The correct answer is 'Business'

Key Points

• The correctly spelled word is 'Business' it is a noun which means 'A regular person's occupation or trade.'
• The other spellings which need to be corrected are-
• Restaurant- A place where people pay to sit and eat meals that are cooked and served on the premises.
• Memoir- It is a noun that means 'a historical account or biography written.'
• Studious- It is an adjective that means 'spending a lot of time studying or reading.'
• So the correct answer is 'Option 3'

The correct answer is 'Vague'

Key Points

• Let's see the meaning of the given words-
• Nebulous→ Vague or ill-defined (which is not clear)
• Example: The concept of time is often perceived as nebulous, as it is difficult to define and comprehend fully.
• Faith→ Complete trust or confidence
• Example: Despite facing numerous challenges, she held onto her faith, believing that everything would work out in the end.
• Stable→ Not likely to give way or overturn, firmly fixed.
• Example: The stock market showed stable growth over the past year, providing investors with a sense of security.
• Dearly→ Very much or at a great cost
• Example: He cherished his grandmother dearly, as she had always been there for him throughout his life.
• Vague→ Of uncertain or imprecise in thought or meaning.
• Example: The instructions given for the assignment were vague, leaving the students confused about what was expected of them.​
• So the correct answer is 'Vague' as it is the exact synonym of the given word.

The correct answer is 'Provincial'

Key Points

• Let's see the meaning of the given words-
• Metropolitan→ Relating to or denoting a metropolis.
• National→ Relating to or characteristic of a nation.
• Federal→ Having or relating to a system of government in which several states form a unity but remain independent.
• Provincial→ Relating to the regions outside the capital city of a country, unsophisticated or narrow-minded.
• Insular→ Uninterested in ideas.
• So according to the meaning of the given options, the correct answer is 'Provincial'

The correct answer is 'Pattern'

Key Points

• In the given blank, we need a noun because before the blank we have an indefinite article.
• Let's see the meaning of the words-
• Structure→ The quality of being well organized.
• Mound→ A large pile or quantity of something.
• Pattern→ A regular form or sequence or an arrangement.
• Design→ The art of action or planning.
• Mosaic→ is a picture or pattern produced by arranging together small pieces of colored stones.
• So according to the meaning of mosaic, the correct answer is 'pattern'

The correct answer is 'was'

Key Points

In the given blank we need to fill the past indefinite tense i.e. 'was'

• According to the rule of grammar, whenever we have things which are built in the past and time reference is also given which is 'the 16th century' then, we need to write the past time.

So the correct sentence is- Fatehpur Sikri was founded in the 16th century by the Mughal Emperor, Akbar.

The correct answer is 'Which'

Key Points

In the given blank we need to fill the relative pronoun 'Which'

• According to the rule of grammar, to mention things we generally use the pronoun 'which'.

So the correct sentence is- It is essentially a fortified city which had been the capital of Akbar

The correct answer is 'for'

Key Points

In the given blank we need to fill 'for'

• According to grammar, to refer to the time we generally use the preposition 'for/since' for is used to show the duration and since is used to show the point in time.
• After the blank, there is a duration which is 'fifteen years.'

So the correct sentence is- It is essentially a fortified city which had been the capital of Akbar for fifteen years.

The correct answer is 'and'

Key Points

In the given blank we need to write 'and'

• According to grammar, we need to connect the same qualities of the subject with the coordinate conjunction 'and'
• In the given sentence, the first quality is  'It is a UNESCO world heritage site' and the other one is a famous tourist attraction'
• So these qualities to be connected with the conjunction 'and'

So the correct sentence is-  Now a UNESCO world heritage site and a famous tourist attraction.

The correct answer is 'example'

Key Points

• Let's see the meaning of the given words-
• Example→ A thing characteristic of its kind or illustrating a general rule.
• Ruin→ A physical destruction.
• Infrastructure→The basic physical and organizational structures.
• Organization→ The action of organizing.
• So according to the meaning of the given words, the correct answer is 'Example' as it is contextually correct.

So the correct sentence is→  it is a fine example of Mughal architecture.

The correct answer is 'BDAC'

Key Points

• The given passage will start with the sentence 'B' because it is the only independent sentence out of four.
• Now the next sentence will be 'Sentence D' because it gives further information on what has really happened.
• The next sentence is 'A' because it tells what the country really does.
• The last sentence is C.

So the correct sequence is- BDAC

The correct answer is 'Since it fell'

Key Points

The given phrase is to be replaced with 'Since it fell'

• In the given sentence there are two clauses the main clause is 'Her dog, a black Labrador, gulped the biscuit down.' and the subordinate clause is 'Since it falls on the floor'
• As we can see that the main clause's verb is in the past tense the verb is 'gulped' so according to the rule of grammar the subordinate clause should be in the past tense.
• So we should replace 'falls' with 'fell'

So the correct sentence is- Since it fell on the floor, her dog, a black Labrador, gulped the biscuit down.

The correct answer is 'A search warrant was brought by the police when they raided his house.'

Key Points

• According to the rule of grammar, the subject of the sentence is 'the police' and the object of the sentence is 'a search warrant' hence the rule says that in the passive voice the subject of the sentence becomes the object and the object of the sentence becomes the subject.
• The main verb of the sentence is 'Brought' which tells that it is in the past tense hence in the passive voice the tense will not be changed.
• Also, the sequence of the clauses should not be changed too. 'When they raided his house' should be at the end position.

So the correct sentence is- A search warrant was brought by the police when they raided his house. i.e. option 3.

The correct answer is 'Gradual'

Key Points

• Let's see the meanings of the given words-
• Instant→ Happening immediately.
• Similar→ Of the same kind in appearance.
• Gradual→ Taking place over an extended period.
• Prompt→ cause or bring about.
• Diverse→ widely varied
• So according to the meaning of the given words the correct sentence is 'Gradual'

​

• आइए देखते हैं दिए गए शब्दों के अर्थ-
• Instant → तुरंत हो रहा है।
• Similar → समान
• Prompt → तात्कालिक
• Diverse → व्यापक रूप से विविध
• तो दिए गए शब्दों के अर्थ के अनुसार सही शब्द है 'Gradual'

The correct answer is 'Gregarious'.

Key Points

• Let's see the meanings of the given words-
• Genial→ Friendly and Cheerful
• Example: The genial host welcomed us into his home with open arms.
• Congruous→ In agreement or harmony
• Example: The congruent colors in the painting created a sense of peace and tranquility.
• Harmonious→ Free from conflict
• Example: The harmonious sounds of the orchestra filled the concert hall.
• Gregarious→ Fond of company or sociable
• Example: The gregarious child made friends with everyone in the class.
• So the correct answer according to the meaning of the words is 'Gregarious'

The correct answer is 'Which is expected to do'

Key Points

The given phrase is to be replaced with 'Which is expected to do'

• According to grammar, Whenever we have an antecedent and it is a thing or a group, then use 'which' as a relative pronoun. 
• Example: She belongs to a great organization, which specializes in saving endangered species.
• In the given sentence, 'who' is incorrect as 'who' is used for the antecedents which are nouns.
• Let's see an example-
• I went over to start up a conversation, asking her who she knew at the party.

So the correct sentence is- This is a class which is expected to do exceptionally well in the quiz next week.

The correct answer is 'Enthralled'

Key Points

• Let's see the meaning of the given words-
• Occupied→ Fill or take up, keep busy, active.
• Absorbed→ Soak up or take in.
• Immersed→ Dip or submerge in liquid.
• Enthralled→ capture the fascinated attention of.
• So according to the meaning of the given words, the correct answer is 'Enthralled'

So the correct sentence is→ The performances of the notable dancers and guest artists Enthralled the audience.

The correct answer is 'Ephemeral'

Key Points

• Let's see the meaning of the given words-
• Endless→ Having or seeming to have no end limits. Innumerable.
• Illusory→ Based on illusion not reality.
• Ephemeral→ Lasting or used for a very short time.
• Infinite→ Limitless in space, extent, or size.
• So according to the meaning of the given words, the correct answer is 'Ephemeral'

The correct answer is 'Peel'

Key Points

• Let's see the meaning of the given words-
• Rind (verb)→ strip the bark from (a tree).
• Example: He removed the thick rind from the watermelon before slicing it into refreshing, juicy pieces.
• Petal→ Each of the segments of the corolla of a flower.
• Example: The delicate rose had beautiful red petals that added a touch of elegance to the flower arrangement.
• Peel(verb)→ Remove the outer covering or skin from (a fruit, vegetable, etc.)
• Example: She used a knife to carefully peel the skin off the orange before enjoying the juicy segments.
• Leaf→ A flattened structure of a plant.
• Example: The autumn breeze blew, causing the colorful leaves to rustle and dance on the ground.
• Shade→ Comparative darkness or coolness caused by shelter from direct sunlight.
• Example: The tall tree provided welcome shade on a hot summer day, offering respite from the scorching sun.​
• So according to the meaning of the given words the correct answer is 'Peel'

The correct answer is 'supportors'

Key Points

The correct spelling is 'Supporters'

• The rest of the spellings are→
• Inclusion→ The action of the state of being included.
• Excess→ An amount that is more than needed.
• Discriminatory→ Showing discrimination or prejudice.
• Hence, the correct answer is 'Option 4'

The correct answer is 'Most of voters' i.e. error lies in this part of the sentence.

Key Points

In the given sentence, the usage of 'Most of voters' is incorrect instead use 'Most voters'

• According to grammar, 'Most' is a determiner which is used for the nouns to determine them as it is determiner hence it has no effect on the verb.
• If we read further the verb of the sentence is 'seem' which is a plural verb. So the subject of the sentence should be a plural noun which is going to be 'Voters'

So the correct sentence is- Most voters in Taiwan seem to have once again voted for the democratic party and President Tsai Ing-wen.

Confusion Points

• 'Most of' is also a quantifier and the structure is Most of + definite article + noun. In this case, the verb should be according to the noun.
• Let's see an example-
• ​Most of the houses in the capital don't have piped water.
• So the given sentence can also be corrected in the other way also- Most of the voters in Taiwan seem to have once again voted for the democratic party and President Tsai Ing-wen.

The correct answer is Nidhi exclaimed, “What a beautiful painting!”

Key Points

• Rules for Changing Exclamatory Sentences into Indirect Speech
• The sentences containing sudden expressions of joy, sorrow, anger, applause, surprise, or contempt are called exclamatory sentences.
• We replace the Reporting verb with ‘exclaimed with joy,’ ‘exclaimed with sorrow’, ‘exclaimed with surprise’ etc according to the sense of the Reported speech.
• The conjunction ‘that’ is used.
• Let's see the examples-
• ​Nidhi said, "Wow! that's beautiful". (Direct speech)
• Nidhi exclaimed with joy that it was beautiful. (Indirect speech)
• Similarly, the given sentence is in 'Indirect speech' and we need to make this sentence into a direct speech.
• So by applying these rules we get option 2.

The correct answer is 'in the mall looking for'

Key Points

 In the given sentence, the usage of 'in the mall looking for' is incorrect Instead, use 'in the mall were looking for'

• According to grammar, 'Most of' is a quantifier which is used to 'to refer to the majority of a group of things or people or the largest part of something.'
• In the given sentence, 'that clause' is used which has its own subject which is 'shoppers' hence we need a verb for this subject because it is not mentioned in the sentence.
• So we need a plural verb which should be in the past tense because the main clause of the sentence is in the past tense.
• So use 'were looking'

So the correct sentence is- We noticed that most of the shoppers in the mall were looking for packets of ready to cook food.

The correct answer is 'receive criticism'

Key Points

• The meaning of the given idiom 'to take the heat' is- to accept blame or withstand disapproval.
• Let's see an example-
• ​If this decision turns out to be a bad one, I'll take the heat for it.
• So the correct answer is 'Option 2'

The correct answer is 'To feel an instinct or intuition'

Key Points

• The meaning of the given idiom 'To have a gut feeling' is- an instinctive feeling, as opposed to an opinion based on facts
• Let's see an example-
• ​My gut feeling was that this woman was a good woman.

So the correct answer is 'Option 2'

The correct answer is 'ACBD'

Key Points

• Let's first understand the meaning of the given words which are given in the sentences-
• Seed→ A seed is the small, hard part of a plant from which a new plant grows.
• Sapling→ A sapling is a young tree.
• Sprout→ When plants, vegetables, or seeds sprout, they produce new shoots or leaves.
• Plant→ A plant is a living thing that grows in the earth and has a stem, leaves, and roots.
• Hence according to the meaning of the words→ 
• We put seed, then sprout will grow or develop, then sapling will come out a small plant and then the plant.

So the correct sentence is- I sow a seed I saw the sprout I saw the sapling I saw the plant.

The paper when unfolded will appear as shown below:

Hence, ‘option 3’ is the correct answer.

The correct mirror image of the given figure when the mirror is placed to the right side of the figure is shown below:

Hence, option 2 is the correct answer.

The pattern followed here is:

1) ADGPI → 1^st and 5^th letters are vowels.

2) ECVMU → 1^st and 5^th letters are vowels.

3) OMKLU → 1^st and 5^th letters are vowels.

4) VDCKA → 1^st letter is a consonant and 5^th letters is a vowel.

Hence, ‘VDCKA’ is the odd one out.

The pattern followed here is:

 

All the letters are arranged according to Alphabetical order in ascending order according to their place values from left to right.

KNOWLEDGE → DEEGKLNOW

Similarly,

SERIAL → AEILRS

Hence, ‘AEILRS’ is the correct answer.

NOTE :

It is not necessary that in coding-decoding you always get the pattern of letter shifting or criss-cross letter shifting. we need to check the options also when no pattern strikes our brain. From the options, we can get the idea that letters are alphabetically arranged here.

The figure that will come next in the following figure series is shown below:

The series is moving in clockwise direction, and with each step, the shaded portion shifts its position.

From 1^st image to 2^nd image – shaded portion shifts by 1 place.

From 2^nd image to 3^rd image - shaded portion shifts by 3 place.

From 3^rd image to 4^th image - shaded portion shifts by 5 place.

From 4^th image to 5^th image - shaded portion shifts by 7 place.

From 5^th image to 6^th image - shaded portion shifts by 9 place.

Hence, ‘option 3’ is the correct answer.

The pattern is:

If the given sequence of letters is divided into four equal parts, we see a particular pattern is repeated.

abccdde / abccdde / abccdde / abccdde

Hence, ‘ddeccdabdccd’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘MOJ’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

 

Similarly,

<br>

Hence, ‘3136’ is the correct answer.

[s1] Use table format for place value type question. Do not use diagram for that

The logic is:

Column 1: (16 + 4) ÷ 2 = 10

Column 2: (30 + 34) ÷ 2 = 32

Similarly,

Column 3: (18 + ?) ÷ 2 = 40

=> 18 + ? = 80

=> ? = 80 – 18

=> ? = 62

Hence, ‘62’ is the correct answer.

According to the given conditions,

 

 

So, Neeta is the mother of Rajiv.

Hence, ‘Mother’ is the correct answer.

The logic is:

Tiger: Felidae → Tiger belongs to the family of Felidae.

Similarly,

1) Lion: Leporidae → Lion belongs to the family of Felidae.

2) Rabbit: Bovidae → Rabbit belongs to the family of Leporidae.

3) Whale: Cetacea → Whale belongs to the family of Cetacea

4) Elephant: Canidae → Elephant belongs to the family of Elephantidae.

Hence, ‘Whale: Cetacea’ is the correct answer.

Let ‘x’ be the number of each denomination.

As the number of each denomination is equal, the equation for the question can be written as:

2x + 5x + 10x + 20x = 740

=> 37x = 740

=> x = 740 ÷ 37

=> x = 20

So, total number of Notes the boy has = 4 × 20 = 80

Hence, ‘80’ is the correct answer.

The least possible Venn diagram is:

I. Some men are rivers. → True (As it is given all men are trees and all trees are rivers → Some men are rivers)

II. All rivers are animals. → False (It can be possible, but it is not definite. As some men are animals and all trees are rivers and all men are trees → Some rivers are animals))

III. All rivers are men. → False (As it is given all men are trees and all trees are rivers → Some rivers are men)

IV. Some men are trees. → True (As it is given all men are trees also means that some men are trees.

Hence, Only conclusion I and IV follows

The Venn diagram that best represents the relationship between Doctor, Neurosurgeons, and Female is shown below:

All Neurosurgeons are Doctors and some Doctors and Neurosurgeons are female.

Hence, ‘option 4’ is the correct answer.

1) × and +

Given expression: 4 – 7 × 28 + 12 ÷ 3 = 4

After replacing the symbols, we get:

L.H.S = 4 – 7 + 28 × 12 ÷ 3

= 4 – 7 + 28 × 4

= 4 – 7 + 112

= 116 – 7

= 109 ≠ R.H.S

2) – and ÷

Given expression: 4 – 7 × 28 + 12 ÷ 3 = 4

After replacing the symbols, we get:

L.H.S = 4 ÷ 7 × 28 + 12 – 3

= 16 + 12 – 3

= 28 – 3

= 25 ≠ R.H.S

3) × and ÷

Given expression: 4 – 7 × 28 + 12 ÷ 3 = 4

After replacing the symbols, we get:

L.H.S = 4 – 7 ÷ 28 + 12 × 3

= 4 – 0.25 + 36

= 40 – 0.25

= 39.75 ≠ R.H.S

4) × and -

Given expression: 4 – 7 × 28 + 12 ÷ 3 = 4

After replacing the symbols, we get:

L.H.S = 4 × 7 – 28 + 12 ÷ 3

= 28 – 28 + 4

= 4 = R.H.S

Hence, ‘× and -’ is the correct answer.

The logic is:

Hence, ‘129’ is the correct answer.

The arrangement of the following words in a logical and meaningful order is:

2. Village
3. City
4. District
5. State
6. Country

A country is divided into different states, which is further divided into districts, districts are further divided into cities and villages.

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

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘LDFL’ is the correct answer.

The option figure that is embedded in the given figure X when rotation is now allowed is shown below:

Hence, ‘option 1’ is the correct answer.

The logic is:

 (6, 42, 1890) → 6 × (6 + 1) = 42 and 42 × (42 + 3) = 1890

Similarly,

1) (7, 23, 1069) → 7 × (7 + 1) = 56 ≠ 23 and 23 × (23 + 3) = 598 ≠ 1069

2) (2, 6, 54) → 2 × (2 + 1) = 6 and 6 × (6 + 3) = 54

3) (9, 102, 1190) → 9 × (9 + 1) = 90 ≠ 102 and 102 × (102 + 3) = 10710 ≠ 1190

4) (4, 20, 420) → 4 × (4 + 1) = 20 and 20 × (20 + 3) = 460 ≠ 420

Hence, ‘(2, 6, 54)’ is the correct answer.

The logic is:

AIDS : VIRUS → AIDS is transmitted by VIRUS. The VIRUS is transmitted through infected blood, semen or vaginal fluids.

Similarly,

MALARIA : ? → Malaria is a disease transmitted by the bite of an infected mosquito. When the mosquito bites a person, the PARASITE is released into the blood stream of the person.

Hence, ‘Parasite’ is the correct answer.

The number of triangles in the given figure is shown below:

Hence, ‘10’ is the correct answer.

Rahul is three times as old as Amar.

Let age of Amar be ‘a’.

So, age of Rahul = 3a

The age of Rahul three years ago = 3a – 3

Age of Amber three years ago = (3a – 3) ÷ 2

After four years from now, Rahul will be 43.

According to the above statement, (3a + 4) = 43

=> 3a = 43 – 4

=> 3a = 39

=> a = 13

So, present age of Amar is 13 years.

Age of Amber three years ago = (3a – 3) ÷ 2

= (3 × 13 – 3) ÷ 2

= (39 – 3) ÷ 2

= 36 ÷ 2

= 18

Present age of Amber = 18 + 3 = 21 years.

The present Ages of Amar and Amber are 13 and 21 years.

Hence, ’13, 21’ is the correct answer.

The logic is:

1^st number × 3^rd number = 2^nd number

(1, 2, 2) → 1 × 2 = 2

(7, 35, 5) → 7 × 5 = 35

Similarly,

(12, 96, ?) → 12 × ? = 96

=> ? = 96 ÷ 12

=> ? = 8

Hence, ‘8’ is the correct answer.

The faces opposite to each other is shown below:

Hence, ‘%’ is the correct answer.

Given:

In ΔPQR, S and T are mid-points of PQ and PR.

∠QPR = 75° and ∠PRQ = 40°

Formula:

If in In ΔPQR, S and T are mid-points of PQ and PR, then

ΔPQR ~ ΔPST 

Sum of all three angles of a triangle is 180°.

Calculation:

In ΔPQR

⇒ ∠QPR + ∠PQR + ∠PRQ = 180°

⇒ 75° + ∠PQR + 40° = 180° 

⇒ ∠PQR = 180° - 115°

⇒ ∠PQR = 65°

As given S and T are mid-points of sides PQ and PR of triangle PQR, then

ΔPQR ~ ΔPST 

∠PST = ∠PQR = 65°

Now,

∠PST + ∠TSQ = 180° [liner pair]

⇒ 65° + ∠TSQ = 180°

⇒ ∠TSQ = 180° - 65°

∴ ∠TSQ = 115°

Given:

tan X = m/n

Formula:

Pythagoras Theorem

H² = B² + P²

Where, Hypotenuse = H, Base = B and Perpendicular = P

tan x = Perpendicular/Base 

sin x = Perpendicular/Hypotenuse

cos x = Base/Hypotenuse 

Calculation:

tan X = Perpendicular/Base = m/n

Perpendicular = m and Base = n

Now,

(Hypotenuse)² = m² + n²

⇒ Hypotenuse = √(m2 + n²)

Now,

sin X + cox X 

⇒ m/√(m2 + n2) + n/√(m2 + n2)

⇒ (m + n)/√(m2 + n2)

(72 + 34) ÷ 2 + [{(75 ÷ 15) + 6} × 2]

⇒ 106 ÷ 2 + [{5 + 6} × 2]

⇒ 53 + [11 × 2]

⇒ 53 + 22

⇒ 75

Given:

3x2 – 5x – 8

Calculation:

3x2 – 8x + 3x – 8

⇒ x(3x - 8) + 1(3x - 8)

⇒ (x + 1)(3x - 8)

Given:

Total expenditure = 7,000 + 13,000 + 25,000 + 10,000 = 55,000

Total income = 22,000 + 30,000 + 20,000 + 38,000 = 1,10,000

Difference between his total income and total expenditure = 1,10,000 - 55,000 = 55,000

∴ Required Percentage =  (55,000/1,10,000) × 100 = 50%

Shortcut Trick

Difference in percentage = 60% − 40% = 20%

Given that this difference in value is 30.

∴ 20% of the number = 30.

∴ The correct answer is 30.

Alternate Method

Given:

Let the number be x.

60% of x − 40% of x = 30

Calculations:

⇒ 0.60x − 0.40x = 30

⇒ 0.20x = 30

⇒ x = 30 ÷ 0.20

⇒ x = 150

Now, find 20% of x:

⇒ 20% of 150 = (20/100) × 150

⇒ 0.20 × 150 = 30

∴ The correct answer is 30.

Additional Information

Percentage Change

To find the percentage change between two values, use: [(New Value − Old Value) ÷ Old Value] × 100.

Fraction to Percentage Conversion

Multiply a fraction by 100 to convert it to a percentage (e.g., 1/5 × 100 = 20%).

Base Value Concept

In percentage problems, the 'number' is always considered as the 100% base value.

Given:

The average of 35 numbers = 22

The average of first 17 numbers = 19

The average of the last 17 numbers = 20

Formula:

Average = (Sum of all observations)/(Total number of all observations)

Calculation:

The sum of 35 numbers = 22 × 35 = 770

Sum of first 17 numbers = 17 × 19 = 323

Sum of last 17 numbers = 17 × 20 = 340 

∴ 18th number = 770 - (340 + 323) = 770 - 663 = 107

Alternate Methodnth Number = Sum of total number - (Sum of first (n - 1) + Sum of Last (n - 1))

∴ 18th number = 770 - (340 + 323) = 770 - 663 = 107

Expenditure of the person from April to July

⇒ 7,000 + 13,000 + 25,000 + 10,000 = 55,000

Income of the person from April to July

⇒ 22,000 + 30,000 + 20,000 + 38,000 = 1,10,000

∴ The percentage of the total expenditure of the total income is

⇒ (55,000/1,10,000) × 100 = 50%

Given:

x2 + y2 = 32 and xy = 16

Formula:

(x + y)² = x² + y² + 2xy

Calculation:

(x + y)2 = x2 + y2 + 2xy

⇒ (x + y)2 = 32 + 2 × 16 

⇒ (x + y)² = 32 + 32

⇒ (x + y)² = 64

⇒ (x + y) = ±8

Given:

sin x - cos x = 0

Calculation:

sin x - cos x = 0

⇒ sin x = cos x

Now,

sin3 x - cos3 x

⇒ sin3 x - sin3 x

⇒ 0

Given:

SP of old scooter = Rs. 18,000

Loss % = 10%

Formula:

CP = SP × [100/(100 - Loss%)

SP = CP × [(100 + Profit%)/100]

Calculation:

CP of the scooter = Rs. 18,000 × (100/90) = 20,000

∴ New SP of the scooter = 20,000 × (115/100) = Rs. 23,000

Given:

CI of 2 years = Rs. 820

Amount = Rs. 8820

Time = 2 years

Formula:

A = P (1 + r/100)^t 

Calculation:

Amount = Rs. 8820 

CI = Rs. 820

Principal = Rs. 8820 - Rs. 820 = Rs. 8000

According to the formula

8820 = 8000 (1 + r/100)²

⇒ (1 + r/100)² = 8820/8000

⇒ (1 + r/100)² = 441/400

⇒ (1 + r/100) = √441/400

⇒ (1 + r/100) = 21/20

⇒ r/100 = 21/20 - 1

⇒ r/100 = 1/20

⇒ r = 5%

∴ The rate of interest is 5%.

Given:

Length of each chord = 8 cm

Distance between chords = 6 cm

Formula:

Pythagoras Theorem

Hypotenuse = H, Base = B and Perpendicular = P

H² = B² + P²

Calculation:

AB and CD are two chords length of each is 8 cm.

O is the center of the circle and M is mid point of AB and Q is the midpoint of CD

Let OB = OD = r (radius of circle)

MQ = 6 cm (Given)

Let OM = x, then

OQ = (6 - x) cm

In right angled ΔMOB

OB² = OM² + MB²

⇒ r² = x² + 4²

⇒ x² = r² - 16     ----(1)

In right angled ΔQOD

OD2 = OQ2 + QD2

⇒ r2 = (6 - x)2 + 42

⇒ r² = 36 + x² - 12x + 16

⇒ x² = r² + 12x - 52     ----(2)

From equation (1) and equation (2)

r2 - 16 = x2 = r2 + 12x - 52 

⇒ 12x = 36

x = 3

Now,

r2 = x2 + 42

⇒ r2 = 32 + 42

⇒ r2 = 9 + 16

⇒ r = √25

⇒ r = 5

∴ Length of radius of the circle is 5 cm.

Given:

To a circle with center at O, two tangents AP and AQ are drawn from an external point A.

∠PAQ = 80°

Concept:

Tangent of a circle is perpendicular to radius.

Calculation:

∠PAQ + ∠OPA + ∠OQA + ∠POQ = 360

⇒ 80° + 90° + 90° + ∠POQ = 360°

⇒ ∠POQ = 360° - 260°

⇒ ∠POQ = 100°

∴  The value of ∠POQ is 100°.

Shortcut Trick

Given a + b = 10 and 3/7 × ab = 9.

Solve for ab: ab = (9 × 7) ÷ 3 = 21.

Apply the algebraic identity: a³ + b³ = (a + b)³ − 3ab(a + b).

Substitute values: 10³ − 3(21)(10) = 1000 − 630 = 370.

∴ The correct answer is 370.

Alternate Method

Given:

Sum of two numbers, a + b = 10

Product relationship, 3/7 of ab = 9

Formula Used:

We use the cubic expansion identity: a³ + b³ = (a + b)³ − 3ab(a + b)

Calculations:

⇒ From the given product ratio: (3/7) × ab = 9

⇒ 3 × ab = 9 × 7

⇒ 3 × ab = 63

⇒ ab = 21

⇒ Now, applying the formula for a³ + b³:

⇒ a³ + b³ = (a + b)³ − 3ab(a + b)

⇒ a³ + b³ = (10)³ − 3 × 21 × 10

⇒ a³ + b³ = 1000 − (63 × 10)

⇒ a³ + b³ = 1000 − 630

⇒ a³ + b³ = 370

∴ The correct answer is 370.

Additional Information

Fundamental Cubic Identities

a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²).

Expansion of (a + b)³

(a + b)³ = a³ + b³ + 3ab(a + b). Rearranging this gives the direct substitution formula used above.

Relationship with Squares

a² + b² = (a + b)² − 2ab. This is often a preliminary step in solving for higher powers like a⁴ + b⁴.

Formula:

cot x = cos x/sin x

cosec x = 1/sin x

sec x = 1/cos x

Calculation:

cotx/(1 + cosec x) + (1 + cosec x)/cotx

⇒ [(cosx/sinx)/(1 + 1/sinx)] + [(1 + 1/sinx)/(cos x/sin x)]

⇒ [(cosx/sinx)/{(sinx + 1)/sinx}] + [{(sinx + 1)/sinx}/(cos x/sin x)]

⇒ [cosx/(sin x + 1)] + [(sinx + 1)/cosx]

⇒ [cos² + (sin x + 1)²]/[(sin x + 1) cos x]

⇒ [cos² + sin² + 1 + 2 sin x]/[(sin x + 1) cos x]

⇒ [2 + 2 sin x]/[(sin x + 1) cos x]

⇒ [2 (1 + sinx)]/[(sin x + 1) cos x]

⇒ 2/cos x

⇒ 2 sec x

Expenditure of the person from April to July = 7,000 + 13,000 + 25,000 + 10,000 = 55,000

Average = Sum of all observations/Total number of all observations

∴ Average expenditure of person = 55,000/4 = Rs. 13,750

Given:

ΔABC, DE is parallel to BC where D and E are points on AB and AC.

AD = 4 cm, DB = 8 cm and AE = 3 cm.

Formula:

If D and E are mid points of sides AB and AC of ΔABC, then ΔABC ∼ ΔADE

If ΔABC ∼ ΔADE, then

AB/AD = BC/DE = AC/AE

Calculation:

According to the formula

AD/AB = AE/AC

⇒ 4/12 = 3/AC

⇒ AC = 9cm

∴ EC = 6 cm

Given:

2794p561 is divisible by 9.

Formula:

Divisibility law of 9 ⇒ A number is divisible by 9 if sum of its digit is divisible by 9.

Calculation:

2 + 7 + 9 + 4 + p + 5 + 6 + 1 

⇒ 34 + p

If we put p = 2, then

⇒ 34 + 2

⇒ 36 (which is divisible by 9)

∴ p = 2

Given:

Length of cuboid = 8 cm

Breadth of cuboid = 6 cm

Height of cuboid = 10 cm

Formula:

Volume of cuboid = lbh

Calculation:

Volume of cuboid = 8 × 6 × 10 = 480 cm³

Given:

Speed of train = 72 km/hr

The train crosses an electric pole = 36 seconds

Formula:

Speed = distance/Time

1 km/hr = 5/18 m/sec

Calculation:

Let length of train be x meter

72 × 5/18 = x/36

⇒ x = 72 × 5/18 × 36

⇒ x = 720 m 

∴ Length of train is 720 m.

Given:

Tap A can fill a tank in = 6 hours

Tap B can fill the same tank in = 8 hours

Tap C can empty the same tank in = 4 hours

Formula:

Total work = Efficiency × Time

Calculation:

Total work = 24 units (LCM of 6, 8 and 4)

Efficiency of tap A = 4 units/day

Efficiency of tap B = 3 units/day

Efficiency of tap C = -6 units/day

∴ Time taken by A, B and C to fill the tank = 24/(4 + 3 - 6) = 24 hours

Given:

Income of the person from April to July = 22,000 + 30,000 + 20,000 + 38,000 = 1,10,000

Formula:

Average = Sum of all observations/Total number of all observations

Calculation:

∴ Average income of person = 1,10,000/4 = Rs. 27,500

Given:

a : b = 3 : 5

b : c = 2 : 3

Calculation:

a : b = 3 : 5      ----(1)

b : c = 2 : 3     ----(2)

Multiply by 2 in equation (1) and multiply by 5 in equation (2)

∴ a : b : c = 6 : 10 : 15

Given:

MP of the book = Rs. 850

SP of the book = Rs. 748

Formula:

Discount % = (Discount/MP) × 100

Calculation:

Discount = Rs. 850 - Rs. 748 = Rs. 102

∴ Discount Percentage = (102/850) × 100 = 12%

The correct answer is Kaushik Basu.

• Kaushik Basu served as the Chief Economist of the World Bank from 2012 to 2016.
• He has also served as the chief economic adviser to Government of India from 2009 to 2012.

Key Points

• Jagdish Bhagwati
• Jagdish Natwarlal Bhagwati is an India-born naturalized American economist.
• Bhagwati currently serves on the Academic Advisory Board of Human Rights Watch (Asia) and on the board of scholars of the Centre for Civil Society.
• Raghuram Rajan
• He was an Indian economist and 23rd Governor of the RBI.
• Also the author of the book 'I Do What I Do'.

The correct answer is Dashavatara Temple.

• Dashavatara Temple has Panchayatana Style of architecture.

Key Points

• Panchayatana Style of architecture:
• The main shrine is built on a rectangular plinth with four smaller subsidiary shrines at the four corners.
• Thus making it a total number of five shrines and hence the name, panchayatana.
• Deogarh temple in Lalitpur District, Uttar Pradesh is also an example of Panchayatana Style of architecture.

Additional Information

• The Sun Temple of Konark has a Kalinga type of architecture.
• King Narsimhadeva constructed the Sun temple at Konarka.
• Brihadeshwara Temple has a Dravidian type of architecture.
• ​It was built by Raja Raja Chola and his sister Kundavai.
• Kashi Vishwanath temple is situated in Varanasi, Uttar Pradesh.

The correct answer is Prakash Padukone.

• Prakash Padukone was awarded the ‘Sportstar LifetimeAchievement Award’ in February 2019.

Key Points

• Prakash Padukone won the Lifetime Achievement Award for his contribution to badminton
• He was awarded at the Sportstar Aces Awards supported by Supreme Committee of Delivery and Legacy.
• Prakash Padukone won a bronze medal at the 1974 Asian Games, gold at the 1979 Commonwealth Games.
• Prakash Padukone was the first Indian shuttler to be ranked number one in the world, and the first Indian to won the prestigious All England Championships in 1980.
• The award was presented by former India captain Sunil Gavaskar.

Additional Information

• Pullela Gopichand is the Chief National Coach for the Indian Badminton team.
• Chetan Anand is a  is a badminton player.
• Sanave Thomas Arattukulam won a bronze medal at the 2006 Commonwealth Games and silver medal at the 2010 Commonwealth Games in the mixed team event in badminton.

The correct answer is Sulfuric acid / sulphuric acid.

• Sulfuric acid is the chemical name of ‘oil of vitriol’.

Key Points

• Sulfuric acid is a dense, colourless, oily, corrosive liquid.
• It is one of the most commercially important of all chemicals.
• It is prepared industrially by the reaction of water with sulfur trioxide.
• Vitriol is any of certain hydrated sulfates or sulfuric acid.
• Uses of Sulphuric acid (H₂SO₄):
• In lead storage battery.
• In the manufacturing of HCl.
• In the manufacturing of Alum.
• In the manufacturing of fertilisers,
  

drugs, detergents and explosives.

Additional Information

• Blue or roman vitriol is cupric sulfate (CuSO4).
• Green vitriol is also called copperas, a name formerly applied to all the vitriols is ferrous sulfate
• White vitriol is zinc sulfate (ZnSO4).
• Red, or rose, vitriol is cobalt sulfate (CoSO4).
• Uran vitriol is a native uranium sulfate [U(SO4)2].

The correct answer is Venus.

• Venus is made up of thick white and yellowish clouds of sulfuric acid.

Key Points

• Venus:
• The planet is nearest to the Earth and is also the brightest planet.
• Venus is known as the “Evening Star” as well as “Morning Star”.
• Known as the “Veiled Planet”.
• Also known as the “Earth’s twin”. It also rotates clockwise like Uranus.
• Venus is the hottest planet (even hotter than Mercury).
• Venus has no water on it. There is no sufficient oxygen on Venus.

Additional Information Mercury, Venus, Earth and Mars are called terrestrial planets.

• Jupiter, Saturn, Uranus and Neptune are called gaseous planets.
• Uranus is about four times the size of the Earth.
• This planet appears Greenish in colour because of methane gas present in its atmosphere.
• Neptune is surrounded by methane rings of sub-zero temperature.

The correct answer is Persian.

Key Points

• The Mughal court chronicles were written in Persian.
• ​Mughal chronicles such as the Akbar Nama were written in Persian, while others, like Babur's memoirs, were translated from Turkish into the Persian Babur Nama.
• Urdu came from the amalgamation of Persian with Hindavi.
• Chronicles commissioned by the Mughal emperors are an important source for studying the empire and its court.
• The authors of Mughal chronicles were mostly courtiers.
• The Mughals were Chaghtai Turks by origin.
• Turkish was their mother tongue hence the first ruler Babur wrote poetry and his memoirs in this language.

The correct answer is Sikkim.

• As per state census 2011, which of the Sikkim is the least populous state of India.

Key Points

• The least populated state in the country was Sikkim with a population of 6.71 lakhs.
• According to Census 2011:
• C M Chandramauli was the Registrar General and Census Commissioner of India for the 2011 Indian Census.
• Uttar Pradesh is the most populous state.
• Maharashtra is the second most populous state in India.
• The sex ratio in the country was is 940 females per 1000 males.
• Haryana has the lowest sex ratio with just 877 women per 1000 males.
• Bihar has the highest population density.
• The overall literacy rate in India is 74% according to the 2011 census.
• Bihar is the least literate state in India, with a literacy of 63.82%.
• Goa was the most urbanized state with 62.17% of the population living in urban areas.

The correct answer is Payal Jangid.

• Payal Jangid became the first Indian to be awarded the ‘Changemaker Award2019’ (given by the Bill and Melinda Gates Foundation) for her work towards the abolition of child marriage in Rajasthan.

Key Points

• Payal Jangid is a 17-year-old youth activist from Rajasthan.
• The Changemaker Award encourages and honours the achievements of young activists, campaigners, and innovators across the world for inspiring social change.
• Payal's activism began when she relented against being married off when she was just 11 years old.
• Payal was mentored by the Nobel Peace Laureate Kailash Satyarthi and child rights activist Sumedha Kailash.

Additional Information

• Goalkeepers Global Goals Award:
• The Goalkeepers Global Goals Award honours individuals for their extraordinary stories of exceptional individuals taking action to bring the Global Goals to life and help achieve them by 2030.
• The awards are presented annually in five categories to leaders and individuals for their efforts in achieving the Sustainable Development Goals (SDGs).
• The categories are Progress, Changemaker, Campaign, Goalkeepers Voice and the Global Goalkeeper.
• The 2019 Goalkeepers Global Goals Award will honour those individuals working to tackle the issues contributing to global inequity.

The correct answer is Kamet.

• Kamet mountain looks like a giant pyramid and has a flat summit area and two peaks.
• Kamet is the second largest mountain of the Garhwal region of Uttarakhand.
• It is for 7,756 metres.
• Kamet, the mountain peak of the Himalayas in Uttarakhand state, northern India, near the border with the Tibet Autonomous Region of China.
• It is part of the Zaskar range.

Additional Information

• Nanda Devi (7816 metres):
• It is a part of Himalayan mountain ranges (Garhwal).
• This is the highest peak located entirely within India.
• The Nanda Devi National Prak, located in vicinity to the peak, consists of the best high altitude flora and fauna.
• Saltoro Kangri (7742 meters):
• ​It is located near the Siachen Region.
• The Saltoro Kangri is ranked the 31st highest independent peak in the world.
• It lies in Saltoro range (a part of Karakoram Mountain range).

The correct answer is Sheila Dikshit.

• Sheila Dikshit wrote the book ‘Citizen Delhi: My Life, My Times’.
• The book was published on 10 February 2018.
• Sheila Dixit was known as the longest-serving Chief Minister of Delhi for a period of 15 years.
• Her books are:
• Citizen Delhi: My Times, My Life
• Dilli Meri Dilli.

Key Points

• Famous Books and Authors

The correct answer is the Airport Authority of India – Navratna.

• Airport Authority of India is a Mini Ratna company.

Key Points

• In February 2009, AAI was granted "Miniratna Category 1 PSE" status by the Government of India.
• Category I CPSEs are the companies which have made profit continuously in the last three years,
• The companies which have made a net profit of Rs. 30 crores or more in one of the three previous years.
• These companies can invest capital expenditure up to Rs. 500 crores or equal to its net worth or which is less without the previous permission of the government.
• The Category I of Miniratna PSU includes 60 companies and Miniratna Category II includes 18 companies.

Additional Information

• A maharatna CPSEs can invest from INR 1,000 crore to INR 5,000 crore.
• PSUs with Maharatna status can invest 15% of their net worth in a project without the prior permission from the Government of India.

The correct answer is Samarendra Kumar Mitra.

• Samarendra Kumar Mitra designed the first analogue computer in India.

Key Points

• The computer was constructed by Samarendra Kumar Mitra and Indian Statistical Institute (ISI) in 1953.
• The first Electronic Analogue Computer could solve linear equations with ten variables.
• The first fully functioning electronic and digital computer was built in the U.S. was ENIAC.
• It was constructed by J. Presper Eckert and John Mauchly at the Moore School of Electrical Engineering, the University of Pennsylvania for the Army Ordnance Department.
• Charles Babbage is known as the Father of the Computer.

The correct answer is Gingee Fort Villupuram District, Tamil Nadu.

• Gingee Fort Villupuram District, Tamil Nadu has not been notified as a National Geo-heritage Monument by the Geological Survey of India (GSI).
• The Geological Survey of India identified 26 geological sites till now.

Additional Information

• The Geological Survey of India (GSI)  is the organisation that studies various aspects of the Earth forming processes and evolution of life.
• GSI is also the primary custodian of the rocks and fossils of the country.
• GSI has been made the sole custodian and curator of all meteorites within the Indian boundary.
• It has been declared as the nodal agency for collection, preservation, registration, and dissemination of all meteorite falls/finds within the country.
• The declaration was made by the Ministry of Mines.
• The GSI is headquartered in Kolkata.

The correct answer is 19 December 1929.

• On 19 December 1929 Indian National Congress passed the Resolution of 'Poorna Swaraj'(total independence) at the Lahore Session.

Key Points

• Lahore Session (1929 AD):
• This session was presided over by Jawaharlal Nehru.
• This session passed a resolution of Poorna Swaraj (complete independence) as its ultimate goal.
• All members of the legislature were asked to resign their seats.
• On 31st December 1929, the newly adopted tricolour was hoisted and 26th January 1930 was fixed as the first Independence Day.
• The Congress Session also announced a Civil Disobedience Movement under the leadership of Mahatma Gandhi.
• Congress decided to boycott the first Round Table Conference.

The correct answer is Seismograph.

• Seismograph records the waves reaching the surface during an earthquake.

Key Points

• Earthquakes:
• The sudden tremors or shaking of the earth's crust is called an earthquake.
• The earth’s crust is made up of different parts of various sizes. They are called plates.
• Most of the earthquakes in the world are caused by the movements of the plates.
• ‘Seismology’ deals with the study of the earthquake.
• ‘Richter scale’ and ‘Mercalli scale’ are the instruments to measure and record the magnitude and the intensity of an earthquake respectively.
• The place where the seismic waves originate beneath the earth’s surface is called the focus of the earthquake.
• The epicenter is that point on the ground surface that is closest to the focus.

Additional Information

• National Earthquake Science Data Centre is located in New Delhi.
• A chronometer is a portable timekeeping device of great accuracy.
• A barograph is a recording aneroid barometer where the changes in atmospheric pressure are recorded.
• A Manometer is a device to measure pressures.

The correct answer is Rohit Sharma.

• Rohit Sharma became the first Indian brand ambassador of La Liga (the top tier of Spanish club football) in December 2019.

Key Points

• Rohit Sharma became the first non-footballer to endorse the La Liga league.
• La Liga is the top tier of Spanish club football.

Additional Information

• The first Football club in India was ‘Dalhousie Club’.
• The apex institution of football is the ‘Federation of International Football Association’ (FIFA), which was formed by seven countries on May 21, 1904.
• The headquarters of FIFA is in Zurich (Switzerland).
• Football was included as a competitive game in the Olympic Games officially in 1908.
• India took part in the World Olympic Football Competition in 1948 in London.

The correct answer is Portugal.

• On December 2019, the Prime Minister of Portugal announced the commencement of the ‘Gandhi Citizenship Education Award’ to be given every year.

Key Points

• The Prime Minister of Portugal Antonio Costa announced the Gandhi Citizenship Education Award.
• The award is inspired by Gandhi's thoughts and life, to help perpetuate the ideals of Mahatma Gandhi.
• He also said that Gandhi Citizenship Award will be dedicated to social welfare.
• Portugal's Prime Minister Antonio Costa said that the first year’s prize will be dedicated to animal welfare.

Additional Information

• Portuguese in India:
• The Cape route was discovered from Europe to India by Vasco da Gama.
• He reached the port of Calicut on May 17, 1498 AD and was received by the Hindu ruler of Calicut (known by the title of Zamorin).
• This led to the establishment of trading stations at Calicut, Cochin and Cannanore.
• Cochin (1502 AD) was the early capital of the Portuguese in India, later on, replaced by Goa.
• In the reign of Mahmud Beghra, Portuguese set up a factory at Diu.
• The first Governor of Portuguese in India was Francisco Almeida (1509 AD). He introduced “The Policy of Blue Water”.
• Alfonso de Albuquerque arrived in India in 1503 AD and became Governor of the Portuguese in India in 1509 AD.
• He captured Goa from the ruler of Bijapur in 1310 AD and introduced the policy of imperialism.
• Nino-da-Cunha (1529 AD-1528 AD) transferred the capital from Cochin to Goa in 1530 AD.
• He acquired Diu and Bassein from Bahadur Shah of Gujarat (1534 AD).
• In the end, they were left only with Goa, Diu and Daman, which they retained till 1961 AD.

The correct answer is Losar festival.

• Losar festival marks the beginning of the Tibetan New Year.

Key Points

• The Losar Festival is celebrated with great zeal and fervour in the Lahaul Valley of Himachal Pradesh.
• It is also known as a festival of happiness and prosperity.
• The celebrates the Ladakhi or Tibetan New Year.
• Reviewer do check this one .......multiple places are found celebrating the same fest

The correct answer is 1991–92.

• The ‘Rajiv Gandhi Khel Ratna Award’ instituted was 1991–92.

Key Points

• Rajiv Gandhi Khel Ratna Award is the highest sporting honour given in India.
• The award is named after Rajiv Gandhi.
• He was the Prime Minister of India who served from 1984 to 1989.
• Chess Grandmaster Viswanathan Anand was the first recipient of this award.
• The other Sports Awards include the Arjuna Award, Dronacharya Award and the Dhyan Chand Award, which are conferred every year by the President of India at the Rashtrapati Bhavan on August 29.
• The National Sports Day is celebrated on August 29.
• It is the birth anniversary of hockey wizard Dhyan Chand.