

⇒ Product Price $=2700-25\%\times 2700$

⇒ Product Price $=2700-\frac{25}{100}\times2700$

⇒ Product Price $=2700-675$

⇒ Product Price = Rs 2025.00

Difference between prices after the discounts = Rs 2065.50 – Rs 2025.00

Difference between prices after the discounts = Rs 40.50

∴ The required difference between the two options is Rs 40.50

Shortcut Trick Apply the Division Algorithm: Dividend − Remainder = Divisor × Quotient. Subtract 3485 from 8675123 to get 8671638. Divide 8671638 by 33611 to find the Divisor. By unit digit check: 1 × 8 = 8, so the last digit of the divisor must be 8. ∴ The correct answer is 258.

Alternate Method Given: Dividend = 8675123 Quotient = 33611 Remainder = 3485 Formula Used: Dividend = (Divisor × Quotient) + Remainder Calculations: ⇒ 8675123 = (Divisor × 33611) + 3485 ⇒ 8675123 − 3485 = Divisor × 33611 ⇒ 8671638 = Divisor × 33611 ⇒ Divisor = 8671638 ÷ 33611 ⇒ Divisor = 258 ∴ The correct answer is 258.

Additional Information Division Algorithm It states that for any two integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < |b|. Remainder Theorem The Remainder is always less than the Divisor. If the remainder is 0, then the dividend is exactly divisible by the divisor. Unit Digit Verification In large divisions, check if (Last digit of Divisor × Last digit of Quotient) + Last digit of Remainder matches the last digit of the Dividend.

Given:

Radius = 6 cm 

∠ARB = 70°

Concept Used:

Sum of the angles of a quadrilateral is 360°

The angle between the radius and the tangent of a circle is 90°

Calculation:

⇒ The 4 points A, B, R and O make a quadrilateral

⇒ ∠RAO = ∠RBO = 90°

⇒ ∠RAO + ∠AOB + ∠RBO + ∠ARB = 360°

⇒ 90° + ∠AOB + 90° + 70° = 360°

⇒ ∠AOB = 360° – 250° = 110°

∴ The value of ∠AOB is 110°.

Given:

 

Concept Used:

Total consumption per day = Sum of all the weights of each item in kilograms

Calculation:

⇒ Total consumption per day in year 1998-2000 = 181 + 50 + 35 + 26 = 292 kg

⇒ Total consumption per day in year 2003-2005 = 167 + 44 + 39 + 17 = 267 kg

⇒ Total consumption per day in year 2008-2010 = 169 + 38 + 49 + 25 = 281 kg

⇒ Total consumption per day in year 2013-2015 = 150 + 45 + 51 + 21 = 267 kg

⇒ Total consumption per day in year 2018-2020 = 147 + 54 + 63 + 24 = 288 kg

∴ The combined consumption per day is equal for the years 2003-2005 and 2013-2015.

Given:

Surface area of cube = 96 cm²

Concept Used:

Surface area of cube = 6a²

Volume of cube = a³

Calculation:

Surface area of cube = 6a²

⇒ Putting the given value of surface area, we get

⇒ 6a² = 96

⇒ a² = $\frac{96}{6}$ = 16

⇒ a = $\sqrt{16}$ = 4 cm

Side of cube, a = 4 cm

Volume of cube = a³

⇒ a³ = 4³

⇒ 64 cm³

∴  The volume of the cube is 64cm³.

Given:

Length = 17m

Breadth = 8m

Height = 3m

Concept Used:

Total Surface area of cuboid = 2(lb + bh + hl)

Calculation:

Surface area of cuboid = 2(lb + bh + hl)

⇒ Putting the values in the formula, we get

⇒  2(17 × 8 + 8 × 3 + 3 × 17)

⇒ 2(136 + 24 + 51)

⇒ 2 × 211 = 422 m².

∴ The value of total surface area of cuboid is 422 m².

Shortcut Trick

Net deviation from the average (180) must be zero.

Monday to Saturday deviations: (−65) + (+32) + (−10) + (−15) + (+5) + (+45) = −8

To balance this −8 deviation, Sunday’s income must be 8 more than the average.

Sunday’s income = 180 + 8 = ₹188.

∴ The correct answer is ₹188.

Alternate Method

Given: Average income for 7 days = ₹180; Incomes of 6 days = ₹115, ₹212, ₹170, ₹165, ₹185, ₹225.

Formula Used: Total Sum = Average × Number of terms; Missing Value = Total Sum − Sum of given values.

⇒ Total income for the week = 180 × 7 = ₹1260

⇒ Sum of income (Mon to Sat) = 115 + 212 + 170 + 165 + 185 + 225

⇒ Sum (Mon to Sat) = ₹1072

⇒ Sunday’s income = Total week income − Sum (Mon to Sat)

⇒ Sunday’s income = 1260 − 1072 = ₹188

∴ The correct answer is ₹188.

Additional Information

Arithmetic Mean Property

The sum of the deviations of a set of values from their arithmetic mean is always zero. ∑(x_i − x̄) = 0.

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the new average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Inclusion/Exclusion Rule

If one value is added to a group, New Value = New Average + (Change in Average × Old Number of items).

Given:

Length of train = 180 m

Speed of train = 54 km/h

Concept Used:

Speed = $\frac{Distance}{Time}$

Calculation:

Firstly, we will change the value of speed from km/h to m/s.

⇒ 54 km/h = $54\times \frac{5}{18}$

⇒ 54 km/h = 15 m/s

Putting the value in the speed formula, we get

⇒ 15 m/s = $\frac{180}{Time}$

⇒ Time = $\frac{180}{15}$

⇒ Time = 12 seconds

∴ The time taken by the train to cross a man standing on the platform is 12 seconds.