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

The correct answer is "Somebody narrated the incident to Naresh."

Key Points

• There are a few things to keep in mind when changing a sentence from passive to active voice.
• The agent in the passive voice becomes the subject(doer of the action) of the active voice.
• In the given sentence, "somebody" becomes the subject in the active voice.
• We can omit the usage of "by" in the active voice. We use the preposition "by" to show the agent in the passive voice.
• We can also omit the usage of "to be" forms in the active voice. So we can omit "was" which is the past tense of "to be" in the given sentence.
• The given sentence is in the simple past tense.

Hence, the correct answer is option 2.

​The correct sentence is: Somebody narrated the incident to Naresh.

Hinglish

• वाक्य को passive to active voice में बदलते समय कुछ बातों का ध्यान रखना चाहिए।
• passive voice में एजेंट active voice का विषय (कार्रवाई का कर्ता) बन जाता है।
• दिए गए वाक्य में, "somebody" सक्रिय आवाज में विषय बन जाता है।
• हम active voice में "by" के उपयोग को छोड़ सकते हैं। एजेंट को passive voice में दिखाने के लिए हम "by" preposition का उपयोग करते हैं।
• हम active voice में "to be" फॉर्म के उपयोग को भी छोड़ सकते हैं।
• इसलिए हम "was" को छोड़ सकते हैं जो दिए गए वाक्य में "to be" का भूत काल है।
• दिया गया वाक्य simple past tense का है।

The correct answer is "sensible".

Key Points

• Let's look at the meaning of the highlighted word.
• impetuous: 

acting or done quickly and without thought or care.

• Example: His decision to confront his manager regarding the promotion was more impetuous than logical.
• ​Let's look at the meaning of the given options.
• ​Dense: 

(of a person) stupid.

• Arguable: 

open to disagreement; not obviously correct.

• Tangible: 

clear and definite; real.

• Sensible: 

done or chosen in accordance with wisdom or prudence; likely to be of benefit.

• As per the meaning of the given words, "sensible" is the antonym of the highlighted word "impetuous".
• Example: He made a sensible decision by buying a house in a developing area.

​Hence, the correct answer is option 4.

The correct answer is "for"

Key Points

• In the given sentence, the usage of the preposition "from" is incorrect.
• We use the preposition 'from' to show where something starts or originates. We also use from to show movement from one thing to another.
• In the given sentence, we need to use the preposition "for".
• We use the preposition 'for' to state how long something lasts or continues.
• Example: I waited at the metro station for about 45 minutes so that I could catch the first metro.
• We also use the preposition "for" as a conjunction to link the first and second clauses of a sentence.
• The implied meaning of the given sentence is that the speaker is expressing how long they waited.

The correct sentence is: I was waiting for two hours.

Hence, the correct answer is option 3.

The correct answer is "accorded".

Key Points

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

compare in such a way as to emphasize differences. (अंतरों को ज़ोर देकर तुलना करना)

• accorded: 

give or grant someone (power, status, or recognition)(किसी को (शक्ति, स्थान या पहचान) देना या अनुदान देना)

• disagreed: 

have or express a different opinion.(अलग मत रखना या व्यक्त करना)

• removed: 

take (something) away or off from the position occupied.((कुछ) किसी स्थान से या ऊपर से हटा देना)

• As per the meaning of the given words, "accorded" is the appropriate word for the blank.
• Example: Sachin was accorded the Padma Vibhushan for his contribution to Indian cricket.

​The correct sentence is: My success was complete and the delighted directors accorded me the privilege of developing automatic regulators which were much desired.

Hence, the correct answer is option 2.

The correct answer is "sheer".

Key Points

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

having all the required or desirable elements, qualities, or characteristics; as good as it is possible to be.

• sheer: not mixed with anything else; pure or complete. It is an adjective used to create emphasis.
• utter: extreme. or absolute.  It also means to express oneself in words.
• total: consisting of the whole number or amount.
• As per the meaning of the given words, "sheer" is the appropriate word choice for the blank.
• Example: It was a moment of sheer bliss for his family and friends when he crossed the finishing line of the marathon.
• The meaning of the given sentence is that the person was laughing as she was completely overjoyed after the performance.

The correct sentence is: She was laughing from the sheer exuberance of the performance.

Hence, the correct answer is option 2.

The correct answer is "Strict".

Key Points

• The meaning of the given idiom is "not to be modified or evaded or strict."
• We use the given idiom in a situation where some rules or something in question is rigid and cannot be changed so easily.
• ​Example: Tina said, "My company has a hard and fast policy when it comes to granting leaves to its employees."

Hence, the correct answer is option 1.

The correct answer is "Omnivorous"

Key Points

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

a person who eats the flesh of other human beings.

• Herbivorous: 

(of an animal) feeding on plants.

• Carnivorous: 

(of an animal) feeding on other animals.

• Omnivorous: (of an animal or person) feeding on a variety of food of both plant and animal origin.
• As per the meaning of the given words, "omnivorous" is the one-word substitute for the underlined group of words.

The correct sentence is: Human beings are usually the ones who are omnivorous..

Hence, the correct answer is option 4.

The correct answer is "A difficult situation in which the solution to a problem is impossible"

Key Points

• The meaning of the given idiom is "a dilemma or difficult circumstance from which there is no escape because of mutually conflicting or dependent conditions."
• We use the given idiom to refer to a situation where one is in a difficult circumstance and there are no easy escapes.
• ​Example: When we discovered that the application we made had some glitches before a major launch, we were caught in a Catch-22 situation.

​Hence, the correct answer is option 1.

The correct answer is "flew away"

Key Points

• The meaning of the idiom "fly away" is "to leave some place or area by flying."
• The first clause of the given sentence is in the past tense.
• So, we need to use the past tense of the verb "fly" which is "flew" in the given sentence.:

​The correct sentence is: As soon as she opened the cages, the birds flew away.

Hence, the correct answer is option 2.

The erroneous spelling is "Appology".

Key Points

• Let's look at the correct spelling and meaning of the marked option:
• Apology: 

a regretful acknowledgment of an offense or failure.(क्षमा, सफ़ाई, दोषस्वीकार)

• Example: Meenal said," I owe you an apology for making you wait for so long".

Hence, the correct answer is option 1.

Additional Information

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

an outgoing, socially confident person.(बहिर्मुखी, 

सामाजिक रूप से आश्वस्त व्यक्ति)

• Lugubrious: looking or sounding sad and dismal. (उदास, दुखपूर्ण, विषादमय)
• Collaborate: 

work jointly on an activity or project. (मिलकर काम करना, सहयोग करना)

All the other words are spelled correctly.

The correct answer is "A grand plan is being floated by Siddharth next week."

Key Points

• There are a few things to keep in mind when changing a sentence from active to passive voice.
• The subject in the active voice becomes the agent in the passive voice. The agent is indicated with the preposition "by" in the given sentence.
• In the given sentence, "Siddharth" becomes the agent in a passive voice indicated with the preposition "by".
• The object in the active voice becomes the subject of the sentence in the passive voice.
• In the given sentence, "A grand plan" is the subject of the passive voice.
• The given sentence is in the present continuous tense so we need to use the present participle of "be" which is "being" in the passive voice sentence.
• The main verb "floating" of the given sentence will take the past participle form (V3) which is "floated" in the passive voice sentence.

 Hence the correct answer is option 2

The correct sentence is:  A grand plan is being floated by Siddharth next week.

The correct answer is "genuine"

Key Points

• Let's look at the meaning of the highlighted word:
• Spurious: 

not being what it purports to be; false or fake. (जाली; नकली) 

• Example: The milk we bought from the roadside stall is spurious.
• Let's look at the meaning of the given options:
• genuine: 

truly what something is said to be; authentic. (वास्तविक)

• curious: 

eager to know or learn something. (जिज्ञासु)

• nefarious: 

(typically of an action or activity) wicked or criminal. (दुष्ट)

• artificial: 

made or produced by human beings rather than occurring naturally, especially as a copy of something natural. (कृत्रिम)

• As per the meaning of the given words, "genuine" is the antonym of "spurious".
• Example: Nidhi is one of the most genuine people I have met in a long time.
• ​Hence, the correct answer is option 1.

The correct answer is "Latter".

Key Points

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

having previously been a particular thing.

• Example: He was a former pilot at a reputed airline but now he is pursuing law.
• Let's look at the meaning of the given words:
• External: belonging to or forming the outer surface or structure of something.
• Additional: 

added, extra, or supplementary to what is already present or available.

• Featured: 

having distinctive attributes or aspects of a specified kind.

• Latter: 

denoting the second or second mentioned of two people or things.

As per the meaning of the given words, "latter" is the antonym of the word "former".

• Example: Among the two new people we met at the party, the former was a cop and the latter was a lawyer.

​Hence, the correct answer is option 4.

The correct answer is "Civilised".

Key Points

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

(of a person or group) primitive and uncivilized.((किसी व्यक्ति या समूह का) आदिम और असभ्य)

• Example: She acted really savage after she lost the title to her rival.
• Let's look at the meaning of the given words.
• Brutal: direct and without attempting to disguise unpleasantness.(प्रत्यक्ष और अप्रियता को छिपाने का प्रयास किए बिना)
• Civilised: bring (a place or people) to a stage of social and cultural development considered to be more advanced(अधिक उन्नत माने जाने वाले सामाजिक और सांस्कृतिक विकास के एक चरण में (एक स्थान या लोगों को) लाना).
• Adequate: satisfactory or acceptable in quality or quantity.(गुणवत्ता या मात्रा में संतोषजनक या स्वीकार्य)
• impartial: 

treating all rivals or disputants equally.(सभी प्रतिद्वंद्वियों या विवादों के साथ समान व्यवहार करना)

• As per the meaning of the given words, "civilised" is the antonym of the word "savage"
• Example: Anirudh acted rather civilised at the party after being drunk, unlike his friends.

​Hence, the correct answer is option 2.

The correct answer is "My elder brother works in a pharmaceutical company."

Key Points

• Let's try to identify the correct sentence.
• Option 1: In the given sentence, the erroneous spelling is "pharmasutical".
• Option 3: In the given sentence, the erroneous spelling is "pharmaetuical".
• Option 4: In the given sentence, the erroneous spelling is "phramaeutical".
• Option 2: In the given sentence, the spelling of "pharmaceutical " is correct.
• Let's look at the meaning of the word.
• Pharmaceutical: relating to medicinal drugs, or their preparation, use, or sale.

​​The correct sentence is: My elder brother works in a pharmaceutical company.

Hence, the correct answer is option 2.

The correct answer is "reconciliation"

Key Points

• Options 1, 2, and 3 have erroneous spellings of the word.
• Let's look at the correct spelling and meaning of the word.
• Reconciliation: 

the restoration of friendly relations.

• Example: The husband and wife were no longer interested in reconciliation so they decided to file for divorce.

​The complete sentence is: The reconciliation of the worksheets is not an easy job.

Hence, the correct answer is option 4.

The correct answer is "Your note book has been lost."

Key Points

• There are a few things to keep in mind before changing a sentence from active to passive voice.
• We can omit the subject in the passive voice if the sentence is meaningful without it.
• In the given sentence, the subject pronoun "your" modifies the meaning of the entire sentence so we don't need to use another relative pronoun for the sentence.
• The object of the active voice becomes the subject of the passive voice.
• In the given sentence, "notebook" is the subject of the sentence in the passive voice.
• The given sentence is in the present perfect tense.  So we need to use "has been" when changing the sentence from active to passive voice.
• We need to use the past particle form of "be" in the given sentence as it becomes the main verb of the sentence. We always use the past participle form of the main verb in passive voice." Been" is the past participle of "be".
• In the given sentence, we need to use the auxiliary verb "has" for the subject-verb agreement as the sentence begins with the singular subject "your notebook".

Hence, the correct answer is option 2.

The correct sentence is: Your note book has been lost.

The correct answer is "bore her up"

Key Points

• Let's look at the meaning of the given phrasal verb:
• ​Carried her up: to sustain someone through a difficult circumstance (कठिन परिस्थिति में किसी को सहारा देकर संभालना।)
• Let's look at the meaning of the given phrasal verbs.
• tore her up: to cause someone much grief. (किसी को बहुत दुःख पहुँचाना।)
• bore her up: To help one to endure or persevere through emotional distress. (भावनात्मक संकट के माध्यम से सहने या दृढ़ रहने में मदद करें।)
• stood her up: to intentionally fails to meet someone when one said they would. (जानबूझकर किसी से मिलने में विफल रहता है जब किसी ने कहा कि वे करेंगे।)
• drove her up: to make (someone) irritated, angry, or crazy. ((किसी को) चिड़चिड़ा, क्रोधित या पागल बनाना।)
• As per the meaning of the given words, "bore her up" is the appropriate option to substitute the underline segment in the given sentence
• ​Example: The presence of her husband at the funeral of her mother bore her up.

​Hence, the correct answer is option 2.

The correct sentence is: The affection of her husband bore her up in the midst of all her problems.

The correct answer is "diversity".

Key Points

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

the state of existing in or containing plentiful quantities of something desirable.

• belongingness: the state or feeling of belonging to a particular group.
• diversity: 

the practice or quality of including or involving people from a range of different social and ethnic backgrounds and of different genders, sexual orientations, etc.

• inclusion: 

the action or state of including or of being included within a group or structure.

• As per the meaning of the words, "diversity" is the appropriate word choice for the blank.
• Example: The variety of food choices at the wedding represents the diversity of Indian culture.

The correct sentence is: The beauty of our festivals lies in **‘**unity in diversity'.

Hence, the correct answer is option 3.

The correct answer is "CDAB"

Key Points

• Let's look at the correct sequence of the passage.
• Statement C is the opening sentence of the passage as it begins with a general opinion about relationships. Opening statements are usually general statements about a topic. The given sentence is a general statement about relationships.
• Statement D is the second sentence of the passage it elaborates on the general statement in the previous sentence. The authors state that arguments, disagreements and conflicts are extremely common even in a healthy relationship.
• Statement A  is the third sentence of the passage as it begins with a conjunction "but" depicting a contrast to the previous statement. The given sentence talks about the negative impact of arguments, disagreements, and conflicts of the parents on their children.
• Statement B is the concluding statement of the passage as it summarizes the core ideas in one sentence. The author states that there is no telling when a squabble between a couple may aggravate and escalate into something ugly, which when witnessed by a child, might devastate them gravely.

​Hence, the correct answer is option 4.

The correct answer is "popular"

Key Points

• Let's look at the meaning of the given options.
• Popular: 

liked or admired by many people or by a particular person or group.

• Desired: 

strongly wished for or intended.

• Influential: 

having a great influence on someone or something.

• Likely: such as well might happen or be true; probable.
• As per the meaning of the given words, "popular" is the appropriate word choice for the blank.
• The implied meaning of the given sentence is that poetry and novels were very 

liked or admired by many people in the 18^th century.

​Hence, the correct answer is option 1.

The complete passage is: Poetry and novels became very (1) popular in the 18^th century. Robinson Crusoe by Daniel Defoe was published in 1719. This is regarded as the first successful English novel. It is partly based on the true-life adventures of a traveller called Alexander Selkirk. Jonathan Swift’s Gulliver’s travels were written in 1726 and (2) describes four imaginary journeys of a ship’s doctor named Gulliver. Poetry (3) revolved around British people and places. Poets also considered nature as a source of (4)inspiration. The poets wrote in a simple style and language so that the (5)ordinary masses could understand it.

The correct answer is "describes".

Key Points

• Let's look at the meaning of the given options.
• ​describes: 

give a detailed account of something in words.

represents: describe or portray in a particular way.

• discloses: 

make (secret or new information) known.

• expresses: 

convey (a thought or feeling) in words or by gestures and conduct.

• As per the meaning of the given words, "describes" is the appropriate word choice for the blank.​
• Example: The tourist describes her experience of travelling in India in a memoir after she returned to her country.
• The implied meaning of the given sentence is that Jonathan Swift’s Gulliver’s travels were written in 1726. It gives a detailed account of four imaginary journeys of a ship’s doctor named Gulliver.

Hence, the correct answer is option 1.

The complete passage is: Poetry and novels became very (1) popular in the 18^th century. Robinson Crusoe by Daniel Defoe was published in 1719. This is regarded as the first successful English novel. It is partly based on the true-life adventures of a traveller called Alexander Selkirk. Jonathan Swift’s Gulliver’s travels were written in 1726 and (2) describes four imaginary journeys of a ship’s doctor named Gulliver. Poetry (3) revolved around British people and places. Poets also considered nature as a source of (4)inspiration. The poets wrote in a simple style and language so that the (5)ordinary masses could understand it.

The correct answer is "revolved"

Key Points

• Let's look at the meaning of the given options.
• ​revolved: 

treat as the most important element.

• encircled: 

form a circle around; surround.

• revolutionized: 

change (something) radically or fundamentally.

• executed: put (a plan, order, or course of action) into effect.
• As per the meaning of the given words, "revolved" is the appropriate word choice for the blank.
• Example: "Me too" is a social movement that revolved around sexual abuse or sexual harassment.
• The implied meaning of the given sentence is that 18^th-century poetry was about British people and places.

Hence, the correct answer is option 1.

The complete passage is: Poetry and novels became very (1) popular in the 18^th century. Robinson Crusoe by Daniel Defoe was published in 1719. This is regarded as the first successful English novel. It is partly based on the true-life adventures of a traveller called Alexander Selkirk. Jonathan Swift’s Gulliver’s travels were written in 1726 and (2) describes four imaginary journeys of a ship’s doctor named Gulliver. Poetry (3) revolved around British people and places. Poets also considered nature as a source of (4)inspiration. The poets wrote in a simple style and language so that the (5)ordinary masses could understand it.

The correct answer is "inspiration".

Key Points

• Let's look at the meaning of the given options.
• ​incentive: 

a thing that motivates or encourages someone to do something.

• inspiration: 

the process of being mentally stimulated to do or feel something, especially to do something creative.

• impulse: 

a sudden strong and unreflective urge or desire to act.

• motivation: 

desire or willingness to do something; enthusiasm.

• As per the meaning of the given words, "inspiration" is the appropriate word choice for the blank.
• The implied meaning of the given sentence is that poets derived their source of mental stimulation from nature.

Hence, the correct answer is option 2.

The complete passage is: Poetry and novels became very (1) popular in the 18^th century. Robinson Crusoe by Daniel Defoe was published in 1719. This is regarded as the first successful English novel. It is partly based on the true-life adventures of a traveller called Alexander Selkirk. Jonathan Swift’s Gulliver’s travels w written in 1726 and (2) describes four imaginary journeys of a ship’s doctor named Gulliver. Poetry (3) revolved around British people and places. Poets also considered nature as a source of (4)inspiration. The poets wrote in a simple style and language so that the (5)ordinary masses could understand it.

The correct answer is "ordinary".

Key Points

• Let's look at the meaning of the given options.
• ​modern: 

relating to the present or recent times as opposed to the remote past.

• traditional: 

habitually done, used, or found.

• ordinary: 

with no special or distinctive features; normal.

• typical:

having the distinctive qualities of a particular type of person or thing.

• As per the meaning of the given words, "ordinary" is the appropriate word choice for the blank.
• The implied meaning of the given sentence is that the style and language of poetry were accessible to the common folks of the time.

​Hence, the correct answer is option 3.

The complete passage is: Poetry and novels became very (1) popular in the 18^th century. Robinson Crusoe by Daniel Defoe was published in 1719. This is regarded as the first successful English novel. It is partly based on the true life adventures of a traveller called Alexander Selkirk. Jonathan Swift’s Gulliver’s travels was written in 1726 and (2) describes four imaginary journeys of a ship’s doctor named Gulliver. Poetry (3) revolved around British people and places. Poets also considered nature as a source of (4)inspiration. The poets wrote in a simple style and language so that the (5)ordinary masses could understand it.

The logic followed here is :

LETTERS REPRESNTION OPERATIONS:

Therefore the equation will be:

(38 × 13) ÷ 19 - 27 + (38 × 3) + 43 - 68 =

 Using BODMAS rule,

B: BRACKETS

O: ORDER OF POWER

D: DIVISION

M: MULTIPLICATION

A: ADDITION

S: SUBTRACTION

(38 × 13) ÷ 19 - 27 + (38 × 3) + 43 - 68 =

494 ÷ 19 - 27 + 114 + 43 - 68

26 - 27 + 114 + 43 - 68

183 - 27 - 68

88

Hence, the correct answer is 88.

Given : 8, 16, 13, ?, 47, 282

In the following series, two operations are going on simultaneously, first multiplication with even number and then subtraction of a prime number.

Therefore, following pattern is followed 

Hence, the correct answer is 52.

Here, we have a paper and the paper is folded three times to make a small square.

In that, they have cut the small square paper as in the image given in the figure 1.

And then when we open one fold of the paper we get the same image but the position of the circle and the triangle is changed.

Next we will open the last fold of the paper and we will get the opposite image in the next half of the paper, as shown below:

Hence, we will get this as the final answer, i.e. option 2.

According to the English alphabets and their positional values:

The pattern followed in the given series is:

• Alphabets placed at even places are decreased to 2 positional values.
• Alphabets placed at odd places are increased to 2 positional values.

Similarly, 

Hence the correct answer is JCCTA.

Given: D E _ W G _ E F _ G D E F U _ D _ F T G

Let's check each option:

1)  F D G V E → D E F W G - D E F G G - D E F U V - D E F T G → Does not follow the pattern

2)  F D V G E → D E F W G - D E F V G - D E F U G - D E F T G → Follow the pattern

Here 4^th letter is decreased by -1.

• W - 1 = V; V -1 = U; U - 1 = T

3)  D F F E V → D E D W G - F E F F G - D E F U E - D V F T G → Does not follow the pattern

4)  D F V G F → D E D W G - F E F V G - D E F U G - D F F T G → Does not follow the pattern

So, Option 2) gives a pattern of D E F W G - D E F V G - D E F U G - D E F T G.

Hence, ‘ F D V G E ’ is the correct answer.

Let us examine each option,

OPTION 1)

34 + 4 × 15 - 51 = 27 ÷ 9 + 40

34 + 60 - 51 = 3 + 40

94 - 51 = 43

43 = 43 

Therefore, LHS = RHS

OPTION 2)

34 - 4 + 15 = 51 × 27 - 9 + 40

34 - 11 = 1377 - 9 + 40

33  is not equal to  1328

OPTION 3)

34 + 4 - 15 = 51 × 27 ÷ 9 - 40

38 - 15 = 51 × 3 - 40

23 = 153 - 40

23 is not equal to 113

OPTION 4)

34 ÷ 4 - 15 = 51 × 27 ÷ 9 - 40

8.5 - 15 = 51 × 3 - 40

-6.5  is not equal to  113

Hence, The correct answer is " +, ×, -, =, ÷, +"

The logic followed here is as follows:

28^th February 2017 was Tuesday,

And  28^th February 2018 = Tuesday + 1(Odd day in 1 year) = Wednesday.

So, 28^th February 2019 = Wednesday + (Odd day in 1 year) = Thursday.

Hence, the correct is Thursday.

Here, we are given a figure.

First, we will count all the triangles which we can see directly, as shown below:

So, in the above figure, we can see there are 22 triangles.

Next, we will combine two triangles to make a big triangle as shown below.

Thus, from the above figure, we can see there are 26 triangles.

Hence, there are 26 triangles in the given figure.

Confusion point: Make sure to first count the small triangles and then see it combine the small ones we get the big triangles or not.

Given: Seven friends M, N, O, P, Q, R, and S

STEP 1: So first in the question, it is given that only two people are older than Q so the resulting framework will be 

__ > __ > Q > __ > __ > __ > __

STEP 2: 5^th line of the question states that only 3 people are younger than S so the resulting formation 

__ > __ > Q > S > __ > __ > __

STEP 3: Now please focus on two lines stating that P is older than Q but younger than O and M is older than R but younger than S and N is the youngest of all so the final formation will be 

O > P > Q > S > M > R >N 

Hence, The age of two persons is between the ages of Q and R.

The logic followed here is:

The mirror image of the given figure will be as follows: 

Detailed Explanation :- 

• The line MN is the mirror.
• The word " em268q"  ends with " 

" So, the mirror image will start with "

"Hence, option 1, 2 and 4 are eliminated.

Hence, Option 3) is the correct answer.

Important Points

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

The pattern followed in the sets is :

First term × 8 = Third term ; First term × 4 - 2 = Second term

Let's apply this in the first row  – 13, 50, 104

First term × 8 = Third term

13 × 8 = 104

104 = 104 

First term × 4 - 2 = Second term

13 × 4   = 52

52 - 2 = 50

Let's apply this in the third row  – 18, 70, 144

First term × 8 = Third term

18 × 8 = 144

144 = 144 

First term × 4 - 2 = Second term

18  × 4  = 72 

72 - 2 = 70

Similarly,

Let's apply this in the second row – 11, 42, ?

First term × 8 = Third term

11 × 8 = Third term 

88 = Third term 

First term × 4 - 2 = Second term

11 × 4  = 44  

44 - 2 = 42 

Hence the correct answer is 88.

Given information: 09 April 2023 is Friday.

Let's add +7 days to the date i.e. 9 so that we get the date which falls on Friday.

9 + 7 = 16 which means 16^th April 2023 is also a Friday.

Now, 16 + 7 = 23 which means 23^rd April 2023 is also a Friday.

So, 23 + 7 = 30 i.e. 30^th April 2023 is also a Friday.

Hence the correct answer is Friday.

The logic followed here is:

The positional value table is as follows:

According to the pattern followed in the series, the third cluster will be:

Hence the correct answer FQNK.

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 answer is option 1)

SOLUTION:

When we unfold the paper once, we get the mirror image of the already existing pattern,

Now when we unfold the paper twice, we get the mirror image of the pattern we got after first step,

Hence the correct answer is option 1)

Given information:

 

Now let's denote the operators in the given equation:

37 L 25 K (14 J 2) L (2 J 13) K (62 I 31) = ?

37 + 25 - (14 × 2) + (2 × 13) - (62 ÷ 31) = ?

Applying the BODMAS rule i.e. Bracket of Division Multiplication Addition Subtraction.

We get,

= 37 + 25 - (28) + (26) - (2) 

= 37 + 25 - 28 + 26 - 2

= 88 - 28 - 2

= 88 - 30

= 58 

Hence, the correct answer is 58.

The code language have a pattern :

The first and second letters are interchanged and the fourth and fifth letters are interchanged.

The code for DANCE is ADNEC

The code for DISCO is IDSOC

Similarly, 

The code for DREAM is RDEMA 

Hence, the correct answer is RDEMA.

The code language have a pattern :

GENIUS : IUNGES 

 

And

HOLDER : DELHOR

 

Similarly, 

Hence, the correct answer is HTGLIS.

Let's compare the options with the given image:

Option 1)

The region in option 1 can be seen in the right half of the given image.

Option 2)

The region in option 2 cannot be seen in the given image. 

Option 3)

The region in option 3 cannot be seen in the given image. 

Option 4)

The region in option 4 cannot be seen in the given image. 

Hence the correct answer is option 1

Let's apply the options into the given equation by using the BODMAS rule :

BODMAS rule is Bracket of Division Multiplication Addition Subtraction.

45 * 9 * 3 * 7 * 5 * 133

Applying option 1) -, +, ×, ÷, =

45 - 9 + 3 × 7 ÷ 5 = 133

45 - 9 + 3 × 1.4 = 133

45 - 9 + 4.2 = 133 

49.2 - 9 = 133 

40.2 = 133 Incorrect

Applying option 2)-, ÷, +, ×, =

45 - 9 ÷ 3 + 7 × 5 = 133

45 - 3 + 7 × 5 = 133

45 - 9 + 35 = 133 

80 - 9 = 133 

71 = 133 Incorrect

Applying option 3) ×, ÷, -, +, =

45 × 9 ÷ 3 - 7 + 5 = 133

45 × 3 - 7 + 5 = 133

135 - 7 + 5  = 133 

140 - 7 = 133 

133 = 133 Correct

Applying option 4) ÷, +, ×, -, =

45 ÷ 9 + 3 × 7 - 5 = 133

5 + 3 × 7 - 5 = 133

5 + 21 - 5 = 133 

26 - 5 = 133 

21 = 133 Incorrect

 Hence the correct answer is "×, ÷, -, +, ="

The pattern given in the series is :

Series 1:

Term 3 = (Term 1) - 3

Term 5 = (Term 3) - 3

Series 2:

Term 4 = (Term 2) + 3

Term 6 = (Term 4) + 3 

In order to get the series correct the difference between second, third and fifth term should be +3.

So adding 3 to the second term we get, 

211 + 3 = 214 i.e the fourth term 

and adding 3 to the fourth term we get,

214 + 3 = 217 i.e the sixth term 

 Hence, the correct answer is 214.

The pattern used in the given pairs :

(First term × 4) + 4 = Second term 

First pair- 19 : 80 

 (First term × 4) + 4 = Second term 

(19 × 4) + 4 = 80 

(76) + 4 = 80 

80 = 80 

Second pair- 23 : 96 

 (First term × 4) + 4 = Second term 

(23 × 4) + 4 = 96 

(92) + 4 = 96

96 = 96

So the third pair becomes, 

(First term × 4) + 4 = Second term 

(16 × 4) + 4 = Second term

(64) + 4 = Second term

68 = Second term

Hence the correct answer is 68

Let's apply the options into the given equation by using the BODMAS rule :

BODMAS rule is Bracket of Division Multiplication Addition Subtraction.

67 * 88 * 8 * 14 * 3 * 19 * 17

Applying option 1) -, ×, =, −, ÷, +

67 - 88 × 8 = 14 - 3 ÷ 19 + 17

67 - 88 × 8 = 14 - 0.15 + 17

67 - 704 = 14 - 0.15 + 17

67 - 704 = 31 - 0.15 

-637 = 30.85 Incorrect

Applying option 2)+, ÷, -, ×, -, =

67 + 88 ÷ 8 - 14 × 3 - 19 = 17

67 + 11 - 14 × 3 - 19 = 17

67 + 11 - 42 - 19 = 17

78 - 42 - 19 = 17 

78 - 61 = 17

17 = 17 Correct

Applying option 3) -, ÷, ×, +, =, -

67 - 88 ÷ 8 × 14 + 3 = 19 - 17

67 - 11 × 14 + 3 = 19 - 17

67 - 154 + 3 = 19 - 17 

70 - 154  = 19 - 17 

-84 = 2 Incorrect

Applying option 4) +, -, =, ×, -, ×

67 + 88 - 8 = 14 × 3 - 19 × 17

67 + 88 - 8 = 42 - 323

155 - 8 = 42 - 323

147 = -281 Incorrect

 Hence, the correct answer is "+, ÷, -, ×, -, ="

The relation between fruit, apple and vegetable is clear.

Let's draw the Venn diagram :

Apple is a kind of fruit that is why it can be classified as a fruit. 

Vegetable is neither a fruit nor related to apple. Therefore, 

So the final Venn diagram is:

Hence the correct answer is option 3)

We observe the small triangle in the corner of each block and we get, 

Small triangle moves to its right in each block and it turns solid in alternate steps:

Now we observe the small box and it's head in each block and we get, 

Small box moves with the small triangle and point towards it in each step:

Therefore we the next step as,

Small triangle faces upwards and is turns solid and the box and it's head point towards it, such the final pattern looks like:

the pattern in the last block is same as the pattern in the first block,

Hence the correct answer is option 4)

Given:

Total monthly income of a family = Rs 70,000

Percentage of expenditure for food = 28%

Percentage of expenditure for house rent = 14%

Percentage of expenditure for child education = 25%

Percentage of expenditure for medical = 10%

Percentage of expenditure for entertainment = 8%

Percentage of expenditure for provident fund = 15%

Concept Used:

Income left = Total Income – Income Spend

Calculation:

Amount spent on food = 28% of 70,000

Amount spent on food = $\frac{28}{100}$ × 70000 = Rs 19,600

Amount spent on medical = 10% of 70,000

Amount spend on medical = $\frac{10}{100}$ × 70000 = Rs 7,000

Total amount spent in food and medical = Rs 19,600 + Rs 7,000 = Rs 26,600

Amount left after spending on food and medical = Rs 70,000 – Rs 26,600 = Rs 43,400

∴ The amount left with the family after only the food and medical expenditures for the month is Rs 43,400

Given:

Speed of boat in still water = 12 km/h

Total distance for downstream = 18 km

Time taken to come back = $6\frac{6}{7}$ hours

Concept Used:

$Speed = \frac{Distance}{Time}$

Downstream speed of the boat = Speed of boat + Speed of stream

Calculation:

Let the speed of the stream be x.

Downstream speed of the boat = 12 + x

Upstream speed of the boat = 12 – x

Time taken by the boat to cover 18 km downstream and 18 km upstream = $6\frac{6}{7}$ = $\frac{48}{7}$ hours

Now, using the formula for speed and putting the values, we get

⇒ $\frac{18}{12 + x} + \frac{18}{12-x}=\frac{48}{7}$

Taking LCM of denominators from LHS,

⇒ $\frac{18×(12-x)+18×(12+x)}{(12+x)(12-x)}=\frac{48}{7}$

By solving the equation,

⇒ 432 × 7 = 48 × (144 - x²) 

⇒ 48 x² = 6912 - 3024

⇒ 48 x² = 3888 

⇒ x² = 81

⇒ x = 9 km / h.

∴  The speed of the stream will be 9 km/h.

Given:

Teak trees planted in 2016 = 25000

Teak trees planted in 2017 = 35000

Concept Used:

Percentage Increase = $\frac{Difference}{Trees}\times 100~$

Calculation:

Increase in teak trees in 2017 as compared to 2016 = Teak trees planted in 2017 – Teak trees planted in 2016

Increase in teak trees in 2017 as compared to 2016 = 35000 – 25000 = 10000

Percentage increase in teak trees from 2016 to 2017

⇒ $\frac{10000}{25000}\times100=\frac{1000}{25}~$= 40%

∴  The percentage increase in the number of teak trees that were planted in 2017 as compared to that by 2016 is 40%.

Given:

$\frac{x^2}{y^2}+\frac{y^2}{x^2}=7$

Concept Used:

$(a+b)^2=a^2+b^2+2ab$

$a^3+b^3=(a+b)(a^2+b^2-ab)$

Calculation:

⇒ $\frac{x^2}{y^2}+\frac{y^2}{x^2}=7$

⇒ Adding both the sides 2 ×  $\frac{x}{y}×\frac{y}{x}$,

⇒ $\frac{x^2}{y^2}+\frac{y^2}{x^2}+2× \frac{x}{y}×\frac{y}{x}=7+2 × \frac{x}{y}×\frac{y}{x}$

⇒ $(\frac{x}{y}+\frac{y}{x})^2=7+2$

⇒ $\frac{x}{y}+\frac{y}{x}=√9=3$

⇒ Now using formula for a³ + b³,

⇒ $\frac{{{x^3}}}{{{y^3}}}, + ,\frac{{{y^3}}}{{{x^3}}}=(\frac{x}{y}+\frac{y}{x})(\frac{x^2}{y^2}+\frac{y^2}{x^2}-\frac{x}{y}×\frac{y}{x})$

⇒ Putting the values, we get

⇒ $\frac{x^3}{y^3}+\frac{y^3}{x^3}=3×(7-1)=18$

∴  The required value of $\frac{x^3}{y^3}+\frac{y^3}{x^3}$ is 18

Alternate MethodCalculation:

If we put x = 1 then,

⇒ $\frac{x^2}{y^2}+\frac{y^2}{x^2}=7$

⇒ ${y^2}+\frac{1}{y^2}=7$

⇒ ${y}+\frac{1}{y}$ = $\sqrt{7 +2} =\sqrt 9$  = 3

⇒ ${y^3}+\frac{1}{y^3}$ = (3)³ - 3 × 3

⇒ ${y^3}+\frac{1}{y^3}$ = 18   ……(1)

If we put x = 1 in the equation, then

⇒ $\frac{{{x^3}}}{{{y^3}}}, + ,\frac{{{y^3}}}{{{x^3}}}$

⇒ ${y^3}+\frac{1}{y^3}$ = 18 [From eq. (1)]

∴ The correct answer is 18.

Given:

Discount percentage = 15%

Selling Price of machine = Rs 1,22,700

Concept Used:

Marked Price = Selling Price ÷ (100% – Discount%)

Calculation:

Putting all the values in MP formula,

Marked Price = 122700 ÷ (100% – 15%)

Marked Price = 122700 ÷ 85%

Marked Price = $122700\times\frac{100}{85}$

Marked Price = $\frac{12270000}{85}=1,44,352.94$

∴ The price at which machine was marked is Rs.1,44,352.94

Given:-

⇒ $\frac{{{\rm{8r}}}}{{{{\rm{r}}^{\rm{2}}},{\rm{ - }},,{\rm{8r}},{\rm{ + }},{\rm{1}}}}, = ,\frac{1}{{14}}$

Calculation:

It is given that 

⇒ $\frac{{{\rm{8r}}}}{{{{\rm{r}}^{\rm{2}}},{\rm{ - }},,{\rm{8r}},{\rm{ + }},{\rm{1}}}}, = ,\frac{1}{{14}}$

Dividing both the numerator and denominator by 'r'

⇒ $\frac{\frac{8r}{r}}{\frac{r^2-8r+1}{r}}=\frac{1}{14}$

⇒ $\frac{8}{r-8+\frac{1}{r}}=\frac{1}{14}$

On solving,

⇒ $r-8+\frac{1}{r}$ = 14×8

⇒ $\left(r+\frac{1}{r}\right)$ = 112+8 = 120

∴ The value of $\left(r+\frac{1}{r}\right)$ is 120.

Given:- 

Average of 15 athletes and 3 trainers (18 people) is 60Kg.

Formula used:- 

$Average=\frac{Sum\ of\ observation}{No.\ of\ observation}$

Calculation:

Average of 18 people (Athletes + trainer) = 60

By using formula of average, 

$Average=\frac{Sum\ of\ observation}{No.\ of\ observation}$

Sum of their weights = 60 × 18 = 1080 kg

Average of 4 more athletes = 63

Sum of their weights = 63 × 4 = 252

Total weight of 19 athlete and 3 trainers = 1080 + 252 = 1332 Kg.

New average = $\frac{total\ sum}{total\ no.\ of\ people }$

New average = $\frac{1332}{22}$ = 60.54kg

New average = 60.54 kg

On rounding off, new average = 61 kg

∴ The average weight of the group is 61 Kg.

Given:-

\left[ {3\frac{6}{7}, ÷ ,\frac{{54}}{7}, - ,\left{ {3, - ,\left( {2\frac{3}{4}, - ,\frac{3}{2}} \right)} \right}} \right], + A ÷ 4 = 0

Concept used:- BODMAS 

Calculation:

 The expression could be written as:

⇒ \left[ {3\frac{6}{7}, ÷ ,\frac{{54}}{7}, - ,\left{ {3, - ,\left( {2\frac{3}{4}, - ,\frac{3}{2}} \right)} \right}} \right]+\frac{A}{4}=0

Solving the expression of () small bracket, 

⇒ $\frac{11}{4}-\frac{3}{2}$ = $\frac{5}{4}$

Now the expression has become, 

⇒\left[ {3\frac{6}{7}, ÷ ,\frac{{54}}{7}, - ,\left{ {3, - \frac{5}{4}} \right}} \right]+\frac{A}{4}=0

Solving the expression inside the curly braces {},

⇒ $3-\frac{5}{4}=\frac{7}{4}$

The simplified expression is,

⇒$\left [3\frac{6}{7} \div \frac{54}{7}- \frac{7}{4}\right]+\frac{A}{4}=0~$

Solving expression of rectangular bracket,

⇒ $3\frac{6}{7} \div \frac{54}{7}- \frac{7}{4}$ = $\frac{27}{7} \div \frac{54}{7}- \frac{7}{4}$

⇒ $\frac{27}{7} \times \frac{7}{54}- \frac{7}{4}$ =  $\frac{1}{2}-\frac{7}{4}$

⇒ $\frac{-5}{4}$

The expression is, 

⇒ $\frac{-5}{4}+\frac{A}{4}=0$

⇒ A = 5

∴ The value of A is 5.

Given:- Dimension of brick= 25 cm × 11.25 cm × 6 cm

To find:- Number of bricks

Formula used:

Volume of cuboid =  Length × width × height

Calculation:

The volume of the brick is

Volume of Brick = 25 cm × 11.25 cm × 6 cm = 1687.5 $cm^3$

The volume of the wall( to be constructed) is,

Volume of wall = 8 m × 6 m × 22.5 cm

(Change the values of dimension in 'cm' as it is given in 'm')

Volume of wall = 800 cm × 600 cm × 22.5 cm      ----(1 m = 100 cm )

⇒ $108 \times 10^5 cm^3$

Number of brick required = $\frac{Volume\ of\ wall}{volume\ of\ brick}$

⇒ $\frac{108 \times 10^5 }{1687.5}$ = 6400

∴ The number of bricks required is 6400.

Shortcut Trick

Since AB = AC in ▵ABC, the angles opposite to these sides must be equal: ∠B = ∠C = 50°.

Given AB = PQ and BC = QR, and since both triangles are isosceles with AB = AC and PQ = PR, it follows that AC = PR.

By the SSS (Side-Side-Side) congruence criterion, ▵ABC ≅ ▵PQR.

In congruent triangles, corresponding angles are equal, thus ∠R = ∠C.

∴ The correct answer is 50°.

Alternate Method

Given:

In ▵ABC: AB = AC and ∠B = 50°.

In ▵PQR: PQ = PR, AB = PQ, and BC = QR.

Formula Used:

1. Isosceles Triangle Property: Angles opposite to equal sides are equal.
2. SSS Congruence: If three sides of one triangle are equal to three sides of another, the triangles are congruent.

Calculations:

⇒ In ▵ABC, since AB = AC ⇒ ∠B = ∠C

⇒ Given ∠B = 50°, therefore ∠C = 50°

⇒ In ▵PQR, since PQ = PR ⇒ ∠Q = ∠R

⇒ Since AB = PQ and AB = AC and PQ = PR, then AB = AC = PQ = PR

⇒ Also given BC = QR

⇒ All corresponding sides are equal: AB = PQ, AC = PR, and BC = QR

⇒ ∴ ▵ABC ≅ ▵PQR by SSS Congruence Rule

⇒ By CPCT (Corresponding Parts of Congruent Triangles), ∠R = ∠C

⇒ ∴ ∠R = 50°

∴ The correct answer is 50°.

Additional Information

SSS Congruence Rule

Two triangles are congruent if all three sides of one triangle are equal to the corresponding three sides of the other triangle.

Isosceles Triangle Theorem

Angles opposite to equal sides of an isosceles triangle are equal (∠B = ∠C if AB = AC).

Angle Sum Property

The sum of all internal angles of any triangle is exactly 180° (∠A + ∠B + ∠C = 180°).

Shortcut Trick

For a dishonest dealer selling at cost price, the profit percentage is calculated on the actual weight delivered.

Profit% = (Error ÷ True Value − Error) × 100

Here, Error = 1000 gm − 900 gm = 100 gm.

Profit% = (100 ÷ 900) × 100 = 100 ÷ 9 = 11¹/₉%.

∴ The correct answer is 11¹/₉%.

Alternate Method

Given: Selling Price (SP) of 900 gm = Cost Price (CP) of 1000 gm.

Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100

⇒ Let the CP of 1 gm be Re 1. Then CP of 1000 gm = Rs 1000.

⇒ The dealer sells 900 gm for Rs 1000 (since he sells at CP of 1 kg).

⇒ CP of 900 gm = Rs 900. SP of 900 gm = Rs 1000.

⇒ Profit = 1000 − 900 = Rs 100.

⇒ Profit% = (100 ÷ 900) × 100 = 11¹/₉%.

∴ The correct answer is 11¹/₉%.

Additional Information

Dishonest Dealer Concept

When a dealer uses less weight, the profit is always calculated on the goods actually leaving the shop (the false weight).

Ratio Method

Ratio of Weight = 1000 : 900 = 10 : 9. Ratio of Price (inverse) = 9 : 10. Profit = 1 unit on 9 units = 11¹/₉%.

Given: 

Average marks=75

Formula used:

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

Calculation:

Total marks scored by a student in 4 subjects = Average × 4

Total marks of 4 subjects = 75 × 4 = 300

Let the marks in English be 'x'

New Average = 70

⇒ $\frac{300+x}{5}$ = New Average

⇒ $\frac{300 + x}{5}$ = 70

⇒ x = 50

∴ The mark scored by students in English is 50.

Given:

0.62 , $\frac{2}{3}$ , 0.57 , $\frac{4}{5}$

Concept Used:

Decimal conversion and comparison.

Calculation:

⇒  $\frac{2}{3}$ could be written as 0.67 in decimal form

and,

⇒ $\frac{4}{5}$ could be written as 0.8 in decimal form.

On comparison between  0.62 , $\frac{2}{3}$ , 0.57 , $\frac{4}{5}$

⇒ 0.8 = $\frac{4}{5}$ > 0.67 = $\frac{2}{3}$ > 0.62 > 0.57

∴  $\frac{4}{5}$ is the greatest among all other options

Given:

P : Q = 10 : 11 and Q : R = 11 : 12

Concept used:

Combining ratios

Calculation:

P : Q = 10 : 11       ----(i)

Q : R = 11 : 12      ----(ii)

Since in both the ratios (i) and (ii) the combining one,Q, has the same value in both the cases 

Hence, P : Q : R = 10 : 11 : 12

Let P , Q , and R be 10x ,11x , and 12x respectively, where x is the factor by which ratio is changing-

then, P + Q = 10x + 11x = 21x

Q + R = 11x +12x = 23x

P + R = 10x + 12x = 22x

⇒ P + Q : Q + R : R + P = 21x : 23x : 22x

⇒P + Q : Q + R : R + P = 21 : 23 : 22    (by putting x = 1)

∴ The value of  P + Q : Q + R : R + P is 21 : 23 : 22

Shortcut Trick

Total Surface Area (TSA) of a hemisphere = 3πr² = 16632 cm².

⇒ πr² = 16632 ÷ 3 = 5544 cm².

⇒ r² = (5544 × 7) ÷ 22 = 252 × 7 = 1764 ⇒ r = 42 cm.

Volume = (2/3)πr³ = (2/3) × (3πr² ÷ 3) × r = (2/9) × 16632 × 42.

⇒ Volume = 2 × 1848 × 42 = 155232 cm³.

∴ The correct answer is 155232 cm³.

Alternate Method

Given:

Total Surface Area (TSA) of solid hemisphere = 16632 cm²

Formula Used:

⇒ TSA of hemisphere = 3πr²

⇒ Volume of hemisphere = (2/3)πr³

Calculations:

⇒ 3 × (22/7) × r² = 16632

⇒ r² = (16632 × 7) ÷ (3 × 22)

⇒ r² = 16632 ÷ 66 × 7

⇒ r² = 252 × 7 = 1764

⇒ r = √1764 = 42 cm

⇒ Volume = (2/3) × (22/7) × 42 × 42 × 42

⇒ Volume = 2 × 22 × 2 × 42 × 42 ÷ 1 (after cancelling 3 and 7 with 42)

⇒ Volume = 88 × 1764 = 155232 cm³

∴ The correct answer is 155232 cm³.

Additional Information

Curved Surface Area (CSA)

The CSA of a hemisphere is exactly half of a sphere's surface area, given by 2πr².

Sphere Properties

For a full sphere, Surface Area = 4πr² and Volume = (4/3)πr³.

Ratio of TSA to CSA

For a solid hemisphere, the ratio of Total Surface Area to Curved Surface Area is 3:2.

Given:

Divisible by 3 or 5

Concept used:

Using the formula of finding the n^th term of an AP

a_n = a + (n - 1) × d

Calculation:

The first two-digit number divisible by 3 is 12

The second two-digit number divisible by 3 is 15

The third is 18

We can see that an AP is formed here, whose first term is 12 and the common difference is 3

By hit and trial we can find the last two-digit number divisible by 3 will 99, which means the last term of an AP is 99

Here, a = 12 , d = 3 and a_n = 99

By putting the values in the formula,

99 = 12 + (n - 1) × 3

n - 1 = 29 

n = 30

The two-digit numbers divisible by 3 are 30

Similarly, by taking 10 as the first and 95 as the last digit we could find the number of two digit numbers divisible by 5,

 Here, a = 10 , d = 5 and an = 95

By putting the values in the formula,

95 = 10 + (n - 1) × 5

n - 1 = 17

n = 18

The two-digit numbers divisible by 5 is 18

It is asked in the question that the two-digit number should either be divisible by 3 or 5 but not by both,

The number of two-digit numbers divisible by both can be found by forming AP(Arithmetic progression) as same as above-

Here, the first term and the common difference will be L.C.M.(3 , 5) i.e. 15

⇒By hit and trial, the last term will be 90

Using n^th term formula of an A.P , an = a + (n +1) × d

⇒90 = 15 + (n - 1) × 15

75 = (n - 1) × 15

5 = (n - 1)

.·. n = 6

The two-digit numbers divisible by both 3 and 5 are 6.

So, The total number of two-digit numbers divisible by 3 or 5 will be,

(Number divisible by 3) + (Number divisible by 5) - (Number divisible by both 3 and 5)

**⇒**30 + 18 - 6 = 42

∴ The two-digit numbers divisible by 3 or 5 are 42.

Given:

Price raised by 45% and two successive discount of 15% is given

Formula used:

Percent change = $\frac{final\ value-initial\ value}{initial\ value}× 100$

Calculation:

Let the cost price of an article is Rs100

As mentioned, the price is raised by 45% that means

New price = Old price + 45% of old price

⇒ 100 + $\frac{45}{100}× 100$

New price = 145 rs

Since two successive discount of 15% has been given on new price,

After first discount,

Discounted Price =145 - 15% of 145

Discounted Price =145 - $\frac{15}{100}×145$

Discounted Price =123.25 rs

After second discount,

Final price = 123.25 - 15% of 123.25 

123.25 - $\frac{15}{100}× 123.25$

123.25 - 18.4875

Final price = 104.7625

Percentage change in price = $\frac{final\ value-initial\ value}{initial\ value}× 100$

% change = $\frac{104.7625-100}{100}× 100$

%change = 4.7625 %

The price of the article is increased by 4.7625 %.

Alternate Method

Let CP be 100

MP = 100 + (45 × 100/100)

⇒ 145

Net Dis = 15 + 15 - (15 × 15/100)

⇒ 27.75%

Final Price = 145 - (145 × 27.75%)

⇒ 104.7625

% change = $\frac{104.7625-100}{100}$ × 100

%change = 4.7625 %

The price of the article is increased by 4.7625 %.