SSC CHSL Tier-1 2021: Official Paper (Held On : 8 June 2022 Shift 2) (Previous Year Paper)

The correct answer is "Cunning"

Key Points Here lets see what the given words refer to:

• Deception - making somebody believe or being made to believe something that is not true(कपट, धोखा)
• Example: He had obtained the secret papers by deception.
• Cunning - clever in a dishonest or bad way(चतुर, शातिर)
• ​Example: He was as cunning as a fox.

Additional Information Here we will see the other words with the help of examples:

• Cruelty - cruel behaviour(क्रूरता, निर्दयता)
• ​Example: Keeping a dog tied up outside all day and all night is animal cruelty.
• Reliability - the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure(विश्वसनीयता) 
• ​Example: If you measure a cup of rice three times, and you get the same result each time, that result is reliable.
• Exception - a person or thing that is not included in a general statement(अपवाद)
• Example:Everybody was poor as a student and I was no exception.

The solution is Serious.

Key Points

• The most appropriate ANTONYM of " Frivolous " is Serious.
• Frivolous - Not having any serious purpose or value. (कोई गंभीर उद्देश्य या मूल्य नहीं होना)
• ​​For example : "Rules to stop frivolous lawsuits."
• Serious - Demanding or characterized by careful consideration or application. (सावधानीपूर्वक विचार या आवेदन द्वारा मांग या विशेषता)
• ​For example : "Her face grew serious."
• Therefore option 4 is the correct option.

Additional Information

• Antonym of Popular is unpopular.
• Popular - Liked or admired by many people or by a particular person or group. (कई लोगों द्वारा या किसी विशेष व्यक्ति या समूह द्वारा पसंद या प्रशंसा की गई)
• ​For example : "These cheese are very popular in USA."
• Antonym of Reputed is Actual.​
• Reputed - Generally believed to exist or be something specified, but not definitely the case. (आम तौर पर माना जाता है कि मौजूद है या कुछ निर्दिष्ट है, लेकिन निश्चित रूप से ऐसा नहीं है।)
• ​For example : "A reputed budget of $500 million."
• Antonym of Nervous is Calm​
• Nervous - Easily agitated or alarmed. (आसानी से उत्तेजित या चिंतित।)
• ​For example : " Riya was very nervous about her interview."$

The solution is Do not exasperate Harsha.

Key Points

• The option that will improve the underlined part of " Don’t provoke Harsha, otherwise, she will give you a slap. " is Do not exasperate Harsha.
• Do not exasperate Harsha, otherwise, she will give you a slap.
• Here the word provoke and exasperate defines irritate and frustrate someone intensely.
• ​*For example : " A teacher can provoke you into working hard."*​
• ​As both the options have similar meaning.
• Therefore, option 2 is the correct option.

Additional Information

• Let's discuss information about other options:
• Vacillate - Waver between different opinions or actions or be indecisive. (विभिन्न विचारों या कार्यों के बीच डगमगाना या अनिर्णय होना)
• ​​For example : "I vacillate between teaching and acting."
• Hesitate - Pause in indecision before saying or doing something. (कुछ कहने या करने से पहले अनिर्णय में रुकें।)
• ​​For example : "He hesitated to give me a ride home."
• Equivocate - Use ambiguous language so as to conceal the truth or avoid committing oneself. (अस्पष्ट भाषा का प्रयोग करें ताकि सच्चाई को छुपाया जा सके या स्वयं को प्रतिबद्ध करने से बचा जा सके)
• ​​For example : "The government have equivocated too often in the past."

​​

Hinglish​

• यहाँ provoke और exasperate  शब्द किसी को तीव्रता से चिढ़ाने और हताश करने को परिभाषित करता है।
• उदाहरण के लिए: "एक शिक्षक आपको कड़ी मेहनत करने के लिए उकसा सकता है।"
• चूंकि दोनों विकल्पों का अर्थ समान है।
• अतः विकल्प 2 सही विकल्प है।

The correct answer is extend.

Key Points

• The most appropriate option to fill in the blank in " We're asking them to ______ the deadline." is extend,
• We're asking them to extend the deadline.​
• Extend - Cause to cover a wider area; make larger. (एक व्यापक क्षेत्र को कवर करने का कारण; बड़ा करना।)
• For example : "The garden has been extended."
• ​Therefore option 4 is the correct option.

Additional Information

• Let's discuss information about other options:
• Increase - Become or make greater in size, amount, or degree. (आकार, राशि या डिग्री में बड़ा होना या बनाना।) 
• ​For example : "They are aiming to increase awareness of social issues."
• Enlarge - Make or become larger or more extensive. (बड़ा या अधिक व्यापक बनाना या बनना)
• ​For example : "They have renovated and enlarged the four-storey building."
• Broaden - Become larger in distance from side to side or widen. (अगल-बगल से दूरी में बड़ा हो या चौड़ा हो।)
• ​For example : "Her smile broadened after seeing her mom."

The correct answer is 'Breach'.

Key Points

• The most appropriate word antonym of the given word 'warrant' is 'breach'.
• Warrant: an official written statement that gives somebody permission to do something. [(किसी काम को करने की) आधिकारिक अनुमति; वॉरंट, अधिपत्र, आज्ञापत्र]
• Example: a search warrant [a document that allows the police to search a house]...
• Breach: an act that breaks an agreement, a law, etc. (नियम, समझौते की शर्तों आदि का उल्‍लंघन; नियम-भंग)
• Example: a breach of confidence...

Correct Answer: Breach.

Additional Information

• Let's look at the meaning of other words:
• triumph: a great success or victory; the feeling of happiness that you have because of this. (महान सफलता या विजय; सफलता या विजय का उल्‍लास)
• support: to help somebody by saying that you agree with him/her/it, and sometimes giving practical help such as money. [किसी को (सहमति के आधार पर) समर्थन देना या किसी की (धन देकर) सहायता करना]
• captivate: to attract and hold somebody’s attention. (किसी का ध्यान आकृष्‍ट रखना; मोहित कर देना)

The solution is When Reema saw her mother, she was in ecstasy.

Key Points

• The sentence which has no spelling error is " When Reema saw her mother, she was in ecstasy."
• Here in this sentence there is no spelling mistake and grammatically correct.
• The word ecstasy is defined as an overwhelming feeling of great happiness or joyful excitement.
• ​​For example : "There was a look of ecstasy on her face."
• ​​​Therefore option 1 is the correct option.

Additional Information

• Let's discuss information about other options:
• ​In the second option the sentence contains a spelling mistake acstasy, the correct spelling is ecstasy.
• In the third option the sentence contains a spelling mistake ektasy, the correct spelling is ecstasy.
• In the fourth option the sentence contains a spelling mistake extasy, the correct spelling is ecstasy.

The solution is Philanthropist.

Key Points

• The option that can be used as a one-word substitute for " One who makes an active effort to promote human welfare." is Philanthropist.
• Philanthropist - A person who seeks to promote the welfare of others, especially by the generous donation of money to good causes.
• For example : "The trust was founded by an American philanthropist."
• Therefore option 1 is the correct option.

Additional Information

• Let's discuss information about other options :
• Philosopher - A person engaged or learned in philosophy, especially as an academic discipline.​
• ​​For example : " Sam was a philosopher."
• Philanderer - A man who readily or frequently enters into casual sexual relationships with women; a womanizer.
• ​For example : "He was known as a philanderer."
• Physicist - An expert in or student of physics.
• ​For example : "Ram choose to become a physicist."

The solution is A new batch of officers is being trained by me.

Key Points

• The option that expresses the " I am training a new batch of officers now." in passive voice is
• Passive voice - If the subject is having the action done to it, then the verb is called passive voice.
• Active voice : I am training a new batch of officers now.
• Passive voice : A new batch of officers is being trained by me.
• Therefore option 4 is a correct option.

Additional Information

• Let's discuss information about voices :
• Passive voice - If the subject is having the action done to it, then the verb is called passive voice.
• Active voice - If the subject is performing the action, then the verb is called active voice.
• ​**For example: Active voice - Aditi cut a tree. Passive voice - A tree was cut by aditi.

The solution is We have been waiting.

Key Points

• The most appropriate option that can substitute the underlined segment in " We are waiting for the minister for the last two hours." is We have been waiting.
• We are waiting for the minister for the last two hours.
• Here the tense of underlined word is incorrect.
• The given sentence tense is Present continuous tense.
• The tense of the sentence should be Present perfect continuous tense.
• Present continuous tense - It is a present continuous tense when the verb form used for action or event that are happening or developing now in present.
• Present perfect continuous tense - It is a present perfect continuous tense when starting in the past and occurring until now with an adverb modifier that indicates the approximate duration or an action occurring until lately or recently with some relevant effect continuing into the present.
• Therefore option 1 is the correct option.

Additional Information

The solution is Students are loved by their teachers.

Key Points

• The option that expresses the "Teachers love their students." in passive voice is
• Passive voice - If the subject is having the action done to it, then the verb is called passive voice.
• Therefore option 2 is the correct option.

Additional Information

• Let's discuss information about voices :
• Passive voice - If the subject is having the action done to it, then the verb is called passive voice.
• Active voice - If the subject is performing the action, then the verb is called active voice.
• **​For example: Active voice - Aditi cut a tree. Passive voice - A tree was cut by aditi.

The solution is Benevolent.

Key Points

• The most appropriate synonym of " Benign " is Benevolent.
• Benevolent - Well meaning and kindly.
• ​For example : "A benevolent smile."
• Benign - Gentle and kindly.
• ​For example : "Her face was calm and benign."
• Therefore option 3 is the correct option.

Additional Information

• Let's discuss information about other options :
• Beneficiary - A person who derives advantage from something, especially a trust, will, or life insurance policy.​
• For example : "They took the beneficiary of his father after he died."
• Boisterous - Noisy, energetic, and cheerful. 
• For example : "A group of boisterous girls."
• Boring - Not interesting or tedious.
• For example : "He has got a boring job in an office."

The solution is to be more difficult.

Key Points

• The option that will improve the underlined part of "I find playing chess to be difficult than playing poker." is to be more difficult.
• I find playing chess to be more difficult than playing poker.
• Here the word "more" is added to the sentence because here the game chess is compared with poker.
• Hence, to show the difficulty level of playing the game we used more.
• Therefore option 1 is the correct option.

Additional Information

The correct answer is 'Not wearing any clothes'.

Key Points

• The most appropriate meaning of the given idiom 'In your birthday suit' is 'Not wearing any clothes'.
• If you are in your birthday suit, you are not wearing any clothes.
• In your birthday suit: not wearing any clothes. (कोई कपड़े नहीं पहने हुए)
• Example: They were sunbathing in their birthday suits.

Correct Answer: Not wearing any clothes.

The correct answer is "Bibliophile".

Key Points

• The appropriate answer which means "a person who loves and collects books" is "Bibliophile".
• A bibliophile is a person who loves books and has deep knowledge about them.
• Example: Dane has his personal library. He is a bibliophile.
• Therefore, this proves that the correct answer is Option 2.

Additional Information

• Booker - a person who hires performance companies. 
• Example: We can ask that booker to know about today's performances.
• Bookworm - a person who loves reading books.
• Example: Gina always tops the class because she is a bookworm.
• Biographer - a person who writes about another's life. 
• Example: Isa will become a biographer if she writes about the President's life.

The correct answer is "to try to force someone to do something". 

Key Points

• The appropriate option which means "to twist the player's arm" is "to try to force someone to do something".
• "Twist someone's arm" means to persuade a person to do an action that they do not want to do. 
• Example: Jake's mother twisted his arm by asking him to clean his room.
• Therefore, the correct answer is Option 1.

Additional Information

• Let's see some other idioms with "twist".

The correct answer is "All the options available need to be evaluated by me by the end of this month".

Key Points

• Lets's look into the sentence "I need to evaluate all the options available by the end of this month".
• Here, "by the end of the month" is the adjunct. Let us keep it aside for some time.
• The remaining part of the sentence is "I need to evaluate all the options available".
• This is in the format "Subject - Predicate - Object".
• In order to change it to the passive form, we need to interchange it as "Object - Predicate - Subject",
• Therefore, the passive form of "I need to evaluate all the options available" is "All the options available need to be evaluated by me".
• If we add the adjunct with this sentence, the appropriate answer is "All the options available need to be evaluated by me by the end of this month".

Additional Information

• Let's see the basic difference between active and passive voice.

The correct answer is "Tolerant".

Key Points

• A fanatic means a person whose enthusiasm for something is beyond normal. 
• Example: Joey was a fanatic when it was to food.
• Tolerant means a person with a lot of patience.
• Example: Nathan becomes tolerant when he is experimenting.
• Therefore, the antonym of "Fanatic" is "Tolerant".

Additional Information

• Extremist - the state of being extreme.
• Example: Harry looks like an extremist because of his decision.
• Lunatic - a person who has lost his mental stability.
• Example: Losing his loved ones made Lee a lunatic.
• Fantastic - Very good. 
• Example: You will look fantastic in this attire.

The correct answer is "Occesion". 

Key Points

• The correct spelling of the word is "Occasion".
• Occasion means a special event.
• Example: The family were colour-coordinated for the occasion.
• Therefore, the appropriate answer is "Occesion".

Additional Information

• Humorous - funny
• Example: The show was humourous.
• Mysterious - suspicious
• Example: The man over there looks mysterious.
• Scissors - a tool that helps to cut things, mostly paper. 
• Example: Open this parcel using scissors.

The correct answer is "to reject".

Key Points

• The appropriate meaning of "Cast aside" is "to reject".
• Cast aside: get rid of someone or something.
• Example: Mary cast aside her neighbours by rising the fence.
• Therefore, the correct answer is Option 4.

Additional Information

• Let's see some idioms starting with "all".

The correct answer is "BACD". 

Key Points

• The given passage is about social media's influence on people.
• Social media is about uploading photos, so "B" will come as its first sentence.
• Next, the type of posts should be discussed and "A" is the next sentence.
• "C" is the next sentence as it contains the matter of the text, that is the influence of social media on people.
• "D" is the final sentence as it gives a conclusion. Moreover, the word "Therefore" also gives a hint that it will be the last sentence of the stanza.

Additional Information

• Certain rules must be followed to arrange sentences in order to frame a meaningful stanza.
• The first step is to read all the sentences and understand their meaning.
• Next, try to find the theme of the stanza.
• There will be a link between each sentence. Try to identify them.
• Connecting words like "although", "therefore", etc will help in ordering them.
• Understanding the opening sentence and closing sentence will make this process easier.

The correct answer is "drinking".

Key Points

• Drinking means the act of consuming liquids. 
• Example: Rina is drinking fruit juice.
• As drinking water is pure and is decreasing constantly, it cannot be used to clean cars.
• Therefore, the appropriate answer is "Drinking".

Additional Information

• Sewage - drainage 
• Example: The sewage water is overflowing.
• Stored - saved
• Example: Let's have the stored food.
• Cold - chill
• Example: The weather is cold today.

The correct answer is "wastage". 

Key Points

• Wastage means loss by using it carelessly. 
• Example: The food wastage after the party was huge.
• Therefore, the appropriate answer is "wastage".

Additional Information

• Extraction - the act of pulling out quickly.
• Example: The tooth extraction was over quickly.
• Greed - selfish desire.
• Example: Tom is always greedy for chocolates.
• Storage - saving things for the future. 
• Example: This food storage will help us ration food.

The correct answer is "judiciously".

Key Points

• "Judiciously" means performing an action wisely and carefully. 
• Example: The judge judiciously solved the case.
• Therefore, the appropriate option is "judiciously".

Additional Information

• Effectively - usefully.
• Example: My teacher advised me effectively.
• Hopefully - want something to be true.
• Example: Amy thinks that she would win the prize hopefully.
• Carelessly - without any care. 
• Example: Tony lost his stationary carelessly.

The correct answer is "Contribution".

Key Points

• "Contribution" means to give according to the person's ability. 
• Example: The pasta is my contribution to the food fest.
• Therefore, the appropriate answer is "Contribution".

Additional Information

• Summation - the act of briefing an incident.
• Example: The summation of the previous meeting was very clear.
• Indication - a signal.
• Example: The cloudy sky is an indication of rain.
• Connection - an association between two or more people or objects. 
• Example: The electric connection is not proper.

The correct answer is "Responsibility". 

Key Points

• "Responsibility" means the duty of being answerable. 
• Example: Harry's responsibility was to make sure that the costumes were good.
• Therefore, the appropriate answer is "responsibility".

Additional Information

• Facility - amenities
• Example: This apartment has all the required facilities.
• Complexity - difficulty
• Example: The complexity of the exam was high.
• Opportunity - a chance
• Example: Gaby got an opportunity to play for the state.

By using BODMAS

and going by the options

Given Equation :-  57 * 35 * 7 * 14 * 2 * 71

Interchanging * with given signs.

Option(1) ×, +, ÷, –, =

⇒ 57 × 35 + 7 ÷ 14 - 2 = 71

⇒ 57 × 35 + 0.5 - 2 = 71

⇒ 1995 + 0.5 - 2 = 71

⇒ 1995.5 - 2 = 71

⇒ 1993.5 ≠ 71

LHS ≠ RHS 

Option(2) –, ÷, +, ×, =

⇒ 57 - 35 ÷ 7 + 14 ×  2 = 71

⇒ 57 - 5 + 14 × 2 = 71

⇒ 57 - 5 + 28 = 71

⇒ 85 - 5 = 71

⇒ 80 ≠  71

LHS ≠ RHS 

Option(3) +, ÷, –, ×, =

⇒ 57 + 35 ÷ 7 - 14 ×  2 = 71

⇒ 57 + 5 - 14 × 2 = 71

⇒ 57 + 5 - 28 = 71

⇒ 62 - 28 = 71

⇒ 34 ≠  71

LHS ≠ RHS 

Option(4) –, +, ×, ÷, =

⇒ 57 - 35 +  7 × 14 ÷  2 = 71

⇒ 57 - 35 + 7 × 7 = 71

⇒ 57 - 35 + 49 = 71

⇒ 106 - 35 = 71

⇒ 71 = 71

LHS = RHS

Hence, the correct answer option(4)

Following logic is followed here,

Logic: Second number = √first number - 3

Option(1)

Second number = √169 - 3 = 13 - 3 = 10

Option(2)

Second number = √196 - 3 = 14 - 3 =11

Option(3)

Second number = √64 - 3 = 8 - 3 = 5

Option(4)

Second number = √36 - 3 = 6 - 3 = 3(not equal to 2)

Hence, the correct answer is option(4)

Following logic is followed here,

REMOVAL : MEROLAV

And,

TYPICAL : PYTILAC

Similarly,

NUCLEAR : ?

Hence, the correct answer is option(4)

When the mirror is placed vertically to the object, then the image formed will be laterally inverted. In other words, the Left Hand Side and Right Hand Side interchange their positions while top and bottom will remain same.

Hence, the correct answer is option (4)

The pattern followed here is:

From the above figure, only option(3) shows the correct answer

Hence, the correct answer is option(3)

When a common digit is on the same face of the same dices, then the digits written after the common digit is opposite to each other .(in the same direction)

Therefore, 1 is opposite to 6

                  4 is opposite to 3

                  2 is opposite to 5(left one)

So, the sum of 2 and 5 is 7

Hence, the correct answer is option(2)

Here, we need to count total number of triangle.

First we will count all the small triangles as:

So, we have 10 triangles.

Next, we will combine two or more triangles, we will have,

So, triangles we have are: PQS, PQT, PQU, PRT, PRU, PSU, PVX, PVY, PVZ, PWY, PWZ, PXZ - total of 12 triangles.

Thus, we have a total of 10 + 12 = 22 triangles.

Hence, we have 22 triangles.

When a mirror is placed vertically to the object, the mirror image so formed will be laterally inverted. In other words, the Left Hand Side and Right Hand Side interchange their positions while top and bottom will remain same.

Hence, the correct answer is option(2)

Here, we will first check all the options one by one

Given equation :- J _ M K L J J _ K L J J _ K L _ J P _ L

Option(1) J N O J K

J J M K L /J J N K L/ J J O K L/ J J P K L

Option(2) J N J K O

J J M K L /J J N K L/ J J J K L/ K J P O L

Option (3) N J K J O

J N M K L /J J J K L/ J J K K L/ J J P O L

Option(4) N J J O K

J N M K L /J J J K L/ J J J K L/ O J P K L

Only option(1) shows the repetition of the series. The middle letter is the next of it in the English Alphabets, while J J and K L is common in all.

Therefore, the correct answer is J N O J K

The logic followed here is:

Logic: The sum of second and third number - 8) is equal to first number.

First pair = 19 + 14 - 8 = 33 - 8 = 25

Second pair = 28 + 30 - 8 = 58 - 8 = 50

Option1) (41, 24, 36)

= 24 + 36 - 8 = 52(not equal to first number)

Option2) (31, 20, 25)

= 20 + 25 - 8 = 37(not equal to first number)

Option3) (24, 17, 21)

= 17 + 21 - 8 = 30(not equal to first number)

Option4) = (35, 22, 21)

= 22 + 21 - 8 = 35(equal to first number)

Therefore, the correct pair is (35, 22, 21)

Hence, the correct answer is option(4)

In any two consecutive ordinary years, date of the next year will be one day ahead of the same date of the previous year.

1^st August 2009 = Saturday

1^st August 2010 = Sunday

1^st August 2011 = Monday

If a leap year comes immediately after an ordinary year, then the day on a certain date of the leap year will be 2 days ahead of the same date on the ordinary year from March to December.

1^st August 2012 = Wednesday

1^st August 2013 = Thursday

Hence, the correct answer is option(2)

Following logic is used in the above question, 

Therefore, '?' will be replaced by 22.

Hence, the correct is option(2)

The pattern followed here is:

The logic is as follows

'GREEN' is written as 'HTHIS'

‘SAFFRON’ is written as ‘TCIJWUU'

'WHITE' be written '?'

'WHITE' be written 'XJLXJ'

Hence, the correct answer is option(1)

Here, we will look at the code

'I' = 'Ha'

'like' = 'Ho'

'you' = 'He'

Therefore, from "you like me" written as "He, Ho, Haa

you = He

like = Ho

me = Haa

Hence, the correct answer is option(1)

Following logic is applied in the above question

Second number = (First number )² + 2(First number)

13 : 195

Second number  = (13)² + 2 (13)

= 169 + 26

= 195

7 : 63

Fourth number =  (7)2 + 2 (7)

= 49 + 14

= 63

18 : ?

Sixth number = (18)2 + 2 (18)

= 324+ 36

= 360

= ? = 360

Therefore, ? will be replaced by 360

Hence, the correct answer is option(1)

Here the given logic is:

9 ÷ 2 = 4.5 + .5 = 5 ⇒ 5³ = 125

11 ÷ 2 = 5.5 + .5 = 6 ⇒ 6³ = 216

13 ÷ 2 = 6.5 + .5 = 7 ⇒ 7³ = 343

7 ÷ 2 = 3.5 + .5 = 4 ⇒ 4³ = 64

As per the given logic, the correct answer is option 2, as 11 : 49 do not follow the pattern that other options do.

Here, we have to find out the day of the given date.

So, 15 Aug 2001 was Wednesday.

Next, we will count all the days = 16 (Aug) + 30 (Sep) + 2 (Oct) = 48 ÷ 7 = 6 weeks and 6 odd days 

Thus, 2 October 2001 = Wednesday + 6 = Tuesday.

Hence, the day will be 'Tuesday' on 2 October 2001.

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

Given: 16 * 2 * 4 * 8 * 10 * 30

First we will check options one by one as below:

1) ÷, ×, +, –,  =

$\Rightarrow$ 16 ÷ 2 × 4 + 8 - 10 = 30

Applying BODMAS rule, we will get,

$\Rightarrow$ 8 × 4 + 8 - 10 = 30

$\Rightarrow$ 32 + 8 - 10 = 30

$\Rightarrow$ 30 = 30, which is possible. This is true.

2) ÷, ×, –, +, =

$\Rightarrow$16 ÷ 2 × 4 - 8 + 10 = 30

Applying BODMAS rule, we will get,

$\Rightarrow$ 8 × 4 - 8 + 10 = 30

$\Rightarrow$ 32 - 8 + 10 = 30

$\Rightarrow$ 34 ≠  30, which is not possible. This is not true.

3) ×, ÷, –, +, =

$\Rightarrow$ 16 × 2 ÷ 4 - 8 + 10 = 30

Applying BODMAS rule, we will get,

$\Rightarrow$ 16 × 0.5 - 8 + 10 = 30

$\Rightarrow$ 8 - 8 + 10 = 30

$\Rightarrow$10 ≠ 30, which is not possible. This is not true.

4) –, +, ×, ÷, =

$\Rightarrow$ 16 - 2 + 4 × 8 ÷ 10 = 30

Applying BODMAS rule, we will get,

$\Rightarrow$ 16 - 2 + 4 × 0.8 = 30 

$\Rightarrow$ 16 - 2 + 3.2 = 30

$\Rightarrow$ 17.2 ≠ 30, which is not possible. This is not true.

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

The least possible Venn diagram is given below:

Conclusion:

I) Some yellows are blues → Does not follow → (As there is no relationship between yellow and blues mentioned in the statements. This is not true.

II) No pink is blue → Does not follow → (As Some pinks are ices, so, some pink is blue. Therefore No pink is blue is possible but does not definitely true.)

III) No yellow is blue → Does not follow → (As there is no relationship between yellow and blue mentioned in the statements. This is not true.

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

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

Given: 14 * 18 * 7 * 79 * 33

First we will check options one by one as below:

1) +, ×, =, −

$\Rightarrow$ 14 + 18 × 7 = 79 - 33

Applying BODMAS rule, we will get,

$\Rightarrow$ 14 + 126 = 79 - 33

$\Rightarrow$ 140 ≠  46, which is not possible. This is not true.

2) +, −, =, ×

$\Rightarrow$ 14 + 18 - 7 = 79 × 33

Applying BODMAS rule, we will get,

$\Rightarrow$ 14 + 18 - 7 = 2607

$\Rightarrow$ 25 ≠  2607, which is not possible. This is not true.

3) =, ×, −, −

$\Rightarrow$ 14 = 18 × 7 - 79 - 33

Applying BODMAS rule, we will get,

$\Rightarrow$ 14 = 126 - 79 - 33

$\Rightarrow$ 14 = 14, which is possible. This is true.

4) −, =, ×, +

$\Rightarrow$ 14 - 18 = 7 × 79 + 33

Applying BODMAS rule, we will get,

$\Rightarrow$ 14 - 18 = 553 + 33

$\Rightarrow$ -4 ≠  586, which is not possible. This is not true.

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

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

Given: 60 * 6 * 3 * 18 * 49 * 5

First we will check options one by one as below:

1) ×, +, ÷, –, =

$\Rightarrow$ 60 × 6 + 3 ÷ 18 - 49 = 5

Applying BODMAS rule, we will get,

$\Rightarrow$ 60 × 6 + 0.16 - 49 = 5

$\Rightarrow$ 360 + 0.16 - 49 = 5

$\Rightarrow$ 311.16 ≠  5, which is not possible. This is not true.

2) ÷, +, –, ×, =

$\Rightarrow$ 60 ÷ 6 + 3 - 18 × 49 = 5

Applying BODMAS rule, we will get,

$\Rightarrow$ 10 + 3 - 18 × 49 = 5

$\Rightarrow$ 10 + 3 - 882 = 5

$\Rightarrow$ -869 ≠  5, which is not possible. This is not true.

3) ×, +, –, ÷, =

$\Rightarrow$ 60 × 6 + 3 - 18 ÷ 49 = 5

Applying BODMAS rule, we will get,

$\Rightarrow$ 60 × 6 + 3 - 0.36 = 5

$\Rightarrow$ 360 + 3 - 0.36 = 5

$\Rightarrow$ 362.64 ≠  5, which is not possible. This is not true.

4) ÷, –, ×, +, =

$\Rightarrow$ 60 ÷ 6 - 3 × 18 + 49 = 5

Applying BODMAS rule, we will get,

$\Rightarrow$ 10 - 3 × 18 + 49 = 5

$\Rightarrow$ 10 - 54 + 49 = 5

$\Rightarrow$ 5 = 5, which is possible. This is true.

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

When a mirror is placed vertically to the object, the image so formed will be laterally inverted. In other words, the Left Hand Side and Right Hand Side interchange their positions while top and bottom will remain same.

Therefore, only option(2) shows the correct image.

Hence, the correct answer is option(2).

The pattern followed here is:

In the above code, letters are given their positional value in increasing order, (addition of 1 for very next number.)

'PENCIL' is written as '1771771418'

And,

'ERASER' is written  as '6204231024'

Similarly,

'SHARPNER'

The code for 'SHARPERNER' is '201042221201226'.

Hence, the correct answer is option(1)

Given series :- 

Here, First letter is the  very next letter of the previous code, second letter is addition of 7 letters, third letter is addition of 13 letters and fourth letter is addition of 19 letters. 

Therefore, '?' will be replaced by 'JGDM'

Hence, the correct answer is option(2)

The logic followed here is:

(First number × 3) - (Second number × 4) = Third number

First row - 67, 25, 101 → (67 × 3) - (25 × 4) = 201 - 100 = 101

Second row - 55, 17, 97 → (55 × 3) - (17 × 4) = 165 - 68 = 97

Similarly,

Third row - 45, 19, ? → (45 × 3) - (19 × 4) = 135 - 76 = 59

Hence, option 4) is the correct answer.

Formula used:

 $\sin2\theta=2\sin\theta.\cos\theta$ 

Calculation:

It is given that $\theta$ is an acute angle, So by trigonometric ratios-

$\sin\theta = {{Perpendicular} \over Hypotenuse}$

Since, $\sin\theta = {{12} \over 13}$ then on comparison,

⇒ Hypotenuse = 13 unit and Perpendicular = 12 unit

Now, by the Pythagorean theorem, 

(Hypotenuse)² = (perpendicular)² + (base)²

⇒ 13² = 12² + (base)²

⇒ (base)2 = 25

⇒ base = 5 unit

⇒ $\cos\theta={base\over hypontenuse}$ = ${5\over13}$

⇒$\tan\theta = {perpendicular\over base}$= ${12\over 5}$

Substituting the values of $\sin\theta$, $\cos\theta$ and $\tan\theta$ into the expression, 

⇒${\left(\frac{12}{13}\right)^2-\left(\frac{5}{13}\right)^2 \over 2.\frac{12}{13}.\frac{5}{13}}\times {1\over \left(\frac{12}{5}\right)^2}$

⇒${\frac{119}{169}\over \frac{120}{169}}\times {25\over144}$

⇒$\frac{119\times25}{120\times144}$= $\frac{119\times 5}{24\times 144}$

⇒${{595} \over 3456}$

The value of the expression is ${{595} \over 3456}$

Concept used:-

Properties of exponents and powers = a2 - b2 = (a + b)(a - b)

Calculation**:-**

Using the exponent property $\frac{a^n}{a^m}=a^{n-m}$ in the given expression,

⇒ $2^2\left(x\right)^{(a-b)(a+b)}\times3^2\left(x\right)^{(b-c)(b+c)}\times6^{-2}\left(x\right)^{(c-a)(c+a)}$

By using the formula, a² - b² = (a + b)(a - b)

⇒ $2^2\left(x\right)^{(a^2-b^2)}\times3^2\left(x\right)^{(b^2-c^2)}\times6^{-2}\left(x\right)^{(c^2-a^2)}$ 

⇒ $2^2\left(x\right)^{(a^2-b^2)}\times3^2\left(x\right)^{(b^2-c^2)}\times(3\times2)^{-2}\left(x\right)^{(c^2-a^2)}$

By using the exponent property, (a × b)^m = a^m × b^m

⇒ $2^2\left(x\right)^{(a^2-b^2)}\times3^2\left(x\right)^{(b^2-c^2)}\times(3)^{-2}\times(2)^{-2}\left(x\right)^{(c^2-a^2)}$

By using the property a^m × aⁿ = a^{(m + n)} 

⇒ $2^{(2+(-2))}\times 3^{(2+(-2)}\times x^{(a^{2}-b^{2})+(b^{2}-c^{2})+(c^{2}-a^{2})}$

By the property of exponents, i.e a⁰ = 1

⇒ 2⁰ × 3⁰ × x⁰ 

⇒ 1 × 1 × 1 = 1

The value of the expression is 1.

Concept used:

Divisibility of 11 = Number is divisible by 11 when the difference between the sum of odd digits and sum of even digits is either 0 or multiple of 11

Calculation:

Odd digits = 6, 4, *, 5

Even digits = 3, 7, 2

According to the rule,

(Sum of odd digits) - (sum of even digits) = 0 or multiple of 11

⇒(6 + 4 + * + 5) - (3 + 7 + 2) = 3 + *

.·.(3 + * ) should be 0 or multiple of 11

⇒Taking 3 + * = 0

• = - 3 which is Impossible as *** will carry only a positive integral value**

⇒Taking (3 + *) = 11, as 11 is the closest to the (3 + *)

⇒(3 + *) = 11

⇒* = 8

The value of * is 8 and the number will be 637825.

Given:

Average weight of the mango box = 35,

Number of apple boxes = 15,

Number of mango boxes = 20

Formula used:

Weighted average = $\frac{w_1× n_1+w_2× n_2}{n_1+n_2}$

Calculation**:**

Let the number of boxes of mango and apples be n₁ and n₂ 

⇒ n₁ = 20 and n₂ = 15

Let the average weight of mango box be w₁ and apple box be w₂ 

⇒ w1 = 35 kg and w2 = ?

By using the formula of weighted average and taking value of weighted average as 30 kg,

⇒ 30 = $\frac{35×20+15× w_2}{15+20}$ 

⇒ 1050 = 700 + 15 × w2

⇒ w2  = $\frac{350}{15}$ = $\frac{70}{3}$

The average weight of a box of apples is $\frac{70}{3}$ kg.

Shortcut Trick

As per the question,  

The average of Mangoes is increasing by 5 from the common average.

It means that the average of Apple is 5 less than the common average.

So we can say that average weight of the apple box 

⇒ 30(avg) - (5(diff) × 20 (box of mango))/15(box of apples)

⇒30 - (100/15) =70/3

Given:

Total number of matches = 20

Total average runs = 30

Formula used:

Average = $\frac{sum\ of\ observation}{total\ number\ of\ observation}$

Calculation**:**

 By using the formula of average we can calculate the total runs scored by player in 20 matches

⇒ Total runs = Average runs × Total number of matches

⇒ Total runs = 30 × 20

⇒ Total runs = 600

Similarly, we can calculate the total runs scored by the player in the first 12 matches,

⇒ R₁₂ = Average runs × Total number of matches

⇒ R12 = 40 × 12 = 480

The difference between the total runs and total runs in the first 12 matches will give the total runs scored by the player in the last 8 matches,

⇒ Total runs in last 8 matches = 600 - 480

⇒ Total runs in last 8 matches = 600 - 480 = 120

By using the formula of average,

⇒ Average = $\frac{120}{8}$

⇒ Average = 15 runs

The average of the last 8 matches is 15 runs.  

Shortcut Trick

Average = 30,

Extra  runs in first 12 matches = 12 × 10 =120 

This means that the average of the remaining 8 matches will be less by 120 runs, only then the common average will be 30 

⇒ Total runs in last 8 matches =  30 -(120/8) = 30 -15 =15

Given:

Calculation:

Total number is students in extra curricular activities in

College A = 150 + 50 + 100 + 250 = 550

College B = 250 + 150 + 50 + 125 = 575

College C = 450 + 150 + 400 + 350 = 1350

College D = 50 + 50 + 125 + 275 = 500

College E = 350 + 50 + 100 + 250 = 750

College F = 250 + 50 + 500 + 150 = 950

College G = 150 + 50 + 150 + 150 = 500

So, the minimum number of students for extra-curricular is from colleges D and G

Shortcut Trick If x − 1/x = k, then x2 − 1/x2 = k × √(k2 + 4) (for x > 0). Here, k = 11. ⇒ x2 − 1/x2 = 11 × √(112 + 4) ⇒ 11 × √(121 + 4) = 11 × 5√5 = 55√5 ∴ The correct answer is 55√5. Alternate Method Given: x − 1/x = 11 and x > 0 Formula Used: a2 − b2 = (a − b)(a + b) (a + b)2 = (a − b)2 + 4ab Calculations: ⇒ x2 − 1/x2 = (x − 1/x)(x + 1/x) First, we find the value of (x + 1/x): ⇒ (x + 1/x)2 = (x − 1/x)2 + 4 ⇒ (x + 1/x)2 = 112 + 4 = 121 + 4 = 125 ⇒ x + 1/x = √125 = 5√5 (Since x > 0, x + 1/x is positive) Now, substituting the values into the formula: ⇒ x2 − 1/x2 = 11 × 5√5 = 55√5 ∴ The correct answer is 55√5. Additional Information Sum and Difference Relation If x + 1/x = k, then x − 1/x = ±√(k2 − 4). Sum of Squares Relation If x − 1/x = k, then x2 + 1/x2 = k2 + 2. Sum of Cubes Relation If x − 1/x = k, then x3 − 1/x3 = k3 + 3k.

Given

Cost price : Marked price = 4 : 7

Discount = 25%

Profit = Rs 50

Formula used

$\frac{C}{M}=\frac{100-D}{100+P}$

C = cost price

M = marked price

D = discount%

P = profit%

Calculation

$\frac{C}{M}=\frac{100-D}{100+P}=\frac{100-25}{100+P}=\frac{4}{7}$

from this P = 31.25%

31.25% of C = 50Rs

then, C is 100% which is $\frac{50}{31.25}\times 100=160Rs$

The cost price of the article is Rs 160

Shortcut Trick

Net multiplier (SP/CP) = (Claimed SP ÷ Actual CP) × (True Weight ÷ Faulty Weight)

Ratio = (27 ÷ 30) × (1000 ÷ 750) = (9/10) × (4/3)

Net Ratio = 36 ÷ 30 = 6 ÷ 5

Profit % = (6 − 5) ÷ 5 × 100 = 20%

∴ The correct answer is 20% profit.

Alternate Method

Given:

Cost Price (CP) of 1000 g rice = ₹30

Selling Price (SP) of 750 g rice (claimed as 1000 g) = ₹27

Calculation:

⇒ Actual Cost Price of 1000 g rice = ₹30

⇒ Actual Cost Price of 750 g rice = (30 ÷ 1000) × 750

⇒ Actual Cost Price of 750 g rice = ₹22.5

⇒ Given Selling Price of 750 g rice = ₹27

⇒ Total Profit = SP − CP = 27 − 22.5 = ₹4.5

⇒ Profit Percentage = (Profit ÷ CP) × 100

⇒ Profit Percentage = (4.5 ÷ 22.5) × 100

⇒ Profit Percentage = (1 ÷ 5) × 100 = 20%

∴ The correct answer is 20% profit.

Additional Information

Dishonest Dealer Concept

When a dealer sells at a profit/loss on price and also uses a faulty weight, the net gain/loss is calculated by the product of individual multiplication factors.

Profit with Weight Manipulation

Profit % = [(True Value − False Value) ÷ False Value] × 100. In this problem, the dealer also changed the price, so we compare the actual CP of the weight delivered with the actual SP received.

Successive Percentage Change

Net Profit % can be viewed as successive changes: price reduction (10% loss) and weight manipulation (33.33% profit). Net = −10 + 33.33 + (−10 × 33.33)/100 = 20%.

Given

length of 1^st train=230 m

length of 2^nd train=240 m

distance between trains=130 m

speed of 1^st train=160 km/h

speed of 2^nd train=200 km/h

Calculation

relative speed=160+200=360 km/h=100 m/s

Total distance for crossing=length of two trains+ distance between trains=470+130=600m

Time taken=$\frac{distance}{speed}=\frac{600}{100}=6$ sec

Total time taken for trains to cross each other = 6 sec

Given:

40% Cost price = 30% Selling price

Calculation:

40% Cost price = 30% selling price

Thus reducing the above equation we get,

4C = 3S

S = 4C/3

Profit or loss %=$\frac{S-C}{C}\times 100$=$\frac{\frac{4C}{3}-C}{C}\times 100 =\frac{4-3}{3}\times 100=33.33\%$

Approximately there is a profit of 33.33%

Formula used:

General form $x^2+y^2+2gx+2fy+c=0$

Radius $r^2=g^2+f^2-c$

Calculation:

Comparing the equations 

g = -2 , f = 3 ,c = -12

Radius=$r=\sqrt{g^2+f^2-c}$=$\sqrt{4+9-(-12)}=\sqrt{25}=5$

The radius of the circle is 5 cm

%students in operating system=16%

%students in java=22%

% students in DBMS=14%

total % students from above specializations=22+16+14=52%

total % of students from all specialization is 100% that is 8000

so 52% is $\frac{8000}{100}\times 52=4160$

The number of students from the above selected specialization is 4160

Given:

Principle = 390625

Amount = 456976

Rate of interest = 8%

Compounded half yearly

Formula used:

$A=P(1+\frac{r}{100})^n$

Calculation:

It is compounded half yearly, for 12 months r = 8%

For 6 months, r = 8/2 = 4%

Substituting,

$A=P(1+\frac{r}{100})^n$=$456976=390625(1+\frac{4}{100})^n$

$\frac{456976}{390625}=(\frac{104}{100})^n$

$\frac{26^4}{25^4}=(\frac{26}{25})^n$

From this we get n = 4  where n is in number of half years

4 half years = 2 years

The amount will be obtained in 2 years.

Given

principle=160000

rate of interest=10% per annum

time =2years

compounded half yearly

Formula used

Amount=Principle$(1+\frac{r}{100})^n$

Calculation

because of interest compounded half yearly the rate of interest will be halved

for 12 months r=10%

for 6 months r=5%

n=time taken=2years which is 4 half years

$A=P(1+\frac{r}{100})^n$=$A=160000(1+\frac{5}{100})^4$=194481

compounded interest=Amount-Principle=194481-160000=34481Rs

The compound interest is Rs. 34,481

Given:

A can do the work in 5 days.

B can do the work in 6 days.

C can do the work in 10 days.

Calculations:

According to the question,

⇒ One day work of A = 1/5 units

⇒ One day work of B = 1/6 units

⇒ One day work of C = 1/10 units

Total Work of A B and C = (1/5) + (1/6) + (1/10)

Total Work = (6 + 5 + 3)/30

Total Work = 14/30 = 7/15 units

A B and C can complete the work in 15/7 days

∴ They will finish the same work in 15/7 or $2{{1} \over 7}$. 

Shortcut Trick