SSC CHSL Tier-1 2021: Official Paper (Held On : 7 June 2022 Shift 3) (Previous Year Paper)

The correct answer is 'train had left already'.

Key Points

• The most appropriate substitute for the underlined segment is 'train had already left'.
• The given sentence, considering the timing, should be in Past Perfect tense.
• The structure of the Past Perfect tense is:
• Subject + had + V3 + Object.
• So, the correct formation of the given sentence should be 'The train had already left before we reached the platform.'

The correct answer is "BCAD". 

Key Points

• Sentence B should come first as it is introducing the characters of the story.
• Sentence C is the second sentence because it is about Chremes.
• Sentence A is the third sentence as it talks about the children and their likeness.
• Sentence D is the last sentence as it is about the closeness of these children after they have become men.

Additional Information

• The paragraph after rearrangement is as follows.
• There was in the city of Rome a noble senator, named Fulvius, who sent his son, called Titus, being a child, to the city of Athens, in Greece (which was the fountain of all manner of doctrine), there to learn good letters: and caused him to be hosted with a worshipful mart of that city, called Chremes. This Chremes happened to have also a son named Gisippus, who not only was equal to the said young Titus in years, but also in stature, proportion of body, favour, and colour of visage, countenance, and speech. The two children were so like, that without much difficulty it could not be discerned of their proper parents, which was Titus from Gisippus, or Gisippus from Titus. These two young gentlemen, as they seemed to be one in form and personage, so shortly after acquaintance, the same nature wrought in their hearts such a mutual affection, and their wills and appetites daily more and more so confederated themselves, that it seemed none other, when their names were declared, but that they had only changed their places, issuing (as I might say) out of the one body, and entering into the other.

The correct answer is 'Sensible'.

Key Points

• The most appropriate antonym for the given word 'Absurd' is 'Sensible'.
• The meaning of the word 'Absurd' is 'wildly unreasonable, illogical, or inappropriate'.
• The meaning of the word 'Sensible' is 'done or chosen in accordance with wisdom or prudence; likely to be of benefit'.
• Hence, the appropriate answer is 'Sensible'.

Additional Information

• Let's understand the other options.
• Amaze- surprise (someone) greatly; fill with astonishment.
• Anxious- feeling or showing worry, nervousness, or unease about something with an uncertain outcome.
• Ramble- talk or write at length in a confused or inconsequential way.

The correct answer is Typical.

Key Points

• The most appropriate synonym for the given word 'Quintessential' is 'Typical'.
• The meaning of the word 'Quintessential' is 'representing the most perfect or typical example of a quality or class'. (किसी गुण या वर्ग के सबसे उत्तम या विशिष्ट उदाहरण का प्रतिनिधित्व करना।)
• The meaning of the word 'Typical' is 'having the distinctive qualities of a particular type of person or thing'. ('किसी विशेष प्रकार के व्यक्ति या वस्तु के विशिष्ट गुण होना'।)
• Hence, the appropriate answer is 'Typical'.

Additional Information

• Let's understand the other options.
• Fantastic- extraordinarily good or attractive. (असाधारण रूप से अच्छा या आकर्षक।)
• Initial- existing or occurring at the beginning. (शुरुआत में विद्यमान या घटित होना।)
• Charming- very pleasant or attractive. (बहुत ही सुखद या आकर्षक।)

The correct answer is 'We are vexed by their behaviour'.

Key Points

• The given sentence is in Present Tense and in Active voice.
• The rule for changing a sentence in Present Tense from Active voice to Passive voice:
• ​Interchange the object and the subject with each other, i.e. Object of the active sentence becomes the subject of the passive sentence.
• The helping verb comes before the object in the passive voice as the passive voice starts with the object of the active voice.
• Convert the verb into past participle or 3^rd form of the verb.
• Structure: Subject + V1 + s/es + Object (Active voice)

​                                       Object + is/am/are/ + V3 + by + Subject (Passive voice)

• Solution: Their behaviour vexes us. (Active Voice)

​                           We are vexed by their behaviour. (Passive Voice)

The correct answer is 'To be brave in a difficult situation'.

Key Points

• The most appropriate meaning of the given idiom 'To bite the bullet' is 'To be brave in a difficult situation'. (कठिन परिस्थिति में बहादुर बनना'।)
• To bite a bullet: to force yourself to perform an unpleasant or difficult action or to be brave in a difficult situation (अपने आप को एक अप्रिय या कठिन कार्य करने के लिए मजबूर करना या कठिन परिस्थिति में बहादुर होना)
• E.g. I decided I had to bite the bullet and take a couple of math classes even though I knew they were hard.
• Therefore, as per the points mentioned above, we find the correct answer is option 3.

Additional Information

• Let's look at some similar idioms.
• Be man enough- to be brave enough to do something (कुछ करने के लिए पर्याप्त बहादुर होना)
• He was man enough to admit he had made a mistake.
• Faint heart never won fair lady- timidity will prevent you from achieving your objective (कायरता आपको अपने लक्ष्य को प्राप्त करने से रोकेगी)
• Rebecca: Remember that faint heart never won fair lady. He'll probably be flattered and impressed if you approach him first.

The correct answer is 'Succesion'.

Key Points

• The correct spelling of 'Succesion' according to the English Dictionary is 'Succession'.
• The word 'Succession' means 'the action or process of inheriting a title, office, property, etc'.
• Hence, the most appropriate answer is 'Succesion'.

Additional Information

• Let's understand the other options.
• Assassinate- murder (an important person) for political or religious reasons.
• Complacent- showing smug or uncritical satisfaction with oneself or one's achievements.
• Aquarium- a transparent tank of water in which live fish and other water creatures and plants are kept.

The correct answer is 'gloomy'.

Key Points

• The most appropriate antonym for the given word 'cheerful' is 'gloomy'.
• The meaning of the word 'cheerful' is 'noticeably happy and optimistic'.
• The meaning of the word 'gloomy' is 'dark or poorly lit, especially so as to appear depressing or frightening'.
• Hence, the most appropriate answer is 'gloomy'.

Additional Information

• Chirpy- cheerful and lively.
• Radiant- sending out light; shining or glowing brightly.
• Jaunty- having or expressing a lively, cheerful, and self-confident manner.

The correct answer is 'disclosed'.

Key Points

• The most appropriate antonym for the given word 'concealed' is 'disclosed'.
• The meaning of the word 'concealed' is 'kept secret; hidden'.
• The meaning of the word 'disclosed' is 'make (secret or new information) known'.
• Hence, the most appropriate answer is 'disclosed'.

Additional Information

• Annoyed- slightly angry; irritated.
• Arrogant- having or revealing an exaggerated sense of one's own importance or abilities.
• Excited- very enthusiastic and eager.

The correct answer is 'unsteadiness'.

Key Points

• The most appropriate synonym for the given word 'giddiness' is 'unsteadiness'.
• The meaning of the word 'giddiness' is 'a sensation of whirling and a tendency to fall or stagger; dizziness'.
• The meaning of the word 'unsteadiness' is 'Loss of one's equilibrium in regard to the environment, often with a feeling of almost falling, or the result of bumping into things'.
• Hence, the most appropriate answer is 'unsteadiness'.

Additional Information

• Opponent- someone who competes with or opposes another in a contest, game, or argument.
• Enthusiasm- intense and eager enjoyment, interest, or approval.
• Pride- consciousness of one's own dignity.

The correct answer is "When the villagers put up a firm resistance to the fearsome bandit with all their might, he ultimately fled the spot. "

Key Points

• The past tense of "flee" is "fled".
• "Fled" means "escape".
• Example: The thief fled from the spot when people began to crowd.
• Moreover, there is no verb in English like "fleed".
• Therefore the appropriate option is "When the villagers put up a firm resistance to the fearsome bandit with all their might, he ultimately fled the spot. "

Additional Information

• The past tense of the verb is formed either by adding "ed" or changing the vowel.
• Not only "ed", but words ending in "e" also has its past tense by simply adding a "-d" and words ending in "y" has its past tense as"-ied". 
• Example: cook - cooked, like - liked, empty - emptied.
• Some verbs change their vowel to get past tense.
• Example: drive - drove, eat - ate, swim - swam.

The correct answer is 'Calligraphy'.

Key Points

• The most appropriate one-word substitute for 'The art of beautiful handwriting' is 'Calligraphy'.
• Let's understand the other options.
• ​Monography- a long article or a short book on a particular subject.
• Epigraphy-  the study of inscriptions, or epigraphs, as writing.
• Catastrophe- an event causing great and usually sudden damage or suffering; a disaster.

The correct answer is 'in'.

Key Points

• The most appropriate option to substitute the underlined word 'on' is 'in'.
• The preposition 'on' is used 'to indicate that something is already in the position'.
• The preposition 'in' is used 'at a point within an area or a space, within the shape of something'.
• Hence, the appropriate preposition is 'in'.

Additional Information

• Let's understand the other options.
• Over- at or to a place that is higher than someone or something
• A beautiful white bird flew over the lake.
• At- expressing location or arrival in a particular place or position
• I will see you at 8:00 pm.
• For- because of or as a result of something
• I'm going for some breakfast. I'm really hungry.

The correct answer is 'Epitaph'.

Key Points

• The most appropriate one-word substitute for 'The work inscribed on the tomb in the memory of the person' is 'Epitaph'.
• Let's understand the other options.
• ​Epigraph- an inscription on a building, statue, or coin.
• Excerpt-  a short extract from a film, broadcast, or piece of music or writing.
• Euphoria- a feeling or state of intense excitement and happiness.

The correct answer is 'The chef is preparing the meal.'.

Key Points

• The given sentence is in the Present Continuous Tense and in Active voice.
• The rule for changing a sentence in Present Continuous Tense from Passive voice to Active voice:
• ​Interchange the object and the subject with each other, i.e. Object of the passive sentence becomes the subject of the active sentence.
• The helping verb comes before the object in the passive voice as the passive voice starts with the object of the active voice.
• Convert the verb into present/base form or 1^st form of the verb.
• Structure: Subject + is/am/are + V1 + ing + Object (Active voice)

​                                       Object + is/am/are/ + being + V3 + by + Subject (Passive voice)

• Solution: The meal is being prepared by the chef. (Passive Voice)

​                           The chef is preparing the meal. (Active Voice)

The correct answer is 'interventions, targeted, inferences'.

Key Points

• The most appropriate options to fill in the blanks are 'interventions, targeted, inferences'.
• The word 'interventions' means 'interference by a state in another's affairs'.
• The word 'targeted' means 'select as an object of attention or attack'.
• The word 'Interference' means 'the action of interfering or the process of being interfered with'.
• Hence, the correct answer is 'interventions, targeted, inferences'.

Additional Information

• Let's understand the other options.
• Option 1:
• Intermissions- a pause or break.
• Directed- control the operations of; manage or govern.
• Injunctions- a judicial order restraining a person from beginning or continuing an action threatening or invading the legal right of another, or compelling a person to carry out a certain act.
• Option 2: 
• Interpolations- the insertion of something of a different nature into something else.
• Disrupted- drastically alter or destroy the structure of.
• Inventions- the action of inventing something, typically a process or device.
• Option 4:
• Interruptions- the action of interrupting or being interrupted.
• Disillusioned- disappointed in someone or something that one discovers to be less good than one had believed.
• Invasions- an incursion by a large number of people or things into a place or sphere of activity.

The correct answer is 'put up with'.

Key Points

• The most appropriate substitute for the underlined segment 'sit up with' is 'put up with'.
• The meaning of the phrasal verb 'put up with' means 'tolerate or endure something'.
• Hence, the appropriate answer is 'put up with'.

Additional Information

• The other options are just to confuse they do not mean anything.

The correct answer is 'toe'.

Key Points

• The most appropriate homonym to fill in the blank is 'toe'.
• The word 'toe' means 'any of the five jointed parts at the front of the human foot'.
• Hence, the correct word is 'toe'.

Additional Information

• Let's understand the other options.
• Toad- a tailless amphibian with a short stout body and short legs, typically having dry warty skin that can exude poison; a species of frogs.
• Tow- (of a motor vehicle or boat) pull (another vehicle or boat) along with a rope, chain, or tow bar.
• To- to indicate a goal or a direction of movement, as well as a place of arrival.

The correct answer is "call a spade a spade". 

Key Points

• The appropriate idiom which means "talking too frankly" is "call a spade a spade".
• Call a spade a spade - speak plainly without leaving out anything. 
• Example: The stand-up comedian was very honest. He called a spade a spade.
• Therefore the correct answer is Option 4.

Additional Information

• Lose one's marbles - become insane.
• Example: John lost his marbles during the fight.
• Go the extra mile - take extra effort.
• Example: Mary went the extra mile to buy a present for her parents.
• Snug as a bug in a rug - in a very comfortable situation. 
• Example: Jim was snug as a bug in a rug in the debate.

The correct answer is 'down'.

Key Points

• The most appropriate word to fill in the blank is 'down'.
• The idiom 'Swallowed down' means 'To eat or drink something, especially very quickly'.
• Hence, the correct option is 'down'.

Additional Information

• Let's look at some similar idioms.
• Made a pig of themselves- When someone eats way too much, then this expression is used informally.

E.g. I made a real pig of myself at the party.

• Eat like a horse- Someone who eats a lot regularly.

E.g. Rohit is thin as a stick yet he eats like a horse.

• Wolf food down- Eating a lot very quickly.

E.g. The kids wolfed the burgers down and then started on the pizza.

The correct answer is 'during'.

Key Points

• The most appropriate word to fill in the blank is 'during'.
• The word 'during' means 'throughout the course or duration of (a period of time)'.
• Hence, the correct answer is 'during'.

Additional Information

• Let's look at the other options.
• By- identifying the agent performing an action.
• At- expressing location or arrival in a particular place or position.
• Through- moving in one side and out of the other side of (an opening, channel, or location).

The correct answer is 'leaving'.

Key Points

• The most appropriate word to fill in the blank is 'leaving'.
• The word 'leaving' means 'go away from'.
• Hence, the correct answer is 'leaving'.

Additional Information

• Let's look at the other options.
• Settling- resolve or reach an agreement about (an argument or problem).
• Reckoning- the action or process of calculating or estimating something.
• Keeping- the action or fact of owning, maintaining, or protecting something.

The correct answer is 'seemed'.

Key Points

• The most appropriate word to fill in the blank is 'seemed'.
• The word 'seemed' means 'give the impression of being something or having a particular quality'.
• Hence, the correct answer is 'seemed'.

Additional Information

• Let's look at the other options.
• Departed- move away from a place into another direction.
• Became- begin to be.
• Kept- the action or fact of owning, maintaining, or protecting something.

The correct answer is 'punishment'.

Key Points

• The most appropriate word to fill in the blank is 'punishment'.
• The word 'punishment' means 'the infliction or imposition of a penalty as retribution for an offense.
• Hence, the correct answer is 'punishment'.

Additional Information

• Let's look at the other options.
• Order- an authoritative command or instruction.
• Accolade- an award or privilege granted as a special honor or as an acknowledgment of merit.
• Oracle- a priest or priestess acting as a medium through whom advice or prophecy was sought from the gods in classical antiquity.

The correct answer is 'sanitary'.

Key Points

• The most appropriate word to fill in the blank is 'sanitary'.
• The word 'sanitary' means 'relating to the conditions that affect hygiene and health, especially the supply of sewage facilities and clean drinking water'.
• Hence, the correct answer is 'sanitary'.

Additional Information

• Let's look at the other options.
• Cultural- relating to the ideas, customs, and social behavior of a society.
• Unhygienic- not clean or sanitary.
• Ongoing- continuing; still in progress.

The pattern followed here is:

• In ANOXIC : ONACIX​
• 
• In EQUITY : UQEYTI​
• 
• Similarly, In **REFUND : ?**​
• 

 We get "FERDNU" .

Hence, "FERDNU" is the correct answer.

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 "

" → Options 2, 4 are eliminated.

• The second last letter of the word is "

". So, the second letter in the mirror image will be "

"→ Options 1 is eliminated.

Hence, Option 3) is the correct answer.

Additional Information

• In a mirror image Left changes to rightand theright changes to leftwheretop 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.

Logic : Cube of first number - Cube of (first number - 1) = Second number

• 3 : 19

⇒ 3³ - (3 - 1)³ 

⇒ 3³ - 2³ = 19

• 2 : 7

⇒ 2³ - (2 - 1)³

⇒ 2³ - 1³ = 7

Similarly, 5 : ?

⇒ 5³ - (5 - 1)³

⇒ 5³ - 4³ = 61

Hence, 61 is the correct answer.

The logic followed here is:

(First number × 3) + (Second number × 2) = Third number

First row: 7, 9, 39 → (7 × 3) + (9 × 2) = 21 + 18 = 39

Second row: 4, 8, 28 →  (4 × 3) + (8 × 2) = 12 + 16 = 28

Third row: 6, 7,? →  (6 × 3) + (7 × 2) = 18 + 14 = 32

Hence, 32 is the correct answer.

The logic followed here is:

Hence, "124" is the correct answer.

When the folder paper is opened, the cuts will appear as follows:

Hence, option 3) is the correct answer.

The logic followed here is:

Hence, 266 is the correct answer.

The pattern followed here is:

Letters are increasing in the order +5.

On continuing the same pattern, we get,

Hence, ‘EILN’ is the correct answer.

The pattern followed here is: (Here, +18 could be replaced by -8)

Hence, ‘GFXA’ is the correct answer.

The logic followed here is:-

• PEN
• 
• ​Therefore, code = OCK
• ZEN
• 
• Therefore, code = YCK
• Similarly, TON
• 
• Therefore, code = SMK

Hence, "SMK" is the correct answer.

Here, we need to find out the pattern to fill the missing letters.

Given: C _ _ r E _ t C U r _ _ n t C _ r _ E n t

First we will check all the options:

1) E r n r E U r: C E r r E n t - C U r r E n t  - C U r r E n t

2) U r U r E U r: C U r r E u t - C U r r E n t  - C U r r E n t

3) U r n r U U r: C U r r E n t - C U r r U n t  - C U r r E n t

4) U r n r E U r: C U r r E n t - C U r r E n t  - C U r r E n t

Thus, we can see that in 'option 4' the letters 'U r n r E U r' are repeating itself.

 

Hence, the correct answer is 'option 4'.

Here, we need to arrange the words in alphabetic order.

So, the dictionary order arrangement would be:

5. Sacrifice
6. Salutation
7. Sanction
8. Sarcastic
9. Satisfaction

Hence, the order of arrangement in alphabetic order is '5, 3, 4, 1, 2'.

Here, we need to apply the combination of signs to get the correct equation.

Given: 

First we will check options one by one as below:

1) +, =, -, ×, ÷, +

$\Rightarrow$ 45 + 17 = 3 - 41 × 81 ÷ 9 + 56

Applying BODMAS rule, we will get, 

$\Rightarrow$ 45 + 17 = 3 - 41 × 9 + 56

$\Rightarrow$ 45 + 17 = 3 - 369 + 56

⇒ 62 = 59 - 369

$\Rightarrow$ 62 = -310, is not possible. This is not true.

2) +, -, =, ×, +, -

$\Rightarrow$ 45 + 17 - 3 = 41 × 81 + 9 - 56

Applying BODMAS rule, we will get,  

$\Rightarrow$ 45 + 17 - 3 = 3321 + 9 - 56 

⇒ 62 - 3 = 3330 - 56

$\Rightarrow$ 59 = 3274, is not possible. This is not true.

3) =, -, ×, +, -, +

$\Rightarrow$ 45 = 17 - 3 × 41 + 81 - 9 + 56

Applying BODMAS rule, we will get,  

$\Rightarrow$ 45 = 17 - 123 + 81 - 9 + 56

⇒ 45 = 154 - 123 - 9

⇒ 45 =  154 - 132

$\Rightarrow$ 45 = 22, is not possible. This is not true.

4) =, ×, +, +, ÷, -

$\Rightarrow$ 45 = 17 × 3 + 41 + 81 ÷ 9 - 56

Applying BODMAS rule, we will get, 

$\Rightarrow$ 45 = 17 × 3 + 41 + 9 - 56

$\Rightarrow$ 45 = 51 + 41 + 9 - 56

⇒ 45 = 101 - 56

$\Rightarrow$ 45 = 45, is possible. This is true.

Hence, the combination of signs ' =, ×, +, +, ÷, -' is used to get correct balanced equation.

 Confusion Points Keep in mind to apply BODMAS rule, while solving these types of problems.

BODMAS rule:

Here, we need to apply the combination of signs to get the correct equation.

Given: 65 * 50 * 5 * 2 * 4 * 63

First we will check options one by one as below:

1) ÷, -, ×, +, =

$\Rightarrow$ 65 ÷ 50 - 5 × 2 + 4 = 63

Applying BODMAS rule, we will get, 

$\Rightarrow$ 1.3 - 5 × 2 + 4 = 63

$\Rightarrow$ 1.3 - 10 + 4 = 63

$\Rightarrow$ 0.3 + 4 = 63

$\Rightarrow$ -4.7 = 63, is not possible. This is not true.

 

2) +, ×, ÷, -, =

$\Rightarrow$ 65 + 50 × 5 ÷ 2 - 4 = 63

Applying BODMAS rule, we will get, 

$\Rightarrow$ 65 + 50 × 2.5 - 4 = 63

$\Rightarrow$ 65 + 125 - 4 = 63

$\Rightarrow$ 186 = 63, is not possible. This is not true.

 

3) +, ×, -, ÷, =

$\Rightarrow$ 65 + 50 × 5 - 2 ÷ 4 = 63

Applying BODMAS rule, we will get, 

$\Rightarrow$ 65 + 50 × 5 - 0.5 = 63

$\Rightarrow$ 65 + 250 - 0.5 = 63

$\Rightarrow$ 314.5 = 63, is not possible. This is not true.

 

4) -, ÷, +, ×, =

$\Rightarrow$ 65 - 50 ÷ 5 + 2 × 4 = 63

Applying BODMAS rule, we will get, 

$\Rightarrow$ 65 - 10 + 2 × 4 = 63

$\Rightarrow$ 65 - 10 + 8 = 63

$\Rightarrow$ 63 = 63, is possible. This is true.

Thus, the combination of signs ' -, ÷, +, ×, =' is used to get correct balanced equation.

Hence, the correct answer is 'option 4'. 

Confusion Point: Keep in mind to apply BODMAS rule, while solving these types of problems.

The logic followed here is:

Here, we have two dices and face number 4 is common in both of them.

Also, both the dice are arranged in such a way that the common faces are at the same place.

So, we can see that, all the numbers except number 1 is not seen here in the image.

Hence, the number 1 will be the face opposite to the face 4.

Here, the alphabets and their positions are shown as below:

The logic here is: The first and the last letter of each word interchange their places and the middle letters are increased by 1 to get the code language of that word.

For the word KITCHEN is written as NJUDIFK

And, for the word RESPECT is written as TFTQFDR

Similarly, for the word WELCOME: 

 

Thus, the code language is 'EFMDPNW' for the given word.

Hence, the correct answer is 'option 2'.

Here, we need to find the pattern to get the odd one out.

The logic here is: The last term is cube root of a number. That number is subtracted by 2 and this number is added to the last term to get the first term of each row.

So, 14 : 512 $\Rightarrow 512 = 8^3$ , 8 + (8 - 2) = 14

22 : 1728 $\Rightarrow 1728 = 12^3$, 12 + (12 - 2) = 22

46 : 23 $\Rightarrow 12167 = 23^3$ , 23 + (23 - 2) = 44, But they have given 46 as the 1^st term

38 : 8000 $\Rightarrow 8000 = 20^3$ , 20 + (20 - 2) = 38

Thus, all except option 3 does not follow the pattern.

Hence, the number pair '46 : 12167' is the odd one out.

Alternate Method14 : 512 → (14 ÷ 2 + 1)³ = 512

22 : 1728 → (22 ÷ 2 + 1)³ = 1728

46 : 12167 → (46 ÷ 2 + 1)³ = 13824 ≠ 12167

38 : 8000 → (38 ÷ 2 + 1)³ = 8000

Hence, the correct answer is "Option 3".

The logic followed here is:

Here, we are given the word and we need to find the mirror image of it.

First keep in mind that, in mirror image the first letter will be the last letter of the given word. Also, the size of the letters will not change i.e. capital letters will appear capital only.

Next, as we can see the given word ends with Z, so the mirror image will have Z as the first word. This shows that, option 2 and 3 are eliminated.

Again, number 5 is water image in option 4, so option 4 is eliminated.. 

Thus, we have only one option left i.e. option 1.

 

Hence, the mirror image of the given word is 'option 1'. 

Confusion Points

Keep in mind what is the difference between mirror image and water image.

The logic followed here :

Here, we are given the word and we need to find the mirror image of it.

First keep in mind that, in mirror image the first letter will be the last letter of the given word. Also, the size of the letters will not change i.e. capital letters will appear capital only.

Next, as we can see the given word ends with 9, so the mirror image will have 9 as the first number. 

Again, number 9 is water image in option 3, so option 3 is eliminated.

Again, letter q is water image in option 2, 3, 4. So, all these options are eliminated.

Thus, we have only one option left i.e. option 1.

Hence, the mirror image of the given word is 'option 1'. 

Confusion Points  Keep in mind what is the difference between mirror image and water image.

The logic followed here is:

Here, we need to apply the combination of signs to get the correct equation.

Given: 93 * 65 * 3 * 56 * 14 * 146

First we will check options one by one as below:

1) ×, +, -, ÷, =  

$\Rightarrow$ 93 × 65 + 3 - 56 ÷ 14 = 146

$\Rightarrow$ 93 × 65 + 3 - 4 = 146

$\Rightarrow$ 6045 + 3 - 4 = 146

⇒ 6048 - 4 = 46

$\Rightarrow$ 6044 = 146, is not possible. This is not true.

2) +, -, ÷, ×, =

$\Rightarrow$ 93 + 65 - 3 ÷ 56 × 14 = 146

$\Rightarrow$ 93 + 65 - 0.053 × 14 = 146 

$\Rightarrow$ 93 + 65 - 0.75 = 146

⇒ 158 - 0.75 = 1436

$\Rightarrow$ 157.25 = 146, is not possible. This is not true.

3) -, +, ×, ÷, =

$\Rightarrow$ 93 - 65 + 3 × 56 ÷ 14 = 146

$\Rightarrow$ 93 - 65 + 3 × 4 = 146

$\Rightarrow$ 93 - 65 + 12 = 146

⇒ 105 - 65 = 146

$\Rightarrow$ 40 = 146, is not possible. This is not true.

4) +, -, ×, ÷, =

$\Rightarrow$ 93 + 65 - 3 × 56 ÷ 14 = 146

$\Rightarrow$ 93 + 65 - 3 × 4 = 146 

$\Rightarrow$ 93 + 65 - 12 = 146

⇒158 - 12 = 146

$\Rightarrow$ 146 = 146, is possible. This is true.

Hence, the combination of signs ' +, -, ×, ÷, =' is used to get correct balanced equation.

Confusion Points

Keep in mind to apply BODMAS rule, while solving these types of problems.

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

First we will check the options one by one.

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

2. 25 : 2 = $\sqrt{25}$ = 5; 5 - 3 = 2

3. 225 : 12 = $\sqrt{225}$ = 15; 15 - 3 = 12

4. 169 : 10 = $\sqrt{169}$ = 13; 13 - 3 = 10

As, we can see all have the same pattern except option 1.

Hence, the number pair '64 : 6' is not related to the given pattern.

Here, we have given a date along with the day and we need to find out the day of the next date given.

For, 28 Feb 2020 was Friday

Since, 2019, 2018, 2017 are ordinary years. All have only 1 odd day.

And, 2016 is a leap year. This will have 2 odd days.

Total days = 1 + 1 + 1 + 2 = 5.

So, 28 Feb 2016 = Friday - 5 = Sunday

Next, we will count the days of the remaining months as:

27 (Feb) + 31 (Jan) + 2 (Dec) = 60 = 8 weeks and 4 odd days.

Thus, 30 Dec 2015 was Sunday - 4 = Wednesday.

Hence, it was 'Wednesday' on 30 Dec 2015.

Confusion Points Keep in mind what are leap years and ordinary year and number of odd days they have. Also, check how to find the leap year too.

Here, we are given the word and we need to find the mirror image of it.

First keep in mind that, in mirror image the first letter will be the last letter of the given word. Also, the size of the letters will not change i.e. capital letters will appear capital only.

Next, as we can see the given word ends with r, so the mirror image will have r as the first letter. 

Again, letter e is water image in option 2 and 3, so both the options are eliminated.

Again, letter r is water image in option 4, so option 4 is eliminated.

Thus, we have only one option left i.e. option 1.

Hence, the mirror image of the given word is 'option 1'. 

 Confusion Points Keep in mind what is the difference between mirror image and water image.

The logic followed here is:

Each term is added by 52 to get the next consecutive numbers.

So,  134 + 52 = 186,

186 + 52 =238,

238 + 52 = 290,

290 + 52 = 342,

Thus, 342 + 52 = 394

Hence, the missing number will be 394.

The logic followed her is:

According to the given statements,

1) W is taller than X but shorter than V.

$\Rightarrow$ X < W < V 

2. T is taller than U but shorter than S.

$\Rightarrow$ U < T < S

3. Y is the shortest among all. 

$\Rightarrow$ Y < All six friends

4) Only three people are taller than V.

$\Rightarrow$ Y < X < W < V

Next, combining all the statements, we will have

$\Rightarrow$ Y < X < W < V < U < T < S

Thus, T and S are taller than U.

Hence, only 2 persons are taller than U.

Given:

Marks scored by Gopal = 15% more than Asha

Marks scored by Asha = 10% more than Sachin

Concept Used:

Percentage Marks Scored = Required Percentage × Total Marks

Calculation:

⇒ Let the marks scored by Sachin be x.

⇒ Marks scored by Asha = x + 10% of x

⇒ Marks scored by Asha = $x+\frac{x}{10}=\frac{11x}{10}$

⇒ Marks scored by Gopal = $\frac{11x}{10}+\frac{15}{100}×\frac{11x}{10}$

⇒ Marks scored by Gopal = $\frac{11x}{10}+\frac{33x}{200}=\frac{220x+33x}{200}=\frac{253x}{200}$

⇒ Difference between Gopal and Sachin marks = $\frac{253x}{200}-x=\frac{53x}{200}$

⇒ Percentage marks Gopal scored more than Sachin = $\frac{\frac{53x}{200}}{{\frac{x}{1}}}×100$

⇒ Percentage marks Gopal scored more than Sachin = $\frac{53}{200}×100=26.5$ %

Hence, Gopal scored 26.5 % more marks than Sachin.

Shortcut TrickLet marks scored by Sachin = 100

Then marks scored by Asha = 100 + 10 = 110

Marks scored by Gopal = 110 + 15% × 110 = 

⇒ 110 + 16.5 = 126.5

So, Gopal scored 26.5% more than Sachin.

Given:

Time taken by Pranjal = Twice as much as Vikram

Time taken by Pranjal = Thrice as much as Ashwin

Time taken to finish work together = 6 days

Calculation:

⇒ Let Pranjal take x days to complete the work.

⇒ So, Vikram takes $\frac{x}{2}$ and Ashwin takes $\frac{x}{3}$ days to complete the work.

⇒ According to the question, all working together

⇒ Then, $\left(\frac{1}{x}+\frac{2}{x}+\frac{3}{x} \right)=\frac{1}{6}$

⇒ $\frac{6}{x}=\frac{1}{6}$

⇒ x = 36 days

⇒ Time taken by Vikram to complete the work = $\frac{x}{2}=\frac{36}{2}=18$ days

Hence, Vikram can complete the work alone in 18 days.

Short trick:

Formula used:

Efficiency = Total unit/No. of days

Time is inversely proportional to efficiency

Calculation:

As , we know that time is inversely proportional to efficiency 

So, let the efficiency of pranjal be x 

Then efficiency of vikram = 2x

Efficiency of Ashwin = 3x

Total efficiencies = x + 2x + 3x = 6x 

Total days taken to work together = 6 

Total unit = 6x × 6 = 36x

Now, vikram can do the work in = 36x/2x = 18

Hence, vikram can do the work in 18 days .

Given:

60% of a number = Three-fourth of another number

Calculation:

⇒ Let the first number be x and another number be y.

⇒ So, 60% of x = $\frac{3}{4}\times y$

⇒ $\frac{60}{100}\times x=\frac{3}{4}y$

⇒ $\frac{x}{y}=\frac{\frac{3}{4}}{\frac{3}{5}}=\frac{3\times5}{4\times3}$

⇒ $\frac{x}{y}=\frac{5}{4}=5:4$

Hence, the ratio of the first number to the second number is 5 : 4

Given:

Average of 19 numbers = 8.5

Correct Number = 63

Incorrect Number = 25

Concept Used:

Average = Sum of all values ÷ Number of values

Calculation:

Total sum of 19 numbers = 19 × 8.5 = 161.5

Removal of Incorrect Number = 161.5 – 25 = 136.5

Now, After adding the correct number

Total sum of 19 numbers = 136.5 + 63 = 199.5

⇒ Corrected Average of 19 numbers = $\frac{199.5}{19}=10.5$

Hence, the corrected average of the 19 numbers is 10.5

Given:

Volume of sphere = 38808 cm³

Concept Used:

Volume of sphere = $\frac{4}{3}π r^3$

Surface Area of sphere = 4πr²

Calculation:

⇒ $\frac{4}{3}π r^3=38808$

⇒ $\frac{4}{3}× \frac{22}{7}× r^3=38808$

⇒ $r^3=\frac{38808× 21}{88}$

⇒ r³ = 9261

⇒ r = 21 cm

Now, the Surface Area of the sphere = $4× \frac{22}{7}× 21× 21$

⇒ 4 × 66 × 21 = 5544 cm²

Hence, the surface area of a sphere is 5544 cm².

Concept Used:

a^x × a^y = a^{x + y}

Calculation:

⇒  (625)0.07× (625)0.18

⇒ (625)^{0.07 + 0.18} 

⇒ (625)^0.25

⇒ (625)^1/4 = (5⁴)^1/4

∴ The value of the given expression is 5

Given:

Divisor = 360

Concept Used:

Divisible by 9 = Sum of all digits of numbers divisible by 9

Calculation:

360 can be expressed in the form of factors 5 × 8 × 9

For numbers to be divisible by 360, it should be divisible by 9 also.

⇒ 171720 = 1 + 7 + 1 + 7 + 2 + 0 = 18

So, it is divisible by 9

⇒ 176600 = 1 + 7 + 6 + 6 + 0 + 0 = 20

So, it is not divisible by 9

⇒ 166200 = 1 + 6 + 6 + 2 + 0 + 0 = 15

So, it is not divisible by 9

⇒ 171080 = 1 + 7 + 1 + 0 + 8 + 0 = 17

So, it is not divisible by 9

Hence, the number which is divisible by 360 is 171720

Given:

Discount % = 20% on the part of the Marked price that was paid in cash

Charged 0.5% on the part marked price paid through a credit card

Suresh paid 40% of the marked price in cash and the rest through a credit card

Formula Used:  

Discount % = Marked Price × Discount Rate

Percentage % = $\frac{\text{Payed}}{\text{Marked Price}}\times100$

Calculation:

Let the marked price = Rs. 100

40% of MP is paid in cash 

⇒ Rs. 40 is paid in cash and Rs. 60 is paid by credit card

According to the question,

20% offered on the part of the marked price that was paid in cash

⇒ 20% of 40 = Rs 8

The discount price of the product paid by cash

⇒ MP - 20% of MP = 40 - 8 = Rs. 32

0.5% charged on the part of the Marked Price that was paid by card

⇒ 0.5% of 60 = 0.3

The increased price the of product paid by credit card

⇒ MP + 0.5% of 60 = 60 + 0.3 = Rs. 60.3

Total payment Suresh has pay = payed by cash + payed by credit card

⇒ Rs. 32 + Rs. 60.3 = Rs. 92.3

Percentage % = $\frac{\text{Payed}}{\text{Marked Price}}\times100=\frac{92.3}{100}\times100$ 

 =  92.3%

The percentage of the Marked Price was his total final payment is 92.3%

Given:

Time taken to row 36 km downstream = 4 hours

Time taken to row 49 km upstream = 7 hours

Concept Used:

Time = Distance ÷ Speed

Calculation:

Let the speed in still water be x km/h and speed of current be y km/h.

Downstream speed = x + y km/h

Upstream speed = x – y km/h

Putting the values in the formula,

⇒ 4 = $\frac{36}{x+y}$ and 7 = $\frac{49}{x-y}$

⇒ x + y = 9 and x – y = 7

Solving, we get

⇒ x = 8 km/h and y = 1 km/h

Hence, the speed of the current is 1 km/h.

Given:

Marked Price of cell phone = Rs 23,000

Successive discounts = 14% and 16%

Concept Used:

Discount = Marked Price – Discount % of Marked Price

Calculation:

On the first discount of 14%

New Marked Price after discount

⇒ 23000 – 14% of 23000

⇒ $23000-\frac{14}{100}\times 23000$ 

⇒ Rs. = 19780

Now, after a discount of 16%

New MP after discount = $19780-\frac{16}{100}\times19780$

⇒ 19780 - 3165

⇒ 16615

Hence, the customer have to pay the amount of Rs 16,615

Given:

Ratio of expenses on rice, vegetables, and cooking oil = 9 : 11 : 5

Increase in prices of item = 10%, 20% and 30%

Concept Used:

New Item Price = Original Price + Percentage Increase of Original Price

Calculation:

Let the prices of rice, vegetables, and cooking oil be Rs 9, Rs 11 and Rs 5 respectively.

⇒ Total Expenditure = Rs 9 + 11 + 5 = Rs 25

Price after increase of 10% in the price of rice

⇒ New Price = 9 + 10% of 9 = $9+\frac{10}{100}\times 9 = 9+0.9=9.9$ 

Price after increase of 20% in the price of vegetables

⇒ New Price = 11 + 20% of 11 = $11+\frac{20}{100}\times 11=11+2.2=13.2$ Rs

Price after increase of 30% in the price of cooking oil

⇒ New Price = 5 + 30% of 5 = $5+\frac{30}{100}\times 5 =5+1.5=6.5$ Rs

⇒ New Total Expenditure = Rs 9.9 + 13.2 + 6.5 = Rs 29.6

⇒ Increase in expenditure = Rs 29.6 – 25 = Rs 4.6

⇒ Percentage increase by new expenditure = $\frac{4.6}{25}\times 100=4.6\times 4=18.4$ %

Hence, the total expense of the family will increase by 18.4 %

Given:

Average visitors on Sundays = 330

Average visitors on the other days = 240

Total days in the month = 30

Concept Used:

Average = Total Sum of Values ÷ Number of values

Calculation:

Starting with Saturday as the first day

Number of Sundays in the month = 5

So, Number of visitors on Sundays in the month

⇒ 330 × 5 = 1650

Number of visitors on the other days = 25 × 240 = 6000

Total visitors in the month

⇒ 6000 + 1650 = 7650

Then, Average visitors per day = $\frac{7650}{30}=255$

Hence, the number of visitors per day in a month is 255

Concept Used:

Calculation:

⇒ ${{3294}\over{(226+506) \ of\ {3\over4}}}+500$

⇒ ${{3294}\over{732 \times\ {3\over4}}}+500$

⇒ $\frac{3294}{549}+500=6+500=506$

Hence, the simplified value of the expression is 506

Concept used:

x² + y² + z² = (x + y + z)² - 2(xy + yz + zx)

Calculations:

According to the question, x + y + z = 0

x = - (y + z)

y = - (x + z)

z = - (x + y)

Now,

 ${{x^2}\over {x^2-yz} }+{{y^2} \over {y^2-zx}}+{{z^2} \over {z^2-xy}}$

⇒  $\frac{x²}{- x(y + z) - yz}$ + $\frac{y²}{- y(x + z) - xz}$ + $\frac{z²}{- z(x + y) - xy}$

⇒ - $\frac{x²}{xy + yz + zx}$ - $\frac{y²}{xy + yz + zx}$ - $\frac{z²}{xy + yz + zx}$

⇒ - $\frac{x²+y²+z²}{xy + yz + zx}$

⇒ - {$\frac{(x+y+z)²-2(xy + yz + zx)}{xy + yz + zx}$} 

Substitute x + y + z = 0 in the above equation

⇒ $\frac{2(xy + yz + zx)}{xy + yz + zx}$

⇒ 2

Hence, the required value is 2.

Concept Used:

Percentage Composition = Percentage Given × Total Time

Calculation:

From the pie chart, we found that the maximum percentage composition is for Sleep.

⇒ Time given for sleeping = 35% of 24 hours

⇒ Time given for sleeping = $\frac{35}{100}\times 24=8.4$ hours

Hence, the maximum number of hours in a day is spent on Sleeping.

Formula used:

sin²ø + cos²ø = 1

sin (90 - ø) = cos ø

cos (90 - ø) = sin ø 

Calculation:

sin 35° cos 55° + cos 35° sin 55°

In the given expression we can write 35 as (90 - 55)

⇒ sin (90 - 55)° cos 55° + cos (90 - 55)° sin 55°

By using the formula, sin ( 90 - ø ) = cos ø and cos ( 90 - ø) = sin ø 

⇒ cos 55° cos 55° + sin 55° sin 55°

⇒ cos² 55° + sin² 55°

⇒ cos2 55° + sin2 55° = 1 (by formula  sin2ø + cos2ø = 1)

The value of the expression is 1

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:

It is given that, $r+{1\over r}=11$

On squaring both sides,

⇒$\left(r+{1\over r}\right)^2=11^2$

⇒ $r^2+{1\over r^2}+2=121$

⇒ $r^2+{1\over r^2}=119$

We have to find the value of ${r^3+{1\over r}} \over r^2-r+1$,

Dividing numerator and denominator by ' r ',

⇒${r^3+{1\over r}} \over r^2-r+1$ = $\frac{r.(r^2+\frac{1}{r^2})} {r.(r-1+\frac{1}{r})}$

⇒$\frac{(r^2+\frac{1}{r^2})} {(r-1+\frac{1}{r})}$

On substituting the values of $r+{1\over r}$ and $r^2+{1\over r^2}$ as 11 and 119 respectively,

⇒$\frac{119}{(11-1)}$ = $\frac{119}{10}$

The value of the expression is $\frac{119}{10}$

Formula used:

Volume of cube = (side)³ 

Surface area of cube = 6(side)²

Calculation:

Volume of larger cube = Volume of smaller cube I + Volume of smaller cube II + Volume of smaller cube III

Volume of larger cube = (3)³ + (4)³ + (5)³

⇒ 216 cm³ 

Let the side of larger cube be 'x' cm

⇒ x³ = 216 cm3 

⇒ x = 6 cm 

Sum of surface areas of cube - I, II and III

⇒ 6(3)² + 6(4)² + 6(5)²

⇒ 6(50)

Surface area of larger cube = 6(x)²

⇒ 6(6)²

Ratio = ${6(50)\over 6(6)^2}$ = 50 : 36

⇒ 25 : 18

The ratio of the smaller cubes' total surface area to the larger cube's total surface area is 25 : 18

\()Given:

CP of machine =  Rs. 5,000

Transportation cost = Rs. 250

SP = Rs. 5,075

Formula used:

% profit = $\frac{SP-CP}{CP} \times 100$ 

% loss = $\frac{CP-SP}{CP}\times 100$

Calculation:

Total amount paid by Rajesh = CP of machine + Transportation of machine

⇒ Rs. 5,000 + Rs. 250 = Rs. 5250

Selling Price =  Rs. 5,075

As it can be noticed that CP > SP

⇒ Hence it is a loss

% loss = $\frac{5250-5075}{5250}\times 100$

% loss = 3.33 %

Rajesh is bearing a loss of 3.33 %

Shortcut TrickRatio to C.P. to S.P.

⇒ 5250 : 5075

⇒ 30 : 29

1 unit of loss out of 30

Loss = 1/30 = 3.33%

Formula used:

 $A = P(1+\frac{r}{n})^{nt}$

Calculation**:**

Let the principal amount of Rs. 100 

It is given that amount is compounded half-yearly

⇒n = 2 and t = 1 year 

So after 1 year the Amount he will be receiving,

⇒A = $100\left(1+\frac{\frac{6}{100}}{2} \right)^{2}~~$

⇒A = 106.09

Effective rate = $\frac{final\ amount - initial\ amount}{100}$

⇒  $\frac{106.09-100}{100}$

⇒ 0.0609

The effective rate of annual interest is 0.0609