SSC CHSL Tier-1 2021: Official Paper (Held On : 31 May 2022 Shift 3) (Previous Year Paper)

The correct answer is: Wish someone good luck.

Key Points

• The idiom 'Break a leg' is used for wishing someone good luck, especially before a performance.

                     ***• Example- “*Danny's family told him to “break a leg” right before he went up on stage.

• So it is clear that the most appropriate meaning of 'Break a leg' is to Wish someone good luck.

Therefore, the correct answer is option 3.

The correct answer is: Miss an opportunity

Key Points

• The idiom 'Miss the boat' means to lose an opportunity to do something by being slow to act.

              • Example- The discounted price sale ended today and I just missed the boat on making a great deal.

• So it is clear that the most appropriate meaning of 'Miss the boat' is to 'Miss an opportunity.'

​Therefore, the correct answer is option 3.

The correct answer is: Grotesque

Key Points

• Comely means pleasurably conforming to notions of good appearance, suitability, or proportion.

             • Example- She is very comely, with the beauty indigenous to this country.

• Marked option Grotesque means a very ugly or comically distorted figure or image.

             • Example- It was something grotesque, but definitely not a skeleton.

• It is clear that Comely and Grotesque are opposite in meaning.

Therefore the correct answer is option 4.

Additional Information

• Grandiloquent means speaking or expressed in a lofty style, often to the point of being pompous or bombastic.
• Gorgeous means splendidly or showily brilliant or magnificent.
• Gregarious means fond of the company of others; sociable.

The correct answer is: Prosecute.

Key Points

• Arraign means to call or bring someone before a court to answer a criminal charge.

             • Example- He was arraigned on charges of aiding and abetting terrorists.

• Marked option Prosecute means to officially accuse someone of committing an illegal act, and to bring a case against that person in a court of law.

              • Example- He was prosecuted for fraud.

• It is clear that Arraign and Prosecute are similar in meaning.

Therefore the correct answer is option 2.

Additional Information

• Arrive means reaching a place at the end of a journey or a stage in a journey.
• Persecute means harassing or annoying someone persistently.
• Arrange means organising or making plans for a future event.

The correct answer is: innovation and spark.

Key Points

• Innovation means a new method, idea, product, etc.

                 • Example- Innovation distinguishes between a leader and a follower.

• Spark means a small amount of quality or intense feeling.

                 • Example- I see a spark in you.

The complete sentence is: Many times innovation starts with the creative spark and the enduring passion of a single individual.

Hence, the correct answer is option 4.

Additional Information

• Tradition means the transmission of customs or beliefs from generation to generation.
• Lethargy means a pathological state of sleepiness or deep unresponsiveness and inactivity.
• Stagnation means a lack of activity, growth, or development.
• Determination means the process of establishing something precisely by calculation or research.
• Renovation means the act or process of repairing and improving something, especially a building.
• Dullness means a lack of interest or excitement.

The correct answer is: Rohan was treated by Alfred’s doctor for his fever.

Key Points

• When an action performed by the subject is expressed by the verb, it is an active voice.
• When the action expressed by the verb is received by the subject, it is passive voice.
• Passive voice is used when the doer of the action is not known and the focus of the sentence is on the action and not the subject.
• Rules:

1. Interchange the object and subject with each other.
2. Object of the active sentence becomes the subject of the passive sentence.
3. Change the base verb in the active sentence into the past participle ie. the third form verb in a passive sentence, preceded by (By, With, to, etc).
4. Base verbs are never used in passive voice sentences.

• ​Example-  Active: Tom changed the flat tire.

                             Passive: The tire was changed by Tom.

Therefore, the correct answer is option 4.

The correct answer is: ADCB

Key Points

• Let's look at the correct sequence of the passage.
• Statement A is the opening sentence of the passage which gives a brief introduction to the legend Birsa Munda.
• Statement D is the second sentence of the passage which says what people thought about and believed in Birsa Munda.
• Statement C is the third sentence of the passage which explains how he took all the responsibilities to save his people from trouble, and free them from the slavery of ‘dikus’.
• Statement B is the last sentence of the passage which explains the rapid popularity of Birsa Munda and how people joined him in his rebellion.

​Hence, the correct sequence is A, D, C, B

The correct passage is:  A. In 1895, a man named Birsa was seen roaming the forests and villages of Chottanagpur in Jharkhand. D. People said he had miraculous powers – he could cure all diseases and multiply grain. C. Birsa himself declared that God had appointed him to save his people from trouble, and free them from the slavery of ‘dikus’. B. Soon thousands began following Birsa, believing that he was God and had come to solve all their problems.

Therefore, the correct answer is option 3.

The correct answer is: Students are sending the flyer for the international symposium to institutes all over the country.

Key Points

• When an action performed by the subject is expressed by the verb, it is an active voice.
• When the action expressed by the verb is received by the subject, it is passive voice.
• Passive voice is used when the doer of the action is not known and the focus of the sentence is on the action and not the subject.
• Rules:

1. Interchange the object and subject with each other.
2. Object of the active sentence becomes the subject of the passive sentence.
3. Change the base verb in the active sentence into the past participle ie. the third form verb in a passive sentence, preceded by (By, With, to, etc).
4. Base verbs are never used in passive voice sentences.

• ​Example-    Active: The teacher always answers the students' questions.

                             Passive: The students' questions are always answered by the teacher.

Therefore, the correct answer is option 3.

The correct answer is: described.

Key Points

• Replace 'describe' with 'described' to make the sentence correct.
• To create a past-tense verb, we usually add –ed or –d to the base form.
• Add "-ed" to a verb to change it to the past tense.
• 'Described' is 2nd form, apparently, it is used in the past tense.
• The second form of the verb is used for a simple past form of a verb.

               • ​Example- Advertising may be described as the science of arresting human intelligence long enough to get money from it.

​Therefore, the correct answer is option 3.

Hence, the corrected sentence is: In its August 1992 issue, the highly respected British Journal of Addiction described three unusual cases of carrot dependence.

The correct answer is: Extremely happy

Key Points

• On cloud nine means being extremely happy and excited.

              • Example- He was on cloud nine after winning the competition.

• So, it is clear that the most appropriate meaning of the given idiom 'On cloud nine' is 'Extremely happy.'

Hence, the correct answer is option 3.

The correct answer is: Weaken

Key Points

• Reinforce means to strengthen by additional assistance, material, or support (सुदृढ बनाना).

                • Example- The captain sent out another squad to reinforce the troops*.***

• Marked option Weaken means make or become weaker in power, resolve, or physical strength (कमज़ोर करना/होना).

                • Example- The disease weakens the immune system.

• So, It is clear that Reinforce and Weaken are opposite in meaning.

Therefore the correct answer is option 2.

Additional Information

• Validate means to check that something is officially true and acceptable, especially in order to approve it (पुष्टि करना).
• Diverge means separate from another route and going in a different direction (दूसरे मार्ग से अलग और एक अलग दिशा में जा रहे हैं).
• Determine means to conclude or ascertain, after reasoning, observation, etc (तय करना).

The erroneous spelling is: Quear

Key Points

• The correct spelling should be 'Queer'.
• Queer (विचित्र) means strange or unusual.

                  • Example-  I had a queer feeling that something bad was about to happen.

Therefore, the correct answer is option 1 which is incorrectly spelled.

Important Points

• The rest of the options are correctly spelled.
• Antibodies (एंटीबॉडीज़): Immune system proteins targeting foreign substances.
• Brag (डींग हांकना): To boast.
• Rascal (शरारती व्यक्ति): Mischievous person.

The correct answer is: Wrangle

Key Points

• Wrangle means a dispute or argument, typically one that is long and complicated.

              • Example- He was involved in a legal wrangle with the Health Secretary.

So, it is clear that the 'Wrangle' can be used as a one-word substitute for 'To dispute angrily.'

Additional Information

• Wrench means a feeling of sadness or distress caused by one's own or another's departure.
• Wreck means destroying or severely damage of a structure, vehicle, or similar.
• Wrack is when something falls into disrepair.

Therefore, the correct answer is option 3.

The correct answer is: Essential

Key Points

• Dispensable means capable of being dispensed with or done without; not necessary or essential.

               • Example- Computers have made typewriters dispensable.

• Marked option Essential means a thing that is absolutely necessary.

               • Example- Mistakes are an essential part of education.

• So, It is clear that Dispensable and Essential are opposite in meaning.

Therefore the correct answer is option 3.

Additional Information

• Acceptable means satisfactory and able to be agreed to or approved of.
• Urgent means requiring immediate action or attention.
• Popular means liked or admired by many people or by a particular person or group.

The correct answer is: Concentratte

Key Points

• The correct spelling should be 'Concentrate.'
• Concentrate means focusing all one's attention on a particular object or activity.

                  • Example-  With his sister's music blaring in the background, it was impossible for Rahul to concentrate on his piano lesson.

Therefore, the correct answer is option 2 which is incorrectly spelled.

Important Points

• The rest of the options are correctly spelled.

The correct answer is: neither

Key Points

• Neither is used to introduce a further negative statement.
• Neither/nor are conjunctions that connect two parts of a sentence to each other.
• They must be used in parallel structures.
• Neither/nor is used when the choice is negative or the person wants to say that more than one thing is not true.

             • Example- I neither speak Spanish nor understand it.

                               It is neither an obsession nor a projection of his mind, although it certainly does compel him.

So, it is clear that the most appropriate word is 'neither'.

Therefore, the correct answer is option 2.

The correct answer is: opened the door.

Key Points

• Replace 'opens' with 'opened' to make the sentence correct.
• Add "-ed" to a verb to change it to the past tense.
• 'Opened' is 2nd form, apparently, it is used in the past tense.
• When we use 'yesterday' in a sentence, we should write it in Simple Past Tense.

               • ​Example- It rained heavily yesterday afternoon.

​Therefore, the correct answer is option 3.

Hence, the corrected sentence is: The children opened the door silently, yesterday.

The correct answer is: Appreciate.

Key Points

• Admire means regard with respect or warm approval.

               • Example- I admire him for his courage.

• Marked option Appreciate means recognising the full worth.

               • Example- I really appreciate everything you've done.

• It is clear that Admire and Appreciate are similar in meaning.

Therefore the correct answer is option 4.

Additional Information

• Neglect means the state of being uncared for.
• Admonish means advising or urging someone earnestly.
• Forget means fail to remember.

The correct answer is: Versatile.

Key Points

• Versatile means able to adapt or be adapted to many different functions or activities.

              • Example- He is a man of versatile abilities.

• So, it is clear that the 'Versatile' can be used as a one-word substitute for 'who has many skills'

Additional Information

• Vulnerable means exposed to the possibility of being attacked or harmed, either physically or emotionally.
• Innovative means introducing new ideas; original and creative in thinking.
• Fragile means easily broken or damaged.

Therefore, the correct answer is option 3.

The correct answer is: Convict.

Key Points

• Exonerate means releasing someone from a duty or obligation.

               • Example- The poor man was exonerated from the accusation of cheating.

• Marked option Convict means a person found guilty of a criminal offence and serving a sentence of imprisonment.

               • Example- The jury convicted them of fraud.

So, it is clear that 'Exonerate' and 'Convict' are opposite in meaning.

Additional Information

• Falsity means the fact of being untrue, incorrect, or insincere.
• Beliefs mean trust, faith, or confidence in someone or something.
• Difficult means characterized by or causing hardships or problems.

Therefore, the correct answer is option 2.

The correct answer is: massive.

Key Points

• Massive means exceptionally large.

              • Example- The bad harvest caused massive food shortages.

So, it is clear that the most appropriate word is 'massive'.

Additional Information

• Passive means receiving or enduring without resistance: submissive.
• Intrusive means causing disruption or annoyance through being unwelcome or uninvited.
• Conclusive means something that puts an end to arguments or that definitively proves something or ends a dispute.

Therefore, the correct answer is option 1.

The correct answer is: elegance.

Key Points

• Elegance means the quality of being graceful and stylish in appearance or manner.

              • Example- They remind us of a time when our culture was sophisticated and full of elegance and beauty.

So, it is clear that the most appropriate word is 'elegance'.

Additional Information

• Harshness means the quality of being cruel or severe.
• Masculinity means qualities or attributes regarded as characteristics of men.
• Vengeance means punishment inflicted or retribution exacted for an injury or wrong.

Therefore, the correct answer is option 4.

The correct answer is: circular

Key Points

• Circular means having the form of a circle.

               • Example- The island was originally circular in shape. 

So, it is clear that the most appropriate word is 'Circular'.

Additional Information

• Perpendicular means a straight line at an angle of 90° to a given line, plane, or surface.
• Peculiar means different to what is normal or expected; strange.
• Vertical means at right angles to a horizontal plane; in a direction, or having an alignment, such that the top is directly above the bottom.

Therefore, the correct answer is option 4.

The correct answer is: equals

Key Points

• Equals mean a person or thing that is the same as another in status or quality.

                • Example- As his adopted brothers in the war against evil, the two of them were his equals.

So, it is clear that the most appropriate word is 'equals'.

Additional Information

• Crossed means passing in an opposite or different direction.
• Unequal means not equal in quantity, size, or value.
• Conical means having the shape of a cone.

Therefore, the correct answer is option 3.

The correct answer is: expression.

Key Points

• Expression means the action of making known one's thoughts or feelings.

                • Example- the prisoners developed a dialect as an everyday means of expression.

So, it is clear that the most appropriate word is 'expression'.

Additional Information

• Depression means a persistent feeling of sadness and loss of interest.
• Inspiration means someone or something that gives you ideas for doing something
• Running means going steadily by springing steps so that both feet leave the ground for an instant in each step..

Therefore, the correct answer is option 2.

Here, we can see that number 5 is common in both the dices. 

Also, we will write the numbers in clockwise direction starting from common number. 

1st dice: 5 - 4 - 6

2nd dice: 5 - 3 - 1

 

Thus, doing so, we will get number 6 which will be opposite to number 1.

 

Hence, the number 6 will be on the face opposite to the one showing '1'.

According to the English alphabet series and its positional value, we will get,

The logic follows here is:

Hence, the answer is 'LHOK'.

Here, we are given some pattern.

Logic: As we can see the second term is the opposite of the first term.

→ Tis is written from the last letter and we get Sit.

And,

→ Tip is written from the last letter and we get Pit.

Similarly,

→ Ten is written from the last and we get Net. 

Hence, the correct answer is "Net".

Here we can see that the given paper is folded three times.

= 

 

Hence, the correct answer is "Option2"

The logic followed here is:

Logic: First number × 14 =  Second number.

1) 9 : 126 ⇒ 9 × 14 = 126

And,

2. 21 : 294 ⇒ 21 × 14 = 294

Similarly,

3. ? : 238 ⇒ ? × 14 = 238 = 238 ÷ 14 = 17

Hence, the correct answer is "17".

We will arrange the given words in alphabetical order as shown below:

4.  Abbreviation 3.  Abduct 2.  Absolutely 1.  Absorption 5.  Accurate

Hence, the correct order is "4, 3, 2, 1, 5".

The logic here is:

As we can see that all the given numbers are prime numbers.

Prime numbers are numbers which have only two factors i.e. 1 and the number itself. 

So, the next prime number after 251 will be 257.

Hence, the correct answer will be 257.

We will also use the letters and their positions as shown below:

The logic here is:

For the word SIMPLE : ISNKEL

For the word PUBLIC: UPYOCI  

Similarly for the word MINUTE: ? we have

Thus, the word IMMFET is related to the fifth term.

Hence, the correct answer is 'option 4'.

The logic followed here is:

Logic: In a row → Second number × 3.5 + First number = Third number

⇒ In row first → 6, 8, 34

⇒ 8 × 3.5 + 6 = 34

And,

⇒ In row second →  3, 2, 10

⇒ 2 × 3.5 + 3 = 10

Similarly,

⇒ In row third → 11, 18, ?

⇒ 18 × 3.5 + 11 = 74

Hence, the correct answer is "74".

Alternate MethodLogic: First number × 2 + Second number × 3 - 2 = Third Number

In row first → 6, 8, 34

= 6 × 2 + 8 × 3 - 2 = 34

In row second →  3, 2, 10

= 3 × 2 + 2 × 3 - 2 = 10

Similarly,

In row third → 11, 18, ?

= 11 × 2 + 18 × 3 - 2 = 74

Hence, the correct answer is "74".

We will arrange the given words in alphabetical order as shown below:

1.  Draft 5.  Dragon 3.  Drain 2.  Drake 4.  Drape

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

BODMAS Rule:

Given : 14 * 5 * 55 * 74 * 12 * 4 * 3

First, we will substitute each option by one by to check the answer.

1) =, +, −, ×, −, ÷

Substitute these signs, we will get,

$\Rightarrow$ 14 = 5 + 55 - 74 $\times$ 12 -  4 ÷  3

$\Rightarrow$ 14 = 5 + 55 - 74 $\times$ 12 - 1.33

$\Rightarrow$ 14 = 5 + 55 - 888 - 1.33

$\Rightarrow$ 14 $\ne$ -829.33,

2) +, −, =, −, ×, +

Substitute these signs, we will get,

$\Rightarrow$ 14 + 5 - 55 = 74 - 12 $\times$  4 + 3

$\Rightarrow$ 14 + 5 - 55 = 74 - 48 + 3

$\Rightarrow$ -36 $\ne$ -829.33

3) ×, +, −, =, ×, +

Substitute these signs, we will get,

$\Rightarrow$ 14 $\times$ 5 + 55 - 74 = 12 $\times$ 4 + 3

$\Rightarrow$ 70 + 55 - 74 = 48 + 3

$\Rightarrow$ 51 = 51

4) ×, −, =, +, −, ×

Substitute these signs, we will get,

$\Rightarrow$ 14 $\times$ 5 - 55 = 74 + 12 - 4 $\times$ 3

$\Rightarrow$ 70 - 55 = 74 + 12 - 12

$\Rightarrow$ 15 $\ne$ 74

Hence, the correct answer is "Option 3".

Here, the alphabetic order and their positions are as shown below:

The logic follows here is:

“CASTLE” is written as “BYPUNH”

And,

“DEMAND” is written as “CCJBPG”

Similarly,

“EITHER” be written as '?'

Hence, the correct answer is "DGQIGU"

The correct mirror image of the given combination when the mirror is placed at MN is as shown below:-

Detailed Explanation:- 

• The line MN is the mirror.
• The last letter '

'. So the first letter in the mirror image will be '

'. → Option 2 is eliminated.

• Again, all the letters will appear in the mirror image. → Options 3 and 4 both are also eliminated.

Hence, 'Option 1' is the correct answer.

Additional Information

• In a mirror image, Left changes to rightand theright changes to leftwheretop and bottom remain the same.
• When placement of the mirror not given, by default we will assume it in vertical direction.
• The starting letter word will be at last after the mirror image drawn with left changes to right and right changes to left.

The correct mirror image of the given combination when the mirror is placed at MN is as shown below:-

Detailed Explanation:- 

• The line MN is the mirror.
• The word '

' ends with the letter '

'. So the mirror image will start with '

'.

• The  numbers ' 

'. So the mirror image will be '

'

.

• → Options 2, 3, and 4 are eliminated.

Hence, 'Option 1' is the correct answer.

Additional Information

• In a mirror image Left changes to right and the right changes to left where top and bottom remains the same.
• When placement of mirror not given, by default we will assume it in vertical direction.
• The starting letter word will be at last after the mirror image drawn with left changes to right and right changes to left.

The logic used here is as:

5 ×  1 + 1 = 6, 

6 × 2 + 2 = 14, which is the answer

14 × 3 + 3 = 45,

45 × 4 + 4 = 184, 

184 × 5 + 5 = 925

Hence, the correct answer is "14".

The pattern followed here is:

Logic: Second number × Third number ÷ 2 = First number.

First we will check all the options.

1) (362, 13, 54) = (13 × 54) ÷ 2 = 351 ≠  362

2) (342, 19, 36) = (19 × 36) ÷ 2 = 342 = 342

3) (369, 15, 78) = (15 × 78) ÷ 2 = 585 ≠ 362

4) (398, 16, 34) = (16 × 34) ÷ 2 = 272 ≠ 362

Hence, the correct answer is "(342, 19, 36)".

The correct mirror image of the given combination when the mirror is placed at MN is as shown below:-

Detailed Explanation:- 

• The line MN is the mirror.
• The word "

"  ends with "

" . So, the mirror image will start with "

" → Option 3 is eliminated.

• The  letter  "

" is used . So, the mirror image will be "

"→ Options 1 and 2 are eliminated.

Hence, Option 4 is the correct answer.

Additional Information

• In a mirror image, the Left changes to rightand theright changes to leftwheretop and bottom remain the same.
• When placement of the mirror is not given, by default we will assume it is in the vertical direction.
• The starting letter word will be at last after the mirror image drawn with left changes to right and right changes to left.

The least possible Venn diagram is given below:

Conclusion:

1) Some apartments are flats → Does not follow → (As Some bungalows are flats and some apartments are bungalows so some apartments are flats is possible but not definite true)

2. Some flats are bungalows → Follow → (As Some bungalows are flats and so some flats are bungalows is true)

Hence, the correct answer is "Only conclusion II follows".

The logic here is:

Hence, the missing number is 164.

BODMAS rule:

Given : 16 * 4 * 8 * 10 * 2 * 52

First, we will substitute each option by one to check the answer.

1) ×, ÷, –, +, =

Substitute these signs, we will get,

$\Rightarrow$ 16 × 4 ÷ 8 - 10 + 2 = 52

$\Rightarrow$ 16 × 0.5 - 10 + 2 = 52

$\Rightarrow$ 8 - 10 + 2 = 52

$\Rightarrow$ 0 $\ne$ 52, which is not possible. This option is not true.

2) –, +, ×, ÷, =

Substitute these signs, we will get,

$\Rightarrow$ 16 - 4 + 8 × 10 ÷ 2 = 52

$\Rightarrow$ 16 - 4 + 8 × 5 = 52

$\Rightarrow$ 16 - 4 + 40 = 52

$\Rightarrow$ 52 = 52, which is possible. This option is true.

3) ÷, ×, –, +, =

Substitute these signs, we will get,

$\Rightarrow$ 16 ÷ 4 × 8 - 10 + 2 = 52

$\Rightarrow$ 4 × 8 - 10 + 2 = 52

$\Rightarrow$ 32 - 10 + 2 = 52

$\Rightarrow$ 24 $\ne$ 52, which is not possible. This option is not true.

4) ÷, ×, +, –, =

Substitute these signs, we will get,

$\Rightarrow$ 16 ÷ 4 × 8 + 10 - 2 = 52

$\Rightarrow$ 4 × 8 + 10 - 2 = 52

$\Rightarrow$ 32 + 10 - 2 = 52

$\Rightarrow$ 40 $\ne$ 52, which is not possible. This option is not true.

Thus, the correct option is "–, +, ×, ÷, =".

Hence, the correct answer is 'option 2'.

The pattern followed here is:

The logic here is:

First, we will take out the difference as :

17 - 13 = 4

24 - 17 = 7

36 - 24 = 12

55 - 36 = 19

85 - 55 = 30

128 - 85 = 43

188 - 128 = 60

So, the logic follows here is as:

17 = 13 + 4

24 = 17 + 4 + 3 (1st prime number is added)

36 = 24 + 7 + 5 (2nd prime number is added)

55 = 36 + 12 + 7 (3rd prime number is added)

85 = 55 + 19 + 11 (4th prime number is added)

128 = 85 + 30 + 13 (5th prime number is added)

188 = 128 + 43 + 17 (6th prime number is added)

Thus, we will add the last number and the difference between the last two numbers and the 7th prime number too, we will get,

188 + 60 + 19 = 267

Hence, the missing number will be 267.

Here, the alphabets and their positions are given below:

The logic follows here is as shown below:

Hence, the correct answer is "ICWB".

Here, we are given with some code of the letters and using that we need to find the answer.

So, the code of the letters are as shown below:

Form the word DIVIDE, we will get,

D = 7, I = 17, V = 43, E = 9

And, from the word SUBTRACT, we will get,

S = 37, U = 41, B = 3, T = 39, R = 35, A = 1, C = 5

Next, the code for the word ADDITION will be:

A = 1, D = 7, D = 7, I = 17, T = 39

But as we can see there is no code for the letters O and N. 

Hence, the correct code is '1 7 7 17 39 17 29 27' for the given word.

Here, we need to count the total number of triangles.

First, we need to count the small triangles.

So, we have 20 triangles.

Next, we will combine more than 2 triangles, we will get,

So, we have 4 triangles as shown in the red line.

Again, we have,

So, we have 4 triangles as shown in the yellow line.

Again, we have,

So. we have 4 triangles as shown in the yellow line.

Thus, we have a total of = 20 + 4 + 4 + 4 = 32.

Hence, we have a total of 32 triangles.

Here, we need to find the pattern to get the odd number pair.

So, we have to check the options one by one.

1. 64 : 6 $\Rightarrow \sqrt{64}$ = 8 - 2 = 6

2. 36 : 5 $\Rightarrow \sqrt{36}$ =  6 - 2 = 4 $\ne$ 5

3. 169 : 11 $\Rightarrow \sqrt{169}$ = 13 - 2 = 11

4. 196 : 12 $\Rightarrow \sqrt{196}$ = 14 - 2 = 12

The logic here is: We take the square root to the 1st term and then the answer is subtracted by 2 to get the 2nd term.

Thus, all except option 2 does not follow the pattern.

 

Hence, the number pair '36 : 5' is the odd one out.

Given:

ΔABC is similar to ΔPQR

Area of ΔABC is 64 cm2

Area of ΔPQR is 121 cm2

QR = 15.4 cm 

Concept: 

The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides & medians. 

Calculations:

According to concept:

area(ΔABC)/area(ΔPQR) = BC2/QR2

⇒ 64/121 = BC2/QR2 

⇒ √(64/121) = BC/QR

⇒ 8/11 = BC/15.4

⇒BC = (15.4 × 8)/11

⇒BC = 11.2

∴ BC = 11.2 cm

Given:

Concept used:

Weighted average = $\sum$(Rating × weightage)

Calculations:

Weighted average = $\sum$(Rating × weightage)

⇒ $\frac{8}{10}$ × 40% + $\frac{6}{10}$ × 20% + $\frac{5}{10}$ × 30% + $\frac{8}{10}$ × 10%

⇒ (0.8 × 0.4) + (0.6 × 0.2) + (0.5 × 0.3) + (0.8 × 0.1)

⇒ (0.32 + 0.12) + (0.15) + (0.08)

⇒ 0.67

∴ The Weighted average is 0.67.

Given:

Ratio of time taken by Anamika and Bani to complete work alone is 1 : 3

Time taken by Anamika is 40 days less than that of Bani to together complete the work.

Formula used:

Efficiency = Total work/Time taken

Calculation:

Let time taken by Anamika and Bani be x and 3x respectively.

Then according to the question,

x + 40 = 3x

⇒ 2x = 40

⇒ x = 20

Hence, Anamika takes 20 days and Bani takes 60 days.

Now, Anamika and Bani together do work in

⇒ $\frac{20×60}{20+60}$

⇒ 15 days.

∴ Anamika and Bani together do the work in 15 days.

Given:

3ab × (a + b)-1 × (a-1 + b-1)

Calculations:

3ab × (a + b)-1 × (a-1 + b-1)

⇒ 3ab × $\frac{1}{(a+b)}$ × $(\frac{1}{a}+\frac{1}{b})$

⇒ 3ab × $\frac{1}{(a+b)}$ × $\frac{(a+b)}{ab}$

⇒ 3

∴ The Required simplified value of 3ab × (a + b)^-1× (a^-1 + b^-1) is 3.

Given:

$x +\frac{1}{x}$= 5

Calculations:

According to question,

$3x\over2x^2 +2-5x$

On dividing both numerator and denominator by x, we get:

⇒$\frac{3}{2x+\frac{2}{x} -5}$               

⇒ $\frac{3}{2(x+\frac{1}{x})-5}$

⇒ $\frac{3}{10-5}$

⇒ $\frac{3}{5}$

∴ The value of $3x\over2x^2 +2-5x$ is $\frac{3}{5}$.

Shortcut Trick

If a sum becomes x times in T years, it becomes xⁿ times in n × T years.

Given: Sum becomes 3¹ times in 4 years (x = 3, T = 4).

To find: Time to become 81 times.

Since 81 = 3⁴, here n = 4.

Required time = n × T = 4 × 4 = 16 years.

∴ The correct answer is 16 years.

Alternate Method

Given: Sum becomes 3 times in 4 years at Compound Interest.

Formula Used: A = P(1 + r/100)^t

⇒ Case 1: 3P = P(1 + r/100)⁴

⇒ 3 = (1 + r/100)⁴ — (Equation 1)

⇒ Case 2: 81P = P(1 + r/100)^t

⇒ 81 = (1 + r/100)^t

⇒ (3)⁴ = (1 + r/100)^t

⇒ [(1 + r/100)⁴]⁴ = (1 + r/100)^t [From Eq. 1]

⇒ (1 + r/100)¹⁶ = (1 + r/100)^t

⇒ t = 16 years

∴ The correct answer is 16 years.

Additional Information

Compound Interest Formula

The amount A on a principal P for t years at rate r% compounded annually is A = P(1 + r/100)^t.

Successive Growth in CI

In compound interest, the amount grows geometrically. If a sum doubles in T years, it becomes 2² times in 2T years, 2³ times in 3T years, and so on.

Rule of 72

A quick shortcut to estimate the time required to double an investment is T ≈ 72 ÷ r, where r is the annual interest rate.

Given:

$2\frac{2}{3}+1\frac{4}{3}\times1\frac{6}{7}\div5\frac{1}{2}$

Concept used:

BODMAS

Calculations:

$2\frac{2}{3}+1\frac{4}{3}\times1\frac{6}{7}\div5\frac{1}{2}$

⇒ $\frac{8}{3}+\frac{7}{3}×\frac{13}{7}÷\frac{11}{2}$

⇒ $\frac{8}{3} + \frac{7}{3}×\frac{13}{7}×\frac{2}{11}$

⇒ $\frac{8}{3}+\frac{26}{33}$

⇒ $\frac{114}{33}$= $\frac{38}{11}$ 

⇒ $3\frac{5}{11}$

∴ The simplified value is $3\frac{5}{11}$.

Given:

Marked price of 12 pair of shoes = Rs. 7, 200

Discount = 20%

Money available = Rs. 1, 440

Formula used:

S.P = $\frac{(100-discount)}{100}$ × M.P

Calculations:

According to the concept:

S.P = $\frac{(100-20)}{100}$ × 7,200

⇒ $\frac{80}{100}$ × 7,200

⇒ Rs.5,760

S.P of 12 pair of shoes is Rs.5,760.

In Rs.1,440 , the pair of shoes can be bought

⇒ $\frac{12}{5760}$× 1440 = 3

∴ The no. of pair of shoes that can be bought at Rs. 1,440 is 3.

Given:

Ratio of the curved surface area and total surface area of a cylinder is 3 ∶ 7.

Formula used:

Curved surface area of cylinder = 2πrh

Total surface area of cylinder = 2πrh + 2πr2

Calculation:

According to question,

Curved surface area/ Total surface area= 3/7

⇒ 2πrh/(2πrh + 2πr2) = $\frac{3}{7}$

⇒ 2πrh/[2πr(h + r)] = $\frac{3}{7}$

⇒ h/(h + r) = $\frac{3}{7}$

⇒ 7h = 3h + 3r

⇒ 7h - 4h = 3r

⇒ 4h = 3r

⇒ h/r = 3/4

⇒ h : r = 3 : 4

∴ The ratio of Height and Radius of a Cylinder is 3 : 4.

Given:

The salaries of P and Q together amount to ₹1,20,000.

P spends 95% of his salary and Q 85% of his.

If their savings are the same

Calculations:

According to the question,

Let the Salary of P be 'x' and that of Q be 'y'

Salary of P + Salary of Q = Rs. 120000

P spends 95% of his salary then his savings are 5% and savings of B is 15%

Savings of P = Savings of Q

⇒ 5% of Salary = 15% of Salary

⇒ 5% × x = 15% × y

⇒ 5x = 15y

⇒ x = 3y

Now,

Salary of P + Salary of Q = Rs. 120000

⇒ x + y = Rs. 120000

⇒ 3y + y = 120000

⇒ 4y = 120000

⇒ y = 120000/4 = 30000

Now Salary of P

Salary of P + Rs. 30000 = Rs. 120000

⇒ Salary of P = Rs. 120000 - Rs. 30000

⇒ Salary of P = Rs. 90000

∴ Salary of P = Rs. 90000

Shortcut Trick⇒ 5% of P's Salary = 15% of Q's Salary

⇒ (P's Salary/Q's Salary) = 3/1

Now,

⇒ P's Salary = 3x 

⇒ Q's Salary = x 

⇒ Total = 3x + x = 4x 

⇒ 4x = 120000

⇒ x = 30000

∴ P's Salary = 3x = 3 × 30000 = 90000.

Given:

The monthly income of Manisha = ₹1,20,000

Her monthly expenditure = ₹55,000.

Next year, her income increased by 22%, and her expenditure increased by 10%.

Calculations:

According to the question,

Monthly savings of Manisha = Income - Expenditure

Savings = 120000 - 55000 = Rs. 65000

After an increment in salary by 22% and expenses by 10% then

⇒ Salary = 120000(1 + 22%)

⇒ Salary = 120000(1 + 0.22)

⇒ Salary = 120000 × 1.22 = Rs. 146400

Now Expenses = 55000(1 + 10%)

⇒ Expenses = 55000(1 + 0.10)

⇒ Expenses = 55000 × 1.10 = Rs. 60500

Now Savings after increment = Rs. 146400 - Rs. 60500 = Rs. 85900

Now for Growth in savings,

⇒ 85,900 - 65,000 = 20,900

%Increase = 20,900/65,000 × 100

⇒ 32.15%

∴ The percentage increase in her savings is 32.15%.

Given:

The Cost Price (CP) of 300 bananas at = ₹18 per dozen

The Selling Price (SP₁) of 200 bananas at = ₹24 per dozen

The Selling Price (SP₂) of remaining bananas at = ₹21 per dozen.

Concept used:

Profit% = $SP - CP\over CP$ × 100

Calculations:

According to the question,

12 banana = 1 dozen

⇒ 300 banana = 300/12 = 25 dozens

Cost Price of 25 dozens = 25 × 18 = Rs. 450

He Sold 200 bananas at Rs. 24 per dozen

⇒ 200 bananas = 200/12 = 16.66 dozens

Cost price of 16.66 dozens of bananas = 16.66 × 24

⇒ Rs. 399.84 ~ Rs. 400

He Sold 100 bananas at Rs. 21 per dozen

⇒ 100 bananas = 100/12 = 8.33 dozens

Cost price of 8.33 dozens of bananas = 8.33 × 21

⇒ Rs. 174.93 ~ Rs. 175

Net Selling Price = 400 + 175 = Rs. 575

Net Profit% = [(575 - 450)/(450)] × 100

⇒ Net Profit% = [125/450] × 100

⇒ Net Profit% = 0.2777 × 100 = 27.77% or ​​​���$27\frac{7}{9}\%$​​​

∴ ​​​His net profit percentage = 27.77% or ​​​​$27\frac{7}{9}\%$​ .

Given:

Input in year 1998 = Rs. 1200 cr.

Total output of years 1998 and 2000 = Rs. 2500 cr.

Calculations:

Let the output for year 1998 be x,

In 1998,

Ratio = input/output

⇒ 0.9 = 1200/x

⇒ x = 1200/0.9 = 4000/3 cr.

Now,

Total output = 2000 output + 1998 output

⇒ 2500 = Output + 4000/3

⇒ Output = 2500 - 4000/3

⇒ Output = (7500 - 4000)/3 = 3500/3

Now, ATQ,

In 2000,

Ratio = input/output

⇒ 1.8 = input/(3500/3)

⇒ Input = 1.8 × 3500/3

⇒ Input = 0.6 × 3500 = Rs. 2100 cr.

∴ The input of the firm in the year 2000 Rs. 2100 cr.

Given:

Concept used:

Considering 360° as 100%

Calculations:

According to the question,

Total central angle showing the share of energy, labor, and transportation cost,

⇒ Energy% + Labour% + Transportation%

⇒ (30% + 10% + 10%) of 360° 

⇒ Angle = 40% × 360° 

⇒ Angle = 4 × 36° = 144° 

∴ The total central angle is 144°.

Given:

When a certain number is multiplied by 11,

the product is a six-digit number containing only 6s

Calculations:

A six-digit number containing only 6s = 666666

Let the no. multiplied by 11 be 'x'

According to the question,

⇒ 11 × x = 666666

⇒ x = 666666/11 = 60606

∴ The number that is multiplied by 11 is 60606.

Calculations:

The maximum aggregate number of participants in all the five different subject Olympiads taken together during that year

Total aggregate of College,

⇒ (Hindi) + (English) + (Maths) + (Science) + (GK) 

Total aggregate of College A,

⇒ 110 + 98 + 130 + 100 + 182 = 632 

Total aggregate of College B,

⇒ 100 + 120 + 110 + 100 + 200 = 630

Total aggregate of College C,

⇒ 125 + 80+ + 250 + 150 + 120 = 725

Total aggregate of College D,

⇒ 103 + 122 + 160 + 200 + 130 = 715

Total aggregate of College E,

⇒ 112 + 105 + 180 + 80 + 183 = 660

∴ College C had the maximum aggregate.

Given:

Discount% on part of MP is 32% 

Credit Card Discount on part of MP is 1.2%

Tanvir paid 75% of the marked price in cash and the rest through a credit card

Calculations:

According to the question,

Payment in cash,

Payment = [(100 - 32)/100] × 75/100 × MP

⇒ 68/100 × 75/100 × MP

⇒ (68 × 75)/10000 × MP

⇒ 5100/10000 × MP

⇒ Payement = 0.51MP

Payment in card,

Payment = [(100 + 1.2)/100] × [(100 - 75)/100] × MP

⇒ 101.2/100 × 25/100 × MP

⇒ (101.2 × 25)/10000 × MP

⇒ 2530/10000 × MP

⇒ Payement = 0.235MP

Total Payment = 0.51MP  + 0.253 MP = 0.763 MP

Now, Percentage = 0.763MP/ MP × 100 = 76.3%

∴ His total final payment was 76.3%.

Given:

Length (l) is 16 m

Breadth (b) is 12 m

Height (h) is 10 m

Concept used:

Diagonal of a cuboid = √(l² + b² + h²)

Calculations:

According to the question,

Diagonal of a cuboid = √(162 + 122 + 102)

⇒ Diagonal = √(256 + 144 + 100)

⇒ Diagonal = √500

⇒ Diagonal = √(5 × 100) = 10√5 m

∴ The longest bamboo pole that can be placed in a room is 10√5 m long.

given: 

Total number of persons 8. Is

Average weight increased by 2.5 kg

Calculation:

total weight increased,

8 x 2.5 kg = 20 kg

Replaced person's weight = 45 kg

new person's weight,

(45 + 20) kg  = 65 kg

The weight of the new person is 65 kg.

Given:

The mean proportional between 6 and another number is 30

Concept used:

Mean proportion of a and b = √ab

Calculations

Let another number be 'a'

Mean proportion = √(6 × a)

⇒ 30 = √(6 × a)

Squaring both sides

⇒ 900 = 6a

⇒ a = 900/6 = 150

∴ The another no. is 150.

Given:

Distance between policeman and thief is 480 m.

Speed of the thief is 19 km/hr

Speed of the policeman is 23 km/hr,

Concept used:

Speed = Distance/Time

Calculations:

Relative speed,

⇒ 23 - 19 = 4 km/hr = 4 × 5/18 = 10/9 m/s 

Time taken by police to overtake the thief,

⇒ 480/(10/9) = 432 sec

Distance travelled by the thief in 432 sec = 432 × 19 × 5/18 

⇒ (432 × 19 × 5)/18

⇒ 41040/18 = 2280 m

∴ The thief have to run 2280 m before he is overtaken.

Given:

Wheat A at is Rs. 20.40/kg

Wheat B at is Rs. 25.50/kg

Calculations:

Let, grocer mixes x kg of Wheat A and y kg of wheat B

Total mixture (x + y) kg worth Rs.23.80 per kg

According to the question,

20.40x + 25.5y = 23.8(x + y)

⇒ 20.40x + 25.5y = 23.8x + 23.8y

⇒ 23.8x - 20.40x = 25.5y - 23.8y

⇒ x(23.8 - 20.40) = y(25.5 - 23.8) 

⇒ 3.4x = 1.7y

⇒ x/y = 1.7/3.4

⇒ x/y = 1/2 = 1 : 2

∴ The proportion of mixer is 1 : 2.

Shortcut Trick Using allegation method:

Therefor the ratio is 1 : 2.

Given:

cos2(90º – θ) – $\frac{cos(90-\theta)cos\theta}{cot\theta}$

Concept used:

cos(90 – θ) = sinθ

Calculations:

cos2(90º – θ) – \()\(\frac{cos(90-\theta)cos\theta}{cot\theta}\)

⇒ sin²θ – $\frac{sin\theta cos\theta}{cot\theta}$

⇒ sin²θ – sin²θ

⇒  0

∴ The Required simplified value is 0.

Given:

Volume of the cube is 1331 cm³ 

Concept used:

Volume of cube = (a)³ 

Diagonal of cube = √3a

Calculations:

According to the question,

⇒ Volume = (a)3 

⇒ 1331 = (a)3 

⇒ a = 11 cm

Now diagonal

⇒ Diagonal = √3a

⇒ Diagonal = 11√3 cm

∴ The length of diagonal (in cm) = 11√3 cm.

Given:

 $x^4$ + $1\over x^4$ = 14159

Formula used:

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

Calculations:

 $x^4$ + $1\over x^4$ = 14159

$\Rightarrow$ (x² +$\frac{1}{x²}$)² = 14161

$\Rightarrow$ x² + $\frac{1}{x²}$ = √14161 = 119

$\Rightarrow$ (x + $\frac{1}{x}$)² = 121

$\Rightarrow$ x + $\frac{1}{x}$ = √121 = 11

∴ x + $\frac{1}{x}$ = 11