SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 1) (Previous Year Paper)

The pattern followed here is:

Interchanging × and ÷, 2 and 6 in the given equation and find which is not correct.

I. 7 – 4 × 3 ÷ 6 + 2 = 8

After interchanging the sign and numbers we get the:

⇒ 7 – 4 ÷ 3 × 2 + 6 = 8

⇒ 7 - 1.333 × 2 + 6 = 8

⇒ 7 - 2.666 + 6 = 8

⇒ 13 - 2.666 = 8

⇒ 10.334 ≠ 8 (Not correct)

II. 6 – 8 × 2 + 9 ÷ 3 = 5

After interchanging the sign and numbers we get the:

⇒ 2 – 8 ÷ 6 + 9 × 3 = 5

⇒ 2 - 1.333 + 9 × 3 = 5

⇒ 2 - 1.333 + 27 = 5

⇒ 29 - 1.333 = 5

⇒ 27.667 ≠ 5 (Not correct)

So, Both I and II are not correct.

Hence, the correct answer is "Option 4".

The correct mirror image of the given figure when the mirror is held on the AB side.

Hence, the correct answer is "Option 4".

Additional Information 1) In the mirror image left side and right side changed vice-versa where the top and bottom remain the same.

2. In a real given mirror image the farthest number or alphabet appears closest in the mirror image.

The pattern followed here is:

Logic: (First number - Third number) = Second number.

1. (70, 14, 56)

⇒ (70 - 56) = 14

2. (88, 30, 58)

⇒ (88 - 58) = 30

Let's check each option one by one.

Option 1) (44, 24, 33)

⇒ (44 - 33) = 11 ≠ 24 (Incorrect)

Option 2) (59, 36, 25)

⇒ (59 - 25) = 34 ≠ 36 (Incorrect)

Option 3) (52, 19, 33)

⇒ (52 - 33) = 19 = 19 (Correct)

Option 4) (38, 16, 24)

⇒ (38 - 24) = 14 ≠ 16 (Incorrect)

Hence, the correct answer is "(52, 19, 33)".

The pattern followed here is:

Logic: (First number)² × 2 = Second number.

1. 8: 128

⇒ 8² × 2

⇒ 64 × 2 = 128

And,

2. 11: 242

⇒ 11² × 2

⇒ 121 × 2 = 242 

Similarly,

3. 6: ?

⇒ 6² × 2

⇒ 36 × 2 = 72

Hence, the correct answer is "72".

The pattern followed here is:

Here in this question interchanging the given two numbers and two signs in the given equation.

Given: – and ×, 6 and 4

I. 7 × 6 + 8 ÷ 2 – 4

After interchanging the two numbers and two signs we get the;

⇒ 7 - 4 + 8 ÷ 2 × 6

⇒ 7 - 4 + 4 × 6

⇒ 7 - 4 + 24

⇒ 31 - 4 = 27

II. 4 – 7 × 6 + 8 ÷ 2

After interchanging the two numbers and two signs we get the;

⇒ 6 × 7 - 4 + 8 ÷ 2

⇒ 6 × 7 - 4 + 4

⇒ 42 - 4 + 4

⇒ 46 - 4 = 42

Hence, the correct answer is "27, 42".

The pattern followed here is:

The least possible Venn diagram is shown below according to the given information.

Statements:

I. Some F are D.

II. No A is D.

Conclusions:

I. Some F are A → Does not follow → As some F are D and No A is D. So some F are A is possible but not definitely followed.

II. No D is A → Follow → As  No A is D. So No D is A is definitely followed.

III. Some F are not A → Follow → As some F are D and No A is D. We can say that part of F which are D definitely not A. So some F are not A is definitely followed.

So, Both conclusions II and III follow.

Hence, the correct answer is "Option 2".

The pattern followed here is:

Logic: (First number - 2)² : Second number.

1. 7 : 25

⇒ (7 - 2)² ⇒ (5)² ⇒ 25

And,

2. 4 : 4

⇒ (4 - 2)² ⇒ (2)2 ⇒ 4

Similarly,

3. 3 : ?

⇒ (3 - 2)2 ⇒ (1)2 ⇒ 1

Hence, the correct answer is "1".

The pattern followed here is:

The given words are arranged as per the English dictionary order.

4. Seniority 5. Senna 1. Sennet 2. Sennight 3. Sennit

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

The pattern followed here is:

Movie: Director → A movie director is a person who controls a film's artistic and dramatic aspects and visualizes the screenplay while guiding the film crew.

Similarly,

Orchestra: Conductor → A conductor conducting is the art of directing a musical performance, such as an orchestral or choral concert.

Hence, the correct answer is "Conductor".

The pattern followed here is:

1. In the every next figures are getting rotated 90º in anti-clockwise direction.

2. One leaf is added in each figure starting from Left then right alternatively.

Hence, the correct answer is "Option 1".

The pattern followed here is:

1. The middle figure is newly formed in every next figure and the number of sides are decrease in every next figure, in first arrow is given, in the second figure in the middle hexagon is given, then the pentagon is given in the third figure, then the square is given in the fourth figure, and the triangle is given in the last figure.

2. Square is shifted towards the left side in middle in the second figure, then shifted right upper corner in the third figure, then shifted left upper in the fourth figure, then shifted right bottom of the corner in the last figure.

3. The phi sign shifted left upper corner in the second figure, then shifted right bottom of the corner in the third figure., then shifted right side in the middle in the fourth figure, then shifted right upper corner in the last figure.

4. Question mark (?) shited the right bottom of the corner in the second figure, then shifted to the left side in the middle in the third figure, then shifted to the right upper corner in the fourth figure, then shifted to left upper corner in the last figure.

5. Star figure shifted right upper corner in the second figure, then shifted left upper corner in the third figure, then shifted right bottom of the corner in the fourth figure, then shifted left side in the middle of the last figure.

Hence, the correct answer is "Option 2".

The position of the English alphabet letters is given below:

Given: AVTE CTRG ERPI GPNK ?

Hence, the correct answer is "INLM".

Preparing the family tree using the following symbol:

Given: 

A ÷ B means that A is the brother of B

A × B means that A is the sister of B

A – B means that A is the father of B

Find:- Which expression shows that P is the paternal uncle of R.

Let's check each option one by one.

Option 1) P - R ÷ Q

P is the father of R, and R is the brother of Q.

Here, P is the Father of R. (Incorrect)

Option 2) P ÷ R × Q 

P is the brother of R, and R is the sister of Q.

Here, P is the Brother of R. (Incorrect)

Option 3) P × R - Q 

P is the sister R, R is the father of Q.

Here, P is the Sister of R. (Incorrect)

Option 4) P ÷ Q - R

P is the brother of Q, Q is the father of R.

Here, P is the Paternal uncle of R. (Correct)

Hence, the correct answer is "Option 4".

The pattern followed here is:

We have to interchange the two numbers to make the given equation correct.

Let's check the option one by one.

Option 1) 6 and 8

Given : (6)2 – 20 + (28 ÷ 7) – $\left[ {\left( {\sqrt 4 } \right) \times 8} \right]$ + (2)2 = 40

After interchanging the numbers we get the:

⇒ (8)2 – 20 + (28 ÷ 7) – $\left[ {\left( {\sqrt 4 } \right) × 6} \right]$ + (2)2 = 40

⇒ 64 - 20 + 4 - 2 × 6 + 4 = 40

⇒ 64 - 20 + 4 - 12 + 4 = 40

⇒ 72 - 20 - 12 = 40

⇒ 40 = 40 

⇒ LHS = RHS

Option 2) 7 and 2

Given : (6)2 – 20 + (28 ÷ 7) – $\left[ {\left( {\sqrt 4 } \right) \times 8} \right]$ + (2)2 = 40

After interchanging the numbers we get the:

⇒ (6)2 – 20 + (28 ÷ 2) – $\left[ {\left( {\sqrt 4 } \right) × 8} \right]$ + (7)2 = 40

⇒ 36 - 20 + 14 - 2 × 8 + 49 = 40

⇒ 36 - 20 + 14 - 16 + 49 = 40

⇒ 99 - 20 - 16 = 40

⇒ 63 ≠ 40

⇒ LHS ≠ RHS

Option 3) 2 and 8

Given : (6)2 – 20 + (28 ÷ 7) – $\left[ {\left( {\sqrt 4 } \right) \times 8} \right]$ + (2)2 = 40

After interchanging the numbers we get the:

⇒ (6)2 – 20 + (28 ÷ 7) – $\left[ {\left( {\sqrt 4 } \right) × 2} \right]$ + (8)2 = 40

⇒ 36 - 20 + 4 - 2 × 2 + 64 = 40

⇒ 36 - 20 + 4 - 4 + 64 = 40

⇒ 104 - 20 - 4 = 40

⇒ 80 ≠ 40

⇒ LHS ≠ RHS

Option 4) 20 and 8

Given : (6)2 – 20 + (28 ÷ 7) – $\left[ {\left( {\sqrt 4 } \right) \times 8} \right]$ + (2)2 = 40

After interchanging the numbers we get the:

⇒ (6)2 – 8 + (28 ÷ 7) – $\left[ {\left( {\sqrt 4 } \right) × 20} \right]$ + (2)2 = 40

⇒ 36 - 8 + 4 - 2 × 20 + 4 = 40

⇒ 36 - 8 + 4 - 40 + 4 = 40

⇒ 44 - 8 - 40 = 40

⇒ - 4 ≠ 40

⇒ LHS ≠ RHS

Hence, the correct answer is "6 and 8".

The correct mirror image of the given figure when the mirror is held on the PQ side.

Detailed Explanation:

• The correct mirror image of the given figure is "

" the second word of the given image is 'O' and the correct mirror image is "

" but it is wrongly given in option 2  and option 4 so option 2 and 4 is eliminated.

• The correct mirror image of the given figure is "

" the sixth number of the given image is '8' and the correct mirror image is "

" but it is wrongly given in option 3 so option 3 is eliminated.

 

Hence, the correct answer is "Option 1".

Additional Information

1. In the mirror image left side and right side changed vice-versa where the top and bottom remain the same.

2. In a real given mirror image the farthest number or alphabet appears closest in the mirror image.

By using the symbols in the table given below, we can draw the following family tree:

Given: 

A + B means ‘A is the father of B’

A – B means ‘A is the mother of B’

A % B means ‘A is the brother of B’

A # B means ‘A is the daughter of B’

Given: P + Q % R % S # T – U

P is the father of Q, Q is the brother of R, R is the brother of S, S is the daughter of T, T is the mother of U.

Find: How is Q related to U?

Clearly, Q is the Brother of U.

Hence, the correct answer is "Brother".

The pattern followed here is:

The least possible Venn diagram is shown below according to the given information.

Statements:

Some ships are cups.

No cup is a stool.

All windows are cups.

Conclusions:

I. Some ships being windows is a possibility → Follow → As some ships are cups and No cup is a stool and all windows are cups. So some ships being windows is a possibility is definitely followed.

II. No window is a stool → Follow → As No cup is a stool and All windows are cups. So No window is a stool is definitely followed.

III. All cups are windows → Does not follow → As all windows are cups. So all cups are windows is not definitely followed.

IV. No ship is a stool → Does not follow → As some ships are cups and No cup is a stool and all windows are cups. So No ship is a stool is not followed because it is a possibility that some ships are stool. So it is definitely not followed.

So, the only conclusions I and II follow.

Hence, the correct answer is "Option 3".

The pattern followed here is:

Here, we have to find the face opposite the face showing '5'.

1. We are taking dice figures (1) & (2) together.

Here, 5 and 3 are common in both figure and 2 is opposite to 4.

2. We are taking dice figure (2) & (3) together.

Here, 5 and 2 are common in both figure and 3 is opposite to 1.

Opposite pairs are:

3 → 1

2 → 4

6 → 5

Clearly, 5 is opposite to 6.

Hence, the correct answer is "6".

The pattern followed here is:

'CHILDREN' is written as ‘FKLOGUHQ’

And,

‘SCHOOL’ is written as ‘VFKRRO’

Similarly,

'CLASSROOM' be written as '?'

Hence, the correct answer is "FODVVURRP".

The pattern followed here is:

Given: 41, 54, 67, 80, 93, ?

Hence, the correct answer is "106".

The pattern followed here is:

Logic: (First number × 2) - 3 =  Second number.

Let's check each option one by one.

Option 1) 17 - 31

⇒ (17 × 2) - 3

⇒ 34 - 3 = 31 = 31 (Correct)

Option 2) 13 - 25

⇒ (13 × 2) - 3

⇒ 26 - 3 = 23 ≠  25 (Incorrect)

Option 3) 15 - 27

⇒ (15 × 2) - 3

⇒ 30 - 3 = 27 = 27 (Correct)

Option 4) 9 - 15

⇒ (9 × 2) - 3

⇒ 18 - 3 = 15 = 15 (Correct)

Hence, the correct answer is "13 - 25".

The pattern followed here is:

1) 'INBOX’ is written as 'MRYCL'

And,

2) 'EMAIL' is written as 'NVZOR'

Similarly,

3. 'DRAFT' is written as '?'

Hence, the correct answer is "IWZGU".

The pattern followed here is:

Logic: First alphabet - 3 = Second alphabet + 1 = Third alphabet.

Option 1) TQR

Option 2) MJK

Option 3) IFG

Option 4) NKI

 

Hence, the correct answer is "NKI".

The pattern followed here is:

Given: LE, OJ, UO, DT, ?

Hence, the correct answer is "PY".

The pattern followed here is:

1. GAIN : HBKP

And,

2. ACHE : BDJG

Similarly,

3. CAKE : ?

Hence, the correct answer is "DBMG".

The correct answer is nickel and iron.

Key Points

Core:

• The innermost layer is the core with a radius of about 3500 km.
• The central core has a very high temperature and pressure.
• The inner core (1200 km) is in the solid state whereas the outer core (2300 km) is in the liquid state.
• The innermost layer is the core with a radius of about 3500 km and divided into Inner and Outer core.
• The inner core is with a radius of 350 km mainly made up of- nickel and iron. The innermost layer is also called ‘nife’ (ni - nickel and fe - ferrous- iron).

Additional Information

The Earth is divided into four main layers: the solid crust on the outside, the mantle, the outer core, and the inner core.

• All those layers are separated from each other through a transition zone.
• These transition zones are called discontinuities.
• Conrad Discontinuity: It lies between the Upper crust and Lower crust.
• Mohorovicic Discontinuity: It lies between crust and mantle.
• Repiti Discontinuity: It lies between the Upper mantle and Lower mantle.
• Gutenberg Discontinuity: It lies between core and mantle.
• Lehman Discontinuity: It lies between the upper core and lower core.

 

Interior of the Earth:

Crust:

• The uppermost layer over the earth’s surface is called the crust.
• It is the thinnest of all the layers.
• on the continental masses, It is about 35 km and on the ocean floors, only 5 km.
• The crust is the thinnest layer of the Earth and it amounts to less than 1% of our planet's volume.
• The earth is made up of several concentric layers with one inside another, just like an onion.
• The crust is the outermost layer of Earth and is made up of igneous, metamorphic, and sedimentary rocks.
• The Earth's crust is unstable because of the exogenic forces.

Mantle:

• The Mantle extends up to a depth of 2900 km below the crust.
• It is the widest section of the Earth.

The correct answer is The principle of National Income.

Key Points

• Principle of National Income:
• The value of the commodities and services a nation produces in a fiscal year is referred to as national income.
• As a result, it represents the sum of all economic activity carried out in a nation over the course of a year.
• It is valued in monetary terms.
• The terms "national income" and "national dividend," as well as "national output" and "national spending," are ambiguous.
• Macro Economics:
• It is the study of how economies function, including changes in the balance of payments, inflation, interest and foreign exchange rates, and economic production.
• Only with solid monetary and fiscal policy are poverty alleviation, social equality, and sustainable growth conceivable.

Additional Information

• Consumer theory:
• Microeconomics includes the field of consumer theory.
• It investigates how people choose what to buy with their money based on their tastes and financial restrictions.
• Producer theory:
• The producers theory looks at how businesses recruit and combine productive inputs to produce goods at reasonable rates.

The correct answer is Abhishek Singh.

Key Points

• ​Abhishek Singh is a senior IAS official.
• He has been promoted to CEO of the National e-Governance Division (NeGD) in march 2022.
• The IAS officer from the Nagaland cadre would hold the position with the rank and salary of Additional Secretary.

Additional Information

• Nitin Chugh:
• To oversee its digital banking activities, State Bank of India (SBI) has recruited Nitin Chugh as Deputy Managing Director (DMD).
• He has been appointed for a three-year first term.
• He served as the CEO of the Ujjivan Small Finance Bank.
• Rajiv Kumar:
• Rajiv Kumar is an economist from India.
• He previously held the position of second vice chairman of the NITI Aayog.
• TS Ramakrishnan:
• On March 1, 2022, LIC Mutual Fund announced the hiring of TS Ramakrishnan as its managing director and CEO.

The correct answer is 1400.

Key Points

• Aihole, Karnataka, India is home to the early eighth-century Hindu temple known as the Durga temple.
• It was originally dedicated to Surya.
• Its relief panels, which feature the artwork of Shaivism, Vaishnavism, Shaktism, and Vedic deities, are the largest and most elaborate in Aihole.
• It is renowned for its apsidal layout, a unique example of early Chalukyan Hindu temple construction.
• It is part of a pending UNESCO World Heritage Site application.

Additional Information

• Aihole
• It was built in 634.
• It was the headquarters of the famous medieval Ayyavole merchants’ guild and was an important commercial centre.
• The earliest stone-built temple is Lad Khan temple.
• A temple dedicated to the goddess Durga was built on the model of Buddha, Chaitya.
• It stands on a raised platform in the form of a semi-circle.
• Badami
• There are four caves in Badami.
• The largest cave temple built by Mangalesa is dedicated to Vishnu.
• The reclining posture of Vishnu on the snake bed and Narasimha are exquisite examples of Chalukya art.
• Pattadakal
• It is a village in the Bagalkot district of Karnataka.
• It is famous for its exquisite temples.
• Pattadakal was a centre for performing royal rituals.
• The Virupaksha temple was built at the order of queen Lohamahadevi to commemorate the conquest of Kanchipuram by her husband Vikramaditya II.

The correct answer is Gandhayukli.

Key Points

• An encyclopaedia written in Sanskrit and published in the sixth century in Ujjain was called Brhat-Samhita.
• In addition to divination, the book covers a wide range of topics, such as astronomy, planetary motion, eclipses, rainfall, architecture, crop development, perfume production, matrimony, household relationships, gems, and ceremonies.
• Varahmihir’s Brihat Samhita** gives references to perfumes and cosmetics.**
• Recipes for hair dying were made from plants, like indigo and minerals like iron power, black iron or steel and acidic extracts of sour rice gruel.
• Gandhayukli describes recipes for making scents, mouth perfumes, bath powders, incense and talcum powder.

Additional Information

• Kamplcica, Pattanga and Jatuka:
• A number of classical texts, like Atharvaveda (1000 BCE) mention some dye stuff, the material used were turmeric, madder, sunflower, orpiment, cochineal and lac.
• Some other substances having tinting properties were Kamplcica, Pattaya and Jatuka.

The correct answer is Carboxylic acid.

Key Points 

• ​A carboxyl group (C(=O)OH) coupled to an R-group makes up a carboxylic acid, an organic acid.
• The general formula of a carboxylic acid is R−COOH or R−CO2H, with R referring to the alkyl, alkenyl, aryl, or other group.
• Carboxylic acids are very common.
• The amino acids and fatty acids are two prime examples.
• A carboxylate anion is produced when a carboxylic acid is deprotonated.
• They produce carboxylate ions when they interact with metals and alkalis.
• The reactions of carboxylic acids show how acidic they are.

Additional Information

• Ester:
• An ester is a substance that is formed from an acid in which an organyl group has been substituted for at least one of the acid's acidic hydrogen atoms.
• Different esters are used in the creation of pheromones, essential oils, and fragrances.
• Ketone:
• A ketone is a functional group that has the formula R-C-R', where R and R' can be any number of substituents that include carbon.
• Ketones have a carbonyl group, or C, in them.
• Acetone is the most basic ketone.
• Aldehydes:
• ​An organic molecule with the functional group RCH=O is known as an aldehyde.
• Natural aldehydes can be found in nuts, spices, fruits, and vegetables.

The correct answer is Article 143.

Key Points

• Article 143: Power of President to consult Supreme Court.

1. If at any time it appears to the President that a question of law or fact has arisen, or is likely to arise, which is of such a nature and such public importance that it is expedient to obtain the opinion of the Supreme Court upon it, he may refer the question to that Court for consideration and the Court may, after such hearing as it thinks fit, report to the President its opinion thereon.
2. The President may, notwithstanding anything in the proviso to article 131, refer a dispute of the kind mentioned in the said proviso to the Supreme Court for opinion and the Supreme Court shall, after such hearing as it thinks fit, report to the President its opinion thereon.

Additional Information

• Article 142 of the Constitution:
• Title: Enforcement of decrees, orders of Supreme Court and orders as to discovery, etc.
• Provisions: This article has 2 provisions –
• 142(1): The Supreme Court may pass an order for doing complete justice. Hence, option 2 is correct.
• 142(2): It confers three different powers on the Supreme Court.
• Article 144
• The Indian Constitution's Article 144 instructs civil and judicial agencies to support the Supreme Court in its work. It states that the Supreme Court shall get assistance from all civil and judicial bodies within the boundaries of India. Additional Reading: Indian Supreme Court.
• Article 145
• Rules of Court
• Subject to the provisions of any law made by Parliament the Supreme Court may from time to time, with the approval of the President, make rules for regulating generally the practise and procedure of the Court.

The correct answer is Red Fort.

Key Points

• On 15 August 1947, the first Prime Minister of India, Jawaharlal Nehru raised the Indian national flag above the Lahori Gate of the Red Fort in Delhi.
• From August 15, 1947, to 1964, he unfurled the Indian flag at Red Fort for continuous 17 years.​
• Every year, the Prime Minister of India unfurls the flag at the Red Fort, but there are some who got a chance to become PM of India but were not able to hoist the flag at the iconic monument.

Additional Information

• List of Prime Ministers who hoisted the flag at Red Fort more than five times:
• Indira Gandhi - From 1966 to 1977, she got the opportunity for nothing less than 11 times.
• Manmohan Singh - Ex-Prime Minister of India unfurled the flag 10 times.
• Narendra Modi - Current Prime Minister of India, Narendra Modi has been hoisting the Indian flag at the Red fort since 2014 till date.
• Atal Bihari Vajpayee - He is the only non-Congress Prime Minister who has unfurled the Indian Flag at Red Fort six times.
• Rajiv Gandhi and Narasimha Rao unfurled the Indian flag five times each.

The correct answer is 1858.

Key Points

• On August 2, 1858, a measure to transfer control of India from the East Indian Company to the British Crown was approved by Parliament.
• For the highest-ranking representative of the British Government in India, the title of viceroy was established.
• This bill's clause asked for the British East India Company, which ruled India with the support of the Parliament, to be dissolved and its authority to be transferred to the British Crown.
• This law was introduced by Lord Palmerston, the UK's prime minister at the time.
• To quell the repercussions of the revolt, this legislation was passed in 1858, the year after India's first war of independence.
• Right till the nineteenth century nothing threatened the rule of the British in the Indian sub-continent, until the first Indian war of Independence in 1857.

Additional Information

• East india company was incorporated in England in 1600 and eventually becoming British.
• East India Company was disbanded in 1874.
• It was established to engage in trade with the East Indies and later, East Asia, in the Indian Ocean region.
• The British East India Company first arrived in India as a spice dealer.
• Other from that, their main commodities were opium, silk, cotton, indigo dye, and tea.
• On August 24, 1608, they arrived in the Indian subcontinent at the port of Surat.

The correct answer is 933.

Key Points

• According to census 2001, sex ratio is 933 females per 1000 males.
• The sex ratio is used to describe the number of females per 1000 males.
• Sex ratio is a valuable source for finding the population of women in India and what is the ratio of women to that men in India.
• In the Population Census of 2011, it was revealed that the population ratio in India in 2011 is 943, little higher than 2001.
• The Sex Ratio 2011 shows an upward trend from the census 2001 data.
• Census 2001 revealed that there were 933 females to that 1000 males.
• For decades India has seen a decrease in the sex ratio in 2011, but in the last two decades, there has been a slight increase in the sex ratio.

Additional Information

• Census 2011
• The Indian Census is the most credible source of information on Demography (Population characteristics), Economic Activity, Literacy and Education, Housing Household Amenities, Urbanization, Fertility and Mortality, etc.
• Census 2011 was the 15^th National Census of the Country.
• Census was introduced in India during the era of Lord Mayo in the year 1872.
• It came into force in 1881.
• This census was conducted under the guidance of Mr. C. Chandramouli.
• The slogan of census 2011 was ‘Our Census, Our future’.

The correct answer is August.

Key Points

• The Central Universities (Amendment) Bill, 2022 was passed in Lok Sabha in August.
• The Central Universities (Amendment) Bill, 2022 was introduced in Lok Sabha on August 1, 2022.
• The Bill amends the Central Universities Act, 2009, which provides for establishing central universities in various states.

Additional Information

• Key features of the Bill include:
• Gati Shakti Vishwavidyalaya: 
• The Bill seeks to convert the National Rail and Transportation Institute, Vadodara (a deemed university) to the Gati Shakti Vishwavidyalaya, which will be a central university.
• Scope of education:
• The Bill provides that Gati Shakti Vishwavidyalaya will take measures to provide quality teaching, research, and skill development in disciplines related to transportation, technology, and management.
• Appointment of a new Vice-Chancellor (VC):
• The existing VC of the National Rail and Transportation Institute will hold office for: (i) six months from when the Act is notified, or (ii) until a new VC for the Gati Shakti Vishwavidyalaya is appointed, whichever is earlier.

The correct answer is Ahmedabad.

Key Points

• Ahmedabad is often referred to as the 'Manchester of India'.
• Favorable locational factors were responsible for the development of the textile industry in Ahmedabad.
• Ahmedabad is situated in the heart of a cotton-growing area. This ensures the easy availability of raw materials.
• Ahmedabad is known as the “Manchester of India” because of its similarity with the well-known cotton textile center of Manchester, Great Britain, and the following reasons. Ahmedabad is situated on the bank of Sabarmati River (like Manchester is located on the banks of River Irwell). Its water is good for dying thread.​​

Additional Information

The correct answer is Sodium thiosulphate.

Key Points

• Sodium thiosulfate 
• Sodium thiosulfate (sodium hyposulfite), Na2S2O3, is used by photographers to fix developed negatives and prints.
• It acts by dissolving the part of the silver salts coated onto film which remains unchanged by exposure to light.

Additional Information

• Sodium bicarbonate
• Baking Soda is the common name for Sodium Bicarbonate.
• Its chemical formula is NaHCO3.
• It is a crystalline white solid that is salty and alkaline.
• It is used for cooking purpose, pest control, and as a fire extinguisher.
• Sodium hydroxide
• Sodium hydroxide (NaOH) is known as 'caustic soda' and it is a 'high-base' alkali.
• It is used in the manufacture of pulp and paper cloth, drinking water, soap, and detergent.
• In the field of medicine, sodium hydroxide is used for the treatment, control, prevention, and improvement of diseases.
• Sodium benzoate is used as a preservative for carbonated drinks, jams and fruit juices, and pickles.
• ​Sodium sulfate
• The formula for sodium is – Na+, and Sulphate is – SO42-. So, the formula for Sodium Sulphate is – Na2SO4.
• Sodium sulfate is used to dry organic liquids.
• As a filler in powdered home laundry detergents.
• Na2SO4 is used in manufactured paper, glass, dyes, and pharmaceuticals.
• It is often used in its decahydrate form, which is also known as Glauber's salt.
• It is also called salt cake.

The correct answer is Muhammad Tughluq.

Key Points

• Muhammad Tughluq appointed Ladha and Pira, two gardeners to high administrative posts.
• Sultan Muhammad Tughluq appointed:
• Aziz Khummar, a wine distiller,
• Firuz Hajjam, a barber,
• Manka Tabbakh, a cook, and
• Two gardeners, Ladha and Pira, to high administrative posts.
• Ziyauddin Barani, a mid-fourteenth-century chronicler, reported their appointments as a sign of Sultan’s loss of political judgment and his incapacity to rule.
• Barani had criticized Muhammad Tughluq for that appointment.
• Tughluq's appointment reflected the socio-economic stereotypes that may have been prevalent in those times.
• The authors of Persian tawarikh criticized the Delhi Sultans for appointing the “low and base-born” to high offices.

Additional Information

• Khizr Khan was the founder of the Sayyid dynasty of the Delhi Sultanate.
• In 1414 AD, Khizr Khan occupied the power of Delhi.
• He did not hold the title of Sultan and declared himself as ‘Rayat-e-Ala’.
• He was the founder of the Sayyid Dynasty in India and ruled as a deputy of Timur’s son and successor, Shah Rukh.
• His reign was marked by utter chaos and disorder.
• The Lodi dynasty was founded by Bahlul Khan Lodi.
• The Lodi dynasty was an Afghan dynasty.
• The Lodi dynasty was the last dynasty in Delhi Sultanate, ruled from 1451 to 1526.
• ​Iltutmish was a king of the Slave dynasty.
• He became a ruler of the Slave dynasty from 1211 to 1236.
• He made Delhi the capital of his kingdom by replacing Lahore.
• He introduced the silver coin(Tanka) and the copper coin(Jital).
• He completed the construction of the Qutb Minar.

The correct answer is Basketball.

Key Points

• Pivoting is related to Basketball.
• Pivoting is when a player stands still and steps with one foot.
• The foot that stays on the ground is called the pivot foot.

Additional InformationList of Sports Terms:

The correct answer is Anil Chauhan.

Key Points

• The Government announced Lt General Anil Chauhan (retired) as the new CDS.
• He is the second CDS of India. ​
• General Anil Chauhan, PVSM, UYSM, AVSM, SM, and VSM assumed office as the Chief of Defence Staff (CDS) on September 30, 2022.

Additional Information

• ​The Chief of Defence Staff (CDS) is the military head and acts as the single-point advisor to the Government of India in matters of India’s military.
• He is also the permanent Chairman of the Chiefs of Staff Committee (CoSC) of the Indian Armed Forces.
• The Chief also heads the Department of Military Affairs.
• The first Chief of Defence Staff, General Bipin Rawat took office on 1 January 2020.
• The creation of the post of CDS was first recommended after the 1999 Kargil War.

The correct answer is 1.

• In all AIBA Boxing competitions, the rest time between each round is 1 minutes.
• A professional boxing match generally consists of 4 to 12 rounds.
• 1 minute is scheduled in between each round for rest.
• This estimate includes fights that ended early, due to knockout or injury.
• The average length of a boxing match is about 5.9 rounds, with each round being 3 minutes long.
• This means the average match would be 17.7 minutes in length, not counting breaks between rounds, which are one minute each.
• This estimate includes fights that ended early, due to knockout or injury. If we don’t consider fights that end early, then the average boxing match is 9.7 rounds, or 29.1 minutes in length.
• Amateur International Boxing Association (AIBA):
• It is also known as the International Boxing Association.
• It was formed in the year 1946.
• Its headquarters is located in Lausanne, Switzerland.

The correct answer is fundamental duty.

Key Points

• List of fundamental duties -
• Abide by the Constitution and respect the national flag & National Anthem
• Follow the ideals of the freedom struggle
• Protect the sovereignty & integrity of India
• Defend the country and render national services when called upon
• Spirit of common brotherhood
• Preserve composite culture
• Preserve natural environment
• Develop scientific temper
• Safeguard public property and abjure violence
• Strive for excellence
• Duty for all parents/guardians to send their children in the age group of 6-14 years to school.

Important Points

• Fundamental Duties:
• Article 51-A, Part IV-A of the Indian Constitution deals with Fundamental Duties.
• This article was added to the Indian Constitution by the 42^nd Constitutional Amendment Act, 1976 on the recommendation of the Swaran Singh Committee.
• Fundamental Duties are Non-justiciable in nature.
• Fundamental Duties in the Indian constitution are inspired by the Constitution of the erstwhile USSR.
• These are confined to Indian citizens only and do not extend to foreigners.
• These are enforceable, which means the parliament is free to enforce them by suitable legislation.
• As of today, there are 11 fundamental duties included in Article 51-A.

The correct answer is Amjad Ali Khan Day.

Key Points

• Ustad Amjad Ali Khan (born 9 October 1945) is an Indian classical sarod player, best known for his clear and fast ekhara taans.
• Khan first performed in the United States in 1963 and continued till 2000
• The U.S. state of Massachusetts proclaimed 20 April as Amjad Ali Khan Day in 1984.
• Khan was awarded the 21^st Rajiv Gandhi National Sadbhavna Award.
• Khan received Padma Shri in 1975, Padma Bhushan in 1991, and Padma Vibhushan in 2001, and was awarded the Sangeet Natak Akademi Award in 1989 and the Sangeet Natak Akademi Fellowship in 2011.

Additional Information

• Some Musical Instrument & related Personalities
• Been - Asad Ali Khan, Zia Moin-ud-din Khan
• Santoor - Shiv Kumar Sharma, Rahul Sharma, Satish Vyas.
• Sarod - Amjad Ali Khan, Hafiz Ali Khan, All Akbar Khan, Tejendar Majumdar, Buddhadev Das Gupta, Bahadur Khan.
• Sarangi - Ustad Binda Khan, Sultan Khan, Sabri Khan, Dhruba Ghosh.
• Sitar - Ravi Shankar, Vilayat Khan, Imran Khan, Hara Shankar Bhattacharya, Nikhil Banerjee, Shahid Parvez
• Veena - Asad Ali khan, Jyoti Hedge, S Bala Chandran, KR Kumaraswamy, Jayanathi Kumaresh.
• Violin - Lalgudi Jayaraman, MS Gopal Krishnan, Ragini Shankar, L. Subramaniam, L. Shankar.

The correct answer is Bharatanatyam.

Key Points

• Rukmini Devi Arundale was a reputed dancer and choreographer of Bharatnatyam
• In 1956, Rukmini Devi was awarded the Padma Bhushan.
• in 1967 she received the "Sangeet Natak Akademi Fellowship".
• Rukmini Devi was the first woman to be nominated as a member of the Rajya Sabha.
• She was featured in India Today's list of 100 people who shaped India.

Additional Information

• Some famous personalities related to Dance
• ​Bharatanatyam - Sonal Mansingh, Bala Saraswati, Narthaki Natraj, CV Chandrasekhar, Leela Samson, Mrinalini Sarabhai, Padma Subramanyam, Rukmini Devi, Yamini Krishnamurti.
• Kathak - Shobhna Narayan, Bharti Gupta, Birju Maharaj, Durga Das, Gopi Krishna, Sambhu Maharaj, Sitara Devi.
• Kuchipudi - Raja, Kaushalaya Reddy, Siddhendra Yogi, Josyula Seetharamaiah, Vempathi Chinna Sathyam, Yamini Krishnamurthy, Ragini Devi.
• Manipuri - Guru Bipin Singh, Indira Devi, Darshana Jhaveri, Rajkumar Singhajit Singh, Nirmala Mehta, Savita Mehta.
• Odissi - Debaprasad Das, Dhirendra Nath Patnaik, Indrani Rahman, Kelucharan Mahapatra, Priyambada Mohanty, Sanjukta Panigrahi, Mayadhar Raut, Ileana Citaristi, Gangadhar Pradhan, Madhavi Mudgal, Sonal mansingh.
• Kathakali - Mrinalini Sarabhai, Thottam Shankaran, Kutti Nayyar, Shankar Kurup, KC (Kavungal Chathunni) Panicker, TT Ram Kulti, Chemancheri Kunhiraman Nair.

The correct answer is Group 17.

Key Points

• Halogens are a group of six elements of Group 17 in the periodic table.
• Fluorine (F)
• Chlorine (Cl)
• Bromine (Br)
• Iodine (I)
• Astatine (At)
• Tennessine (Ts)
• Halogens are nonmetals.
• Halogens are very reactive, the reactivity decreases from Fluorine to Astatine.
• Physical Properties of Halogens:
• They have a strong and often nasty smell.
• They are extremely toxic.
• They are poor conductors of heat and electricity.
• They have low melting and boiling points.
• Chemical Properties of Halogens:
• Their Molecules are diatomic.
• They have seven valence electrons as their one electron missing, they form negative ions and are highly reactive.
• They can gain an electron by reacting with atoms of other elements.

The correct answer is  Gross domestic product.

Key PointsGross domestic product (GDP)

• It is the standard monetary measure of the value-added created through the production of goods and services in a country during a certain period
• As such, it also measures the income earned from that production or the total amount spent on final goods and services (fewer imports)
• As a broad measure of overall domestic production, its functions as a comprehensive scorecard of a given country's economic performance.
• In India, the GDP is released by the National Statistical Office (NSO). Ministry of Statistics and Programme Implementation on a quarterly and yearly basis.
• The formula to calculate GDP is of three types: Expenditure Approach, Income Approach, and Production Approach.
• Expenditure Approach
• GDP = Consumption + Investment + Government Spending + Net Export
• Income Approach
• GDP = Total National Income + Sales Taxes + Depreciation + Net Foreign Factor Income
• Production or Value-Added Approach
• Gross Value Added = Gross Value of Output – Value of Intermediate Consumption

Additional Information

• Gross national product (GNP) is an estimate of the total value of all the final products and services turned out in a given period by the means of production owned by a country's residents. GNP is commonly calculated by taking the sum of personal consumption expenditures, private domestic investment, government expenditure, net exports, and any income earned by residents from overseas investments, then subtracting income earned by foreign residents.
• Net national product (NNP) is the monetary value of finished goods and services produced by a country's citizens, overseas and domestically, in a given period. It is the equivalent of the gross national product (GNP), the total value of a nation's annual output, minus the amount of GNP required to purchase new goods to maintain existing stock.
• The gross national product at factor cost is the difference between the gross national product and net indirect taxes. It is also called gross national income. Gross national income is the total compensation of employees, operating surplus, mixed income, depreciation and net factor income from abroad.

The correct answer is Healthy fats.

Key Points

• Monounsaturated fats and polyunsaturated fats are known as the “good fats” because they are good for your heart, your cholesterol, and your overall health.
• These fats can help to lower the risk of heart disease and stroke, cholesterol levels, and Prevent abnormal heart rhythms.
• Monounsaturated fat good sources include olive, canola, peanut, and sesame oils, Nuts (almonds, peanuts, macadamia, hazelnuts, pecans, cashews), avocados etc.
• Polyunsaturated fat good sources include Sunflower, sesame, and pumpkin seeds, Walnuts, Fatty fish (salmon, tuna, mackerel, herring, trout, sardines) fish oil, Soybean and safflower oil, etc.

Additional Information

• Unhealthy fats 
• Trans fat. Small amounts of naturally occurring trans fats can be found in meat and dairy products but it's artificial trans fats that are considered dangerous.
• This is the worst type of fat since it not only raises bad LDL cholesterol but also lowers good HDL levels.
• Carbohydrates
• They're the body's primary source of energy and the brain's preferred energy source. Carbs are broken down by the body into glucose.
• Minerals
• Minerals are those elements in foods that our bodies need to develop and function normally.
• Those essential for health include calcium, phosphorus, potassium, sodium, chloride, magnesium, iron, zinc, iodine, etc.
• Protein
• Protein is considered the building block of life and is found in every cell of the body.
• Protein is made up of amino acids that are attached to one another in long chains.

The correct answer is 1907.

Key Points 

• In 1907, the session of the Indian National Congress was held in Surat, in which the Congress was divided into two parties called the Extremist Party and the Moderate Dal.
• This is called the Surat division.
• The session of 1907 was presided over by Rash Behari Ghosh.

Additional Information 

• ​In 1907, the Congress session was held in Surat on the banks of the Tapti River under the chairmanship of Rash Behari Ghosh.
• In this, the differences between the moderates and the extremists led to a split in Congress.
• The Muslim League was formed in 1906 by Aga Khan and Mohsin Mulmuk.
• A separate electorate was introduced by the Morley–Ralley Minto Reform Act of 1909.

Important Points

• Resolutions passed in the Calcutta session of the Indian National Congress in 1906 were about: 
• Use of Swadeshi
• Boycott Videshi
• Focus on National Education
• And Self Government
• Resolutions on all four issues were passed in the 1906 Congress session, and also swaraj was announced as the aim.
• The Calcutta session of 1906 was a conciliation attempt for both factions (moderates and extremists).
• Presided by Dadabhai Naoroji.
• Four compromise resolutions on the Swadeshi, Boycott, National Education, and Self- Government demands were passed.
• The major bone of contention was the Extremist demand to extend the boycott in both severities and extend it throughout India.
• While the moderates wanted to limit the boycott only to Bengal and with less severity.
• Throughout 1907 the two sides fought over differing interpretations of the resolutions.
• Moderates did not want to be tagged as radical.
• They also toned down the resolution in a compromised state and made it - self-government means that obtaining the self-governing British Colonies.
• Thus the whole meaning of Swaraj of the extremists was changed.
• The extremists felt cheated and the difference became apparent.
• Congress was now bound to split, which actually happened next year in Surat.

The correct answer is Terence Lewis.

Key Points

• Terence Lewis is an Indian dancer and choreographer.
• Lewis won the 2002 American Choreography Award for choreographing the songs of the movie Lagaan along with Saroj Khan, Raju Khan, Ganesh Hegde and Vaibhavi Merchant
• The WEB Europe Scholarship programme offers young professional dancers and choreographers from mainly European but also from non-European countries the possibility to participate in an intense multinational further training programme.

Additional Information

• Ashley Lobo is an Indian-Australian choreographer and is considered an introducer to International dance in India.
• Padmini Chettur has a background in the classical Indian form Bharatanatyam. She was trained by the famous choreographer Chandralekha.
• Shakti Mohan is a famous Indian dancer and choreographer.

Calculation:

As the expression given is C₁C₂ = r₁ + r₂

C1C2 represents the distance between the centers of the circles.

r₁ represents the radius of the first circle

r₂ represents the radius of the second circle.

C1C2 = r1 + r2 represents that the distance between the centers of the circle is equal to the sum of the radius, which means the circle touches each other externally.

When the circle touches each other externally then there are only three tangents are possible.

i.e. two direct common tangents and one transverse tangent.

∴ The correct answer is Option 3.

Given:

674pq0 is divisible by both 3 and 11

Concept used:

If the sum of digits of a number is a multiple of 3, the number will be completely divisible by 3

If the difference of the sum of alternative digits of a number is 0 or divisible by 11, then that number is divisible by 11 completely.

Calculation:

As 674pq0 divisible by 3

So, 6 + 7 + 4 + p + q + 0

⇒ 17 + p + q also divisible by 3

Now,

Possible values of p + q = 4, 7, 10, 13, 16

From the options

Option 1 and Option 4 is satisfying

Now,

For Option 1

The number is 674220

So, 6 + 4 + 2 - 7 - 2 = 3 Not divisible by 11

For Option 4

The number is 674520

So, 6 + 4 + 2 - 7 - 5 = 0 divisible by 11

∴ The required answer is Option 4.

Shortcut Trick

When time is constant, distance is directly proportional to speed.

Ratio of speeds (Thief : Policeman) = 7 : 8 ⇒ Ratio of distance = 7 : 8.

Difference in distance units = 8 − 7 = 1 unit.

Given 1 unit = 450 m. Distance covered by Policeman = 8 units = 8 × 450 m = 3600 m.

3600 m = 3.6 km.

∴ The correct answer is 3.6 km.

Alternate Method

Given: Initial distance between policeman and thief = 450 m = 0.45 km. Speed ratio (Thief : Policeman) = 7 : 8.

Formula Used: Relative Speed = Speed_P − Speed_T | Distance = Speed × Time.

⇒ Let speeds be 8x and 7x. Relative speed = 8x − 7x = x.

⇒ Time to catch = Initial distance ÷ Relative speed = 0.45 / x.

⇒ Total distance covered by Policeman = Speed_P × Time.

⇒ Distance = 8x × (0.45 / x) = 8 × 0.45.

⇒ Distance = 3.6 km.

∴ The correct answer is 3.6 km.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction, the relative speed is the difference of their speeds (S₁ − S₂).

Distance-Speed Relationship

If time of travel is the same for both entities, the ratio of distances covered is equal to the ratio of their speeds (D₁/D₂ = S₁/S₂).

Unit Conversion

Always ensure units are consistent; to convert meters (m) to kilometers (km), divide by 1000.

Shortcut Trick

For the largest sphere inside a cube, the diameter of the sphere is equal to the side of the cube.

Side (a) = 5.6 cm → Radius (r) = 2.8 cm

Volume = (4/3) × π × r³

Volume ≈ 1.33 × 3.14 × 21.952 ≈ 91.98 cm³

∴ The correct answer is 91.98 cm³.

Alternate Method

Given:

Side of the cube (a) = 5.6 cm

Formula Used:

Volume of sphere = (4/3) × π × r³

Calculations:

⇒ For the largest sphere, Diameter (d) = Side of cube = 5.6 cm

⇒ Radius (r) = d/2 = 5.6/2 = 2.8 cm

⇒ Volume = (4/3) × (22/7) × (2.8) × (2.8) × (2.8)

⇒ Volume = (4/3) × (22/7) × 21.952

⇒ Volume = (4/3) × 22 × 3.136

⇒ Volume = (88 × 3.136) / 3

⇒ Volume = 275.968 / 3

⇒ Volume ≈ 91.9893...

∴ The correct answer is 91.98 cm³.

Additional Information

Cube properties

Volume of cube = a³ | Total Surface Area = 6a² | Diagonal = a√3

Sphere properties

Surface Area of sphere = 4πr² | Volume of hemisphere = (2/3)πr³

Inscribed and Circumscribed

Radius of sphere inscribed in cube = a/2 | Radius of sphere circumscribing cube = (a√3)/2

Given:

The curved surface area of the sphere is 154 cm2

Concept used:

Surface area of a sphere = 4πr²

Volume of a sphere = 4/3πr³

Here,

r = radius

Calculation:

4πr² = 154

⇒ 4 × 22/7 × r2 = 154

⇒ r2 = 49/4

⇒ r = 7/2

So, volume = 4/3 × 22/7 × (7/2)³

⇒ 4/3 × 22 × 49/8

⇒ 11 × 49/3

⇒ 539/3

⇒ 179.66 ≈ 179.7

∴ The volume of the sphere is 179.7 cm³.

Given:

${\rm x} + \frac{1}{{\rm x}} = - 14$

Concept used:

(a² - b²) = (a + b)(a - b)

Calculation:

${\rm x} + \frac{1}{{\rm x}} = - 14$

⇒ ${\rm x^2} + \frac{1}{{\rm x^2}} +2= 196$

⇒ ${\rm x^2} + \frac{1}{{\rm x^2}} +2-4= 196-4$

⇒ ${\rm x^2} + \frac{1}{{\rm x^2}} -2= 192$

⇒ $({\rm x} - \frac{1}{{\rm x}})^2= 192$

⇒ ${\rm x} - \frac{1}{{\rm x}} =\pm 8√3$

As x < -1 So, ${\rm x} - \frac{1}{{\rm x}} =- 8\sqrt3$

Now,

${{\rm x}^2} - \frac{1}{{{{\rm x}^2}}}$ = (- 14) × ($-8\sqrt 3$)

⇒ $112\sqrt 3$

∴ The required answer is $112\sqrt 3$.

Calculation:

Total number of donuts sold by stores P and R together in October = 125 + 960

⇒ 1085

Total number of donuts sold by stores R and Q together in October = 905 + 960

⇒ 1865

Ratio = 1085 : 1865

⇒ 217 : 373

∴ The required answer is 217 : 373.

Calculation:

x% of 20 = 0.5

⇒ x = (0.5/20) × 100

⇒ 5/2

⇒ 2.5

∴ The required answer is 2.5%.

Shortcut Trick

The ratio of the sides AB : AC = 8.4 : 5.6 = 3 : 2.

By the Angle Bisector Theorem, the ratio of the segments BD : DC must also be 3 : 2.

Given DC = 2.8 cm, which represents 2 units, thus 1 unit = 1.4 cm.

The total length of side BC is (3 + 2) = 5 units.

Length of BC = 5 × 1.4 = 7 cm.

∴ The correct answer is 7 cm.

Alternate Method

Given:

In triangle ABC, AD is the angle bisector of angle A.

AB = 8.4 cm, AC = 5.6 cm, DC = 2.8 cm.

Formula Used:

Internal Angle Bisector Theorem: The internal bisector of an angle of a triangle divides the opposite side into segments that are proportional to the adjacent sides. ⇒ AB / AC = BD / DC

Calculations:

⇒ AB / AC = BD / DC

⇒ 8.4 / 5.6 = BD / 2.8

⇒ (84 / 56) = BD / 2.8

⇒ 1.5 = BD / 2.8

⇒ BD = 1.5 × 2.8

⇒ BD = 4.2 cm

Now, side BC = BD + DC

⇒ BC = 4.2 + 2.8

⇒ BC = 7 cm

∴ The correct answer is 7 cm.

Additional Information

Internal Angle Bisector Theorem

In any triangle, the angle bisector divides the opposite side into two segments whose lengths have the same ratio as the other two sides of the triangle.

Length of the Angle Bisector

The length of the internal bisector AD can be calculated using the formula: AD² = (AB × AC) − (BD × DC).

External Angle Bisector Theorem

If the external bisector of angle A intersects the extended side BC at E, then AB / AC = BE / CE.

Given:

A hotel is giving a discount of 12% on the booking of 2 or more rooms

Additionally, the hotel is offering a 5% discount only on payment using any card of SBI.

Actual cost of each room = Rs. 1500

Calculation:

Price after 1^st discount = (1500 × 2) × 88%

⇒ 3000 × 88%

⇒ 2640

Price after 2^nd discount = 2640 × 95%

⇒ 2508

∴ He had to pay Rs. 2508.

Given:

R jogs at twice the speed of walking and runs at twice the speed of jogging.

The distance between his office and home is 10 km

He walks at the speed of 5 km/h

Concept used:

Average speed = Total distance/Total time taken

Calculation:

R's jogging speed = 5 × 2

⇒ 10 km/h

R's running speed = 10 × 2

⇒ 20 km/h

Now,

At the time of going to his office time taken = 5/5 + 5/10

⇒ 1 + 0.5

⇒ 1.5 hours

At the time of returning to his home time taken = 5/10 + 5/20

⇒ 0.5 + 0.25

⇒ 0.75 hour

So, total time = 1.5 + 0.75

⇒ 2.25 hours or 9/4 hours

Total distance = 20 km    [To and fro]

Average speed = 20/(9/4)

⇒ $\frac{{80}}{9}$

∴ His average speed (in km/h) in a complete round from his home to office and back home is $\frac{{80}}{9}$.

Shortcut Trick

Present ratio of Ram and Ramesh = 3 : 5 (Difference = 2 units).

Ratio after 7 years = 4 : 5 (Difference = 1 unit).

To equate differences, multiply the future ratio by 2: (4 : 5) × 2 = 8 : 10.

Change in Ramesh’s age units = 10 − 5 = 5 units.

Given that 5 units = 7 years, then Ramesh’s present age (5 units) is 7 years.

∴ The correct answer is 7 years.

Alternate Method

Given:

Present age ratio of Ram and Ramesh = 3 : 5

Ratio after 7 years = 4 : 5

Calculations:

⇒ Let the present ages of Ram and Ramesh be 3x and 5x respectively.

⇒ After 7 years, their ages will be (3x + 7) and (5x + 7).

⇒ According to the problem: (3x + 7) ÷ (5x + 7) = 4 ÷ 5

⇒ 5 × (3x + 7) = 4 × (5x + 7)

⇒ 15x + 35 = 20x + 28

⇒ 20x − 15x = 35 − 28

⇒ 5x = 7

⇒ Ramesh’s present age = 5x = 7 years.

∴ The correct answer is 7 years.

Additional Information

Age Difference Consistency

The difference between the ages of two individuals remains constant throughout their lives. If the difference is 'd' now, it will remain 'd' after any number of years.

Ratio Adjustment Method

When the time gap is the same for both people, adjust the ratios such that the numerical difference between the terms of each ratio is identical.

Cross-Multiplication in Ratios

For a ratio a : b changing to c : d after 'n' years, the value of one part x = [n × (d − c)] ÷ [ad − bc].

Shortcut Trick

If k⁴ + 1/k⁴ = a, then k² + 1/k² = √(a + 2).

If k² + 1/k² = b, then k + 1/k = √(b + 2).

If k + 1/k = x, then k³ + 1/k³ = x³ − 3x.

Here, x = √(√(47 + 2) + 2) = √(7 + 2) = 3.

Required value = 3³ − 3(3) = 27 − 9 = 18.

∴ The correct answer is 18.

Alternate Method

Given: k⁴ + 1/k⁴ = 47

Formula Used: (a + b)² = a² + b² + 2ab and (a + b)³ = a³ + b³ + 3ab(a + b)

⇒ k⁴ + 1/k⁴ + 2 = 47 + 2

⇒ (k²)² + (1/k²)² + 2(k²)(1/k²) = 49

⇒ (k² + 1/k²)² = 49

⇒ k² + 1/k² = 7

⇒ k² + 1/k² + 2 = 7 + 2

⇒ (k + 1/k)² = 9

⇒ k + 1/k = 3

Now, finding the value of k³ + 1/k³:

⇒ (k + 1/k)³ = k³ + 1/k³ + 3(k)(1/k)(k + 1/k)

⇒ (3)³ = k³ + 1/k³ + 3(3)

⇒ 27 = k³ + 1/k³ + 9

⇒ k³ + 1/k³ = 27 − 9

⇒ k³ + 1/k³ = 18

∴ The correct answer is 18.

Additional Information

Algebraic Reciprocal Square Identity

If k + 1/k = x, then k² + 1/k² = x² − 2.

Algebraic Reciprocal Cube Identity

If k + 1/k = x, then k³ + 1/k³ = x³ − 3x.

Negative Reciprocal Identity

If k − 1/k = x, then k² + 1/k² = x² + 2 and k³ − 1/k³ = x³ + 3x.

Power 4 from Power 1

If k + 1/k = x, then k⁴ + 1/k⁴ = (x² − 2)² − 2.

Given:

SP = Rs. 4,00,000

Loss% = 20%

New Profit = 5%

Calculation:

Let CP be 100x

Now, SP after 20% loss = Rs. 100x × (100 – 20)%

⇒ Rs. 80x

And, SP after 5% profit = Rs. 100x × (100 + 5)%

⇒ Rs. 105x

According to the question, ⇒

80x = Rs. 4,00,000

⇒ 105x = Rs. (4,00,000/80) × 105

⇒ Rs. 5,25,000

∴ The required selling price is Rs. 5,25,000.

Given:

Two numbers are 110 and 1980

Calculation:

110 = 2 × 5 × 11

1980 = 2² × 3² × 5 × 11

So, HCF = 2 × 5 × 11

⇒ 110

∴ The required answer is 110.

Given:

(x + 2y)3 + (x - 2y)3

Concept used:

a³ + b³ = (a + b)(a² + b² - ab)

Calculation:

(x + 2y)3 + (x - 2y)3 = (x + 2y + x - 2y)[(x + 2y)2 + (x - 2y)2 - (x + 2y)(x - 2y)]

⇒ (x + x)[(x² + 4y2 + 4xy + x² + 4y2 - 4xy - x² + 4y²)]

⇒ 2x(x2 + 12y2)

⇒ 2x3 + 24 xy2

∴ The required answer is 2x3 + 24 xy2.

Given:

Sum = Rs. 5250

Amount = Rs. 9870

Rate = 11%

Concept used:

S.I = (P × T × R)/100

Here,

P = Sum

T = Time 

R = Rate

Amount = Sum + S. I

Calculation:

Interest = 9870 - 5250

⇒ 4620

Now,

Let the time be T years

4620 = (5250 × T × 11)/100

⇒ 420 = 210T/4

⇒ T = 4 × 2 = 8

So, time is 8 years

∴ The required time is 8 years.

Calculation:

Total production of trucks in H and I = 400 + 300

⇒ 700

Total production of bikes in J and K = 350 + 400

⇒ 750

Ratio = 700 : 750

⇒ 14 : 15

∴ The required answer is 14 : 15.

Given:

$\sin θ + \cos θ = \frac{{\sqrt 3 - 1}}{{2\sqrt 2 }}$

Concept used:

sin²θ + cos²θ = 1

Calculation:

$\sin θ + \cos θ = \frac{{\sqrt 3 - 1}}{{2\sqrt 2 }}$

⇒ $(\sin θ + \cos θ)^2 = \left(\frac{{\sqrt 3 - 1}}{{2\sqrt 2 }}\right)^2$

⇒ $\sin ^2θ + \cos ^2θ +2sinθ .cosθ = \left(\frac{{3 + 1-2\sqrt3.1}}{{8 }}\right)$

⇒ $1+2sinθ .cosθ = \frac{{4-2\sqrt3}}{{8 }}$

⇒ $2sinθ .cosθ = \frac{{4-2\sqrt3}}{{8 }}-1$

⇒ $2sinθ .cosθ = \frac{{4-2\sqrt3-8}}{{8 }}$

⇒ $sinθ .cosθ = \frac{{-(\sqrt3+2)}}{{8 }}$

Now,

tan θ + cot θ = $\rm \frac{sinθ}{cosθ}+\frac{cosθ}{sinθ}$

⇒ $\rm \frac{sin^2θ+cos^2θ}{sinθ.cosθ}$

⇒ $\rm \frac{1}{sinθ.cosθ}$

⇒ $\rm \frac{1}{\frac{{-(\sqrt3+2)}}{{8 }}}$

⇒ $\rm \frac{-8}{{{(\sqrt3+2)}}{}}$

⇒ $\rm \frac{-8(\sqrt3-2)}{{{(\sqrt3+2)(\sqrt3-2)}}{}}$

⇒ $\rm \frac{-8(\sqrt3-2)}{{{3-4}}{}}$

⇒ $\rm \frac{-8(\sqrt3-2)}{{{-1}}{}}$

⇒ $8\left( {\sqrt3 - 2} \right)$

∴ The required answer is $8\left( {\sqrt3 - 2} \right)$.

Shortcut Trick

By the Internal Angle Bisector Theorem, the ratio of the base segments equals the ratio of the adjacent sides.

BD / DC = AB / AC = 10 / 14 = 5 / 7

Let BD = 5 parts and DC = 7 parts, which means the total length BC = 5 + 7 = 12 parts.

Therefore, the required ratio of BD to BC is 5 : 12.

∴ The correct answer is 5 : 12.

Alternate Method

Given:

⇒ Length of side AB = 10 cm

⇒ Length of side AC = 14 cm

⇒ AD is the angle bisector of angle BAC

Formula Used:

⇒ Internal Angle Bisector Theorem: BD / DC = AB / AC

θ θ

A B C D

10 cm 14 cm

5x 7x

BD : BC = 5 : 12

Calculations:

⇒ By the Internal Angle Bisector Theorem: BD / DC = 10 / 14

⇒ Simplifying the fraction, we get: BD / DC = 5 / 7

⇒ Let the lengths be BD = 5x and DC = 7x

⇒ The total length of the base BC = BD + DC

⇒ BC = 5x + 7x = 12x

⇒ Now, substitute these into the required ratio BD : BC

⇒ Ratio = 5x / 12x = 5 / 12

⇒ BD : BC = 5 : 12

∴ The correct answer is 5 : 12.

Additional Information

Internal Angle Bisector Theorem

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

External Angle Bisector Theorem

The bisector of an external angle of a triangle divides the opposite side externally in the ratio of the adjacent sides. If AD is the external bisector meeting BC extended at D, then BD/DC = AB/AC.

Incenter of a Triangle

The point of intersection of all three internal angle bisectors of a triangle is called the Incenter. It forms the center of a circle inscribed within the triangle and is equidistant from all three sides.

Area Ratio of Sub-Triangles

Since triangles ABD and ADC share the same height drawn from vertex A to the line BC, the ratio of their areas is equal to the ratio of their base lengths: Area(ABD) / Area(ADC) = BD / DC = AB / AC.

Given:

$\sin θ = \frac{8}{{17}}$

Concept used:

(H)Hypotenuse² = (P)Perpendicular² + (B)Base²

Calculation:

sinθ = P/H

So, H² = P² + B²

⇒ 17² = 8² + B²

⇒ 289 = 64 + B2

⇒ 225 = B2

⇒ 15 = B

Now,

tanθ = P/B

So, tanθ = $\frac{8}{{15}}$

∴ The required answer is $\frac{8}{{15}}$.

 Shortcut Trick

sinθ = 8/17 = P/H, we know the triplet P = 8, B = 15, H = 17

Now, tanθ = P/B So, tanθ = 8/15

Given:

sec 2θ = cosec (θ – 36°)

Concept used:

Calculation:

sec 2θ = cosec (θ – 36°)

⇒ sec 2θ = sec (90° – θ + 36°)

⇒ sec 2θ = sec (126° – θ)

⇒ 2θ = 126° – θ

⇒ 3θ = 126°

⇒ θ = 42°

∴ The required answer is 42°.

Calculation:

The total number of students who opted for Yoga and Painting taken together = 300 × (18 + 12)%

⇒ 300 × 30%

⇒ 90

The total number of students who opted for Music and Dance taken together = 300 × (24 + 16)%

⇒ 300 × 40%

⇒ 120

Difference = 120 - 90

⇒ 30

∴ The required answer is 30.