WBP Lady Constable (Prelims) 10 Sept 2023 Official Paper (Previous Year Paper)

The correct answer is Emiliano Martínez

Key Points

• Emiliano Martinez, the acclaimed goalkeeper who played a crucial role in Argentina's World Cup triumph in Qatar, arrived at Kolkata's Netaji Subhas Chandra Bose International Airport to an exuberant reception from passionate supporters.

Given:

We need to find the largest number that divides 303 and 207 and leaves remainders of 3 in both cases.

Concept:

To find the largest number that divides two numbers and leaves the same remainder, we first subtract the remainder from each number and then find the greatest common divisor (GCD) of the resulting numbers.

Calculation:

We have,

⇒ 303 - 3 = 300

⇒ 207 - 3 = 204

Now, we find the GCD of 300 and 204.

Prime factorization:

⇒ 300 = 2² × 3 × 5²

⇒ 204 = 2² × 3 × 17

The common factors are 2² × 3.

Hence, GCD = 2² × 3 = 4 × 3 = 12

∴ The largest number that divides 303 and 207 and leaves remainders of 3 in both cases is 12.

The correct answer is Amir Khusharu.

Key Points

• Amir Khusro, also known as Abul Hasan Yaminuddin Khusro, was an Indo-Persian Sufi singer, musician, poet, and scholar who flourished under the Delhi Sultanate.
• He is a legendary person in the Indian subcontinent's cultural history.
• He was a mystic and spiritual follower of Delhi"s Nizamuddin Auliya.
• He mostly wrote poetry in Persian, although he also wrote in Hindavi.
• Khusrau is known as the "Voice of India" or the "Parrot of India," and has been dubbed the "Father of Urdu Literature."

Additional Information The Navratnas of Akbar were as follows-

• Raja Birbal- Foreign Minister
• Miyan Tansen- Culture Minister
• Abul Fazal- Prime Minister
• Faizi- Education Minister
• Raja Man Singh- Chief of Staff of Mughal Army
• Raja Todar Mal- Finance Minister
• Mullah Do Piyaza- Home Minister
• Fakir Aziao-Din- Religious Minister
• Abdul Rahim Khan-I-Khana- Defence Minister

The correct answer is ​Bal Gangadhar Tilak

Key Points

• Kesari is a Marathi newspaper which was founded on 4 January 1881 by Lokmanya Bal Gangadhar Tilak, a prominent leader of the Indian Independence movement.
• The newspaper was used as a spokespiece for the Indian national freedom movement, and continues to be published by the Kesari Maratha Trust and Tilak's descendants.
• Bal Gangadhar Tilak used to run his two newspapers, Kesari, in Marathi and Mahratta in English from Kesari Wada, Narayan Peth, Pune.

Additional Information 

• The editors of Kesari included a number of freedom fighters and social activists / reformers, including Agarkar (its first editor), Chiplunkar and Tilak.
• Agarkar left Kesari in 1887 to start his own news paper, Sudharak (The Reformer) after which Tilak continued to run the paper on his own.
• Narasimha Chintaman Kelkar, a close associate of Tilak, served as editor twice when Tilak was imprisoned in 1897 and 1908.

Given:

a + 2b = 5 and a2 + 4b2 = 13

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:

We have,

a + 2b = 5

On squaring both sides,

(a + 2b)² = 5²

⇒ a2 + 4b2 + 2 × a × 2b = 25

⇒ a2 + 4b2 + 4ab = 25

⇒ 13 + 4ab = 25

⇒ 4ab = 25 - 13 = 12

⇒ ab = 12/4 = 3

Hence, ab = 3

The logic followed here is:

→√64 + √25 + √144 + √36 = 8 + 5 + 12 + 6 = 31

→√81 + √9 + √25 + √361 = 9 + 3 + 5 + 19 = 36

→ √49 + √169 + √36 + √81 = 7 + 13 + 6 + 9 = 35

Hence the correct answer is Option 2:35

The correct answer is 1556.

Key Points

• The Second Battle of Panipat took place on 5^th November 1556, between the emperor of north India, Hemu, and the forces of the Mughal emperor Akbar.
• On January 24, 1556, the Mughal ruler Humanyun died in Delhi and was succeeded by his son, Akbar at Kalanaur, who was only thirteen years old.
• Akbar and his guardian Bairam Khan did not participate in the battle and were stationed 8 miles away from the war zone.
• The 13 year old child King was not permitted to be present on the battlefield in person, instead he was provided with a special guard of 5000 well trained and most faithful troops and was stationed at a safe distance far behind the battle lines.
• The Mughal Vanguard consisted of 10,000 cavalry, out of which 5000 were experienced veteran soldiers and were ready to meet the advancing army of Hemu.
• Hemu led his army himself and his army consisted of 1500 war elephants and a vanguard of artillery.
• Hemu marched in excellent order with 30,000 practiced horsemen composed of Rajputs and Afghans.
• But Hemu died in this battle and his army was in disarray and defeated in the ensuing confusion.

Additional Information

• The First Battle of Panipat was fought on April 21, 1526, between the forces of Babur and Ibrahim Lodhi.
• The Third Battle of Panipat was fought on 14^th January 1761 between the Marathas and the Durrani Empire (Afghanistan).

The logic followed here is:

\

Hence, the correct answer is "159".

Given:

The number is 6351.

We need to find the smallest number to be added to 6351 to make it a square number.

Concept Used:

To determine the smallest number to be added to make a perfect square, we can calculate the nearest square greater than 6351 and subtract 6351 from it.

Calculation:

We have,

⇒ 6351

Find the smallest integer greater than or equal to √6351:

⇒ √6351 ≈ 79.68

Next integer is 80:

⇒ 80² = 6400

Difference between 6400 and 6351:

⇒ 6400 - 6351 = 49

∴ The smallest number to be added to 6351 is 49.

The correct venn diagram representing the relationship between wife, mother and doctor is shown below:

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Hence, the correct answer is "C".

The correct answer is Surendranath Banerjee

Key PointsIndian National Conference

• Indian Association and Indian National Conference are considered the precursors of the Indian National Congress.
• The Indian National Conference was the first recognized nationalist organization founded in British India by Surendranath Banerjee and Ananda Mohan Bose in 1876.
• The primary objective of the Association was to encourage people by legitimate means i.e. the political, intellectual, and material advancement of the people.
• The first session of the National Conference, held in Calcutta on December 28 - 30, 1883, was attended by more than a hundred delegates from different parts of India.
• Immediately after the conclusion of the second session of the National Conference in Calcutta, the first session of the Indian National Congress was held in Bombay (December 28, 1885).

Additional Information The Indian Association of Calcutta

• It was founded by Surendranath Banerjee and Anand Mohan Bose in 1876.
• This association was aimed to unify Indian people on a common political program.

British Indian Association

• It was founded on October 29, 1851, at Calcutta with Raja Radhakanta Dev and Debendranath Tagore as its President and Secretary respectively.
• The object of the Association was 'to secure improvements in the local administration of the country and in the system of government laid down by Parliament'.

Given:

A box contains 52 coins of 1 rupee and 50 paise. The ratio of their value is 3 ∶ 5.

Concept:

Let the number of 1 rupee coins be x and the number of 50 paise coins be y.

According to the problem,

x + y = 52 (Total number of coins)

Value of 1 rupee coins = x × 1 = x rupees

Value of 50 paise coins = y × 0.5 = 0.5y rupees

The ratio of their value is given as 3 ∶ 5.

Formula Used:

Value ratio: (x / (0.5y)) = 3 / 5

Calculation:

We have,

⇒ x + y = 52  ...(i)

⇒ x / (0.5y) = 3 / 5  ...(ii)

From equation (ii):

⇒ x / (0.5y) = 3 / 5

⇒ 2x / y = 3 / 5

⇒ 10x = 3y

⇒ y = (10/3)x  ...(iii)

Substitute equation (iii) into equation (i):

⇒ x + (10/3)x = 52

⇒ (3x + 10x) / 3 = 52

⇒ 13x / 3 = 52

⇒ 13x = 156

⇒ x = 156 / 13

⇒ x = 12

Substitute x = 12 into equation (iii):

⇒ y = (10 / 3) × 12

⇒ y = 40

∴ The number of 1 rupee coins is 12 and the number of 50 paise coins is 40.

The correct answer is Nana Sahib.

Key Points

• Nana Saheb led the revolt of 1857 from Kanpur.
• The rebellion of 1857 was spread across the areas of Meerut, Agra, Mathura, and Lucknow near Kanpur.
• Nana Saheb, the adopted heir of Baji Rao II joined the struggle as he was denied the pension and honours on the ground that he was not the natural-born heir.
• Tantia Tope assisted Nana Saheb in Kanpur as the Commander in Chief.

Additional InformationThe Sepoy Mutiny

• The First War of Independence, known as Sepoy Mutiny, was the first rebellion against the British troops in India in 1857.
• The revolt began in Meerut and was led by Bahadur Shah II from Delhi, Begum Hazrat Mahal from Lucknow, Nana Sahib, and Tantya Tope from Kanpur, and Rani Laxmibai from Jhansi.

The reasons behind the revolt were:

• Destruction of Indian Economy and Land Reforms
• Policies of Subsidiary Alliance and Doctrine of Lapse
• Introduction of Enfield Rifles with fat coatings

The correct answer is yellow coloured.

Key Points

• Hydrogen is the most abundant gas in the universe.
• The chemical element hydrogen has the symbol H and the atomic number 1.
• It is the very first element in the periodic table.
• The hydrogen nucleus contains one proton but no neutron.
• It is insoluble in water and lighter than the air.
• In nature, hydrogen gas is colourless, odourless, non-toxic, and tasteless.
• It is a combustible gas, but it does not support combustion Thus, the colour of the hydrogen gas is colourless.

The logic followed here is:

Logic: It is the logical sequence of events, typically in the context of a person's career progression.

The correct meaningful order of the words is shown below:

E) Education

D) Application

C) Examination

A) Appointment letter

B) Income

Hence, the correct answer is "EDCAB".

Given:

A can do a piece of work in 20 days

A leaves after 5 days of work

The rest of work B can do in 22\(\frac{1}{2}\)  = 45/2 days

Calculation:

5A + 45/2B = 20A

⇒ 45/2 B = 15A

⇒ 45 B = 30 A

⇒ B/A = 30/45 = 2/3

Total work = 20A = 20 × 3 = 60

Time take by (A + B) together = 60/(3+ 2) = 60/5 = 12 days.

∴ The correct answer is 12 days.

Given that

A is shorter than B but taller than E. C is taller than B → C>B > A >E

D is shorter than B but taller than A → B >D >A

The final arrangement → C>B >D >A >E

The shortest is E

Hence the correct answer is option 2: E

The correct answer is ​Sir William Jones

Key Points

• ​Sir William Jones (an Anglo philologist) created the Asiatic Society to promote oriental research and studies in India.
• The Asiatic Society publishes books in different series, viz.,
• Bibliotheca Indica,
• Monograph,
• Seminar & Public Lecture,
• Catalogues
• Bibliographical Works besides some books under Miscellaneous publications.
• Moreover, it publishes periodicals, i.e. a quarterly Journal of the Asiatic Society and Monthly Bulletin of the Asiatic Society.
• James Prinsep bought the first issue of the journal, The Journal of the Asiatic Society of Bengal, which appeared in March 1832.

Additional InformationDavid Hare:

• In 1817, David Hare, who had come out to India in the 1800 as a watchmaker but spent his entire life in the propagation of modern education in the country, founded the famous Hindu College.
• He spent his entire life in the promotion of modern education in the country, founded the famous Hindu College.
• Rammohun Roy gave most enthusiastic assistance to Hare in this and his other educational projects.
• In addition, he maintained at his own cost an English school in Calcutta from 1817.
• In this school, among other subjects, mechanics and the philosophy of Voltaire were taught.

The given series is: 1 3 4 3 5 2 2 3 3 4 1 5 6 7 4 6 2 3 2 5 7 2 5 6 7 9 

Here, the numbers which are equal to the sum of the immediately preceding and immediately following numbers:

→ 1 3 4 3 (5) 2 2 3 3 (4) 1 5 6 7 4 (6) 2 3 2 5 (7) 2 5 6 7 9 

Here, we can see that there are four such numbers.

Hence, the correct answer is "4".

The correct answer is Lysosome.

Key Points

• Lysosomes are single membrane-bound organelles present in animal cells.
• Lysosomes have acidic internal pH about 5 and are filled with hydrolytic enzymes.
• They contain about 40 different types of hydrolytic enzymes (including lipases, proteases, nucleases, phosphatases etc.) which are responsible for digestion of intracellular macromolecules.
• Lysosomes are of two types: **Primary lysosomes (**do not contain material for intracellular digestion) and secondary lysosomes (contain materials that are undergoing digestion or that already have been digested).
• The process by which substances are taken into the cell from external environment and broken down by lysosome is called heterophagy.
• In contrast, the degradation of cytoplasmic components within lysosomes is called autophagy.

Additional Information

 Ribosome: The ribosomes are large ribonucleoproteins consists of RNAs and proteins, ubiquitous in all cells, that translates genetic information stored in the mRNA into the polypeptides.

Different types of ribosomes and their rRNAs.

The ribosomes are app. globular in structure.

 Centrosome: In animal cells, a pair of centrioles present in MTOC (microtubule-organizing center.) MTOC with a pair of centrioles is known as centrosome.

Mitochondria: Mitochondria (term coined by C. Benda) are energy converting organelles, which are present in virtually all eukaryotic cells. 

• They are sites of aerobic respiration. They produce cellular energy in the form of ATP. So, they are known as powerhouse of the cell.

Given:

The sum of the present ages of father and son is 50 years. When the age of the son becomes equal to the present age of the father, the sum of their ages will be 110 years.

Concept:

We need to set up equations based on the given conditions and solve for the present ages of the father and the son.

Calculation:

Let the present age of the father be F years and the present age of the son be S years.

From the given information:

⇒ F + S = 50  ...(1)

When the son's age becomes equal to the present age of the father, the son's age will be F years. At that time, the father will be F + (F - S) years old (since the difference in their ages remains constant).

The sum of their ages at that time will be:

⇒ F + (F + (F - S)) = 110  ...(2)

Simplifying equation (2):

⇒ F + F + F - S = 110

⇒ 3F - S = 110  ...(3)

Now we have two equations:

1. F + S = 50

2. 3F - S = 110

Adding equations (1) and (3):

⇒ (F + S) + (3F - S) = 50 + 110

⇒ 4F = 160

⇒ F = 40

Substitute F = 40 into equation (1):

⇒ 40 + S = 50

⇒ S = 10

∴ The present age of the father is 40 years and the present age of the son is 10 years.

The logic followed here is:

Logic: The coding has been done by the square of the digits.

Let's check,

249 = 41681

\

357 = 92549

\

856 = 642536

\

Similarly,

973 = ?

\

Hence, the correct answer is "81499".

The correct answer is Kerala.

Key Points

• The Vikram Sarabhai Space Centre is a major space research centre of the Indian Space Research Organisation, focusing on rockets and space vehicles for India's satellite programme. It is located in Trivandrum, in the Indian state of Kerala. It was established in 1963.
• The UR Rao Satellite Centre, formerly ISRO Satellite Centre is an Indian Space Research Organisation centre for the design, development, and construction of Indian satellites. It was established in the year of 1972 as Indian Scientific Satellite Project in Peenya Industrial Estates of Bengaluru.
• National Remote Sensing Centre, or NRSC, located in Hyderabad, Telangana is one of the centres of the Indian Space Research Organisation. NRSC manages data from aerial and satellite sources.
• The Indian Institute of Remote Sensing is a premier institute for research, located in Dehradun, Uttrakhand, higher education and training in the field of Remote Sensing, Geoinformatics and GPS Technology for Natural Resources, Environmental and Disaster Management under the Indian Department of Space, which was established in the year 1966.

Additional InformationThe table below is correctly matched:

Given:

Rs.1550 divided into two parts and deposited at the rate of 5% and 8%. Interest of Rs. 300 was obtained after 3 years.

Concept:

Simple Interest (SI) formula is used:

SI = (P × R × T) / 100

Where P is the principal amount, R is the rate of interest, and T is the time period.

Calculation:

Let the two parts be Rs. x and Rs. (1550 - x).

⇒ Interest from the first part at 5%:

SI₁ = (x × 5 × 3) / 100 = (15x) / 100

⇒ Interest from the second part at 8%:

SI₂ = ((1550 - x) × 8 × 3) / 100 = (37200 - 24x) / 100

⇒ Total interest from both parts:

(15x) / 100 + (37200 - 24x) / 100 = 300

⇒ Simplifying the equation:

(15x + 37200 - 24x) / 100 = 300

⇒ (37200 - 9x) / 100 = 300

⇒ 37200 - 9x = 30,000

⇒ 9x = 7200

⇒ x = 800

Therefore, the two parts are:

1550 - 800 = 750

∴ The correct answer is option 3 (800, 750)

The correct answer is Special Leave Petition

Key Points

• Writs are a written order from the Supreme Court or High Court that commands constitutional remedies for Indian Citizens against the violation of their fundamental rights.
• Article 32 in the Indian Constitution deals with constitutional remedies that an Indian citizen can seek from the Supreme Court of India and the High Court against the violation of his/her fundamental rights.
• The same article gives the Supreme Court power to issue writs for the enforcement of rights whereas the High Court has the same power under Article 226.
• The writs- Habeas Corpus, Mandamus, Certiorari, Quo Warranto, and Prohibition

The correct answer is 1907.

Key Points

• At the Surat conference in 1907, congress split.
• The moderate leaders have captured the machinery of the Congress excluded the militant extremist elements from it.
• The Congress split into 2 separate groups moderates and extremists.

Additional Information The INC was formed during the tenure of Lord Dufferin (Viceroy of India from 1884-1888).

The correct answer is Charles Darwin

Key Points

• Charles Darwin proposed the theory of Natural selection in 1859 in his book **The Origin of Species.**​
• Darwin coined the term natural selection. To describe the process by which organisms with favorable variations survive and reproduce at higher rate.
• An inherited variation that increases an organisms' chance of survival in a particular environment is called an adaptation.
• Over many generations, an adaptation could spread throughout the entire species.
• In this way, according to Darwin, evolution by natural selection.

Darwin concluded **that individuals having advantageous variations are more likely to survive and reproduce than those of without the advantageous variations (**survival of fittest). 

Darwin's theory invariably had a combination of some the following five theories:

1. Evolution as such
2. Common descent
3. Multiplication of species
4. Gradualism
5. Natural selection.​

Additional Information

• Newton: Sir Issac Newton was a great mathematician and physicist. who gave the law of motion and gravitation.
• Newton gave 3 laws of motion=

1. A body at rest will remain at rest, and body in motion will remain in motion unless it is acted upon by an external force.
2. The force acting on an object is equal to the mass of mass of that object times its acceleration, F=ma
3. For every action, there is an equal and opposite reaction.

• ​Mendel: Gregor John Mendel known as the father of genetics.

1. In 1856, he published the results of the hybridization experiments titled Experiments on Plant Hybrids in a journal 'The proceeding of Brunn society of natural history'. and postulated the principles of inheritance which are popularly known as Mendel's law.
2. Mendel's law of inheritance: These laws of inheritance are applicable to sexually reproducing eukaryotic organisms.

• On the basis of hybridization experiment on Pisum sativum. Mendel proposed the laws of inheritance.
• These laws are- 1) Law of segregation.

                                   2) Law of independent assortment.

Characters studied by Mendel.

​

Important Points

• Flower color is correlated with seed coat colors. Seeds with white seed coats were produced by plants that had white flowers and those with grey seed coats came from plants that had violet flower.
• Lamarck:
• Jean-Baptiste de Lamarck, a French biologist, published the first truly mechanistic theory of evolution in his book called the use and disuse of acquired characteristics.

The logic followed here is:

Mississippi ∶ America

→ Mississippi is a state in America.

Similarly,

Congo ∶ ?

→ Congo is a state in Africa.

Hence, the correct answer is "Africa".

The logic followed here is:

Logic: The number inside the box is the sum of the outer numbers.

→ (7 + 4 + 3 + 6) = 20

→ (8 + 2 + 9 + 5) = 24

Similarly,

→ (7 + 9 + 6 + 10) = 32

Hence, the correct answer is "32".

Calculation:

Square root of 6466849 = 2543.

The family tree can be drawn using the given information,

Here, we can see that Soma is the wife of the Basab's father.

Hence, the correct answer is "Wife".

The correct answer is 65 years.

Key PointsSupreme Court

• It is the highest constitutional court in India.
• It has the power of judicial review of the acts passed by the Parliament.
• The Supreme Court of India came into existence on 26^th January 1950.
• The judges of the Supreme Court are appointed through a collegium system.
• It is the custodian of the Constitution of India.
• The current strength of the Supreme Court is 34**(33 judges + 1 Chief Justice)**
• The retirement age of the judge of the Supreme Court is 65 years (and for judges of the High Court, it is 62 years).
• First Chief Justice of Supreme Court: H.J.Kania
• Current Chief Justice: Dr. Justice D.Y. Chandrachud

Jurisdiction of Supreme Court:

1. Original Jurisdiction
2. Appellate Jurisdiction
3. Advisory Jurisdiction

Given that:

Since the color of milk is white and white is coded as black.

Hence the correct answer is Option 2: Black

The correct answer is 21 March.

Key Points

• Definition of Equinox – An equinox occurs when the Sun is directly above the equator, resulting in nearly equal day and night durations across the globe.
• Dates of Equinoxes – Equinoxes occur twice a year: around March 21 (Spring or Vernal Equinox) and September 22 (Autumn or Fall Equinox).
• Global Effect – During an equinox, all places on Earth experience roughly 12 hours of daylight and 12 hours of darkness, as the Earth's axial tilt is neither towards nor away from the Sun.
• Seasonal Transition – In the Northern Hemisphere, the March equinox marks the start of spring, while the September equinox marks autumn. In the Southern Hemisphere, these seasons are reversed.

The logic followed here is:

Hence the correct answer is Option 4: G

The correct answer is the Ministry of Finance.

Key Points 

• The revenue estimates of the Budget in India are prepared by the Ministry of Finance.
• The budget is an instrument of the Fiscal policy of the Government.
• The budget is the annual financial statement of a government.
• It lays out a fiscal roadmap for the country for the next year.
• It is prepared by the ministry of finance in consultation with Niti Aayog and other concerned ministries.
• The Budget division of the department of economic affairs (DEA) in the finance ministry is the nodal body responsible for producing the Budget.
• The finance minister presents the Budget in Lok Sabha. Until 2016, it was presented on the last day of February. However, since 2017 the Budget has been presented on 1 February every year.

The logic followed here is:

Hence the correct answer is Option 2: IX

The correct answer is Mewar.

Key Points

• Chittaurgarh, formerly called Chitrakut (for Chitrang, a chieftain of the Rajputs), lies at the foot of a hillslope on which stands Chitor (or Chittorgarh) hill fort.
• From the 8^th century to the 16^th it remained the capital of the Rajput state of Mewar and was the stronghold of the Sisodia Rajputs
• Chittorgarh is home to the Chittor Fort, the largest living fort in India and Asia.
• It was sacked thrice; first in 1303 by Alauddin Khalji, again in 1535 by Bahadur Shah of Gujarat.
• The Sisodiya Capital of Chittor was seized by the forces led by Akbar on 23 February 1568.
• In 1567, the campaign of the Mughal Empire against the Kingdom of Mewar was called as ‘Siege of Chittorgarh’.

Given:

Total cost of 3 chairs and 2 tables is Rs.2900.

Total cost of 4 chairs and 3 tables is Rs.4200.

Concept:

We need to find the cost of one chair and one table using a system of linear equations.

Formula Used:

Let the cost of one chair be C and one table be T.

We have two equations:

3C + 2T = 2900          (1)

4C + 3T = 4200          (2)

Calculation:

Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of T equal:

⇒ 9C + 6T = 8700          (3)

⇒ 8C + 6T = 8400          (4)

Subtract equation (4) from equation (3):

⇒ 9C + 6T - (8C + 6T) = 8700 - 8400

⇒ C = 300

Substitute C = 300 back into equation (1):

⇒ 3(300) + 2T = 2900

⇒ 900 + 2T = 2900

⇒ 2T = 2000

⇒ T = 1000

Hence, the total cost of 1 chair and 1 table is:

⇒ C + T = 300 + 1000

⇒ 1300

∴ The correct answer is option 1.

Calculation:

1 - \(\frac{1}{2}\) - \(\frac{1}{4}\) + \(\frac{1}{8}\) - \(\frac{1}{16}\) 

⇒ \(\frac{16-8-4+2-1}{16}\)

⇒ \(\frac{5}{16}\)

∴ The correct answer is 5/16.

The correct answer is Copper.

Key Points

• HCL or Hindustan Copper Limited is the company for extracting the majority of copper in India .
• This mineral is found mainly in Rajasthan, Madhya Pradesh and in the Chotanagpur region . Khetri mines is one of the famous copper mines of India hence it is the correct option.
• : Mining is done by both opencast and underground methods in India. The major copper mines are the Khetri copper belt in Rajasthan, Singhbhum copper belt in Jharkhand and Malanjkhand copper belt in Madhya Pradesh which are mined by HCL.

The logic followed here is:

Logic: The end of the line represents the square of the number on the other end.

4: 16 → (4)² = 16

9: 81 → (9)2 = 81

12: 144 → (12)2 = 144

Similarly,

24: ? → (24)2 = 576

Hence, the correct answer is "576".

The correct answer is Dr B.R. Ambedkar.

Key Points 

• Dr. Bhimrao Ambedkar  is known as the "Father of the Indian Constitution".
• The Constitution of India was adopted on 26 November 1949.
• The National Anthem of India was adopted on 24 January 1950.
• It was decided to declare 26 November as Constitution Day.

Important Points 

• Vallabhbhai Patel is known as the “Bismarck of India”.
• Sarojini Naidu is known as the nightingale of India.
• Dr Sarvapalli Radhakrishnan was known as the bridge builder between India and the West.
• Mahatma Gandhi is known as the father of nation.

Given:

Speed of boat in still water = 10 km/hr

Distance covered downstream = 150 km

Time taken downstream = 10 hours

Concept:

Speed downstream = Speed of boat + Speed of stream

Speed upstream = Speed of boat - Speed of stream

Calculation:

⇒ Distance = Speed × Time

⇒ 150 = (10 + Speed of stream) × 10

⇒ 150 = 10 × 10 + 10 × Speed of stream

⇒ 150 = 100 + 10 × Speed of stream

⇒ 50 = 10 × Speed of stream

⇒ Speed of stream = 5 km/hr

⇒ Speed upstream = 10 - 5 = 5 km/hr

⇒ Time taken upstream = Distance / Speed upstream

⇒ Time taken upstream = 150 / 5

⇒ Time taken upstream = 30 hours

∴ The boat will take 30 hours to cover the same distance upstream.

The correct answer is Third.

Key Points

• According to Newton's third law of motion, every action has an equal and opposite reaction.
• These two forces act on two different bodies.
• For example, while swimming, you push the water backward.
• The water, in turn, pushes you forward.
• Similarly, while walking, you push the ground backward.
• The ground then exerts a reaction force on you in the forward direction.

Additional Information

• Newton: Sir Issac Newton was a great mathematician and physicist. who gave the law of motion and gravitation.
• Newton gave 3 laws of motion=
• A body at rest will remain at rest, and body in motion will remain in motion unless it is acted upon by an external force.
• The force acting on an object is equal to the mass of mass of that object times its acceleration, F=ma
• For every action, there is an equal and opposite reaction.

The logic followed here is:

Hence the correct answer is Option 2: 15859103

The correct answer is Rajasthan.

Key Points

• Kota previously known as Kotah, is a city in the southeast of the northern Indian state of Rajasthan.
• It is located about 240 kilometres (149 mi) south of the state capital, Jaipur, situated on the banks of Chambal River.
• The city of Kota was once the part of the erstwhile Rajput kingdom of Bundi. It became a separate princely state in the 16^th century.
• Apart from the several monuments that reflect the glory of the town, Kota is also known for its palaces and gardens.
• The city was also included among 98 Indian cities for Smart Cities Mission initiated by Indian Prime Minister Narendra Modi in 2015[1

The correct answer is Alluminum

Key Points

• Aluminum (blended with small quantities of other metals) is used on most types of aircraft because it is lightweight and strong. Aluminum alloys don't corrode as readily as steel. ..
• . It has also been used for the skin of some high-speed airplanes, because it holds its strength at higher temperatures better than aluminum.
• Because the metal resists corrosion, some airlines don't paint their planes, saving several hundred of kilograms in weight.Aircraft manufacturers use high-strength alloys (principally alloy 7075) to strengthen aluminium aircraft structures.

The logic followed here is:

Logic: Red, Blue, and Green are primary colors in the RGB color model which is widely used in digital displays. Given this analysis and usual categorizations, Pink stands out as it is not considered a primary color in the RGB color model, unlike Red, Blue, and Green.

Thus, the odd word is Pink.

Hence, the correct answer is "Pink".

The logic followed here is:

POLICE: GAKJQN

Similarly,

ARREST: ?

Hence, the correct answer is "VQGPTY".

The correct answer is Pallava dynasty.

Key Points

• The monuments were built during the Pallava dynasty.
• Known as the Seven Pagodas in many colonial-era publications, they are also called the Mamallapuram temples or Mahabalipuram temples in contemporary literature.
• The site, restored after 1960, has been managed by the Archaeological Survey of India.
• The Group of Monuments at Mahabalipuram is a collection of 7^th- and 8^th-century CE religious monuments in the coastal resort town of Mahabalipuram, Tamil Nadu, India and is a UNESCO World Heritage Site.
• It is on the Coromandel Coast of the Bay of Bengal, about 60 kilometres (37 mi) south of Chennai.
• The site has 40 ancient monuments and Hindu temples,including one of the largest open-air rock reliefs in the world: the Descent of the Ganges or Arjuna's Penance.
• The group contains several categories of monuments: ratha temples with monolithic processional chariots, built between 630 and 668; mandapa viharas (cave temples) with narratives from the Mahabharata and Shaivite, Shakti or Shaaktha and Vaishnava inscriptions in a number of Indian languages and scripts; rock reliefs (particularly bas-reliefs); stone-cut temples built between 695 and 722, and archaeological excavations dated to the 6^th century and earlier.

Given:

13 + 23 + 33 + ... + 103 = 3025

Calculation:

4 + 32 + 108 + ... + 4000

⇒ 4(1 + 8 + 27 + .....+ 1000)

⇒ 4(13 + 23 + 33 + ... + 103)

⇒ 4 × 3025 = 12100

∴ The correct answer is 12100.

The correct answer is President.

Key Points

• Article 61 of the Indian Constitution is the procedure for impeaching the President, as and when applicable. In such a case, either House of Parliament has the authority to prevent the President from being impeached.
• The Indian Constitution specifies a course of action to be taken if the President violates constitutional norms. In such a case, Article 61 of the Constitution empowers either House of Parliament to impeach the President
• When one House of Parliament prefers a charge, the other House must investigate the charge or cause it to be investigated. The President is entitled to attend the investigation and be represented.
• The President will be removed from office as of the date the resolution is so passed if, as a result of the investigation, a resolution is passed by a majority of not less than two-thirds of the entire membership of the House by which the charge was investigated or caused to be investigated, declaring that the charge preferred against the President has been sustained

Given:

A person's salary has been reduced by 10% and 20% twice in a row and the last time it has increased by 10% and it became Rs 9,900.

Concept Used:

Successive percentage changes can be calculated using the formula for successive percentage change.

Formula Used:

If a value is changed by x% and then by y%, the overall percentage change is given by:

Overall Change = (1 + x/100) × (1 + y/100) - 1

Calculation:

Let the original salary be Rs. S.

First Reduction:

⇒ Salary after 10% reduction = S × (1 - 10/100) = S × 0.90

Second Reduction:

⇒ Salary after 20% reduction = S × 0.90 × (1 - 20/100) = S × 0.90 × 0.80 = S × 0.72

Increase:

⇒ Salary after 10% increase = S × 0.72 × (1 + 10/100) = S × 0.72 × 1.10 = S × 0.792

Given that the final salary is Rs 9,900:

⇒ S × 0.792 = 9,900

⇒ S = 9,900 / 0.792

⇒ S = 12,500

Hence, the person's original salary was Rs 12500.

Given:

A tank is filled in 18 minutes by three tubes A, B, and C. After running all three tubes together for 6 minutes, tube C is stopped and the tank is filled by tubes A and B in 24 minutes.

Concept:

Work done by tubes A, B, and C together in 1 minute = 1/18

Work done by tubes A and B together in 1 minute = 1/24

Calculation:

⇒ Work done by A, B, and C together in 6 minutes = 6 × (1/18) = 1/3

⇒ Remaining work to be done by A and B = 1 - 1/3 = 2/3

⇒ Time taken by A and B to complete 2/3 of the work = 24 minutes

⇒ Work done by A and B together in 24 minutes = 2/3 × (1/24) = 1

⇒ Work done by A and B together in 1 minute = 1/36

⇒ Work done by C in 1 minute = (1/18) - (1/36)

⇒ Time taken by C alone to fill the tank = 1 / (1/36) = 36 minutes

∴ The correct answer is option 2 (36 minutes).

Given:

Buying a carriage with a horse for Rs 4000 makes a profit of 3.5% if the horse is sold at a profit of 20% and the carriage at a loss of 10%.

Concept:

To find the cost price of the horse, we need to set up equations based on the given profit and loss percentages and solve them.

Formula Used:

Profit Percentage = (Profit / Cost Price) × 100

Loss Percentage = (Loss / Cost Price) × 100

Calculation:

Let the cost price of the horse be Rs H and the cost price of the carriage be Rs C.

Given, H + C = 4000

Horse is sold at a profit of 20%:

⇒ Selling Price of Horse = H + 0.20H = 1.20H

Carriage is sold at a loss of 10%:

⇒ Selling Price of Carriage = C - 0.10C = 0.90C

Total Selling Price = 1.20H + 0.90C

Given, the total profit is 3.5%:

⇒ Total Selling Price = 4000 + 0.035 × 4000 = 4000 + 140 = 4140

We have the equation:

1.20H + 0.90C = 4140

We also have H + C = 4000

Solving these two equations:

From H + C = 4000, we get C = 4000 - H

Substitute C in the first equation:

⇒ 1.20H + 0.90(4000 - H) = 4140

⇒ 1.20H + 3600 - 0.90H = 4140

⇒ 0.30H = 540

⇒ H = 540 / 0.30

⇒ H = 1800

Hence, the cost price of the horse is Rs 1800.

∴ The correct answer is option 4.

The correct answer is 1971.

Key Points

• Independence of Bangladesh was declared on 26 March 1971, celebrated as Independence Day, from Pakistan.
• The Independence Day of Bangladesh is celebrated on 26 March when Sheikh Mujibur Rahman declared the independence of Bangladesh.
• The Bangladesh Liberation War started on 26 March and lasted till 16 December 1971 which is celebrated as Victory Day in Bangladesh.
• There is a dispute along partisan line on who declared the Independence of Bangladesh.
• The Awami League claim Sheikh Mujibur Rahman while the Bangladesh Nationalist Party claim it was Ziaur Rahman

The family tree can be drawn using the given information:

Here, we can see that Ram is the Paternal uncle's son of Rama.

Hence, the correct answer is "Paternal uncle's son".

The correct answer is KNO3.

Key Points

• KNO3 is a chemical compound with the chemical name Potassium Nitrate.
• Potassium nitrate also called saltpetre or nitre is a white solid soluble in water formed by fractional crystallisation of sodium nitrate and potassium chloride solutions.
• It is made from potassium chloride and a source of nitrate, such as sodium nitrate, ammonium nitrate, or nitric acid. Potassium nitrate is sold as a water-soluble, crystalline material for hydroponics and in a prilled form for soil applicatio

The correct answer is Uttarakhand.

Key Points

• Kedarnath is a town and Nagar Panchayat in Rudraprayag district of Uttarakhand, India, known primarily for the Kedarnath Temple.
• It is approximately 86 kilometres from Rudraprayag, the district headquarter.
• Kedarnath is the most remote of the four Chota Char Dham pilgrimage sites.
• It is located in the Himalayas, about 3,583 m (11,755 ft) above sea level near the Chorabari Glacier, which is the source of the Mandakini river.
• The town is flanked by snow-capped peaks, most prominently the Kedarnath Mountain.
• The nearest road head is at Gaurikund about 16 km away.
• The town suffered extensive destruction during June 2013 from the Flash Floods caused by torrential rains in Uttarakhand state

The letter P is the 16^th letter in the English alphabet. Counting 10 letters to the left of P: O (15), N (14), M (13), L (12), K (11), J (10), I (9), H (8), G (7), F (6). The 10^th letter to the left of P is F. 

The letter F is the 6^th letter in the English alphabet. Counting 13 letters to the right of F: G (7), H (8), I (9), J (10), K (11), L (12), M (13), N (14), O (15), P (16), Q (17), R (18), S (19). The 13^th letter to the right of F is S. 

So, the 13^th letter to the right of the 10^th letter to the left of P is S.

Hence, the correct answer is "S".

Given:

Sum (Principal + Interest) = Rs. 3540

Rate of Interest (R) = 6% per annum

Time (T) = 3 years

Concept:

In Simple Interest, the formula for Interest (I) is:

I = P × R × T / 100

Where P is the Principal amount.

Formula Used:

Sum (Principal + Interest) = Principal + (Principal × Rate × Time / 100)

Let Principal = P

3540 = P + (P × 6 × 3 / 100)

Calculation:

We have,

⇒ 3540 = P + (P × 18 / 100)

⇒ 3540 = P + 0.18P

⇒ 3540 = 1.18P

⇒ P = 3540 / 1.18

⇒ P ≈ 3000

Interest (I) = P × R × T / 100

⇒ I = 3000 × 6 × 3 / 100

⇒ I = 540

∴ The interest will be Rs. 540.

The correct answer is Prime Minister.

Key Points

• Foremost, Leader: This is the original meaning of the word, derived from the Persian word پیشوا (pēshwā) meaning "foremost, leader".
• It was used in various Persianate empires operating in the Deccan region of India before the rise of the Maratha Empir
• Chief Minister of the Maratha Empire: In the context of Indian history, Peshwa specifically refers to the title of the chief minister or Prime Minister of the Maratha Empire between 1674 and 1818.
• The Peshwa held immense power and often acted as the de facto ruler of the empire even while the titular Chhatrapati (emperor) remained in place.

According to the given direction,

1) My house is on the south side of the market and post office is on the east side of my house and the distance from my house to market and post office is equal.

2) I first went to the market and then started walking towards the post office, met my friend in the middle of the street and we decided we would go back home.

Here, we can see that now we are walking in south-west direction.

Hence, the correct answer is "South-West".

Given:

Average age of 6 members in a family is 25 years. Among them, the youngest member is 5 years old.

Concept:

To find the average age at the time of the youngest member's birth, we need to determine the total age of the family members at that time and then divide it by the number of members.

Formula Used:

Total age of family members = Average age × Number of members

Average age at the time of the youngest member's birth = (Total age of family members - Age of youngest member) / Number of members

Calculation:

We have,

⇒ Average age = 25 years

⇒ Number of members = 6

⇒ Youngest member's age = 5 years

⇒ Total age of family members = 25 × 6 = 150 years

⇒ Total age of family members at the time of the youngest member's birth = 150 - 5 = 145 years

⇒ Average age at the time of the youngest member's birth = 145 / 6

⇒ Average age at the time of the youngest member's birth ≈ 24.17 years

Since we are looking for the closest whole number, we approximate to 24 years.

∴ The average age of the members at the time of the youngest member's birth was 24 years.

The correct answer is South America.

Key Points

• The Andes Mountains line the western edge of South America, from Venezuela all the way along Chile to South America's southern tip, crossing through Ecuador, Peru, and Bolivia.
• There’s no other location on the surface of the Earth that is farther from the Earth’s centre than the peak of Chimborazo in the Ecuadorean Andes, located in Ecuador, Mount Chimborazo is a dormant volcano. It last erupted over 10 centuries ago.
• The Andes are the world's longest continental mountain range, about 9,000 km in all. They lie as a continuous chain of highlands along the western coast of South America, along that route, they cross through Ecuador, Peru, and Bolivia .

The given equation is: 2 < 4 > 3 ≠ 32 = 8 = 2 ≠ 3 > 4 < 2

The equation we get after replacing the signs: 2 + 4 - 3 × 32 ÷ 8 ÷ 2 × 3 - 4 + 2

→ 2 + 4 - 3 × 32 ÷ 8 ÷ 2 × 3 - 4 + 2

→ 2 + 4 - 3 × 2 × 3 - 4 + 2

→ 2 + 4 - 18 - 4 + 2

→ 8 - 18 - 4

→ - 10 - 4 = - 14

Hence, the correct answer is "- 14".

Calculation:

LCM of {8, 16, 40, 80} = 80

\(\frac{7}{{8}}\) = \(\frac{7\times10}{{8\times 10}}\) = \(\frac{70}{{80}}\)

\(\frac{13}{{16}}\)= \(\frac{13\times5}{{16\times5}}\) = \(\frac{65}{80}\)

\(\frac{31}{{40}}\) = \(\frac{31\times2}{{40\times2}}\) = \(\frac{62}{{80}}\)

\(\frac{63}{{80}}\)

Since, \(\frac{70}{{80}}\) is the largest fraction among these.

Thus, \(\frac{7}{{8}}\) is the largest fraction.

The correct answer is Cauliflower.

Key Points

• From the given options, cauliflower is not an example of an underground stem.
• Ginger: Ginger is a rhizome, which is a type of underground stem with horizontal growth and nodes where new shoots and roots can sprout.
• Potato: A Potato is a tuber, which is a swollen underground stem that stores food reserves.
• Amorphophallus campanulatus: This plant, also known as the corpse flower, has a corm, which is another type of underground stem that is solid and bulb-like shape.

Given:

Distance between two places: 50 km

Speed of first friend: 5 km/hr

Speed of second friend: 6 km/hr

Time traveled: 3 hours

Concept Used:

Relative speed is the sum of individual speeds when moving towards each other.

Formula Used:

Distance covered together = Relative speed × Time

Calculation:

⇒ Relative speed = 5 km/hr + 6 km/hr

⇒ Relative speed = 11 km/hr

⇒ Distance covered together in 3 hours = 11 km/hr × 3 hours

⇒ Distance covered together = 33 km

⇒ Distance remaining between them = 50 km - 33 km

⇒ Distance remaining = 17 km

∴ The correct answer is option 1 (17 km).

The correct answer is Vitamin D.

Key Points

• Vitamin D, first identified as a vitamin early in the 20^th century, is now recognized as a prohormone.
• The scientific name for Vitamin D is calciferol.
• The two major forms are vitamin D2 and vitamin D3.
• Vitamin D2 (ergocalciferol) is largely human-made and added to foods.
• vitamin D3 (cholecalciferol) is synthesized in the skin of humans and is also consumed in the diet via the intake of animal-based foods.
• It is a fat-soluble vitamin that plays a crucial role in several important bodily functions.

Additional InformationVitamins, Their Chemical Names And Deficiency Disease.

Given that:

Five boys A, B, C, D and E are sitting in a circle facing the centre. E sits between A and D, A sits to the right of B

As per the information given

So B and D are sitting on both sides of C.

Hence the correct answer is Option 2: B and D

The Logic followed here is: Sum of the positional values of the opposite alphabet​ according to English Alphabet series.

O(15) → opposite alphabet is L and is coded as 12.

Similarly,

Hence the correct answer is Option 4: 81

The correct answer is Mercury.

Key Points

• Mercury is a chemical element; it has the symbol Hg and atomic number 80.
• It is also known as quicksilver and was formerly named hydrargyrum
• Mercury: Mercury is the only metal that is liquid at room temperature. Its melting point is -38.8°C, meaning it's even liquid well below freezing.
• The ore of mercury is cinnabar.
• Mercury is used in thermometers, barometers, manometers, sphygmomanometers, float valves, mercury switches, mercury relays, fluorescent lamps and other devices.

Additional Information

• Silver: Silver has a melting point of 961°C, which is well above room temperature (25°C).
• The most important ore mineral of silver is argentite (Ag2S, silver sulfide). Silver is commonly extracted from ore by smelting or chemical leaching.
• Sodium: Sodium has a melting point of 97.7°C, also significantly higher than room temperature.
• It occurs abundantly in nature in compounds, especially common salt—sodium chloride (NaCl)
• Gold: Gold has a melting point of 1064°C, making it a solid at room temperature.
• usually found in nature in a comparatively pure form.

According to the given information,

Here, we can see that the code for 'leaf' is 2, and the code for 'is' is 4.

Hence, the correct answer is "2 and 4".

The correct answer is Cuttack.

Key Points

• Subhas Chandra Bose was born to Bengali parents Prabhavati Bose (née Dutt) and Janakinath Bose on 23 January 1897 in Cuttack—in what is today the state of Odisha in India, but was then part of the Bengal Presidency in British India.
• Subhas Bose was born into wealth and privilege in a large Bengali family in Orissa during the British Raj.
• The early recipient of an Anglocentric education, he was sent after college to England to take the Indian Civil Service examination.
• He stood for unqualified swaraj (independence), and opposed the Motilal Nehru Report which spoke for dominion status for India.
• He actively participated in the Salt Satyagraha of 1930 and vehemently opposed the suspension of Civil Disobedience Movement and signing of the Gandhi-Irwin Pact in 1931.
• In the 1930s, he was closely associated with left politics in Congress along with Jawaharlal Nehru and M.N. Roy.
• Bose won the congress presidential elections at Haripura in 1938.
• Again in 1939 at Tripuri, he won the presidential elections against Gandhi's candidate Pattabhi Sitarammayya. Due to ideological differences with Gandhi, Bose resigned and left congress. Rajendra Prasad was appointed in his place.
• He founded a new party, 'the Forward Bloc'. The purpose was to consolidate the political left and major support base in his home state Bengal.

The correct answer is Namibia.

Key Points

• Recently Prime Minister, Shri Narendra Modi released wild Cheetahs which had become extinct in India - in Kuno National Park. Cheetahs brought from Namibia - are being introduced in India under Project Cheetah, which is the world's first inter-continental large wild carnivore translocation project. Out of the eight Cheetahs, there are five female and three male Cheetahs.
• The release of wild Cheetahs by the Prime Minister in Kuno National Park is part of his efforts to revitalise and diversify India’s wildlife and its habitat.
• The Cheetah was declared extinct from India in 1952. The Cheetahs that would be released are from Namibia and have been brought under an MoU signed earlier this year.
• The introduction of Cheetah in India is being done under Project Cheetah, the world’s first inter-continental large wild carnivore translocation project.

The pattern followed here is:

Hence the correct answer is Option 3: bbabaa

The correct answer is Air.

Key Points

• Loesses are homogeneous; porous; friable; pale yellow or buff; slightly coherent; typically, non-stratified; and often calcareous.
• Loess grains are angular, with little polishing or rounding, and composed of quartz, feldspar, mica, or other mineral crystals. Loesses have been described as rich, dust-like soil
• Loess deposits may become very thick: at more than a hundred meters in areas of Northwestern China and tens of meters in parts of the Midwestern United States.
• Loesses generally occur as blanket deposits that cover hundreds of square kilometres. The deposits are often tens of meters thick. Loesses often have steep or vertical faces
• In several areas of the world, loess ridges have formed that had been aligned with the prevailing winds during the last glacial maximum.
• These are called "paha ridges" in America and "greda ridges" in Europe. The formation of these loess dunes has been explained as a combination of wind and tundra conditions.

Given:

Average income of A and B is Rs.3300. The average income of B and C is Rs 3000 and the average income of A and C is Rs 2700.

Solution:

Sum of A and B Income = 3300 × 2 = 6600

Sum of B and C Income = 3000 × 2 = 6000

Sum of A and C Income = 2700 × 2 = 5400

⇒ 2(A + B + C) = 18000

⇒ A + B + C = 9000

Average of A, B and C = 9000/3 = 3000

The average income of these three people is Rs. 3000

∴ The average income of these three people is 3000.

Given:

8a3 - (pb)3 = (2a - 3b) (4a2 + 6ab + 9b2)

Formula used:

a³ - b³ = (a -b)(a² + ab + b2)

Calculation:

(2a - 3b) (4a2 + 6ab + 9b2)

⇒ (2a - 3b) [(2a)2 + 2a × 3b + (3b)2]

⇒ (2a)³ - (3b)³

⇒ 8a3 - (3b)3 =  8a3 - (pb)³

So, p = 3

∴ The correct answer is option (2).

The correct answer is Anthracite.

Key Points

• Coal is a fossil fuel that mainly contains carbon.
• It is formed by the decay of vegetation that existed millions of years ago.
• The best quality of coal is Anthracite.
• “Anthracite is the highest rank of coal.”
• It is a hard/brittle/black lustrous coal, also known as hard coal.
• It has the highest percentage of carbon i.e. 92%-98%

 and a low percentage of volatile matter.

• It ignites slowly with a blue flame.

Additional Information

• Bituminous- It is the most widely available coal in India. It is of medium quality. It contains about 40 to 75 per cent carbon. In India, much of the coal comes under this category.
• Lignite- It is of low quality. It is brown. It contains about 30 to 40 per cent coal.
• Peat- It is the middle stage in the process of coal formation. It contains less than 40 per cent carbon. It has more impurities. The parts of the wood are remarkably present in it.

Given:

5 years ago, the ratio of ages of A and B was 6 ∶ 7.

After 5 years, the ratio of their ages will be 8 ∶ 9.

Concept:

Let the ages of A and B 5 years ago be 6x and 7x respectively.

Hence, the present age of A is (6x + 5) and B is (7x + 5).

Formula Used:

After 5 years, their ages will be (6x + 10) and (7x + 10) respectively.

The new ratio given is 8 ∶ 9.

Calculation:

We have,

⇒ (6x + 10)/(7x + 10) = 8/9

⇒ 9(6x + 10) = 8(7x + 10)

⇒ 54x + 90 = 56x + 80

⇒ 56x - 54x = 90 - 80

⇒ 2x = 10

⇒ x = 5

Hence, the present age of A is:

⇒ 6x + 5 = 6(5) + 5 = 30 + 5 = 35

∴ The present age of A is 35 years, which corresponds to option 2.

Given:

In a joint business, the capitals of A, B, and C are in the ratio \(\dfrac{1}{4}\) ∶ \(\dfrac{1}{3}\) ∶ \(\dfrac{1}{2}\).

At the end of the year, they make a profit of Rs. 11700.

Concept used:

Ratio of investments is the same as the ratio of profits or losses.

Calculation:

The capitals of A, B, and C are in the ratio  \(\dfrac{1}{4}\) ∶ \(\dfrac{1}{3}\) ∶ \(\dfrac{1}{2}\) = 3 : 4 : 6.

∴ The ratio of profit = 3 : 4 : 6

Let the profits of A, B, and C be 3x, 4x and 6x respectively.

Total profit = Rs. 11700

∴ Profit of B = \(11700\times \dfrac{4x}{13x} \) = Rs. 3600

Hence, the profit of B is Rs. 3600.

The given word is: MEDITERRANEAN

Now, let's check each option,

1) READER → Can be formed.

2. ARRANGE → Cannot be formed (Because there is no 'G' in MEDITERRANEAN)

3. DINNER → Can be formed.

4. MEDIATE → Can be formed.

Hence, the correct answer is "ARRANGE".

Given:

10 cows or 7 buffaloes can gaze a field in 60 days working 8 hours a day.

We need to find the number of days required for 25 cows and 14 buffaloes working 12 hours a day to do 9 times their work.

Concept:

Work done is directly proportional to the number of animals and the number of hours worked.

If W is the work done by one cow in one hour, then 10 cows work in 60 days for 8 hours each day is:

Formula Used:

Total Work = Number of Animals × Number of Days × Number of Hours

Calculation:

We have,

⇒ 10 cows × 60 days × 8 hours = 4800 cow-hours

Similarly,

⇒ 7 buffaloes × 60 days × 8 hours = 3360 buffalo-hours

Assuming 1 buffalo = (4800 cow-hours) / (3360 buffalo-hours) = 1.428 cows

Now, for 25 cows and 14 buffaloes working 12 hours a day to do 9 times the work:

Total equivalent cows = 25 cows + 14 buffaloes × 1.428 = 25 + 20 = 45 cows

Total work required = 9 × 4800 cow-hours = 43200 cow-hours

Let the number of days required be D. Then,

⇒ 45 cows × D days × 12 hours = 43200 cow-hours

⇒ 540D = 43200

⇒ D = 43200 / 540

⇒ D = 80

∴ The number of days required is 80.

Hence, the correct answer is option 1.

The correct answer is ​Regelation

Key Points

• Regelation is defined as the phenomenon in which the ice melts to the water below 0°C on the application of pressure and refreezes back to ice on the removal of pressure.
• Regelation demonstrates the idea of compressing the ice and turning it into water under pressure and when the pressure is removed, it solidifies again.

Other Examples

• Glacier acts as a source of a river due to regelation. The mass of the glacier exerts pressure on the lower surface lowering the melting point of the ice at its base. This results in the melting of ice and propels the glacier to slide over the liquid. Under appropriate conditions, liquid water flows from the base of the glacier to lower altitudes when the temperature of the air is above the freezing point of water.

The logic followed here is:

Logic: The resultant is the product of the sum of digits of both numbers.

324 × 150 = 54

→ (3 + 2 + 4) = 9

→ (1 + 5 + 0) = 6

Resultant = 9 × 6 = 54

251 × 402 = 48

→ (2 + 5 + 1) = 8

→ (4 + 0 + 2) = 6

Resultant = 8 × 6 = 48

Similarly,

735 × 866 = ?

→ (7 + 3 + 5) = 15

→ (8 + 6 + 6) = 20

Resultant = 15 × 20 = 300

Hence, the correct answer is "300".

Given:

Product of HCF and LCM of two numbers = 24

Subtraction of the two numbers = 2

Concept:

If two numbers are a and b, then HCF(a, b) × LCM(a, b) = a × b

Given, a - b = 2

Calculation:

⇒ Let the two numbers be a and b, and a > b

⇒ a - b = 2

⇒ HCF(a, b) × LCM(a, b) = a × b

⇒ 24 = a × b

⇒ Since a - b = 2, let b = x and a = x + 2

⇒ (x + 2) × x = 24

⇒ x² + 2x = 24

⇒ x² + 2x - 24 = 0

⇒ Solving the quadratic equation:

⇒ x = [-2 ± √(2² - 4×1×(-24))] / 2×1

⇒ x = [-2 ± √(4 + 96)] / 2

⇒ x = [-2 ± √100] / 2

⇒ x = [-2 ± 10] / 2

⇒ x = 4 (since x must be positive)

⇒ Therefore, b = 4 and a = 4 + 2 = 6

∴ The larger number is 6.

Calculation:

(0.5)² = 0.25

\(\sqrt {0 \cdot 49} \) = \(\sqrt {0.7\times0.7} \) = 0.7

\(\sqrt[3]{{0 \cdot 008}}\) = \(\sqrt[3]{0.2\times0.2\times0.2}\) = 0.2

0.23

Here, 0.2 is the least value among all of them.

Thus, \(\sqrt[3]{{0 \cdot 008}}\) is the least value.

∴ The correct answer is option(4).

The correct answer is Refraction

Key Points

• When a fish is underwater and you observe it from above the water surface, the apparent position of the fish appears closer to the surface than its actual position.
• When light travels from one medium (such as water) to another (such as air), it changes direction due to refraction.
• This phenomenon occurs because light travels at different speeds in different materials.
• The refractive index (or index of refraction) describes how fast light travels through a material.

Additional Information

 Diffraction:

• Diffraction involves the interference or bending of light around the corners of an obstacle or through an aperture into the region of geometrical shadow created by the obstacle or aperture.
• In classical physics, diffraction is described by the Huygens–Fresnel principle, which treats each point in a propagating wavefront as a collection of individual spherical wavelets.

Total Internal Reflection:

• Total internal reflection occurs when light rays travel from a more optically dense medium (like water) to a less optically dense medium (like air) and are reflected back at the surface of the denser medium.
• The angle of incidence must be greater than the critical angle .

Reflection:

• Reflection involves the change in direction of a light ray at an interface between two different media so that the ray returns to the medium from which it originated.
• The laws of reflection determine how incident light rays behave on reflecting surfaces, such as mirrors, smooth metal surfaces, and clear water:
• The incident ray, the reflected ray, and the normal all lie in the same plane.
• The angle of incidence (the angle between the incident ray and the normal) equals the angle of reflection (the angle between the reflected ray and the normal).

The correct answer is Eichhornia crassipes.

Key Points

• Breathing roots are the modified roots which are also called pneumatophores.
• Eichhornia crassipes medical function -Water hyacinth is reported to have anti-inflammatory, antifungal, and antibacterial functions.

Additional Information

• Examples of plants with breathing roots are banyan, money plants, rubber plants, ficus, peepal tree, pakad tree, and many more.

The logic followed here is:

2, 7, 13, 23, 34, 47 →Except 34 all other numbers are prime numbers.

Hence the correct answer is 34.

Additional Information Prime number - The number that is divisible by only 1 and itself.

**Given:**

Question: How many faces does a triangular prism have?

Options: 1) 6, 2) 4, 3) 3, 4) 5

Correct Option: 4

**Concept:**

A triangular prism is a 3-dimensional solid shape with two parallel and congruent triangular bases and three rectangular faces joining them.

**Calculation:**

We need to find the total number of faces of a triangular prism.

⇒ A triangular prism has:

⇒ 2 triangular faces (one at the base and one on top)

⇒ 3 rectangular faces joining the sides of the triangles

⇒ Total faces = 2 (triangular) + 3 (rectangular)

⇒ Total faces = 5

**Hence, the triangular prism has 5 faces.**

``` Explanation: - **Given**: Summarizes the key data from the question. - **Concept**: Describes the main concept needed to solve the problem. - **Calculation**: Provides a step-by-step solution to the problem, using arrows (⇒) to start each step. - **Conclusion**: Summarizes the result with "Hence" and states the final answer.

Given:

The product of two digits of a two-digit number is 12. Adding 36 to the number the digits interchange their place.

Concept:

Let the two-digit number be 10a + b, where 'a' and 'b' are the digits.

Given, ab = 12 and 10a + b + 36 = 10b + a

Calculation:

We have,

⇒ ab = 12

⇒ 10a + b + 36 = 10b + a

⇒ 9a - 9b = -36

⇒ a - b = -4

Now, solve the equations:

From ab = 12, we get possible pairs (a, b) as (2, 6) or (6, 2).

Check each pair:

For (a, b) = (2, 6):

⇒ a - b = 2 - 6 = -4 (valid)

For (a, b) = (4, 3):

⇒ a - b = 6 - 2 = 4 (not valid)

Hence, the number is 23 (since 10a + b = 10×2 + 6 = 26).

∴ The correct answer is option 4 (26).

Formula used:

a³ + b³ = (a + b)(a² + b² - ab)

Calculation: 

\(\frac{{8 \cdot 73 × 8 \cdot 73 × 8 \cdot 73 + 4 \cdot 27 × 4 \cdot 27 × 4 \cdot 27}}{{8 \cdot 73 × 8 \cdot 73 - 8 \cdot 73 × 4 \cdot 27 + 4 \cdot 27 × 4 \cdot 27}}\)

⇒ (8.73)³ + (4.27)³ / [(8.73)2 + (4.27)2 - 8.73 × 4.27]

⇒ (8.73 + 4.27)[(8.73)2 + (4.27)2 - 8.73 × 4.27] / [(8.73)2 + (4.27)2 - 8.73 × 4.27]

⇒ (8.73 + 4.27) = 13

∴ The correct answer is 13.