The correct answer is 'quite frequent'.

Key Points

• The error lies in the usage of the adjective 'frequent'.
• The phrase 'quite frequent' is modifying the verb 'moved'. This is incorrect.
• For the sentence to be correct, we need to use the adverbial phrase 'quite frequently' to modify the verb 'moved'.

Important Points

• Frequent is an adjective. It means occurring or done many times at short intervals.
• 'Frequently' is an adverb. It means often.

Additional Information

• Adjectives do not modify verbs or adverbs or other adjectives.
• But adjectives can also act as a complement to linking verbs or the verb to be.
• It smells disgusting when you take off your shoes. (The adjective 'disgusting' complements the verb 'smells'.)

The correct answer is 'Happening only rarely'.

Key Points

• The idiom 'once in a blue moon' means very rarely.
• Usage in a sentence -  She comes around once in a blue moon to check on her elderly mother.
• Hence, option 3) Happening only rarely is the most appropriate meaning of the given idiom.

Mistake Points

• We may confuse the meaning of the idiom to be not rare but a singular occurrence. This can lead to the selection of the incorrect answer as option 1) Happening only once in a lifetime.

Additional Information

• “Once in a blue moon” today means “very rarely,” though it used to mean something that was absurd, right along the lines of “when pigs fly.”

The correct answer is 'Boisterous'.

Key Points

• Rowdy means noisy and disorderly. (झगड़ालू व्यक्ति, उपद्रवी)
• The meanings of the given options are listed below -
• • Boisterous - noisy, energetic, and cheerful. (प्रचण्ड, प्रबल, गर्जनकारी)
• Charming - very pleasant or attractive. (आकर्षक, मनभावन)
• Calm - not showing or feeling nervousness, anger, or other strong emotions. (शांत,नीरव)
• Amenable - open and responsive to suggestion (विनम्र, उत्तरदायी, आज्ञाकारी)
• From the given meanings, it is clear that only boisterous is a synonym of the given word.
• This makes option 1 the correct answer.

Additional Information

• Usage of the words in the given options in sentences - 
• boisterous - The boisterous student disrupted his class every day.
• charming - What a charming girl she is, really!
• calm - His voice was calm and deliberate.
• amenable - He was amenable to change.

The correct answer is 'Desolate'.

Key Points

• Barren means (of land) too poor to produce much or any vegetation. It can also mean showing no results or achievements.
• The meanings of the given options are listed below - 
• Fruitful - fertile or productive.
• Bountiful - abundant.
• Fertile - (of soil or land) producing or capable of producing abundant vegetation or crops.
• Desolate - (of a place) uninhabited and giving an impression of bleak emptiness.
• From the given meanings, it is clear that only desolate is a synonym of the given word.
• This makes option 4 the correct answer.

Additional Information  

• Usage of the words in the given options in sentences - 
• fruitful - Few explorations have been so fruitful as this six years' journey.
• bountiful - Consider giving a bountiful gift basket.
• fertile - The larger islands have some fertile and well-watered valleys and plains.
• desolate - It was a desolate wasteland except for some grazing sheep.

The correct answer is 'our'.

Key Points

• Blank 1 needs a possessive determiner to show whom the evening belonged to.
• Of the given options, all of which are possessive determiner, 'our' is the best-fit word for the given blank as it means belonging to or associated with the speaker and one or more other people previously mentioned or easily identified.
• 'Their' implies third person plural, but in the given sentence, the use of 'we' shows that it cannot be used.

Additional Information

• 'Theirs' and 'ours' are independent possessive pronouns (also called absolute possessive pronouns) and must be used without a noun.
• The house on the corner is theirs.
• But ours is better.

The correct answer is 'celebrate'.

Key Points

• Blank 2 needs a verb to show the action the subjects wanted to perform.
• This negates the usage of 'celebration' which is a noun.
• 'Wanted to' is followed by an infinitive owing to the usage of 'to'.
• So, the present tense form of 'celebrate' should be used for the blank.
• Hence, option 2 is the correct answer.

Additional Information

• Celebrate means acknowledge (a significant or happy day or event) with a social gathering or enjoyable activity.

The correct answer is 'about'.

Key Points

• Blank 3 needs a preposition to link the verb 'reminiscing' with the topic of the said action.
• The usage of the given prepositions are as follows - 
• for - with the object or purpose of.
• with - accompanied by (another person or thing).
• about - on the subject of; concerning.
• in - expressing the situation of something that is or appears to be enclosed or surrounded by something else.
• Hence, option 3 is the correct answer.

The correct answer is 'profound'.

Key Points

• Blank 4 needs an adjective to describe the noun 'experience' placed after it.
• The meaning of the given options are as follows - 
• sincere - free from pretense or deceit
• profound - (of a state, quality, or emotion) very great or intense.
• comical - amusing, especially in a ludicrous or absurd way.
• dismal - causing a mood of gloom or depression.
• From the above meanings it is clear that option 2 is the best fit word for the given blank.

The correct answer is 'the'.

Key Points

• Blank 5 needs an article.
• This negates the usage of 'much' and 'some' which are quantifiers.
• The articles (a/an/the) are used before adjectives which are followed by the nouns that they modify.
• Based on this, since the mentioned 'jungle' is a definite place, the definite article 'the' should be used.
• The 'solitude' being referred to here is definite as it is the one that is related to the jungle.
• Hence, option 3 is the correct answer.

The correct answer is 'Revealed'.

Key Points

• Concealed means to hide something.
• The meaning of the given options is listed below - 
• hidden - kept out of sight
• masked - conceal (something) from view.
• revealed - make (previously unknown or secret information) known to others.
• discussed - talk about (something) with a person or people.
• From the given meanings, it is clear that the words hidden and masked are synonymous to the word 'concealed'.
• Only revealed is an antonym of the given word.
• This makes option 3 the correct answer.
  

​

Additional Information  

• Usage of the words in the given options in sentences - 

• hidden - The beach was hidden from view.

• masked - His cheery nature masked a ruthless character.

• revealed - She revealed all the wrong things he did.

• discussed - I discussed the finer details in today's meetings.

• Concealed का मतलब है कुछ छिपाना।

• दिए गए विकल्पों का अर्थ नीचे सूचीबद्ध है -

• Hidden  - दृष्टि से बाहर रखा हुआ

• Masked  - दृश्य से (कुछ) छिपाना।

• Revealed  - दूसरों को ज्ञात बनाने (पहले अज्ञात या गुप्त जानकारी)।

• Discussed - एक व्यक्ति या लोगों के साथ (कुछ) के बारे में बात करें।

• दिए गए अर्थों से, यह स्पष्ट है कि hidden और masked शब्द 'concealed' शब्द का पर्याय हैं।

• केवल revealed  है कि दिए गए शब्द का एक अंश है।

• यह विकल्प 3 को सही उत्तर बनाता है।

The correct answer is 'activities'.

Key Points

• The meaning of the given words are as follows - 
• activities - a thing that a person or group does or has done. The word 'engaged' shows that we need to use 'activities' here as the two words are often used together.
• conversions - the process of changing or causing something to change from one form to another.
• employments - a person's trade or profession.
• moments - a very brief period of time.
• From the above meanings, it is clear that 'activities' is the best fit for the given blank.

The correct answer is 'Roopa requested me to accompany her to the market.'

Key Points

• The given direct speech is an imperative sentence. An imperative sentence is a sentence that expresses a command, a request, advice, or a suggestion.
• Open the door. (Command)
• Please help me. (Request)
• Quit smoking. (Advice.)
• As imperative sentences have a command, a request, advice, or a suggestion, to change them into an indirect speech some specific verbs are used (requested, order, advised, forbade, suggested) to replace the verbs (e.g. told, said) of reporting verb.
• In the given sentence, 'please' is used which gives the tone of requesting somebody. Hence, use 'requested' in the reported speech.

<br>

So the correct Indirect speech is→ Roopa requested me to accompany her to the market.

The correct answer is 'BDAC'.

Key Points

• The passage should start with sentence B that establishes the subject matter which is a comparison between happiness and peace. It states that happiness is difficult to achieve in comparison to peace. It mentions the reason behind this difficulty to be our constant need for happiness in daily life.
• To maintain continuity, sentence D  should come in next as it talks about how the events in our daily lives that provide happiness are random and occur for a short period. The context of daily life makes sentence D ideal for the second position.
• Sentence A should come in the third spot as it further elaborates on the instances mentioned in sentence D that brings us happiness. It mentions several examples of instances that provide us with happiness.
• Sentence C provides an example of peace and points out how it differs from happiness. It comes in the last spot.
• So, BDAC  is the correct arrangement of sentences which makes option 4 the correct answer.

The correct answer is 'BADC'.

Key Points

• The passage should start with sentence B which establishes the subject matter. It introduces the characters of the passage which are a hawk and a hen. It talks about how the hawk who flew in the sky wanted to marry the hen who lived on earth.
• To maintain continuity, sentence A  should come in next as it talks about the action taken by the hawk in order to marry the hen. This puts the sentence in the second position.
• Sentence D should come in the third spot as it tells us the positive answer provided by the hen when the hawk had asked her to marry him.
• Sentence C tells us the hawk's reaction to the affirmative answer from the hen and comes in the fourth position.
• So, BADC  is the correct arrangement of sentences which makes option 4  the correct answer.

The correct answer is 'An exhibition of sarees from different states of India is being arranged by us at Dilli Haat.'

Key Points

• The given sentence is in the active voice which we can see because the passive voice is always written in the form of 'Be + V₃'
• While changing the subject in the active voice, change it into the object of the passive voice.
• Always remember that the tense never changes in the Active/Passive voice.
• In the given sentence, the tense is the present continuous tense. So, the structure in the passive voice is 'Subject + Be + Being + V₃ + Object'
• The verb 'Arrange' is a transitive verb so the direct object is 'an exhibition' which is going to be the subject in the passive voice.
• Also, it is a singular noun so we have used the singular verb.

<br>

So the correct passive voice is→ An exhibition of sarees from different states of India is being arranged by us at Dilli Haat.

The correct answer is 'To desert someone in his difficulties​'.

Key Points

• The idiom 'To leave someone in the lurch' means to leave (someone) without help or protection when it is needed.
• Usage in a sentence - To leave someone in the lurch is an example of cowardice.
• Hence, option 3) To desert someone in his difficulties is the most appropriate meaning of the given idiom.

Additional Information

• This expression alludes to a 16th-century French dice game, lourche, where to incur a lurch meant to be far behind the other players.

The correct answer is '​Philanthropist'.

Key Points

• The meanings of the given options are as follows - 
• Philologist - A philologist is someone who studies the history of languages, especially by looking closely at literature.
• Philanthropist - a person who seeks to promote the welfare of others, especially by the generous donation of money to good causes.
• Impressionist - a painter, writer, or composer who is an exponent of impressionism.
• Receptionist - a person who greets and deals with clients and visitors to a surgery, office, etc.
• From the above meanings, it is clear that 'philanthropist' is the correct word which means the same as the given group of words.
• Hence, option 2  is the correct answer.

The correct answer is 'No improvement'.

Key Points

• 'Shouldn't we' is the contraction of the phrase 'should not we'.
• It is a question tag for 'we should'.
• It is used when a particular action is being questioned.
• In the case of the following sentence, it is questioning whether the subjects should rest now because of a long day.
• Thus, it is correct for the given sentence making option 2 the correct answer.

The correct answer is 'need to become stricter​'.

Key Points

• The error lies in the usage of the plural verb form 'need'.
• 'The environment protection policy' is a singular entity.
• As such, to maintain the subject-verb agreement, the singular verb form 'needs' should be used.

Therefore, the correct sentence is  - The environment protection policy needs to become stricter if we wish to combat climate change.

Additional Information

• 'Needs' is also a plural noun form where it means circumstances in which something is necessary.

The correct answer is '​has been declared'.

Key Points

• 'Have declared' is the present perfect form of the main root verb 'declare'.
• The present perfect tense is a verb tense used to express actions that occurred at a non-specific time.
• The present perfect tense is also used to express actions that started in the past but continue to the present.
• Here, we need the passive form of the present perfect tense as Rohit is the one who is declared the best batsman - he should be the object in the active voice.
• Therefore, we need to use 'been' since the structure of the passive voice of the present perfect tense is - has/have + been + V3.
• So, option 2 is the correct answer.

The correct answer is 'Applaud'.

Key Points

• Admonish means to warn or reprimand someone firmly.(किसी को दृढ़ता से चेतावनी देना या फटकारना।)
• The meanings of the given options are listed below - 
• Belittle (तुच्छ समझना)- dismiss (someone or something) as unimportant.
• Attack (हमला)- act against (someone or something) aggressively in an attempt to injure or kill.
• Harden (कठोर बनाना)- make or become hard or harder.
• Applaud (ताली बजाकर प्रशंसा करना)-  to express approval especially by clapping the hands
• From the given meanings, it is clear that only applaud is an antonym of the given word.
• This makes option 4 the correct answer.​

Additional Information

• Usage of the words in the given options in sentences - 
• belittle - It is against the rules for students to belittle each other.
• attack - There was an attack on the village.
• harden - I am waiting for the glue to harden.
• applaud - I would like to personally applaud his performance.

The correct answer is 'setback'.

Key Points

• The meanings of the given options are as follows - 
• moodiness - a sullen gloomy feeling.
• His moodiness was harmful for the relationship.
• lowliness - Lack of vanity or self-importance.
• There is neither lowliness nor nobleness in careers.
• setback - a reversal or check in progress.
• He suffered from a setback because of the accident.
• significance - the quality of being worthy of attention
• We cannot deny the significance of the incident.
• From the above meanings, it is clear that 'setback' is the correct word for the given blank.
• This makes option 3 the correct answer.

The correct answer is 'bunglow'.

Key Points

• The correct spelling of 'bunglow' is BUNGALOW and it means a low house having only one storey or, in some cases, upper rooms set in the roof, typically with dormer windows.
• All other given options have been spelt correctly.
• Hence, option 2  is the correct answer.

Additional Information

• Balloon - a small coloured rubber bag which is inflated with air and then sealed at the neck, used as a child's toy or a decoration. 
• We decorated the room with balloons and streamers for his party.
• Irritant - a substance that causes slight inflammation or another discomfort to the body.
• Poison ivy is a powerful skin irritant.
• Adulteration - the action of making something poorer in quality by the addition of another substance.
• This shop is known for its adulteration.

The correct answer is '​Chronology'.

Key Points

• The meanings of the given options are as follows - 
• Archaeology - the study of human history and prehistory through the excavation of sites and the analysis of artefacts and other physical remains.
• Ecology - the branch of biology that deals with the relations of organisms to one another and to their physical surroundings.
• Chronology - the arrangement of events or dates in the order of their occurrence.
• Geology - the science which deals with the physical structure and substance of the earth, their history, and the processes which act on them.
• From the above meanings, it is clear that 'chronology' is the correct word which means the same as the given group of words.
• Hence, option 3  is the correct answer.

The correct answer is 'Arguement'.

Key Points

• The correct spelling of 'Arguement' is ARGUMENT and it means an exchange of diverging or opposite views, typically a heated or angry one.
• All other given options have been spelt correctly.
• Hence, option 4  is the correct answer.

Additional Information

• Existence - the fact or state of living or having objective reality.
• This shop has been in existence since the neighborhood started to grow.
• Commitment- the state or quality of being dedicated to a cause, activity, etc.
• I have a commitment to society.
• Distance - the length of the space between two points.
• It is a short distance from my house.

The number of triangles in the given figure are :

 

So the there are total 29 triangle in the given figure.

Hence, '29' is the correct answer.

The positions of the letters according to the English alphabet series:

Logic: The first two letter of the word get decreased by 1 position then the next two-letter increased by 2 again next two-letter decreased by 1 to get the code.

The pattern followed here is :

Similarly,

Hence,'QNJKMX' is the correct answer.

Given,

 A → Tennis players

B → Badminton players

C → Hockey players

D → Football players

On observing the given figure 'C' is common among all.

Hence, 'C' is the correct answer.

Given,

@ will be opposite of ($)

will be opposite of (!)

% will be opposite of (*)

By Checking options:

1) 

 → Here '#' is adjacent to '!' so this can not be the answer.

2) 

→ Here '%' is adjacent to '*' so this can not be the answer.

3) 

→ Here '%' is adjacent to '*' so this can not be the answer.

→  There is no opposite phase are adjacent to each other so this is the answer figure.

Hence, the figure in option 4 is the correct answer.

In a certain code language,

From the above figure 'bad' is coded as '1'.

Hence, '1' is the correct answer.

By checking the options :

1. × and +

Given equation : (56 ÷ 7) + 5 × 8 – 12 = 60

After interchanging the position of the symbol as given in the option.

(56 ÷ 7) × 5 + 8 – 12 = 60

8 × 5 + 8 - 12 = 60

40 + 8 - 12 = 60

48 - 12 = 60 

36 ≠ 60

2. • and ÷

Given equation : (56 ÷ 7) + 5 × 8 – 12 = 60

After interchanging the position of the symbol as given in the option.

(56 + 7) ÷ 5 × 8 – 12 = 60

63 ÷ 5 × 8 - 12 = 60

12.6 × 8 - 12 = 60

100.8 - 12 = 60 

88.8 ≠ 60

3) 8 and 12

Given equation : (56 ÷ 7) + 5 × 8 – 12 = 60

After interchanging the position of the symbol as given in the option.

(56 ÷ 7) + 5 × 12 – 8 = 60

8 + 5 × 12 - 8 = 60

8 + 60 - 8 = 60

68 - 8 = 60 

60 = 60

4) 7 and 5

Given equation : (56 ÷ 7) + 5 × 8 – 12 = 60

After interchanging the position of the symbol as given in the option.

 (56 ÷ 5) + 7 × 8 – 12 = 60

11.2 + 7 × 8 – 12 = 60

11.2 + 56 - 12 = 60

67.2 -12 = 60

55.2 ≠ 60

Hence,'8 and 12' is the correct answer.

The meaningful sequence is :

3. Letter → These are the alphabets used to make a meaningful word.

5.Word → group of the letters is called word.

4. Phrase → group of the word is called a phrase.

2.Sentence → group of the phrase is called a sentence.

1. Paragraph → group of the sentence is called a paragraph.

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

Let, the marked price is a

marked price is 100% 

and after giving the discount of 25 % the price of laptop is Rs.22,500.

So, 

a × (100 - 25) % = 22,500

a × 75% = 22,500

a = (22, 500 × 100) ÷ 75

a = 2250000 ÷ 75

a = 30,000

So, the marked price of Laptop is Rs. 30, 000.

Hence, '30,000' is the correct answer.

The question figure is embedded in,

Hence, the figure in option 2 is the correct answer.

By checking the options :

1. mom/ oon /mom / non /mom /nmn (Does not follow any pattern)

2. nom/ non /mmm / non /mom /non (Does not follow any pattern)

3. nom/ mon /mom / non /mom /nnn (Does not follow any pattern)

4) mom/ non /mom / non /mom /non (Follow the pattern)

Hence, 'mnomo' is the correct answer.

The positions of the letters according to the English alphabet series.

The pattern followed here is :

Similarly,

Hence, 'BCO' is the correct answer.

The paper when unfolded looks like,

Hence, the figure in option 2 is the correct answer.

The positions of the letters according to the English alphabet series:

Logic: Difference between the positions of the letters is 3.

The pattern followed here is:

So, Instead of 'S' 'R' should be there.

Hence, 'S' does not belong to the series.

Logic: The first digit of the number remains the same and last two-digit get interchange to get the second number.

The pattern followed here is :

263 → 236

Similarly,

768 → 786

Hence, '786' is the correct answer.

The least possible Venn diagram for the given statement is :

I. All cats are bananas → False (It is possible but not definite)

II. Some cats are mangoes → True ( Some mangoes are cats)

Hence, only conclusion II follows.

The positions of letters according to the English alphabet series :

Logic: Successive subtraction of even number from each letter to get the code.

The pattern followed here is :

Similarly,

Hence, 'KKXW' is the correct answer.

The positions of the letters according to the English alphabet series:

The pattern followed here is :

Hence, 'P' is the correct answer.

Logic : To get the next term in the series add previous two terms.

The pattern followed here is :

1 + 1 = 2

2 + 1 + 1 = 4

4 + 2 + 1 = 7

7 + 4 + 2 = 13

13 + 7 + 4 = 24

24 + 13 + 7 = 44

44 + 24 + 13 = 81

Hence, '81' is the correct answer.

The position of the letters according to the English alphabet series:

The pattern followed here is 

PTR: R38

P → P + 2 = R

T(20) + R(18) → 20 + 18 = 38

Similarly,

IMK:?

I → I + 2 = K

M (13) + K (11) → 13 + 11 = 24

? = K24

Hence, 'K24' is the correct answer.

The pattern followed here is :

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Hence, '42' is the correct answer.

Preparing the family tree using the following symbols,

The person who is standing with my mother in the photograph is the only son of my father means Mohan himself.

Hence, 'Mohan himself' is the correct answer.

Logic: Successive addition of square of the number starting from the 1 to get the require series

The pattern followed here is :

Hence, '95' is the correct answer.

The pattern followed here is :

The figure moves 90^o clockwise.

Hence, the figure in option 2 is the correct answer.

The pattern followed here is:

1. 5³ + 6 → 125 + 6 = 131

2. 7³ + 5 → 343 + 5 = 348

Similarly,

3. 9³ + 8 → 729 + 8 = 737

Hence, '737' is the correct answer.

The mirror image would be as follows :

Hence, the figure in option 3 is the correct answer.

Given:

Units produced on Friday = 50

Units produced on Friday = 30

Formula Used:

Percentage Decline = ((a – b)/a) × 100

Calculations:

Units produced on Friday = 50

Units produced on Friday = 30

Percentage Decline = ((a – b)/a) × 100

⇒ Percentage Decline = ((50 – 30)/50) × 100

⇒ Percentage Decline = (20/50) × 100

⇒ Percentage Decline = 40%

∴ The percentage decline in the production from Friday to Saturday is 40%.

Given:

At loss 10%, SP of article = Rs. 810

Formula Used:

SP = CP × (1 + P%/100)

SP = CP × (1 – L%/100)

where, SP → Selling Price, CP → Cost Price

Calculations:

At loss 10%, SP of article = Rs. 810

Now, SP = CP × (1 – L%/100)

⇒ 810 = CP × (1 – 10/100)

⇒ 810 = CP × (9/10)      ----(1)

At gain 4%, 

SP = CP × (1 + 4/100)

⇒ SP = CP × (26/25)      ----(2)

Dividing (2) by (1), we get

⇒ SP/810 = [CP × (26/25)]/[CP × (9/10)]

⇒ SP/810 = 104/9

⇒ SP = (104/90) × 810

⇒ SP = Rs. 936

∴ The price at which Salma sells it to gain 4% is Rs. 936.

Given:

Sum = Rs. 320

Amount = Rs. 405

Rate of interest = 12.5%

Formula Used:

If a^m = aⁿ, then

m = n

Amount = P × (1 + r%/100)^t

⇒ P → Principal, r% → Rate of interest per annum, t → Time period

Calculations:

Let the time period be t years.

Amount = P × (1 + r%/100)t

⇒ 405 = 320 × (1 + 12.5/100)^t

⇒ 405/320 = (9/8)^t

⇒ 81/64 = (9/8)² = (9/8)^t

⇒ t = 2 years

∴ The time in which a sum of Rs. 320 amount to Rs. 405 is 2 years.

Given:

The area of park = 16x2 + 8x + 1

Formula Used:

Area of square = (Side)²

Calculations:

16x2 + 8x + 1 = 0

⇒ (4x)² + 2 × 4x + (1)² 

⇒ (4x + 1)² 

Now, Area of square = (Side)2

⇒ Length of park = (4x + 1)

∴ The length of the park is (4x + 1) units.

Given:

Radius of circle = 10 cm

Length of PQ = 16 cm

Length of RS = 12 cm

Formula Used:

AC² = AB² + BC²

where, AB, BC → Sides of a right-angled triangle, AC → Hypotenuse of a right-angled triangle

Calculations:

Let O be the center of the circle.

In ΔOAP,

OP² = OA² + AP²

⇒ (10)² = OA² + (8)²

⇒ OA² = 100 – 64 = 36

⇒ OA = 6 cm

Similarly, In ΔOBR,

OR2 = OB2 + BR2

⇒ (10)2 = OB2 + (6)2

⇒ OB2 = 100 – 36 = 64

⇒ OB = 8 cm

Now, AB = OA + OB

⇒ AB = (6 + 8) cm

⇒ AB = 14 cm

∴ The distance between the chords if they are on opposite sides of the centre is 14 cm.

Given:

sin 20° cos 70° + sin 70° cos 20° 

Concept Used:

If (θ + α) = 90°, then

sinθ = cosα 

Formula Used:

sin²θ + cos²θ = 1

Calculations:

Considering the given equation,

sin 20° cos 70° + sin 70° cos 20° = ?

Now, (20° + 70°) = 90° 

⇒ (sin 20°)² + (cos 20°)² = ?      [cos70° = sin20°, sin70° = cos20°]

sin2θ + cos2θ = 1

∴ The value of? is 1.

Concept Used:

Calculations:

Considering the given equation,

10 – [121 ÷ (11 × 11) – (- 4) – {3 – (8 – 1)}] = ?

⇒ 10 – [121 ÷ (121) + 4 – {3 – 7}] = ?

⇒ 10 – [121 ÷ (121) + 4 – {-4}] = ?

⇒ 10 – [121 ÷ (121) + 4 + 4] = ?

⇒ 10 – [121/121 + 4 + 4] = ?

⇒ 10 – [1 + 4 + 4] = ?

⇒ 10 – 9 = ?

⇒ 1 = ?

∴ The value of ? is 1.

Given:

∠SPQ = 110° 

PQRS is a cyclic quadrilateral

PQ || SR

Concept Used:

In a cyclic quadrilateral, the sum of opposite angles is 180°.

If AB || CD, then

θ + α = 180° 

Calculations:

In cyclic quadrilateral PQRS,

∠SPQ + ∠SRQ = 180° 

⇒ 110° + ∠SRQ = 180° 

⇒ ∠SRQ = 180° – 110° 

⇒ ∠SRQ = 70°

Now, ∠SRQ + ∠PQR = 180°      

⇒ 70° + ∠PQR = 180°

⇒ ∠PQR = 180° – 70° 

⇒ ∠PQR = 110°

∴ The measure of the angle PQR is 110°.

Calculations:

From the graph,

Teachers above the age of 45 yrs and below 50 years = 5

∴ The teachers who are aged 45 years or more but less than 50 years is 5.

Given :

The ratio of angles of a triangle is 3: 4 : 8  

Concept used :

The sum of all angles of a triangle is 180° 

Calculations :

Let the values of angles be 3x, 4x and 8x

3x + 4x + 8x = 180° 

15x = 180° 

⇒ x = 12° 

3x = 36° , 4x = 48° and 8x = 96° 

One of the angles is more than 90° 

∴ The triangle will be obtuse

Concept used :

(a + b)² = a² + b² + ab

Calculations :

(ax + by)² = a²x² + 2abxy + b²y²

Out of all options, we can see only one option matches the value 

∴ Option 3 will be the right answer

Given :

The selling price of a mobile phone is Rs. 31500 

Discounts offered were 30% and 10% 

Concept used :

Total discount = a + b – (a × b)/100 (where a and b are the discounts offered on the same item)

Selling price = marked price - discount on Marked price 

Calculations :

Total discount % = 30% + 10% – (30% × 10%)/100 = 37% 

According to the question,

⇒ 31500 = Marked price – discount on the marked price 

⇒ 31500 = Marked price – 37% of marked price 

⇒ 31500 = 63% of the marked price 

Marked price = (31500/63) × 100 

⇒ Rs. 50000  

∴ The marked price of the item was Rs. 50000   

Concept used:

S.P = M.P ×  (100 – D₁)/100 × (100 – D₂)/100

Calculations:

Let the Marked price be x 

S.P = M.P ×  (100 – D1)/100 × (100 – D2)/100

⇒ 31500 = x × (100 – 30)/100 × (100 – 10)/100

⇒ 31500 = x × 70/100 × 90/100

⇒ x = 5 × 100 × 100

⇒ x = 50000

∴ The marked price of the item was Rs. 50000

Given :

tan4A = cot(A – 20°)

Formula used :

tanθ = cot (90° – θ)

Calculations :

cot (90° – 4A) = cot (A – 20°)

⇒ 90°– 4A = A – 20° 

⇒ 5A = 110° 

⇒ A = 22° 

∴ The value of A will be 22°

Shortcut Trick

The angle between the altitude (AP) and the angle bisector (AQ) from the same vertex is given by the formula:

∠PAQ = 1/2 |∠B − ∠C|

From the given figure, assuming standard values ∠B = 60° and ∠C = 30°:

⇒ ∠PAQ = 1/2 |60° − 30°| = 15°

In the right-angled triangle APQ, ∠APQ = 90°.

⇒ ∠PQA = 90° − ∠PAQ = 90° − 15° = 75°.

∴ The correct answer is 75°.

Alternate Method

Given: In ΔABC, AP ⊥ BC and AQ is the angle bisector of ∠BAC.

Formula Used: Sum of interior angles of a triangle = 180°.

In ΔABC, let ∠B = 60° and ∠C = 30°.

⇒ ∠A = 180° − (60° + 30°) = 90°

⇒ Since AQ is the bisector, ∠BAQ = ∠A ÷ 2 = 90° ÷ 2 = 45°

In right-angled ΔABP:

⇒ ∠BAP = 90° − ∠B = 90° − 60° = 30°

Now, find ∠PAQ:

⇒ ∠PAQ = ∠BAQ − ∠BAP = 45° − 30° = 15°

In right-angled ΔAPQ:

⇒ ∠PQA = 180° − (∠APQ + ∠PAQ)

⇒ ∠PQA = 180° − (90° + 15°)

⇒ ∠PQA = 180° − 105° = 75°

∴ The correct answer is 75°.

Additional Information

Angle between Altitude and Bisector

In any triangle, the angle formed between the altitude and the angle bisector drawn from the same vertex is equal to half the absolute difference of the other two angles: ∠ = 1/2 |∠B − ∠C|.

Angle Bisector Theorem

The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle: BQ/QC = AB/AC.

Exterior Angle Property

The exterior angle of a triangle is equal to the sum of the two opposite interior angles. In this case, ∠AQC = ∠B + ∠BAQ.

Given :

A can do a work in 12 days 

B can do the same work in 16 days 

They work on alternate days 

Concept used :

work done each day = total work/total number of days

Calculations :

Total work = LCM of 12 and 16 

⇒ 48 units 

A's per day work = 48/12 = 4 units 

B's per day work = 48/16 = 3 units 

Total work done in 13 days  (7 days of A and 6 days of B) = 7 × 4 + 6 × 3 = 46 units 

Remaining work = 48 – 46 = 2 units 

Time is taken by B to complete the remaining work = 2/3  (B's turn to do the work)

⇒ 2/3 days

Total time taken = 13 + 2/3 

⇒ $13{2\ \over3}$  days

∴ Total $13{2\ \over3}$ days will be taken to complete the work

Given :

Volume of the tank = 72 m³

Water is poured at a rate of 60 litres/minute 

Formula used :

1 m³ = 1000 litres 

Calculations :

Total volume of Water (in litres) = 72 × 1000 = 72000 litres 

Total time taken = Total volume/Rate of water poured per minute  

⇒ Total time = 72000/60

⇒ 1200 minutes 

⇒ 20 hours (1 hour = 60 minutes) 

∴ The total time taken was 20 hours

Concept used :

(a - b)² = a² + b² - 2ab 

Calculations :

(2x - 3y)²  = 4x² + 9y² - 12xy 

we can see that option 1 has the same value 

∴ option 1 is the correct answer

Given :

Two trains start from point A and B 

Distance between them is 1800 km

Speed of trains are 44 and 46 km/hour respectively 

Concept and formula used :

Time = Distance/Speed 

Relative speed  

Speeds are added when vehicles run in the opposite direction 

Speeds are subtracted when vehicles run in the same direction

Calculations :

Relative speed = 44 + 46 = 90 km/hour 

Time taken to meet = 1800/90 = 20 hours 

Distance travelled by train running from A = speed × time 

⇒ 44 × 20 

⇒ 880 km

∴ Distance from station A will be 880 km

Given :

2²⁰ + 1 is completely divisible by a whole number 

Formula used :

a³ + b³ = (a + b)(a² + b² - ab)

Calculations :

We will expand the numbers 

2⁹⁰ + 1 = 2⁹⁰ + 1⁹⁰ = (2³⁰ + 1)(2⁶⁰ + 1⁶⁰ - 2³⁰)

2¹⁵ + 1 = 2¹⁵ + 1¹⁵ = (2⁵ + 1) (2¹⁰ + 1¹⁰ - 2⁵)

2⁶⁰ + 1 = 2⁶⁰ + 1⁶⁰ = (2²⁰ + 1)(2⁴⁰ + 1⁴⁰ - 2²⁰)

We can see that in if a number divides (220 + 1) then it will surely divide (260 + 1)

∴ The answer will be the option D

Given:

The volume ratio of A, B is 6 ∶ 5

The volume of A is increased by 30%

Calculation:

Let the volume of A, B be 60, 50

New volume of A = 60(1 + 30/100) = 78

Difference between the volumes of A, B is 78 – 50 = 28

∴ Percentage Increase in volume = 100 × 28/50 = 56%

Calculation:

Total teacher = 4 + 5 + 6 + 3 + 2 + 5 = 25

Total teachers whose age is less than 45 = 25 - 5 = 20

∴ Percent required = 100 × 20/25 = 80%

Formula Used:

Componendo dividendo rule

Calculation:

Let x be the number that to be added

⇒ (8 + x)/(13 + x) = (26 + x)/(40 + x)

By applying componendo dividend

⇒ (8 + x + 13 + x)/(13 + x – (8 + x)) = (26 + x + 40 + x)/(40 + x – (26 + x))

⇒ (21 + 2x)/5 = (66 + 2x)/14

⇒ 294 + 28x = 330 + 10x

⇒ 18x = 36

⇒ x = 2

∴ The number that should be added is 2.

Given:

The score in the 16^th innings is 120

The increase in average is 6

Formula Used:

Total score = Average × No. of Innings

Calculations:

Let the initial average be ‘k’

⇒ New average = k + 6

⇒ Total Score after 15 innings = 15k

⇒ Total Score after 16 innings = 16(k + 6) = 16k + 96

⇒ 15k + 120 = 16k + 96

⇒k = 24

⇒ k + 6 = 24 + 6 = 30

∴ New Average = k + 6 = 30

Calculation:

Total production = 25 + 40 + 60 + 45 + 50 + 30 = 250

⇒ 1/5^th of total production = 250/5 = 50

∴ Friday is the answer

Given:

sinθ + cosecθ = 2

Formula Used:

cosecθ = 1/sinθ

Calculation:

Let sinθ = x

⇒ sinθ + cosecθ = x + 1/x = 2

⇒ (x + 1/x)² = 2²

⇒ x² + 2 + 1/x² = 4

⇒ x² + 1/x² = 2

∴ sin²θ + cosec²θ = 2

The correct answer is Three.

• Three Indian bowlers - Harbhajan Singh, Irfan Pathan, and Jasprit Bumrah have managed to bag a hat-trick in Test cricket.
• An occasion when a player scores three times (wickets, goals, sixes) in the same game is known as hat trick.

Important Points

• Deepak Chahar is the only Indian to have taken a hat-trick in T20Is.
• Chetan Sharma was the first Indian bowler to take a hat-trick in ODI cricket, against New Zealand in the 1987 World Cup.
• Kapil Dev was the second Indian bowler to take a hat-trick in ODI cricket.
• He achieved this feat in the Asia Cup final against Sri Lanka, played at the Eden Gardens in 1991.

Additional Information

• A hat-trick is a rare occurrence in any form of cricket, An occasion when a player scores three times (wickets, goals,sixes) in the same game is known as hat trick, and only 49 hat-tricks have been taken in the history of ODI cricket.
• Pakistan's Jalal-ud-Din became the first bowler to take a hat-trick in ODI cricket.
• He did so against Australia in 1982.
• Sri Lanka's bowler, Lasith Malinga has taken 3 hat-tricks in ODI cricket.

The correct answer is Macroeconomics.

• Macroeconomics is a branch of economics that studies how an overall economy:
• Inflation.
• Price levels.
• Rate of economic growth.
• National income.
• Gross domestic product (GDP).
• Changes in unemployment.
• The two main areas of macroeconomic research are long-term economic growth and shorter-term business cycles.

Important Points

• Microeconomics is the social science that studies the implications of incentives and decisions, specifically about how those affect the utilization and distribution of resources.
• Microeconomics provides a more complete and detailed understanding than macroeconomics.
• Public finance is the management of a country’s revenue, expenditures, and debt load through various government and quasi-government institutions.
• The main components include:
• Tax collection.
• Budget.
• Expenditures.
• Deficit/Surplus.
• National Debt.
• International economics deals with the economic activities of various countries and their consequences.
• It studies economic and political issues related to international trade and finance.

The correct answer is Satyapal Malik.

• Satya Pal Malik is the 21^st and current Governor of Meghalaya.
• He was the 18^th Governor of Goa (3 November 2019 - 18 August 2020).
• Bhagat Singh Koshyari is now Governor of Goa as an additional charge.

Important Points

• Bhagat Singh Koshyari is the current Governor of Maharashtra.(Nov 2020)
• Shripad Yesso Naik is a member of the Lok Sabha since 1999.
• He is the Union Minister of State in the Ministry of Ayurveda, Yoga & Naturopathy, Unani, Siddha, and Homoeopathy and Minister of State for Defence.
• Pramod Pandurang Sawant is the 11^th and current Chief Minister of Goa.

The correct answer is Kalidasa.

• Malavikagnimitra, (Sanskrit: “Malavika and Agnimitra”) five-act drama written by Kalidasa.
• Kalidasa is one of the greatest classical Sanskrit poets and dramatists of ancient India.
• His writings reveal that he was a pious Brahmana of Ujjain, and had acquired a knowledge of the various branches of Brahmanical learning.
• His poetic talent is very well reflected in all his works, which are Malavikagnimitra, Vikramorvasiya, Abhijñana-Sakuntala, and poems like Raghuvamsa, Kumarasambhava, and Meghaduta.

Important Points

The correct answer is Gulbadan Begum.

• Gulbadan Begum was a Mughal princess and the daughter of Emperor Babur and sister of Humayun.
• She is best known as the author of Humayun Nama.

Important Points

The correct answer is Sachin Tendulkar.

• Sachin Tendulkar was scoring 673 runs in the 2003 World Cup.
• It including a hundred and 6 fifties, at an average of 61.18, and bagged the ‘Man of the Tournament’ award.
• Sachin Tendulkar was scoring 482 runs in the 2011 World Cup.
• It including 2 hundred and 2 fifties, at an incredible average of 53.55.
• Sachin was scoring 523 Runs in the 1996 World Cup.
• It including 2 hundred and 3 fifties at a colossal average of 87.17.

Important Points

• Rohit Sharma was scoring 648 Runs in the 2019 World Cup.
• Kapil Dev is a former Indian cricketer.
• Kapil Dev led the Indian cricket team to their maiden World Cup triumph on June 25, 1983.

The correct answer is Beriberi.

Important Points

Additional Information

• Pellagra is a disease caused by a lack of vitamin B3 (niacin).

The correct answer is N Chandrasekaran.

• The chairman of Tata Sons, N. Chandrasekaran, and his co-author, Roopa Purushothaman wrote the book 'Bridgital Nation – Solving Technology's People Problem'.
• Natarajan Chandrasekaran is Chairman of the Board of Tata Sons.
• Roopa Purushothaman is the chief economist and head of policy advocacy at the Tata Group, and the founder of Avasara Leadership Institute.

Important Points

The correct answer is =.

Important Points

• Microsoft Excel shortcut keys:

 

The correct answer is Shipki la.

Key Points

• Shipki La is a mountain pass and border post on the India-Tibet border.
• The river Sutlej enters India through this pass.
• It is located in the Kinnaur district in the state of Himachal Pradesh, India, and Tibet.
• This pass is India's third border post for trade with Tibet after Nathu La in Sikkim, and Lipulekh in Uttarakhand.

Important Points

The correct answer is Kolkata.

• The 5th edition of India International Science Festival (IISF) 2019 was held in Kolkata from 5th to 8th November 2019.
• The Union Minister for Science & Technology, Earth Sciences, and Health & Family Welfare, Dr Harsh Vardhan announced this at a curtain-raiser Press Conference in New Delhi.
• It is being organized in collaboration with Vigynana Bharati, an RSS-linked scientific body.
• The IISF will also host 28 different events such as Agriculture Scientists' Meet, Vigyan Samagam, Young Scientists Conference, Vigyanika-International Science Literature Festival, International Science Film Festival of India.
• The theme for this year's festival is 'RISEN India - Research, Innovation, and Science Empowering the Nation'.

The correct answer is 11.

Important Points

• The total number of Fundamental Duties provided by Article 51A of the Constitution of India is 11.
• Part IVA of the Indian Constitution deals with Fundamental Duties.
• There are 11 Fundamental duties.

Article 51A: Fundamental duties:

1. To abide by the Constitution and respect its ideals and institutions, the National Flag and the National Anthem.
2. To cherish and follow the noble ideals which inspired our national struggle for freedom.
3. To uphold and protect the sovereignty, unity, and integrity of India.
4. To defend the country and render national service when called upon to do so.
5. To promote harmony and the spirit of common brotherhood amongst all the people of India transcending religious, linguistic, and regional or sectional diversities; to renounce practices derogatory to the dignity of women.
6. To value and preserve the rich heritage of our composite culture.
7. To protect and improve the natural environment including forests, lakes, rivers, and wildlife, and to have compassion for living creatures.
8. To develop the scientific temper, humanism, and the spirit of inquiry and reform.
9. To safeguard public property and to abjure violence.
10. To strive towards excellence in all spheres of individual and collective activity so that the nation constantly rises to higher levels of endeavor and achievement.
11. To provide opportunities for education by the parent the guardian, to his child, or a ward between the age of 6-14 years as the case may be.

The correct answer is non-luminous.

• Objects that do not emit light on their own are called non−luminous objects.
• Moon is a non-luminous object because it does not emit its own light and glows by reflecting the light of the sun.
• It is the fifth-largest natural satellite in the Solar System and the largest among planetary satellites relative to the size of the planet that it orbits.
• The Moon is the second-densest satellite.
• The first densest is Jupiter's satellite.
• The Moon is made of rock and metal—just like the Earth and the other rocky planets (Mercury, Venus, and Mars).

Additional Information

• The first uncrewed mission to the Moon was in 1959 by the Soviet Lunar Program with the first crewed landing being Apollo 11 in 1969.
• Sun is a luminous object because it a source of light and consequently emits light of its own.

The correct answer is Alla Rakha.

• Ustaad Allarakha Qureshi popularly known as Alla Rakha was an Indian tabla player who specialized in Hindustani classical.
• Trippunithura Narayanaiyer Krishnan was an Indian Carnatic music violinist.
• Pandit Bhimsen Gururaj Joshi was a legendary Hindustani classical vocalist.
• He is renowned for the khayal form of singing, as well as for his popular renditions of devotional music.

Important Points

The correct answer is Article 123.

• Article 123 of the Indian Constitution grants the President of India the power to promulgate ordinances when either of the two Houses of the Parliament is not in session.
• An Ordinance may relate to any subject that the Parliament has the power to legislate on. Conversely, it has the same limitations as the Parliament to legislate, given the distribution of powers between the Union, State, and Concurrent Lists.

Important Points

The correct answer is Madhya Pradesh.

• The 'Matki' dance form has been developed by nomadic tribes in Madhya Pradesh.
• Performed using a “small pitcher” is a folk dance originating from central India known as the “Matki Dance”.
• This “pitcher dance” belongs to the state of Madhya Pradesh, and is mainly performed in the Malwa region.

Important Points

The correct answer is Beginner’s All-purpose Symbolic Instruction Code.

Important Points

• BASIC is one of the simplest and earliest high-level programming language supports in all operating systems.
• John G. Kemeny and Thomas E. Kurtz designed the original BASIC language DartmouthBasic in 1964.
• The main moto is that all students should be able to use computers in every field.
• With the use of BASIC, people started developing custom software on their personnel computer for their business, profession, etc.

Additional Information

• QuickBasic (QB) is the compiler for the BASIC developed by Microsoft in 1985 which runs mainly on DOS.

The correct answer is Rani Rampal.

• Indian women’s hockey team captain Rani Rampal has been announced as one of the candidates to win the title of ‘Athlete of the Year 2019’ by the International World Games Association (IWGA).
• She will be competing for the honour with 25 other athletes from various sports.

Important Points

The correct answer is Sulphur dioxide.

Important Points

• According to a new analysis by Greenpeace, India is the largest emitter of SO₂ in the world with more than 15% of all the anthropogenic sulfur dioxide (SO₂)  hotspots detected by NASA OMI (Ozone Monitoring Instrument) satellite.
• The largest source of SO₂ in the atmosphere is the burning of fossil fuels and other industries' activities.
• In 2019, India emitted 21% of global anthropogenic SO₂ emissions, nearly double that of the second-ranked global emitter, Russia.
• The major SO₂ emission hotspots in India are:
• Singrauli in Madhya Pradesh.
• Neyveli and Chennai in Tamil Nadu.
• Talcher and Jharsuguda in Odisha.
• Korba in Chhattisgarh.
• Kutch in Gujarat.

The correct answer is Bharat Petroleum Corporation Limited.

Important Points

• A new LPG bottling plant was set up for Rs 103 crore by Bharat Petroleum Corporation Limited (BPCL) in Odisha Balangir district.
• It was inaugurated by Vice President M Venkaiah Naidu on December 27, 2019.
• The foundation stone of the Balangir LPG bottling plant was laid on May 21, 2018, by Petroleum Minister Dharmendra Pradhan.
• The plant with a capacity to produce 42 lakh cylinders per year.
• BPCL already has an LPG bottling plant at Khurda and the new plant at Balangir is the second company plant in Odisha.

The correct answer is diastrophism.

• All processes that move, elevate or build up portions of the earth’s crust come under diastrophism.
• It includes Orogenic processes and Epeirogenic processes.
• Orogenic processes involving mountain building through severe folding and affecting long and narrow belts of the earth’s crust. They act tangentially to the earth's surface, as in plate tectonics.
• Epeirogenic processes involving uplift or warping of large parts of the earth’s crust, thus it is a continental building process. They act along the earth’s radius and thus are also called radial movements.

Important Points