SSC CHSL Tier-1 2021: Official Paper (Held On : 26 May 2022 Shift 2) (Previous Year Paper)

The correct answer is 'Harmony'.

Key Points

• Variance is a noun that means the fact or quality of being different, divergent, or inconsistent. (भिन्न, भिन्न या असंगत होने का तथ्य या गुण।)
• The meaning of the given options is as follows - 
• Convention - a way in which something is usually done. (एक तरीका जिसमें आमतौर पर कुछ किया जाता है।)
• Equal - having the same quantity, value, or measure as another. (समान मात्रा, मान या माप दूसरे के रूप में होना।)
• Harmony - a combination of parts into a pleasing or orderly whole; congruity. (एक मनभावन या व्यवस्थित पूरे में भागों का संयोजन; अनुरूपता।)
• Intellectual -   relating to the ability to understand things and think intelligently (चीजों को समझने और समझदारी से सोचने की क्षमता से संबंधित)
• From the above meanings, it is evident that harmony is the correct antonym for the word variance.
• Hence, option 3 is the correct answer.

The correct answer is 'motivated'.

Key Points 

• Inclined means to be favourably disposed towards or willing to do something. (कुछ करने के लिए अनुकूल या इच्छुक होना)
• The meaning of the given options are as follows - 
• struggled - make forceful or violent efforts to get free of restraint or constriction. (संघर्ष किया)
• mystified - utterly bewilder or perplex (someone). (किसी को पूरी तरह से भ्रमित करना)
• motivated - cause (someone) to have interest in or enthusiasm for something. (प्रेरित)
• declined - politely refuse (an invitation or offer). (अस्वीकृत)
• From the above meanings it is evident that motivated is the correct synonym for the word inclined.
• Hence, option 3 is the correct answer.

The correct answer is 'harder than'.

Key Points

• There is an error in the adjective usage in the underlined part of the given sentence.
• There is a comparison happening in the sentence between the work done by an individual and the work done by others.
• To make it correct we need to substitute it with the correct comparative adjective form of hard.
• Adjectives with two syllables can form the comparative either by adding -er or by preceding the adjective with more.
• So, harder is the correct comparative degree of the adjective for the given sentence.
• So, either option 1 or option 3 is the correct substitute.
• But the given sentence has two clauses - The independent clause 'One should work hard' and the dependent clause 'other to succeed'.
• We need to join the two parts with a conjunction.
• Than is a conjunction while to is a preposition.
• Hence, option 1 or harder than is the most appropriate option that can substitute the underlined segment in the given sentence.

Correct sentence - One should work harder than others to succeed.

The correct answer is 'GB Shaw wrote Pygmalion.'

Key Points

• The given sentence is in passive voice. As per the question we have to change it into active voice.
• The structure of the given sentence is as follows:
• Subject (objective case) + was + past participle + by Object (subjective case) (Passive voice)
• Subject + past participle + Object (Active voice)
• Example: 
• A large house was built by her.(Passive voice)
• She built a large house. (Active voice)
• The subject of the given sentence is ‘Pygmalion’.
• The object of the given subject is ‘GB Shaw’.
• The subject will be put in place of the object and the object will be put in place of the subject.
• was written will be changed to wrote.

Correct sentence - GB Shaw wrote Pygmalion.

The erroneous part is 'There is many ways'.

Key Points

• There is an error in the use of the linking verb in the segment 'There is many ways'.
• many ways is a plural phrase and using the singular linking verb violates the subject-verb agreement.
• Thus, option 2 is the correct answer.
• We can correct the erroneous part by using the plural linking verb are.

Correct sentence - There are many ways / to make / a stranger feel / welcome in the community.

The incorrectly spelled word is 'Mamorial'.

Key Points

• The correct spelling for the word is memorial which means a statue or structure established to remind people of a person or event.
• The meanings of the other options are as follows - 
• Acquaint - make someone aware of or familiar with.
• Guarantee - a formal assurance (typically in writing) that certain conditions will be fulfilled, especially that a product will be repaired or replaced if not of a specified quality.
• Monotonous - dull, tedious, and repetitious; lacking in variety and interest.
• Hence, option 2 is the correct answer.

The correct answer is 'fewer marbles'.

Key Points

• There is an error in adjective usage in the underlined part of the given sentence.
• Less is an adjective of quantity used with uncountable nouns. - less sugar, less time, etc.
• But, marbles is a countable noun.
• Marbles means small balls of coloured glass or similar material used as a toy.
• In such a case we need to use the adjective few which is used with nouns for countable objects and concepts.
• Since a comparison between two entities is happening (the number of marbles Robin has versus the number George has) we need to use the comparative degree of few which is fewer.
• Hence, option 4 or fewer marbles is the option that will improve the underlined part of the given sentence.

Correct sentence - Robin has fewer marbles than George.

The correct answer is 'compromising, mediocrity, strive, ensure'.

Key Points

• From the given incomplete passage, we can infer from the beginning part that it is talking about how if we start tolerating something negative it becomes the new norm.

• Thus, the second blank will have a word that implies a negative trait.

• From the given options let us look into the meanings of each second word -

• | Option | Second Word | Meaning | | --- | --- | --- | | 1 | excellence | the quality of being outstanding or extremely good. | | 2 | mediocrity | the quality or state of being mediocre. | | 3 | transcendence | existence or experience beyond the normal or physical level. | | 4 | distinction | a difference or a contrast between similar things or people. |

• From the above table it is clear that only mediocrity is a word that implies a negative trait and it falls under option 2.

• Let us look into the meaning of the other words under option 2 - 

• ​compromising - expediently accept standards that are lower than is desirable.

• strive - make great efforts to achieve or obtain something.

• ensure - make certain that (something) will occur or be the case.

• From the above meanings it is clear that each word of option 2 fits the corresponding blanks correctly.

• Hence option 2 is the correct answer.

Correct passage - The minute you start compromising and tolerating mediocrity, it becomes the new norm and the slide begins therefore, we must constantly strive to give our best and be recognized, not simply aim to do just enough to ensure that we don’t get found out.

The correct answer is 'route'.

Key Points

• Let us look into the meaning of the given homonyms - 
• riot - a violent disturbance of the peace by a crowd.(भीड़ द्वारा हिंसक रूप से शांति भंग करना।)
• rot - (chiefly of animal or vegetable matter) decay or cause to decay by the action of bacteria and fungi; decompose.((मुख्य रूप से पशु या वनस्पति पदार्थ) बैक्टीरिया और कवक की क्रिया से क्षय या क्षय का कारण बनता है; विघटित।)
• root - the part of a plant that attaches it to the ground or to a support, typically underground.(एक पौधे का वह भाग जो इसे जमीन से या किसी सहारे से जोड़ता है, आमतौर पर भूमिगत।)
• route - a way or course is taken in getting from a starting point to a destination.(एक प्रारंभिक बिंदु से एक गंतव्य तक पहुंचने में एक रास्ता या पाठ्यक्रम लिया जाता है।)
• The given sentence implies that a question is being asked about the road taken by the minister to reach the Assembly.
• Hence, route is the correct homonym for the given blank.
• So, option 4 is the correct answer.

Correct sentence - Which route does the minister take to reach the Assembly?

The sentence with no spelling error is 'Neeta represented Global School in the state level debate competition.'

Key Points

• The word competition which means the activity or condition of striving to gain or win something by defeating or establishing superiority over others has been incorrectly spelled in options 1, 3 and 4.
• ​Option 1 - competetoin
• Option 3 - compettion
• Option 4 - compitition
• Only option 2 has the correct spelling for the word, making it the correct answer.

The correct answer is 'Botanist'.

Key Points

• Let us look into the meaning of the words in the options - 
• Florist - a person who sells and arranges cut flowers.
• Gardener - a person who tends and cultivates a garden as a pastime or for a living.
• Vegetarian - a person who does not eat meat or fish, and sometimes other animal products, especially for moral, religious, or health reasons.
• Botanist - an expert in or student of the scientific study of plants.
• From the above meanings it is clear that botanist is the best word to substitute for the given group of words.
• Hence, option 4 is the correct answer.

The incorrectly spelt word is 'Collaegue'.

Key Points 

• The correct spelling for the word is colleague which means a person with whom one works in a profession or business.
• The meanings of the other options are as follows - 
• Opportunity - a time or set of circumstances that makes it possible to do something.
• Warrant - a document issued by a legal or government official authorizing the police or another body to make an arrest, search premises, or carry out some other action relating to the administration of justice.
• Conversation - a talk, especially an informal one, between two or more people, in which news and ideas are exchanged.
• Hence, option 4 is the correct answer.

The correct answer is 'To gain honour'. 

Key Points

• Win laurels is an idiom that means to obtain achievements or honors.
• ​Example - Anand is a very hard-working boy, he is sure to win laurels in life.
• So, to gain honour is the most appropriate meaning of the given idiom.
• Hence, option 1 is the correct answer.

The correct answer is 'Barely managed to escape'. 

Key Points 

• By the skin of your teeth is an idiom that means to just barely, very narrowly manage to do something. ( बहुत ही संकीर्णता से कुछ कर पाना।)
• ​Example - He won, but only by the skin of his teeth.
• So, barely managed to escape is the most appropriate meaning of the given idiom.
• Hence, option 1 is the correct answer.

The correct answer is 'the sun rises in the east'.

Key Points

• There is an error in the verb usage in the underlined segment of the given sentence.
• The segment incorrectly uses the verb raise.
• Raise is a transitive verb that is it must have a direct object.
• If you raise something, it means that you elevate it - you move it up or lift it to a higher level. - If you have a question, please raise your hand.
• But in the given segment raise does not have a direct object.
• The correct verb, in this case, is the intransitive verb rises. If something rises, it means that it elevates itself - it goes up itself. No external force is needed to lift it.
• Hence, option 2 , or the sun rises in the east is the most appropriate option that can substitute the underlined segment in the given sentence.

Correct sentence - The teacher said, “the sun rises in the east every day”.

The incorrectly spelt word is 'Equillibrium'.

Key Points 

• The correct spelling for the word is equilibrium which means a state in which opposing forces or influences are balanced.
• The meanings of the other options are as follows - 
• Equine - relating to or affecting horses or other members of the horse family.
• Equilateral - having all its sides of the same length.
• Equanimity - calmness, and composure, especially in a difficult situation.
• Hence, option 3 is the correct answer.

The incorrectly spelt word is 'Encouregement'.

Key Points 

• The correct spelling for the word is encouragement which means the action of giving someone support, confidence, or hope.
• The meanings of the other options are as follows - 
• Achievement - a thing is done successfully with effort, skill, or courage.
• Advertisement - a notice or announcement in a public medium promoting a product, service, or event or publicizing a job vacancy.
• Environment - the surroundings or conditions in which a person, animal, or plant lives or operates.
• Hence, option 1 is the correct answer.

The correct answer is 'explore'.

Key Points

• Let us look into the meanings of the given options - 
• determine - cause (something) to occur in a particular way or to have a particular nature.
• deploy - move (troops or equipment) into position for military action.
• invent - create or design (something that has not existed before); be the originator of.
• explore - travel through (an unfamiliar area) in order to learn about it.
• The given sentence implies that the subject (Ramu) was traveling with his friends to find and tour new paths.
• From the above meanings it is clear that explore is the most appropriate option to fill in the blank.
• Hence, option 4 is the correct answer.

Correct sentence - Ramu went with his friends on a trip to explore new paths.

The correct answer is 'carried away'.

Key Points

• There is an error in the verb usage in the given sentence.
• Based on the given options, we need to replace the verb carried with the appropriate phrasal verb.
• Let us look into the meanings of the given options - 
• carried off - to succeed in doing or achieving something difficult
• carried away - to arouse to a high and often excessive degree of emotion or enthusiasm.
• carried of - to take or bear (something) from one place to another. (Note - this is not a phrasal verb)
• carried to - support and move (someone or something) from one place to another. (Note - this is not a phrasal verb)
• From the above meanings it is clear that carried away is the most appropriate option to substitute the underline segment in the given sentence.
• Hence, option 2 is the correct answer.

Correct sentence - I was carried away by her rapturous song.

The correct answer is 'a, c, b, d'.

Key Points

• From the given jumbled parts, we can make out that the sentence is related to non-verbal communication.
• The sentence should start with part a which introduces the topic.
• It should be followed by part c which mentions what this form of communication means.
• Part b which points out how to communicate without speaking through visual clues should come after part c.
• Part d becomes the concluding part of the passage.
• So, we get the sequence a, c, b, d, making option 1 the correct answer.

So, the correct paragraph is: a) Non-verbal communication is a means c) By which you are able to communicate without speaking b) This is possible by using visual clues d) Such as facial expressions, eye contact, postures, gestures, etc.

The correct answer is 'process'.

Key Points

• Let us look into the meaning of the given options - 
• aspect - a particular part or feature of something.
• process - a series of actions or steps taken in order to achieve a particular end.
• tool - a device or implement, especially one held in the hand, used to carry out a particular function.
• mechanism - a system of parts working together in a machine; a piece of machinery.
• From the line with the blank, we can infer that the blank 1 needs a word that would describe the procedure of tree plantation.
• Hence, process is the most appropriate option for blank 1.
• So, option 2 is the correct answer.

Correct paragraph - Tree plantation is the (1)process of transplanting saplings or seeds to maximise the amount of greenery and focus on promoting (2)afforestation. Planting trees can be a very rewarding and fruitful (3)endeavour! Not only is it (4)ecologically beneficial for this planet, but it also contributes to helping create an environmentally friendly place to live, as trees help reduce pollutant (5)concentration.

The correct answer is 'afforestation'.

Key Points 

• Let us look into the meaning of the given options - 
• vegetation - plants considered collectively, especially those found in a particular area or habitat.
• afforestation - a process where new forests are planted across land without trees.
• land reservation - tract of land set aside by a government for the use of one or more aboriginal peoples.
• deforestation - the action of clearing a wide area of trees.
• From the line with the blank, we can infer that the blank 2 needs a word that would describe the process of creating new forests.
• Hence, afforestation is the most appropriate option for blank 2.
• So, option 2 is the correct answer.

Correct paragraph - Tree plantation is the (1)process of transplanting saplings or seeds to maximise the amount of greenery and focus on promoting (2)afforestation. Planting trees can be a very rewarding and fruitful (3)endeavour! Not only is it (4)ecologically beneficial for this planet, but it also contributes to helping create an environmentally friendly place to live, as trees help reduce pollutant (5)concentration.

The correct answer is 'endeavour'.

Key Points 

• Let us look into the meaning of the given options - 
• plan - a detailed proposal for doing or achieving something.
• labour - work, especially physical work.
• order - the arrangement or disposition of people or things in relation to each other according to a particular sequence, pattern, or method.
• endeavour - earnest, prolonged, and industrious effort.
• From the line with the blank, we can infer that the blank 3 needs a word that would describe the effort of planting trees which is rewarding.
• Hence, endeavour is the most appropriate option for blank 3.
• So, option 4 is the correct answer.

Correct paragraph - Tree plantation is the (1)process of transplanting saplings or seeds to maximise the amount of greenery and focus on promoting (2)afforestation. Planting trees can be a very rewarding and fruitful (3)endeavour! Not only is it (4)ecologically beneficial for this planet, but it also contributes to helping create an environmentally friendly place to live, as trees help reduce pollutant (5)concentration.

The correct answer is 'ecologically'.

Key Points 

• Let us look into the meaning of the given options - 
• ecologically - in a way that concerns the relation of living organisms to one another and to their physical surroundings.
• physically - in a manner relating to the body as opposed to the mind.
• socially - in a way that relates to society or its organization.
• economically - in a way that relates to economics or finance.
• From the line with the blank, we can infer that blank 4 needs a word that would refer to the natural benefit of tree plantation.
• Hence, ecologically is the most appropriate option for blank 4.
• So, option 1 is the correct answer.

Correct paragraph - Tree plantation is the (1)process of transplanting saplings or seeds to maximise the amount of greenery and focus on promoting (2)afforestation. Planting trees can be a very rewarding and fruitful (3)endeavour! Not only is it (4)ecologically beneficial for this planet, but it also contributes to helping create an environmentally friendly place to live, as trees help reduce pollutant (5)concentration.

The correct answer is 'concentration'.

Key Points

• Let us look into the meaning of the given options - 
• problem - a matter or situation regarded as unwelcome or harmful and needing to be dealt with and overcome.
• concentration - the relative amount of a particular substance contained within a solution or mixture or in a particular volume of space.
• method - a particular procedure for accomplishing or approaching something, especially a systematic or established one.
• calculation - a mathematical determination of the amount or number of something.
• From the line with the blank, we can infer that blank 5 needs a word that would describe the presence of pollutants in the environment.
• Hence, concentration is the most appropriate option for blank 5.
• So, option 2 is the correct answer.

Correct paragraph - Tree plantation is the (1)process of transplanting saplings or seeds to maximise the amount of greenery and focus on promoting (2)afforestation. Planting trees can be a very rewarding and fruitful (3)endeavour! Not only is it (4)ecologically beneficial for this planet, but it also contributes to helping create an environmentally friendly place to live, as trees help reduce pollutant (5)concentration.

The pattern followed in the given series is :

According to the pattern the next term in the series will be,

Hence the correct answer is 1311.

According to the sequence in the dictionary.

The correct order of the given words is:

3. Beggar
4. Beginner
5. Beheld
6. Behind
7. Belief

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

The logic followed here is:

Step 1: P is older than only U and R.

Step 2: R is older than U.

P > R > U

Step 3:Q is older than S but younger than T. 

T > Q > S

Now on combining all the above steps we get:

T > Q > S > P > R > U

Step 4: T is not the oldest among all.

V > T > Q > S > P > R > U

Here when we observe that there are 2 person between R and Q.

Hence the correct answer is 2.

When we compare the codes we get :

Here we can see the word "code" is coded as "3".

And in the options, we can see only one option that consist of code "3"

Hence the answer for "make one code" is "13 15 3".

The mirror image of the given combination is :

   

We can clearly see the the mirror image of the given combination matches with option 3).

Hence the answer is option 3).

The logic followed here is:

Fathers and mothers both can be doctors, so both mother and father can have a common factor, thus, the Venn diagram representing the relation are as follows:

   

Hence, the above Venn diagram that is represented in option 2 is the correct answer.

The logic followed here is:

Replacing the given equation with the given signs, 

and by using BODMAS RULE,

option 1) 

78 * 43 * 2 * 56 * 27 * 4

78 + 43 = 2 + 56 × 27 - 4

78 + 43 = 2 + 1512 - 4

121 = 1514 - 4

121 is not equal to 1510.

Thus, LHS is not equal to RHS.

option 2)

78 * 43 * 2 * 56 * 27 * 4

78 - 43 ÷ 2 = 56 + 27 × 4

78 - 21.5 = 56 + 27 × 4

78 - 21.5 = 56 + 108

78 - 21.5 = 164

56.5 is not equal to 164. 

Thus, LHS not equal to RHS.

option 3)

78* 43 * 2 * 56 * 27 * 4

78 - 43 × 2 = 56 + 27 × 4

78 - 86 = 56 + 108

78 - 86 = 164

-8 is not equal to 164.

Thus, LHS is not equal to RHS

option 4)

78 * 43 * 2 * 56 * 27 * 4

78 + 43 × 2 - 56 = 27 × 4

78 + 86 - 56 = 108

164 - 56 = 108

108 =108

Thus, LHS is equal to RHS.

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

The logic followed here is:

By using BODMAS rule,

OPTION 1)

230 × 1 ÷ 5 + 16 - 41 = 21

230 × 0.2 + 16 - 41= 21

46 + 16 - 41 = 21

62 - 41 = 21

21 = 21

Therefore, LHS is equal to RHS

OPTION 2)

230 + 1 ÷ 5 × 16 - 41 = 21

SOLVING LHS:

230 + 0.2 ×16 - 41

230 + 3.2 - 41

233.2 - 42

192.2

Thus, LHS is not equal to RHS.

OPTION3)

230 – 1 + 5 ÷ 16 × 41 = 21

SOLVING LHS,

230 - 1 + 0.3125 × 41

230 - 1 + 12.8

230 - 13.8

216.2

Thus, LHS is not equal to RHS.

OPTION4)

230 ÷ 1 + 5 – 16 × 41 = 21

Solving LHS

230 + 5 - 16 × 41

230 + 5 - 656

235 - 656

• 421

Thus, LHS is not equal to RHS"

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

The logic followed here is:

   

 

In a mirror image LEFT changes to right and the RIGHT changes to left.

When placement of mirror not given, by default we will assume it in VERTICAL DIRECTION.

The letter adjacent to the right side of mirror,  will be adjacent to it on the left side  but direction will be changed as left changes to the right and the right changes to the left.

Hence,  

   will be the correct answer

The logic followed here is:

By using BODMAS RULE,

OPTION 1) −, ×, +, =, ÷, +

41 - 4 × 39 + 73 = 25 ÷ 4 + 30

41 - 4 × 39 + 73 = 6.25 + 30

41 - 156 + 73 = 6.25 + 30

41 - 229 = 36.25

-188 is not equal to 36.25

OPTION 2) ×, +, −, =,  ×, +

41 × 4 + 39 - 73 = 25 × 4 + 30

164 + 39 - 73 = 100 + 30

203 - 73 = 130

130 = 130

Thus, LHS is equal to RHS

OPTION 3) ÷, +, =, ×, −, +

41 ÷ 4 + 39 = 73 × 25 - 4 + 30

10.25 + 39 = 1825 - 4 + 30

40.25 = 1825 - 34

40.25 is not equal to 1791

OPTION 4) −, =, +, ×, −, ×

41 - 4 = 39 + 73 × 25 - 4 × 30

37 = 39 + 1825 - 120

37 = 1864 - 120

Thus, LHS is not equal to RHS

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

The logic followed here is:

OPTION 1) 4 ∶ 48

4³ - 4² = 48

64 - 16 = 48

OPTION 2) 6 ∶ 180

6³ - 6² = 180

216 - 36 = 180

OPTION 3) 8 ∶ 448

8³ - 8² = 448

512 - 64 = 448

OPTION4) 9 ∶ 639

9³ - 9² = 648

729 - 81 = 648

639 is not equal to 648.

As it should be 648 and not 639, it will be the odd number - pair.

Hence, the correct answer is 9 ∶ 639.

The logic followed here is:

A particular pattern is observed after every five letters and after every fourth letter the sixth letter is the succeeding letter of the first one.

Option 1) I E W P N

I P N I E / X E N I E / Y P N W E / Z P P I N

No pattern is seen here.

Option 2) N I E W P

N P N I E / X I N I E / Y P N E E / Z P W I P

No pattern is seen here.

Option 3) W P I N E

W P N I E / X P N I E / Y P N I E/ Z P N I E

Thus, this option is correct. 

Option 4) E W P N I

E P N I E / X W N E / Y P N P E / Z P N I I

No pattern is seen here

Hence, W P I N E is the correct answer.

The logic followed here is:

BROWSER : SERWBRO :: CAPTURE : URETCAP :: DESKTOP : ?

If you see the pattern carefully the middle letter remains at the same position and the three letters on the left side shift to the right side and vice versa. 

BROWSER : SERWBRO

CAPTURE : URETCAP

Similarly,

DESKTOP : TOPKDES

Hence, the correct answer TOPKDES

Let's take each pair individually to obtain the identical operation:

Pair 1- 8 : 64 

Operation- (First number × First number) = Second number

 8 × 8 = 64

Pair 2- 8 : 512 

Operation- (First number × First number × First number) = Second number

 8 × 8 × 8 = 512

Pair 3- 6 : 216

Operation- (First number × First number × First number) = Second number

 6 × 6 × 6 = 216

Pair 4- 4 : 64 

Operation- (First number × First number × First number) = Second number

 4 × 4 × 4 = 64

The pattern is common in pair 2, 3 and 4.

Therefore the odd pair is 8 : 64.

Hence, the correct answer is 8:64.

The logic followed here is:

(First term + 1) × 5 = Second term 

Option 1) 6 : 36

(6 + 1) × 5 = 36

7 × 5 = 36

35 ≠ 36

Thus, the logic does not apply to this pair.

Option 2) 2:15

(2 + 1) × 5 = 15

3 × 5 = 15

15 = 15

Option 3) 3:20

(3 + 1) × 5 = 20

4 × 5 = 20

20 = 20

Option 4) 5 : 30

(5 + 1) × 5 = 30

6 × 5 = 30

30 = 30

Hence the correct answer is option 1)

From the given information:

I denotes ÷

J denotes ×

K denotes ‘−’ 

L denotes ‘+’

Now we solve the equation using BODMAS rule:

Now we substitute the values,

42 + 18 - (7 × 4) + (21 ÷ 3) × 9 + 22 = ?

42 + 18 - 28 + 7 × 9 + 22 = ?

42 + 18 - 28 + 63 + 22 = ?

145 - 28 = ?

117 = Answer

Hence the correct answer is option 1)

Given: _ a _ _ W a L W _ L _ W a L _ a _ a W _ L

Let's check each option:

1)  W L a a L W L a → W a L a W a L W a L L W a L W a L a W a L

2)  W L a a a W L a → W a L a W a L W a L a W a L W a L a W a L

3)  W L a a a W L W → W a L a W a L W a L a W a L W a L a W W L

4)  L L a a a W L a → L a L a W a L W a L a W a L W a L a W a L

So, In option 2 "W a L a W a L" is repeating itself.

Hence, ‘W L a a a W L a’ is the correct answer.

We unfold the paper step by step:

Now we consider the given options:

Option 1) The pattern in the option is not symmetrical.

Option 2) The pattern is incorrect.

Option 3) The positioning of the shapes is wrong.

Option 4) The pattern matches completely.

Hence the correct answer is option 4)

In a mirror image LEFT CHANGES TO RIGHT AND THE RIGHT CHANGES TO LEFT and vice-versa.

                              

From the given options,

Option 1) The pattern is inverted and it does not match.

Option 2) The pattern is inverted and it is reversed so it does not match.

Option 3) The pattern matches completely.

Option 4) The pattern is mirrored but in the wrong order.

Hence the correct answer is option 3)

Lets count the number of squares step by step:

      

Hence, the correct answer is "18".

We unfold the paper step by step:

Now we consider the given options:

Option 1) There is no symmetry.

Option 2) There is no symmetry.

Option 3) The pattern matches completely.

Option 4) There is no symmetry.

Hence the correct answer is option 3)

The pattern used in the given series is:

 First term + (first term ÷ 2) = Second term

Let's apply the pattern n the series:

14 : 21 :: 6 : 9 :: 12 : ?

14 + (14 ÷ 2) = 21

14 + 7 = 21

21 = 21

14 : 21 :: 6 : 9 :: 12 : ?

6 + (6 ÷ 2) = 9

6 + 3 = 9

9 = 9

14 : 21 :: 6 : 9 :: 12 : ?

12 + (12 ÷ 2) = ?

12+ 6 = ?

18 = Answer

Hence the correct answer is option 3).

For the year 2021:

Total number of odd days from 20 July to 28 November:

July=11; odd days = 4

August = 31; odd days = 3

September=30; odd days = 2

October=31; odd days = 3

November=28; odd days = 0

Total number of odd days = 4 + 3 + 2 + 3 + 0 = 12 i.e. 5 

So, Tuesday + 5 = Sunday. 

Hence the correct answer is option 1)

The pattern used in the given codes is:

 First and second alphabets are interchanged. 

 Third and fourth alphabets are interchanged.

 

Similarly,

Hence the correct answer is option 4)

From the given information:

A denotes ‘+’

‘B’ denotes ‘×’

‘C’ denotes ‘–’

‘D’ denotes ‘÷’

Now we substitute the values and solve the equation using BODMAS rule:

71 A 3 B 2 C 6 B (65 D 13) C 7 B 4 = ?

71 + 3 × 2 - 6 × (65 ÷ 13) - 7 × 4 = ?

71 + 3 × 2 - 6 × 5 - 7 × 4 =?

71 + 6 - 30 - 28 =?

77 - 30 - 28 = ?

19 = Answer

Hence the correct answer is option 2)

GIVEN:

Difference between number and square root of  the number = 2.

CALCULATION :

Let the number be x 

then , According to the question 

⇒ x - √x = 2 -------------(1)

On rearranging the equation we get 

⇒ (x - 2) = √x

on squaring  we get

⇒ (x - 2)² = (√x)²

On apply the formula (a - b)² = a² + b² - 2ab, we get

⇒ x² + 4 - 2x (-2) = x   

⇒ x2 - 5x + 4 = 0

⇒ x(x - 4) - (x - 4) = 0

⇒ (x - 1)(x - 4) = 0

⇒  x = 1 or x = 4

Now on putting the value of x in equation 1, we get 

For x = 1,  

⇒  x - √x = 2

⇒  1 - √1 = 2

⇒  1 - 1 = 2

⇒  0 ≠ 2

For x = 4,

⇒  x - √x = 2

⇒  4 - √4 = 2

⇒  4 - 2 = 2

⇒  2 = 2

So the required number is 4.

Hence the correct answer is option 4)

GIVEN:

 a² - 4a + 1 = 0 

FORMULA USED:

(a + b)² = a² + b² + 2ab

Where a and b are 1^st and 2^nd term respective

CALCULATION:

 a² - 4a + 1 = 0

⇒ on taking a common we get,

⇒ a (a -4 +1/a ) = 0 

⇒ a - 4 + 1/a = 0

⇒ a + 1/a = 4  ...................( 1)

Now, on  squaring  both the sides we get,

 ( a + 1/a)² =   a² + 1/a² + 2 × a × 1/a

⇒ 16 = a² + 1/a² + 2 

a² + 1/a² = 14 .........................(2)

Now,  on adding the  equations  (1) and (2) the value of a + 1/a + a² + 1/a² = ( 4 + 14) = 18.

Hence, the value is 18.

Given:

$(x - \frac{1}{x}) = \frac{7}{3}$

Formula used:

 $(a - b)^3 = a^3 - b^3 - 3ab(a -b)$ where a and b are 1^st and 2^nd term respectively.

Calculation:

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

⇒ $(\frac{7}{3})^3$ = $\left( {{x^3} - \frac{1}{{{x^3}}}} \right)$ - 3 × $\frac{7}{3}$ 

⇒ $x ^3 - \frac{1}{x}^3$ = 532/27 = $19 \frac{19}{27}$ .

⇒ Hence, the value is $19\frac{19}{27}$.

Shortcut Trick

Ratio of students in the three batches = 30 : 50 : 70 ⇒ 3 : 5 : 7

Combine the batches with the same average marks (70): 5 + 7 = 12 units.

New simplified ratio of students = 3 : 12 ⇒ 1 : 4

Using Deviation Method (Base = 55): Net Deviation = 4 × (70 − 55) = 60

Average increase = 60 ÷ (1 + 4) = 12 marks

Total Average = 55 + 12 = 67

∴ The correct answer is 67.

Alternate Method

Given:

Number of students (n₁, n₂, n₃) = 30, 50, 70

Average marks (A₁, A₂, A₃) = 55, 70, 70

Formula Used:

Combined Average = (n₁A₁ + n₂A₂ + n₃A₃) ÷ (n₁ + n₂ + n₃)

Calculations:

⇒ Total marks of all students = (30 × 55) + (50 × 70) + (70 × 70)

⇒ Total marks = 1650 + 3500 + 4900

⇒ Total marks = 10050

⇒ Total number of students = 30 + 50 + 70 = 150

⇒ Combined Average = 10050 ÷ 150

⇒ Combined Average = 67

∴ The correct answer is 67.

Additional Information

Weighted Average Principle

When multiple groups are combined, the overall average is the sum of products of values and their respective weights, divided by the total weight: A_w = Σn_ia_i ÷ Σn_i.

Deviation Method for Averages

Pick an assumed average (A). The true average = A + (Σdeviations ÷ total count). This simplifies calculations with large numbers.

Combined Average with Same Mean

If two or more groups have the exact same average, their combined average will always be that same value, regardless of the number of students in each group.

GIVEN:

numbers divisible by 11

CONCEPT USED :

Divisibility of 11: Difference between the sums of the alternate digits of the given number is either 0 or divisible by 11.

CALCULATION :

Considering option (1) , we have 

⇒ 28171 = (2 + 1 + 1) - (8 + 7) = (4 - 15)  = -11, which is divisible by 11 

⇒ Hence, 28171 is divisible by 11.

Considering option (2), we have 

⇒ 27667 = (2 + 6 + 7) - (7 + 6) = (15 - 13) = 2, which is not divisible by 11

⇒ Hence, 27667 is not divisible by 11

Considering option (3), we have 

⇒ 29817 =  (2 + 8 + 7) - (9 + 1) = (17 - 10) = 7, which is not divisible by 11

Considering option (4), we have 

⇒ 28196 = (2 +1 + 6) - (8 + 9) = (9 - 17) = -8 , which is also not divisible by 11

Hence, 28171 is divisible by 11.

GIVEN:

Sum = Rs 8400 $(1 +\frac{6}{100})^3$

Time = One and a half years

Rate = 12% per annum compounded half early 

FORMULA USED:

Compound Interest = P $( 1 + \frac{r}{100})^n$ - P where n = time and P = principal or sum 

When it is compounded half-yearly, then time becomes double i.e. = 3 years in this case

and the rate becomes half i.e. 6% in this case.

CALCULATION:

Principal = 8400 

C.I. = 8400 $( 1+ \frac{6}{100})^3$ - 8400 

⇒ (8400 × 106/100 × 106/100 × 106/100) - 8400 = 1604.5 

Hence, compound interest is Rs1604.5

Shortcut Trick⇒ Principle → Amount

⇒ 50 → 53

⇒ 50 → 53

⇒ 50 → 53

⇒ Total → 125000 → 148877

Now, 

If, Principle = 125000x, then Amount = 148877x

∴ Compound Interest = 148877x - 125000x =23877x

⇒ 125000x = 8400

⇒ x = 8400/125000

∴ Compound Interest = 23877x = 23877 × (84/1250) = 1604.5

GIVEN:

Two Δ ABC and Δ PQR are similar to each other.

Side BC = 5 cm , Side QR = 12.5 cm, Side PQ = 6.25 cm 

CONCEPT USED:

When two triangles are similar, their corresponding sides are in the same ratio.

CALCULATION :

Since Δ ABC is similar to Δ PQR

Hence, their corresponding sides are in the same ratio such as,

AB/PQ = BC/QR =AC/PR  

⇒ Now, AB/PQ = BC/QR 

⇒  AB/6.25 = 5/12.5 

⇒ AB = 2.5 cm 

Hence, the value of side AB is 2.5 cm.

GIVEN:

x : y = 1 : 2

CALCULATION :

x/y = 1/2 

Hence, on putting the value of x and y, we get

⇒ (2x + 4y) : (x + 4y)  = (2 × 1 + 4 × 2) : ( 1 + 4 × 2) 

⇒ (2x + 4 y) =  10 : 9.

Hence, the value is (2x + 4y) = 10 : 9.

GIVEN :

Speed = 108 km/h

Time  = 11 seconds

FORMULA USED:

Distance = Speed × Time 

CALCULATION :

Speed = 108 km/h 

To convert km/h into m/s multiply the number by 5/18.

 speed = 108 × 5/18 m/s = 30 m/s.

Distance = Speed × Time =  30 × 11 = 330 m

Hence, the distance covered by the train is 330m.

GIVEN:

Height of wooden solid cone = 12cm 

Circumference = 44cm 

FORMULA USED:

Volume =  $\frac{1}{3}π r^2h$, where r is radius and h is height respectively

Circumference =  $2π r$

CALCULATION :

Circumference = 2πr = 44

⇒ 2 × 22/7 × r = 44 

⇒ r = 7 cm  

The volume of the cone = $\frac{1}{3}π r^2h$ 

⇒ 1/3 × 22/7 × 7 × 7 × 12

⇒ 616 $cm^3$ 

Hence, the volume is 616 cm³

GIVEN :

Man completes the project in 16 days

Women complete the same work in 12 days

they worked on alternate days.

CALCULATION :

Man's 1-day work = 1/16 days

Woman's 1-day work = 1/12 days

(man + woman)'s work in 2 days = ( 1/16 + 1/12) = (4 + 3)/48 = $\frac{7}{48}$ 

⇒ In 6 pairs of 2 days they will complete  = $\frac{7}{48}$ × 6 = $\frac{7}{8}$  i.e. after 6 × 2 = 12 days

Remaining work

(1 - 7/8) = 1/8 work is left .

On the 13^th day, A will do the work,

⇒ 1/16 work done  by A in 1 day  

Then, remaining work = (1/8) - (1/16) = 1/16 

On the 14^th day, it is B's turn,

⇒ 1/12 work done by B in 1 day 

Hence, 1/16 work will be done in (12 × 1/16) = 3/4 day

⇒ Total days = (12 + 1  + 3/4) = $13 \frac{3}{4}$ days or 55/4 days.

Hence, they will take 55/4 days to complete the work.

GIVEN :

The sides of a triangle are 5 cm,12 cm and 13 cm 

FORMULA USED:

Area of the triangle = $\sqrt {s (s-a)(s-b) (s-c)}$ where a, b and c are the sides of the triangle respectively

and s is the semi- perimeter  and s = (a  + b + c) /2.

CALCULATION:

S = (5 + 12 + 13) /2 = 15 cm

Area of the triangle = $\sqrt{15 (15 -5)(15-12)(15 -13)}$  = $\sqrt{15 (10)(3)(2)}$  = $\sqrt900$ = 30 cm².

Hence, the area of the triangle is 30 cm².

Alternate Method

 $13^2$ = 169  and $( 5^2 + 12 ^2)$ = 169 . 

Hence, as both are equal and the square of the bigger side is equal to the sum of the square of the smaller sides

$13^2 = 5^2 + 12^2$ it is a right-angled triangle and hence, as in this $h^2 = p^2 + b^2$ where h = hypotenuse, b= base and  p= perpendicular.

⇒ here, h = 13, b = 12 and p = 5 

⇒ Hence, Area of the triangle = 1/2 × b × h  = 1/2 × 12 × 5 = 30 cm² .

Hence, the area of the triangle is 30 cm²

Given:

tan48° tan23° tan42° tan67°

Formula used: 

tanθ  × cotθ = 1

tan(90 - θ) = cotθ 

Calculation:

⇒ The value can be rewritten as 

tan48 tan42 tan23 tan67

⇒ tan48 tan(90 - 48) tan23 tan(90 - 23)

⇒ tan48 cot48 tan23 cot23

⇒ 1

Hence, the value is 1

Given:

240 donors of blood group  A, B , O and AB

Formula used:

360 degrees = Total donors 

Calculation:

As, 360 degree represents 240 donors 

Hence, blood group O has 80 degree 

Blood group O has = 240/360 × 80 donors = 160/3

Now, blood group A represents  90 degree

Blood group A has = 240/360 × 90 = 60 

Now, blood group AB represents 70 degrees

Blood group AB has = 240/360 × 70 = 140/3

Now, average of A and AB = Sum of values/Total number of values = (60 + 140/3) ÷ 2 =  160/3.

Hence, the ratio between O and the average of A and AB = 160/3 : 160/3 = 1:1.

Hence, the ratio is 1:1.

GIVEN:

The total number of students in coaching  R = 300.

Percentage of students of school M enrolled in coaching R = 34

CALCULATION:

35% of the students in coaching  R are female = 35% × 300 = 105.

20% of the female enrolled with Coaching R belongs to the school

20% of 105 = 21 

Total students are in the school M = 34% of 300 = 102.

Hence, female in school M = 21 

No. of male students of school M who have enrolled with coaching R = (102 - 21) = 81.

Hence, the number of male students of school M who enrolled with coaching R = 81.

Given:

Rohan scored 70 and 75 in two exam .

Average given = 70

Concept used:

Average = Sum of all the terms/Total number of terms

Calculations:

Let the marks obtained in the third test be x.

According to the question,

$\frac{70+75+x}{3}=70$

$\Rightarrow$ 145 + x = 210

$\Rightarrow$ x = 65

$\therefore$ Marks obtained in the third test are 65 marks.

Given:

C.P = Rs. 48,000

Loss% on first S.P = 15 %

Profit on second S.P = 22.5 %

Concept used:

S.P = $\frac{(100-loss)}{100}×$ C.P

S.P = $\frac{(100+profit)}{100}×$ C.P

Calculations:

First S.P = $\frac{(100-15)}{100}×48,000$

⇒ Rs. 40,800

Hence, First S.P = Second C.P = Rs. 40,800

Now, Second S.P = $\frac{(100+22.5)}{100}×40,800$

$⇒$ Second S.P = Rs. 49,980

Now, Total profit = Second S.P - C.P = 49,980 - 48,000 = 1,980

Hence, total profit = Rs. 1, 980

Now, Profit % = $\frac{1,980}{48,000}×100$

$⇒$ Profit % = 0.04125 × 100 = 4.125 %

$\therefore$ Overall Profit % is 4.125%.

Shortcut Trick

Successive discounts of 28% and 30% give a combined multiplier.

SP Multiplier = (100 − 28)% × (100 − 30)% = 0.72 × 0.70

SP Multiplier = 0.504

SP = 4875 × 0.504 = 2457

∴ The correct answer is ₹2,457.

Alternate Method

Given: Marked Price (MP) = ₹4,875, First Discount (d₁) = 28%, Second Discount (d₂) = 30%

Formula Used: SP = MP × (100 − d₁)/100 × (100 − d₂)/100

MP: ₹4875

−28%

₹3510

−30%

SP: ₹2457

⇒ Price after 1^st discount = 4875 × (100 − 28) ÷ 100

⇒ Price after 1^st discount = 4875 × 0.72 = ₹3,510

⇒ Selling Price (SP) = 3510 × (100 − 30) ÷ 100

⇒ SP = 3510 × 0.70

⇒ SP = ₹2,457

∴ The correct answer is ₹2,457.

Additional Information

Successive Discount Formula

The single equivalent discount for two successive discounts a% and b% is given by (a + b − (a × b) ÷ 100)%.

Selling Price and Marked Price Relationship

SP = MP × (1 − Discount/100). For multiple discounts, multiply each factor: SP = MP × (1 − d₁/100) × (1 − d₂/100)...

Discount Amount

Total Discount = Marked Price − Selling Price. It is always calculated on the Marked Price unless otherwise specified.

Given:

Final amount = Rs. 19,320

Gain% = 15 % 

Calculations:

Let the amount be x.

Then, according to the question,

x + 15% of x = 19,320

$\Rightarrow x + \frac{15x}{100}=19,320$

$\Rightarrow \frac{115x}{100}=19,320$

$\Rightarrow x =\frac{(19,320×100)}{115}$

$\Rightarrow$ x = 16,800

$\therefore$ The initial sum of money is Rs. 16,800.

Given:

Selling Price (M.P) = Rs. 480

Two successive Discount = 25% and 10%

Formula used:

Net Discount = $(-X-Y+\frac{XY}{100})$

S.P = M.P × $\frac{(100-D\%)}{100}$

Calculations:

Net Discount = $(-X-Y+\frac{XY}{100})$

⇒ - 25 - 10 + 25 × $\frac{10}{100}$

⇒ - 35 + 2.5

⇒ - 32.5

Net discount% = 32.5 %

Selling Price(S.P) = Marked Price(M.P) × $\frac{(100-D\%)}{100}$

⇒ 480  = Marked Price  × $\frac{(100-32.5)}{100}$

⇒ 480 = Marked Price × $\frac{67.5}{100}$

⇒ 480 = Marked Price × 0.675

⇒ Marked Price = $\frac{480}{0.675}$= 711.11 ≈ 711

∴ The original Price of the Shirt is Rs. 711.

Shortcut TrickLet the original price be Rs. 'x'

⇒ x × 75% × 90% = 480

⇒ (3x/4) × (9/10) = 480

∴ x = (480 × 10 × 4)/ (9 × 3) = 711.11 ≈ 711.

Given:

The mean of three numbers $\frac{a}{3}$, b and c is the same as the mean of the numbers $\frac{b}{3}$, $\frac{c}{3}$ and x.

Concept used:

Mean = $\frac{Sum \space of \space observations}{No. \space of \space observation}$

Calculations:

According to the question,

$\frac{\frac{a}{3}+b+c}{3}=\frac{\frac{b}{3}+\frac{c}{3}+x}{3}$

$\Rightarrow \frac{a}{3}+b-\frac{b}{3}+c-\frac{c}{3}=x$

$\Rightarrow \frac{a+2b+2c}{3}=x$

$\Rightarrow 3x = a+2b+2c$

$\therefore$The value of 3x = a + 2b + 2c.

Given:

The ratio of number of boys and girls = 11 : 9

30% of boys and 20% of girls passed the examination

Calculation:

Let the ratio of boys and girls be 11x and 9x.

Total number of students = 20x

According to the question,

Number of passed students = 11x × 30% + 9x × 20%

⇒ $\frac{33x}{10}+\frac{18x}{10}$

⇒ $\frac{51x}{10}$

Number of passed students = $\frac{51x}{10}$

Now, the percentage of passed students = $\frac{\frac{51x}{10}}{20x}×100$

⇒ 25.5 %

∴ The percentage of the passed student is 25.5 %.

Given:

The ratio between their radii of the bases = 3 : 4

The ratio between their volume = 11 : 16

Formula used:

The volume of the cone = $\frac{1}{3}$πr2h, where r is the radius of the base and h is the height of the cone.

Calculation:

Let V1 and V2 are the volumes of two cones

and H1 and H2 are their height.

V1 =$\frac{1}{3}$ × π × (R1)2 × H1

V2 =$\frac{1}{3}$ × π × (R2)2 × H2

According to the question,

V₁ : V₂ = 11 : 16

⇒ [$\frac{1}{3}$ × π × (R1)2 × H1] : [$\frac{1}{3}$ × π × (R2)2 × H2] = $\frac{11}{16}$

⇒ $\frac{3²}{4²}$ × (H₁ : H2)= $\frac{11}{16}$

⇒ $\frac{9}{16}$ × (H1 : H2)= $\frac{11}{16}$

⇒ (H1 : H2) = 11 : 9

∴ The ratio between their heights is 11 : 9.

Given:

The number is 2143251

Concept used:

Divisibility law of 3 ⇒ A number is divisible by 3 if the sum of its digit is divisible by 3.

Divisibility law of 7 ⇒ A number is divisible by 7 if the difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to 0

Calculations:

Sum of digits of 2143251 = 2 + 1 + 4 + 3 + 2 + 5 + 1 = 18

Now, 18 is divisible by 3 therefore, the Number 2143251 is divisible by 3.

Here in the options, two numbers are not available so we don't need to check divisibility from other numbers.

$\therefore$The number 2143251 is divisible by 3.

Given:

Table showing the survey on students loving sports.

 

Calculations:

Total number of boys = 542 + 438 = 980

Total number of girls = 358 + 372 = 730

Now, the difference between the number of boys and girls  in  the school = 980 - 730 = 250

$\therefore$ The difference between no. of boys and girls in the school is 250.