The logic followed here is:-

1) 4174 → 4 + 1 + 7 + 4 = 16 ⇒ Even

2) 5459 → 5 + 4 + 5 + 9 = 23 ⇒ Odd

3) 2126 → 2 + 1 + 2 + 6 = 11 ⇒ Odd

4) 9637 → 9 + 6 + 3 + 7 = 25 ⇒ Odd

∴ Here, '4174' is different from other three alternatives.

Hence, the correct answer is "4174".

Alternate Method The logic followed here is:-

The first number × the Last(fourth) number gives the middle two numbers.

4174 → 4 × 4 = 16 ≠ 17,

5459 → 5 × 9 = 45

2126 → 2 × 6 = 12

9637 → 9 × 7 = 63

So, '4174' is different from other three alternatives.

The logic followed here is :-

The prime number between 1 to 50 are :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

• There are two prime numbers in between the given pairs.

Hence, the correct answer is "19".

The correct answer is Chlorophyll, sunlight, carbon dioxide, and water.

Key Points

• Photosynthesis is the process by which plants use sunlight, water, and carbon dioxide to create oxygen and energy in the form of sugar.
• Steps of photosynthesis:

1. CO2 and H2O enter the leaf.
2. Light hits the pigment in the membrane of a thylakoid, splitting the H2O into O2.
3. The electrons move down to enzymes.
4. Sunlight hits the second pigment molecule allowing the enzymes to convert ADP to ATP and NADP+ gets converted to NADPH.
5. The ATP and NADPH are used by the Calvin cycle as a power source for converting carbon dioxide from the atmosphere into simple sugar glucose.
6. The Calvin cycle converts 3CO2 molecules from the atmosphere to glucose.
7. The second of two major stages in photosynthesis (following the light reactions), involves atmospheric CO2 fixation and reduction of the fixed carbon into carbohydrates.

Additional Information

• There are three main types of photosynthetic pathways: C3, C4, and CAM. They all produce sugars from CO2 using the Calvin cycle, but each pathway is slightly different.
• Green plants and trees use photosynthesis to make food from sunlight, carbon dioxide and water in the atmosphere:
• It is their primary source of energy.
• The importance of photosynthesis in our life is the oxygen it produces.
• Without photosynthesis, there would be little to no oxygen on the planet.

CONCEPT USED:

Highest Common Factor(H.C.F)

CALCULATION:

Here, the length of the three pieces given is 48m, 56m, and 72 m respectively

⇒Greatest possible length of each plank = H.C.F (48, 56, 72) 

Prime factorization:

48 = 2 × 2 × 2 × 2 × 3 

56 = 2 × 2 × 2 × 7 

72 = 2 × 2 × 2 × 3 × 3 

⇒ H.C.F = Product of  the smallest power of each common prime factor involved in the numbers = 2 × 2 × 2  = 8

Hence, the greatest possible length of each plank is 8 m.

GIVEN:

Cost price of some toffee at the rate of 15 toffees = Rs. 3 

Selling price of some toffee at the rate of 3 toffee = Rs. 2 

FORMULA USED:

Gain percent = (Gain/C.P.) × 100 

Gain = (S.P. - C.-P.)

Where, S.P. = Selling Price  C.P.= Cost price.

CALCULATION:

Let us assume the person buys 45 toffees 

(you can assume any number but for the sake of calculation, we have taken L.C.M of 15 and 3)

⇒ C.P. of 15 toffees =  Rs. 3

⇒ C.P. of 45 toffees = ( 3/15) × 45 =  Rs. 9

⇒ S.P. of 3 toffee =  Rs. 2

⇒ S.P. of 45 toffees = (2/3) × 45  = Rs. 30

⇒ Gain = (S.P. - C.P.) = (30 - 9 ) = Rs. 21

⇒ Gain% = (Gain/C.P.) × 100 = (21/ 9) × 100  = 700/3 = 233 $\frac{1}{3}$% gain

Hence, gain% is 233$\frac{1}{3}$%.

The mirror image of the given figure is as shown below :

∴ Here, the figure D is the mirror image of given figure.

Hence, the correct answer is "D".

Confusion Points

The Water image of the given figure is as shown below :

CONCEPT USED:

Place value =  value of each digit in a number 

CALCULATION:

Here, the given number is 71,624 

⇒ Place value of 7  in 71,624 = 70,000  ( as place value represents a digit in a number on the basis of its position in the number).

Hence, the place value is 70,000.

The correct answer is Half a byte.

Key Points

• Nibble is also known as half-byte or trade and has sixteen possible values represented by a hex digit.
• It is used to state the memory consumption to store a digit in packed decimal format within an IBM mainframe to enhance the computation and the process of debugging.
• In a networking or telecommunication context, the nibble is often called a semi-octet, quadbit, or quartet. A nibble has sixteen possible values.

Additional Information

 Unit Conversion Table

• 4 bit = 1 Nibble
• 8 bit = 1 byte
• 1 KB (kilobyte) = 1024 byte
• 1 MB (megabyte) = 1024 KB
• 1 GB (gigabyte) = 1024 MB
• 1 TB (terabyte) = 1024 GB
• 1 PB (petabyte) = 1024 TB
• 1 XB (Exabyte) = 1024 PB
• 1 ZB (zettabyte) = 1024 XB
• 1 YB (yottabyte) = 1024 ZB

GIVEN:

Salary of A =  25% more than that of B 

CALCULATION:

Let us assume B's salary to be 100

⇒ Here, the Salary of A = 25% more than that of B 

⇒ Salary of A =  100 + 100 × 25/100 = 125 

⇒ Now, Salary of B lower than that of A = (Difference of A - Difference of B) = ( 125 - 100 ) = 25 

⇒ Required percent = (25/125) × 100 = 20% 

Hence, the required percentage is 20%.

The correct answer is Vikram Sarabhai.

Key Points

• The Indian Space Research Organisation is the national space agency of India.
• It's headquartered in Bangalore.
• It operates under the Department of Space which is directly overseen by the Prime Minister of India, while the Chairman of ISRO acts as the executive of DOS as well.
• Dr. Vikram Sarabhai, the founding father of the Indian space program, quickly recognized the benefits of space technologies for India.
• Vikram Ambalal Sarabhai was an Indian physicist and astronomer who initiated space research and helped develop nuclear power in India.
• He was honoured with Padma Bhushan in 1966 and the Padma Vibhushan in 1972.

Additional Information

• ISRO was formed in 1969 with a vision to develop and harness space technology in national development while pursuing planetary exploration and space science research.
• It is one of the elite space agencies in the world over the years.
• The major ISRO achievements of 2021:
• PSLV-C51/Amazonia-1
• Indian student satellites UNITYsat and Satish Dhawan SAT (SDSAT)
• GSLV-F10/Gisat-1 (renamed to EOS-3): Failed mission.

CALCULATION:

Let the required number be x 

⇒ Hence, we have x % of 50 = 40 

⇒ x/100 × 50 = 40 

⇒ x = 80 .

Hence, 80% of 50 = 40.

GIVEN:

In mathematics = 70% marks

In science = 60% marks

CALCULATION:

Here, we have equal maximum marks

 Hence, let us assume equal maximum marks in both subjects to be 100 

 Sachin secures 70% marks in mathematics = 70/100 × 100 (as maximum marks is 100 ) = 70 marks

 Sachin secures 60% marks in Science = 60/100 × 100 (as maximum marks is 100 ) = 60 marks

 Total maximum marks = 100 + 100 = 200 

 Total marks secured by Sachin in both the subjects together = 70 + 60 = 130

 Percentage of marks secured by Sachin in both the subjects together =(130/200) × 100 = 65%.

 The percentage of marks secured by Sachin in both subjects together is 65%.

CALCULATION:

Let us assume,

x/5 = y/6 = z/11 = k 

⇒ x = 5k,  y = 6k, z = 11k 

⇒ x + y + z = ( 5k + 6k + 11k ) =  22k

⇒ Hence, ( x + y + z ) / z = 22k/ 11k = 2 

Hence, the required value is 2.

The correct answer is Bombay (now Mumbai).

Key Points

• Aruna Asaf Ali
• Aruna Asaf Ali was born on July 16, 1909, into a Bengali Brahmin family in Kalka, Punjab, British India (now in the Indian state of Haryana).
• She was a publisher, political activist, and educator from India.
• She was an ardent member of the fight for Indian independence, and she is well known for hosting the Indian National flag at the Gowalia Tank Maidan in Bombay in 1942, during the Quit India Movement.
• In the Indian Independence Movement, Aruna Asaf Ali played a significant role.
• After getting married to Asaf Ali, she joined the Indian National Congress and took part in the Salt Satyagraha's public processions.
• She was imprisoned in 1931 in violation of the Gandhi-Irwin Pact, which called for the release of all political prisoners, since she was accused of being a wanderer.

Additional Information

• Quit India Movement
• On August 8, 1942, during World War II, Mahatma Gandhi began the August Kranti Movement, also known as the Quit India Movement, calling for the end of British rule in India at the Bombay session of the All India Congress Committee.
• Gandhi issued a call to Do or Die in his Quit India address.
• Gandhi's "An Orderly British Withdrawal" from India was the demand of the All India Congress Committee, which organised the massive demonstration.
• Within hours of Gandhi's speech, virtually the entire Indian National Congress leadership was detained without charge.
• The Golden Jubilee of the Quit India Movement was commemorated in 1992 by the Reserve Bank of India by issuing a one rupee commemorative coin.

GIVEN:

A and B finish work in 20 days

A is twice as efficient as B 

FORMULA USED:

Efficiency = Total work/  No. of days

CALCULATION:

Here, A's efficiency = 2 B's efficiency 

⇒ A's efficiency/ B's efficiency = 2/1  ⇔ Total efficiencies taken together by A and B = (2 + 1) = 3

⇒ No. of days taken together by A and B = 20 days 

⇒  Total work = Efficiency × No. of days =  3 ×  20 = 60 unit.,

⇒ A alone can finish the work in = Total unit of work/ Efficiency =  60/2 = 30 days. ( as  Efficiency of A = 2 )

A alone can finish the work in 30 days.

The correct answer is Virus attack.

Key Points

• A Trojan Horse Virus is a type of malware that downloads onto a computer disguised as a legitimate program.
• The delivery method typically sees an attacker use social engineering to hide malicious code within legitimate software to try and gain users' system access with their software.
• A computer virus is a type of malicious software, or malware, that spreads between computers and causes damage to data and software.
• Computer viruses aim to disrupt systems, cause major operational issues, and result in data loss and leakage.

Additional Information

• The Slammer worm exploits the stack buffer overflow vulnerability in a pair of functions offered by the SQL Server Resolution Service.
• Melissa worm It then used a macro to hijack their Microsoft Outlook email system and send messages to the first 50 addresses in their mailing lists.
• A Denial-of-Service (DoS) attack is an attack meant to shut down a machine or network, making it inaccessible to its intended users.

CONCEPT USED:

Lowest Common Multiple (L.C.M) = Smallest positive integer that is divisible by both a and b.

CALCULATION:

L.C.M. of 7,14,28,35 and 42 

⇒Prime factorization 

7 = 7 × 1

14 = 7 × 2 × 1 

28 = 2 × 2 × 7 × 1 = 2² × 7 × 1 

35 = 5 × 7 × 1 

42 = 2 × 3 × 7 × 1 

⇒ L.C.M = Product of all factors in the greatest number of their occurrence = 7 × 2² × 5 × 3 =  420. ( as  prime factors of 5, 7, 3  occur one time while 2 occurs more than once) 

Hence,  the smallest number is 420.

The correct answer is Chand Bibi.

Key Points

• Sultana Chand Bibi was an Indian ruler and warrior.
• She acted as the Regent of Bijapur Sultanate during the minority of Ibrahim Adil Shah II in 1580-1590, and regent of Ahmednagar Sultanate during the minority of her great nephew Bahadur Shah in 1595-1600.
• She was born in 1550 in Ahmadnagar Sultanate and died in1599 in Ahmednagar
• Chand Bibi was a contemporary of Emperor Akbar, well known as the heroic defender of Ahmadnagar against the Mughal forces of Emperor Akbar in 1595.
• Due to her heroic defense, Chand Bibi came to be known as “Chand Sultana”.

Additional Information

• Razia Sultana was the first woman Sultanate of India and ruled the court of Delhi from the end of 1236 to 1240. The only ever woman to do so, she defied all odds to occupy the throne, including overcoming conflicts over her gender and her slave ancestry.
• Rani Durgavati was the ruling Queen of Gondwana from 1550 until 1564. She was born in the family of Chandel Rajput king Salibahan at the fort of Mahoba. She was married to Dalpat Shah Kacchwaha, the adopted son of king Sangram Shah of the Garha Kingdom.
• Rani Roopmati was a poet and the consort of the Sultan of Malwa, Baz Bahadur. Roopmati features prominently in the folklores of Malwa, which talk about the love between the Sultan and Roopmati. Adham Khan was prompted to conquer Mandu partly due to Roopmati's beauty.

The logic followed here is :-

∴ Here, Dog : Bark (Dog's sound) has given in option which is different from other three alternatives.

Hence, the correct answer is "Dog : Bark".

The correct answer is Faizpur.

Key Points

• The Fiftieth (50^th) Session of the Indian National Congress was held between 26 to 28 December 1936 at Faizpur.
• It was the first congress session to be held in a village.
• A large number of peasants (Almost 40,000) participated in the session.
• Dhanajinana Choudhari and Sane Guruji played an important role in organizing this session.
• The Faizpur Session was important for the Congress which had been raising demands for the welfare of the peasants.
• The Faizpur Session was also important because it was presided over by Jawaharlal Nehru who was at his peak of influence in Congress.

Additional Information

• The Indian National Congress is colloquially the Congress Party but often simply the Congress.
• It is a political party in India with widespread roots.
• It was founded in 1885.
• it was the first modern nationalist movement to emerge in the British Empire in Asia and Africa.

The correct answer is Central.

Key Points.

• A unitary government is often described as a centralized government.
• All powers held by the government belong to a single, central agency.
• The central (national) government creates local units of government for its convenience.
• A unitary government is one in which all the powers of administration are vested in a single centre.
• The centre is omnipotent.

Additional Information

• Countries with a unitary system include the United Kingdom, Japan, and Saudi Arabia.
• Countries with much larger regions, such as the United States, usually have federal systems of government.
• A unitary state may be divided into small units for the sake of administrative convenience but the units do not have any constitutional status of their own

GIVEN:

A and B together dig a tank = 12 days

A alone dig = 24 days 

FORMULA USED:

Efficiency = Total work /No. of days

CALCULATION:

Let us assume total work done be 24 unit

( you can assume any number but for the sake of calculation, it is advised to take the L.C.M of the given numbers .Here, the given numbers are 12 and 24 and hence, the required L.C.M is 24 )

⇒ No. of days taken by A and B together = 12 days

⇒ Now, Efficiency of both A and B = Total unit of work done/ No. of days  = 24/12 = 2 uniit/day

A alone takes 24 days to dig

⇒ Efficiency of A = 24/24 = 1unit/day

Now, Efficiency of B =  ( Efficiency of A and B - Efficiency of A ) = ( 2 - 1) = 1 unit/day 

⇒  Hence, B can dig a tank = 24/ 1 = 24 days

⇒ In 24 days, B can dig a tank 

⇒ In 1 day B can dig = 1/24 

Hence, B can dig 1/24 of the tank in 1 day.

The correct answer is 1857.

Key Points

• Tantia Tope's original name is Ramchandra Panduranga.
• He was born in1813 in Pune, India, and died on April 18, 1859, in Shivpuri.
• He was a leader of the Indian Mutiny of 1857–58.
• Although he had no formal military training, he was probably the best and most effective of the rebels' generals.

Additional Information

• The Indian Rebellion of 1857 was a major uprising in India in 1857–58 against the rule of the British East India Company, which functioned as a sovereign power on behalf of the British Crown.
• The rebellion began when sepoys refused to use new rifle cartridges, which were thought to be lubricated with grease containing a mixture of pigs' and cows' lard and thus religiously impure for Muslims and Hindus.
• It was begun in Meerut by Indian troops (sepoys) in the service of the British East India Company, it spread to Delhi, Agra, Kanpur, and Lucknow.

GIVEN:

X and Y completes work = 16 days

Y and Z completes work = 24 days 

X, Y and Z together completes work = 12 days

FORMULA USED:

Efficiency = Total work done/ No. of days

CALCULATION:

Let us assume the total work done be 48 unit

( you  can assume any number , but for the sake of calculation, it is advised to take the L.C.M of the given numbers. Here L.C.M of 16, 24 and 12 = 48 )

As X and Y  completes the work = 16 days

⇒ Efficiency of X and Y = 48/16 = 3 unit/ day

Now, Y and Z completes the work = 24 days

⇒ Efficiency of Y and Z = 48/24 = 2 unit/ day

Now, As X,Y and Z completes the work together  = 12 days

⇒ Efficiency of X,Y and Z = 48/12 = 4 unit/day

Now, Efficiency of X =( Efficiency of X,Y and Z - Efficiency of Y  and Z ) = ( 4 - 2 ) = 2 unit/day

     Efficiency of Z  = ( Efficiency of X,Y and Z - Efficiency of X and Y ) = ( 4 - 3) = 1 unit/day

⇒ Total Efficiencies of X and Z = ( 2 +1) = 3 unit / day

Since, total work = 48 unit

⇒ No. of days taken by X and Z to complete the work = 48/3 = 16 days.

Hence, X and Z takes 16 days to finish the work.

The correct answer is Ethiopia.

Key Points

• The Ethiopian Empire, also known as Abyssinia.
• It was a kingdom that spanned a geographical area in the current state of Ethiopia.
• It began with the establishment of the Solomonic dynasty in approximately 1270 and lasted until 1974.
• When the ruling Solomonic dynasty was overthrown in a coup d'état by the Derg.

Additional Information

• The Solomonid dynasty founded the medieval Kingdom of Abyssinia.
• It was founded in 1270 CE.
• Their first ruler was Yekuno-Amlak (r. 1270-1285 CE), a local leader at Amhara.

The correct answer is Halite.

Key Points

• Halite commonly known as rock salt, is a type of salt, the **mineral (**natural) form of sodium chloride (NaCl).
• Halite forms isometric crystals.
• Halite is mainly a sedimentary mineral that usually forms in arid climates where ocean water evaporates.
• Salt is widely used in cooking as a taste enhancer and in the curing of a number of foods, including bacon and fish.

Additional Information

• Limonite is a general term for a mixture of fine-grained iron oxides, generally dominated by goethite, but also possibly containing hematite, lepidocrocite, and other minerals.
• Hematite, also spelt haematite, heavy and relatively hard oxide mineral, ferric oxide (Fe2O3), that constitutes the most important iron ore because of its high iron content (70 per cent) and its abundance.
• Siderite, also called chalybite, is an iron carbonate (FeCO3), a widespread mineral that is iron ore. The mineral commonly occurs in thin beds with shales, clay, or coal seams (sedimentary deposits) and in hydrothermal metallic veins (gangue, or waste rock).

The correct answer is simple permanent.

Key Points

• Permanent tissues are derived from meristematic tissue once they lose the ability to divide.
• They are classified as simple and complex tissues.
• Parenchyma, collenchyma, and sclerenchyma are three types of simple tissues.
• Parenchyma tissue is involved in photosynthesis, secretion, food storage, and other activities of plant life.
• Collenchyma tissue provides support, structure, mechanical strength, and flexibility to the petiole, leaf veins, and stem of young plants, allowing for easy bending without breakage.
• Sclerenchyma is one of the three types of ground, or fundamental, tissue in plants; the other two types are parenchyma (living thin-walled tissue) and collenchyma (living support tissue with irregular walls).

Additional Information

• Vascular tissue is comprised of the xylem and the phloem, the main transport systems of plants. They typically occur together in vascular bundles in all plant organs, traversing roots, stems, and leaves.
• Nervous tissue is found in the brain, spinal cord, and nerves. It is responsible for coordinating and controlling many body activities. It stimulates muscle contraction, creates an awareness of the environment, and plays a major role in emotions, memory, and reasoning.
• The tissue system that gives mechanical support to the whole plant and its growing organs against different external and internal forces is called the mechanical tissue system.

The logic followed here is :-

∴ Here, 'Cricket' is played by maximum number of players.

Hence, the correct answer is "Cricket".

GIVEN:

Time = 12 years

Amount = Sum of money double

FORMULA USED:

S.I. =( P × R × T) /100 

Amount = S.I. + P 

Where, S.I. = Simple Interest, P = Principal,  R = Rate of interest,, T = Time in years

CALCULATION:

Let us assume the sum of money be P, 

According, to the given Question, Amount = double of sum of money = 2P, Time = 12 years

⇒ S.I. = (Amount - Principal) = ( 2P - P) = P 

⇒ S.I. =( P × R × T)/100 

⇒ P = ( P × R × 12)/100

⇒ R = 25/3 = 8 $\frac{1}{3}$%.

Hence, the required Rate of percent is 8 $\frac{1}{3}$%.

The correct answer is Malaysia.

Key Points

• Among the options, only Malaysia is NOT a permanent member of the United Nations Security Council.
• The United Nations Security Council is one of the principal organs of the United Nations.
• United Nations Security Council has 15 Members, and each Member has one vote. Among these 15 members, 5 are permanent members and 10 are non-permanent members.
• Permanent members:

1. China.
2. France.
3. Russia.
4. The United Kingdom.
5. The United States.

• Non-permanent members:

1. Estonia.
2. India.
3. Ireland.
4. Kenya.
5. Mexico.
6. Niger.
7. Norway.
8. Saint Vincentand the Grenadines.
9. Tunisia.
10. Vietnam.

Additional Information

• The Security Council held its first session on 17 January 1946 at Church House, Westminster, London.
• Since its first meeting, the Security Council has taken permanent residence at the United Nations Headquarters in New York City.
• In August 2021, India took over the presidency of the United Nations Security Council (UNSC) for a duration of one month.
• India’s next month of the Council presidency will be in December 2022.

FORMULA USED:

If  1² + 2² + 3² + ..........+ n²  then, sum  = $n ( n +1) ( 2n +1)\over 6$

CALCULATION:

Here,  3 + 12 + 27 + ----------------- + 3n²  

Now, on  taking 3 common 3 ( 1 + 4 + 9 + ------------------- + n² ).................(1)

Now, equation (1) can be written as

⇒ 3 ( 1² + 2² + 3² + ------------- + n² ) = 3  $n ( n+1) ( 2n+1_)\over 6$  =  $n ( n+1) ( 2n +1)\over2$

Hence, the required value is [n(n+1) (2n +1)]/2.

The correct answer is anaerobic.

Key Points

• Anaerobic exercise is a type of exercise that breaks down glucose in the body without using oxygen; anaerobic means "without oxygen".
• In practical terms, this means that anaerobic exercise is more intense, but shorter in duration than aerobic exercise.
• Anaerobic exercises involve quick bursts of energy and are performed at maximum effort for a short time.
• Examples include jumping, sprinting, or heavy weight lifting.
• The anaerobic energy system (also called the lactic acid system) is the body's way of creating energy in the form of ATP quickly.

Additional Information

• The blood circulatory system is a system of organs that includes the heart, blood vessels, and blood which is circulated throughout the entire body of humans or other vertebrates. It includes the cardiovascular system, or vascular system, which consists of the heart and blood vessels.
• If you contract a disease, you catch it but only use this if it's something serious. You catch a cold, but contract malaria. The contract also means "shrink."
• Aerobics is a form of physical exercise that combines rhythmic aerobic exercise with stretching and strength training routines with the goal of improving all elements of fitness.

The logic followed here is :-

• RAW : WAR

Similarly,

• STAR :  ?

Hence, the correct answer is "RATS".

GIVEN:

Ratio of radii of two circles = 1:4

FORMULA USED:

Area of circle = πr²

CALCULATION:

Let, the radii of two circles be r₁ and r₂ respectively

Now, here r₁ = 1 and r₂ = 4 

Since, Area of circle = πr²

Ratio of Area of two circles = πr₁²/  πr₂²  =  r₁² / r₂²   ⇔ 1²/4²  =  1/16  

Hence, Ratio of radii of two circles is 1 : 16

The correct answer is Veena.

Key Points

• The veena also spelt vina, comprises various chordophone instruments from the Indian subcontinent.
• Ancient musical instruments evolved into many variations, such as lutes, zithers, and arched harps.
• Veena is a musical instrument that is not Indo-Islamic in origin.
• One who plays the veena is referred to as a vainika.
• It remains an important and popular string instrument in classical Carnatic music.

Additional Information

• Sitar is a stringed instrument of the lute family that is popular in northern India, Pakistan, and Bangladesh.
• Rubab, robab, or rabab is a flute-like musical instrument. The rubab is one of the national musical instruments of Afghanistan; and is also commonly used in Pakistan.
• A tabla is a pair of twin hand drums from the Indian subcontinent. Since the 18^th century, it has been the principal percussion instrument in Hindustani classical music, where it may be played solo, as an accompaniment with other instruments and vocals, and as a part of larger ensembles.

The logic followed here is :-

∴ Here, '46' given in the series instead of '47'.

Thus 46 DOES NOT belong to the following series.

Hence, the correct answer is "46".

The correct answer is Anandmath.

Key Points

• Bankim Chandra Chattopadhyay wrote the national song 'Vande Mataram'.
• It was a part of his novel Anandamath (1882).
• It is a political novel depicting a Sanyasi army fighting British soldiers.
• The poem was first sung by Rabindranath Tagore in the 1896 session of the Indian National Congress.
• On 24 January 1950, the Constituent Assembly of India has adopted "Vande Mataram" as a national song.
• On this occasion, the first President of India, Rajendra Prasad stated that the song should be honoured equally with the national anthem of India, Jana Gana Mana.

Additional Information

• Durgeshnandini is a Bengali historical romance novel written by Indian writer Bankim Chandra Chattopadhyay in 1865.
• Devi Chaudhurani is a Bengali novel written by Bankim Chandra Chatterjee and published in 1884. It was later translated to English by Subodh Chunder Mitter.
• Kapalkundala is a Bengali romance novel by Indian writer Bankim Chandra Chattopadhyay. Published in 1866.

GIVEN:

Ratio of two numbers = 2:3 

Product of LCM and HCF = 9600

FORMULA USED:

L.C.M × H.C.F = Product of two numbers 

CALCULATION:

Let us take the numbers to be 2x and 3x 

Since, L.C.M × H.C.F = product of two numbers 

Now, L.C.M × H.C.F  = 2x × 3x

 So, 9600 =  6x² 

⇒ x² = 1600

⇒ x = 40

Now, the numbers are 2x  = 2 × 40 = 80 and 3x = 3 × 40 = 120

Now, sum of the numbers  = ( 80 +120) = 200.

Hence, sum of the numbers are 200.

The logic followed here is :-

∴ Here, All players except 'Sophia' plays cricket thus Sophia does not play cricket.

Hence, the correct answer is "Sophia".

The correct answer is Nagpur.

Key Points

• Nagpur Airport, also known as Dr. Babasaheb Ambedkar International Airport, serves Nagpur in Maharashtra state in India.
• It was named in 2005 after B. R. Ambedkar, Dr. "Babasaheb" Ambedkar, the chief architect of the Indian Constitution.
• Dr. B. R. Ambedkar:
• B. R. Ambedkar was popularly known as Babasaheb Ambedkar.
• He was one of the architects of the Indian Constitution.
• He was a very well-known political leader, eminent jurist, Buddhist activist, philosopher, anthropologist, historian, orator, writer, economist, scholar, and editor, too.

Additional Information

• Airports in Maharastra:
• There are 12 Airports in Maharastra.
• Chhatrapati Shivaji International Airport (BOM), Mumbai
• Pune International Airport (PNQ), Pune
• Dr Babasaheb Ambedkar International Airport (NAG), Nagpur
• Shri Guru Gobind Singh Ji Airport (NDC), Nanded
• Akola Airport (AKD)
• Aurangabad Airport (IXU)
• Shirdi Airport (SAG)
• Kolhapur Airport (KLH), Kolhapur
• Gandhinagar Airport
• Solapur Airport
• Jalgaon Airport
• Ozar Airport in Ozar

The correct answer is Russia.

Key Points

• Saudi Arabia has led the world in annual oil exports, but that changed in 2019 when the United Arab Emirates overtook it as the world's biggest oil exporter.
• The United States has also increased its share of global oil exports, accounting for 8.17% of exports in 2020, up from 5.71% in 2019.
• Russia takes the second spot.
• In 2019, it accounted for 11.6% of global exports, totalling $74.4 billion.
• Production reached an annual average of 10.5 million barrels per day.
• Produced by major names like Rosneft, Surgutneftegas, and Gazprom. This accounts for 11% of global oil production.

Additional Information

• Oil is the third largest exported product in the world, by revenue. In 2019, crude petroleum accounted for 3.82% of global trade.
• Crude oil is unrefined petroleum that's used to manufacture many products, including gasoline, heating fuel, and plastics. As of 2019, global oil production reached 4.2 billion metric tons.
• Top countries list:
• Saudi Arabia
• Russia
• United States
• Canada
• Iraq
• United Arab Emirates
• Nigeria
• Kuwait
• Kazakhstan
• Norway$

The logic followed here is :-

CALM is coded as XZON

Similarly,

LOVE will be coded as:

Hence, the correct answer is "OLEV".

The logic followed here is :-

Checking options:

1. 87 → 8 - 7 = 1 

2. 75 → 7 - 5 = 2 

3) 72 → 7 - 2 = 5 

4. 96 → 9 - 6 = 3 

Hence, the correct answer is "72".

The correct answer is 2^nd Five Year Plan.

Key Points

• Mahalanobis Plan was India's second five-year plan (1956-61) proposed by Professor Prasanta Chandra Mahalanobis.
• PC Mahalanobis established the Indian Statistical Institute (ISI) in Calcutta in 1931 and for the same reason, he is known as the father of Indian Statistics.
• He was a member of the first Planning Commission of free India.
• This plan gave priority to investment goods, as they were crucial for the further economic growth of India.
• The plan explores the allocation of investment between the different sectors of the economy.
• Two sectors are considered in the model; the production goods-producing sector (K-sector) and the consumption goods-producing sector (C-sector).

Additional Information

• Basic information about the planning commission and 5- year plans:
• The planning commission was founded: in 1950.
• Planning Commission head: Prime Minister
• First five-year plan launched: 1951
• A total number of 5- year plans: 12.
• Planning Commission dissolved: 2014 (By PM Narendra Modi)

The correct answer is PARAM 8000.

Key Points

• PARAM is a series of supercomputers designed and assembled by the Centre for Development of Advanced Computing (C-DAC) in Pune, India.
• PARAM means "supreme" in the Sanskrit language, whilst also creating an acronym for "PARAllel Machine". As of June 2021, the fastest machine in the series is the PARAM Siddhi AI which ranks 89^th in the world with a Rpeak of 5.267 petaflops.
• The PARAM 8000 was the first machine in the series and was built from scratch. A prototype was benchmarked at the "1990 Zurich Super-computing Show" of the machines that ran at the show it came second only to one from the United States.
• It was created in three months at a cost of ₹160 million (US$2 million) - the first Indian supercomputer.

Additional Information

• ENIAC was the first programmable, electronic, general-purpose digital computer, completed in 1945. It was Turing-complete and able to solve "a large class of numerical problems" through reprogramming.
• SAGA-220 is a supercomputer built by the Indian Space Research Organisation. It was unveiled on 2 May 2011 by Dr. K. Radhakrishnan, Chairman, ISRO.$

The correct answer is religious.

Key Points

• The Phad Painting is practised in Rajasthan.
• It is a style of painting in which scroll painting and folk painting is done on a canvas or a long cloth, termed as 'phad'.
• Generally, the narratives of the folk deities of the state are depicted in this style of painting.

Additional Information

• The famous Madhubani paintings belong to the Indian state of Bihar.
• Kalighat paintings originated in the vicinity of Kalighat Kali Temple, Kalighat, Kolkata.
• Madhubani Paintings originated from the Madhubani district, Mithila region of Bihar.
• Kalamkari originated in Andhra Pradesh and Telangana.

The correct answer is operating system.

Key Points

• Operating System
• An operating system (OS) serves as an interface between the computer user and the hardware.
• Operating System software is responsible for controlling computer hardware, managing software resources, and offering standard services for computer programs.
• By utilising the hardware drivers as the interface between the two, it sits in between the applications you execute and the hardware.
• For instance, when an application wants to print something, it defers to the OS to handle that operation.
• The following are some of the key functions that an operating system should perform:
• Memory management,
• Device management,
• Processor management,
• Security,
• File management,
• Coordination between other software and users**,**
• Error detection tools,
• and Job accounting.

Additional Information

• Operating systems are present on a wide range of computing devices, including supercomputers, web servers, mobile phones, and gaming consoles.
• Some of the most popular operating systems include:
• Apple macOS
• Apple's iOS
• Microsoft Windows
• Linux
• UNIX
• Android
• With a market share of roughly 76.45%, Microsoft Windows is the most popular operating system for general-purpose personal computers.
• In second place (17.72%) is Apple Inc.'s macOS, followed by all of the Linux distributions in third (1.73%).
• In the year 2020, Android's market share in the mobile industry (which includes smartphones and tablets) is up to 72%.

GIVEN:

The ratio of angles of a quadrilateral = 2:4:6:8

CONCEPT USED:

The sum of all angles of a quadrilateral = $360^\circ$

CALCULATION:

Let the angles of a quadrilateral be 2x , 4x, 6x and 8x

Now, Sum of the angles in a quadrilateral = $360^\circ$

So, 2x + 4x + 6x + 8x = $360^\circ$ 

20x = $360^\circ$ 

x = $18^\circ$ 

Now, the smallest of these angles is 2x = 2 × $18^\circ = 36^\circ$ 

Hence, the smallest of these angles is  $36^\circ$.

CONCEPT USED:

Co- prime numbers: The numbers which have no common factors except 1, is called co- prime number.

H.C.F of two co- prime number will always be 1 

L.C.M of two co- prime number will be the product of them

Here L.C.M = Least Common Multiple

       H.C.F = Highest Common Factor

CALCULATION:

As, 119 can be factorized as  119 =  17 × 7 

As, 17 and 7 are two- co -prime numbers as they have no common factors except 1

Since, L.C.M of two co- prime numbers are the product of two co-prime  numbers 

L.C.M = 17 × 7 = 119

Hence, L.C.M is 119.

The correct answer is Mural.

Key Points

• Mural Paintings
• Mural paintings are the only form of art that truly alters and shares space, making them appear three-dimensional.
• They must be painted on the walls of big buildings like caverns and temples since they are too big to fit on paper.
• The three main religious themes depicted by the paintings are Hinduism, Buddhism, and Jainism.
• Their natural relationship to architecture and wide-ranging public importance are two key characteristics that set them apart.
• The colour pigments used in ancient Indian mural paintings were made by combining natural materials like chalk, terracotta, red ochre, and yellow ochre with animal fat.
• Mural paintings can be found in places like Ajanta, Thiruvarur, Bagh Caverns, Sittanavasal Caves, Kailasanatha Temple in Ellora, Armamalai Cave, and Ravan Chhaya Rock Shelter.

Additional Information

• Ajanta Paintings 
• One of the earliest existing murals on the Indian subcontinent was carved out of volcanic rocks in the 4^th century AD in the Ajanta caves.
• It consists of 29 horseshoe-shaped caverns.
• These caves are well-known for their magnificent mural paintings, which were produced during the Mauryan Empire's rule and took four to five centuries to complete.
• The paintings show the social fabric and human ideals as well as historical fashions.

The correct answer is Ankleshwar.

Key Points

• Ankleshwar
• Ankleshwar is the largest and most famous petroleum site located in the Bharuch district of Gujarat, India.
• The Ankleshwar field, located roughly 80 km south of Vadodara and nearly 160 km south of Khambhat, was the first significant oil find and was made in 1958.
• The anticline at Ankleshwar is 4 km wide and 20 km long.
• Oil can be found between 1000 and 1200 metres below the surface.
• It is such a productive oilfield that Jawaharlal Nehru, India's former prime leader, referred to it as the fountain of prosperity.
• This field has the potential to produce 2,500,000 million tonnes of oil annually.
• The refineries in Trombay and Koyali receive oil from this field.

Additional Information

• Oil and Gas Industry
• The discovery of the nation's first oil resources in the town of Digboi in the state of Assam in 1889 marked the beginning of India's oil and gas sector.
• After the discovery of gas fields in Assam and Gujarat, the natural gas industry in India got its start in the 1960s.
• Gujarat is home to 4% of India's estimated total natural gas reserves and 20% of the country's projected total crude oil reserves.
• The largest oil field in India, known as Bombay High, is situated at the coast of Mumbai, Maharashtra.
• The first refinery in India's public sector is the Guwahati Refinery.
• The largest refinery in the world at present is the Jamnagar Refinery in India, which is owned and run by Reliance Industry.

The correct answer is 448.

Key Points

• Constitution of India
• The Indian Constitution is the country's highest law.
• The document outlines the framework that defines the fundamental political code, as well as the fundamental rights, directive principles, and responsibilities of citizens.
• It also lays out the structure, methods, powers, and duties of governmental institutions.
• It is the world's longest-written national constitution.
• On 26 November 1949, the Indian Constituent Assembly approved it, and it went into effect on 26 January 1950.
• It comprised 395 articles in 22 parts and 8 schedules at the time of its implementation.
• As of October 2020, there are 448 articles in the Constitution of India.
• Currently (2021), it has 470 articles, 25 parts, 12 schedules, and 105 amendments.

Additional Information

• Dr. B. R. Ambedkar served as the Constitution of India's principal architect.
• India is proclaimed to be a sovereign, socialist, secular, and democratic republic in the constitution
• It also guarantees its citizens justice, equality, and liberty while working to foster fraternity.
• The 42^nd amendment act, passed in 1976 during the Emergency, added the phrases "secular" and "socialist" to the preamble.
• At the Parliament House in New Delhi, the original 1950 constitution is kept in a helium-filled box.

The correct answer is 1510 AD.

Key Points

• Conquest of Goa by the Portuguese
• With the aid of Krishnadev Raya (ruler of the Vijaynagar empire), Afonso de Albuquerque defeated Ismail Adil Shah, the Sultan of Bijapur, and captured Goa in 1510 AD.
• He is also credited with ending the Sati tradition in Goa.
• Goa was officially taken over by the Portuguese and Albuquerque on February 17, 1510, with no resistance
• Under penalty of death, Albuquerque reaffirmed that the city was not to be taken over and that its citizens were not to be injured.
• Timoji's intelligence of the enemy's preparations was confirmed when the Portuguese discovered more than 100 horses belonging to the ruler of Bijapur, 25 elephants, and partially finished new ships within the city.
• Goa served as the principal Portuguese base in the East for four and a half centuries and eventually became the capital of the Portuguese East Indies and Portuguese Indian territories.

Additional Information

• History of Goa 
• Despite being the geographically smallest state in India, Goa has a lengthy and varied history.
• With regard to colonial influences and a multicultural aesthetic, it has many similarities to Indian history.
• During the Iron Age, Goa was governed by the Mauryan and Satavahana Empires.
• The Kadamba dynasty, the Vijayanagara Empire, the Bahmani Sultanate, and the Bijapur Sultanate all ruled over Goa during the Middle Ages.
• After a 36-hour fight, India conquered Goa in 1961 and seized it.
• In 1987, Goa received statehood as a result of the Konkani language agitation.
• Among the Indian states, Goa has one of the highest Human Development Index and GDP per capita.

FORMULA USED:

cosec²$\theta$ - cot²$\theta$ = 1

CALCULATION:

Here, cosec$\theta$  = 3x and cot$\theta$ = 3/x

Since, we have cosec²$\theta$ - cot²$\theta$ = 1

So, (3x)² - ( 3/x)²  = 1

⇒ 9x² - (9/x² ) = 1 

⇒ 9 ( x² - 1/x² ) = 1`.

Hence, the required value is 1.

GIVEN:

Number of girls in a class = 7 times the number of boys

CALCULATION:

Let the number of boys be  x

Then, According to the given Question, 

Number of girls = 7 times the number of boys 

Number of girls = 7× x=  7x

So, the total number of children = x + 7x = 8x

So, in the given options, 72, 8 , 48 ,52 .Only 52  is not divided by 8x  

Hence, 52 cannot represent  the total number of children.

Hence, the number which cannot represent the total number of children in the class is 52.

GIVEN:

$sin\theta$ = 5/13

FORMULA USED:

sin$\theta$ =  p/h 

$cos\theta$ = b/h 

tan$\theta$ = p/b 

cot$\theta$ = b /p 

h² = p² + b²

Where, h = hypotenuse, p = perpendicular, b= base 

CALCULATION: 

Here, sin$\theta$  = 5/13 = p/h 

Now, h² = p² + b²

⇒  13² = 5² + b²

⇒ 169 - 25 = b² 

⇒ 144 = b²

⇒ 12 = b 

Cos$\theta$  = b/h = 12/13

tan$\theta$ = p/b = 5/12 

cot$\theta$ = b\p = 12/5 

$cos\theta - tan\theta \over 2cot\theta$ = $(12/13 - 5/12)\over 2 \times 12/5$ =  $(144 -65)\over 156$ × 5/24 = 79/156 $\times$ 5/24 = 395/ 3744

Hence, the required value is 395/3744.

The correct answer is ADSL.

Key Points

• ADSL
• Asymmetric Digital Subscriber Line (ADSL) is a technology that enables high-bandwidth, fast data transmission to homes and businesses over copper wire telephone wirings.
• ADSL is asymmetric, as it uses the majority of its channels to transport data downstream to the user and only a tiny portion of them to upload data from the user.
• On the same phone line, ADSL supports both analogue (voice) and digital (data) traffic.
• It is usually provided with downstream internet connection data speeds ranging from 512 Kbps to around 6 Mb/s.
• Compared to a conventional dial-up connection, it is a more affordable way to access the internet at faster speeds.
• Download and upload speeds are not similar in ADSL technology.
• The Digital Subscriber Line (DSL) modem's primary function while using an ADSL connection is to download the content; it is not intended to distribute it to others.

Additional Information

• In order to enable simultaneous usage of the landline and the ADSL modem, ADSL operates on existing copper phone lines by utilising a DSL filter, also known as a splitter, to isolate the bands with higher frequencies.
• The one-way nature of most multimedia communication, in which a lot of data flows in the user's direction and just a little bit of interactive control data is returned, is something that ADSL was created to take advantage of.
• Symmetric Digital Subscriber Line (SDSL), which is less widespread, is different from ADSL.
• SDSL
• Broadband technology that delivers data via a phone network is known as SDSL.
• SDSL, however, has downstream bandwidth that is identical to upstream bandwidth from the network to the subscriber.

Given

Sum of two numbers = 75

Difference of squares of the numbers=300

Formula 

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

Calculation

a + b=75

$a^2-b^2=$300

Substituting in the equation

$300=(75)(a-b)$

a-b=$\frac{300}{75}=4$

The difference between the given numbers is 4

The correct answer is Universal Postal Union.

Key Points

• Universal Postal Union
• One of the specialised institutions of the United Nations, the Universal Postal Union (UPU), coordinates postal policies among its member's countries.
• Under the influence of the Treaty of Bern, it was established in 1874 under the name General Postal Union, but in 1878 the name was modified to Universal Postal Union.
• The Congress, the Council of Administration (CA), the Postal Operations Council (POC), and the International Bureau are the four bodies that make up the UPU.
• Additionally, it is in charge of the telematics and EMS cooperatives.
• The UPU's main office is in Bern, Switzerland.

Additional Information

• In 1948, it became a specialised agency of the UN, making it the second-oldest global international organization.
• The UPU's official language is French. In 1994, English was included as a working language.
• The majority of the UPU's records and publications are available in the six official languages  (French, English, Russian, Mandarin Chinese, Spanish, and Arabic) of the United Nations, including its flagship magazine, Union Postale.
• The treaty stated that;
• There should be a standard flat charge for mailing letters anywhere in the world.
• Postal authorities should handle both domestic and international mail equally.
• Each nation should keep all funds gathered for international postage.

The correct answer is be amended.

Key Points

• Kesavananda Bharti Case
• The Kesavananda Bharati case, which established the basic structure theory of the Indian Constitution, is a landmark judgment of the Supreme Court of India.
• The landmark decision was made on April 24^th, 1973, by a narrow majority of 7:6.
• It holds that any provision of the Indian Constitution can be amended by the Parliament in order to fulfil its socio-economic obligations that were guaranteed to the citizens as stated in the Preamble
• It provides that such an amendment did not alter the Constitution's fundamental structure.
• However, the minority had a divergent view and cautioned against handing the Parliament unrestricted altering authority.
• The court ruled that the 24^th Constitutional Amendment was fully lawful.
• But it deemed the second section of the 25^th Constitutional Amendment to be excessive.

Additional Information

• Kesavananda Bharati
• He fought against the Kerala land reforms Act, which placed limitations on the management of religious property, in 1970.
• The ability to administer religiously owned property independently of the government was in dispute in this case under Article 26.
• The Supreme Court assembled the largest-ever bench of 13 judges to hear the case.
• The case had been heard for 68 days.
• The Kesavananda Bharati case, which had a severe dispute between the government and the judiciary, is popularly referred to as the fundamental rights case.

The correct answer is Fateh Burj.

Key Points

• Fateh Burj
• The Fateh Burj, the tallest minar in India, is located in the Punjabi province's SAS Nagar district (Mohali district), near the old village of Chappar Chiri.
• In 2011, it was finished and inaugurated by the former Punjab chief minister Parkash Singh Badal.
• The village of Chappar Chiri is located along National Highway 205A (India), also known as Banda Singh Bahadur Road, which connects Kharar and Banur.
• The tower, which stands at 328 feet (100 meters), is dedicated to the Sikh Misls, which were established in 1711 and spread throughout most of Punjab.
• It is located just outside of Mohali, a short distance from Landran and 20 kilometres from Sirhind.
• Here, one of the most renowned Sikh fighters, Banda Singh Bahadur, defeated the Mughal army's leader, Wazir Khan, in a crucial conflict.

Additional Information

• Jhulta Minar
• One of India's most well-known minars is Jhulta Minar, located in Ahmedabad, Gujrat.
• Because both minarets shakes, Jhulta Minar is sometimes referred to as a shaking minaret.
• The mosque is thought to have been built in 1452 AD either by Sidi Bashir, a slave of Sultan Ahmed Shah, or by Malik Sarang, another Sultan of Gujarat.
• Qutub Minar
• The Qutub complex, a UNESCO World Heritage Site in Delhi's Mehrauli area, contains the Qutub Minar, a minaret or triumph tower.
• Qutub Minar is the second-tallest landmark in Delhi, standing at a height of 72.5 metres (238 feet).
• Qutb Ud-Din-Aibak, who founded the Delhi Sultanate after overthrowing Delhi's final Hindu ruler, started constructing it in 1192 and finished it in 1193.
• Vijay Stambh
• In Chittor Fort in Chittorgarh, Rajasthan, India, there is an impressive victory monument called the Vijaya Stambha.
• In 1448, the Hindu Rajput king Rana Kumbha of Mewar built the tower to mark his victory over Mahmud Khalji's army of Malwa in the Battle of Sarangpur.
• The Hindu God Vishnu is honoured by the tower.

The correct answer is extinct.

Key Points

• Extinct Species
• A species that cannot be found after a prolonged search in its area of habitation is said to be extinct species.
• A species loses all of its genetic heritage when it goes extinct.
• In order to adapt to alterations in the environment or genetic inheritance, species evolve into new species.
• According to estimates, there are currently between 10 and 14 million species, of which more than 1.2 million have been researched and more than 86% have yet to be discovered.
• Causes of Extinction
• Climate change
• Loss of habitat
• Diseases
• Lack of genetic diversity
• Some common examples of extinct species are Passenger Pigeon, Dodo, Tasmanian Tiger, Baiji White Dolphin, Pyrenean Ibex, etc.

Additional Information

• Rare Species
• A species is considered rare if its population is so limited that it could become vulnerable or endangered.
• Examples: the wild Asiatic buffalo the Himalayan brown bear, the desert fox, the hornbill, etc.
• Endangered Species
• Species in risk of going extinct are referred to as endangered species.
• Examples: Indian wild ass, Indian rhino, lion-tailed macaque, black buck, crocodile, and sangai (brow anter deer in Manipur).
• Vulnerable Species 
• The term "vulnerable species" refers to those species whose populations have dropped to the point where they are likely to become endangered.
• Examples: Gangetic dolphin, blue sheep, Asiatic elephant, etc.

The correct answer is Doddabetta.

Key Points

• Doddabetta 
• The Nilgiri Hills' highest peak, Doddabetta, has an elevation of 2637 meters.
• Around the mountain, there is a protected forest area.
• It is located in the Nilgiris District of Tamil Nadu, South India, 9 kilometres from Ooty on the Ooty-Kotagiri Road.
• According to the Badugu language, the name Doddabetta literally translates to "Big mountain."
• Along with Anamudi, Mannamalai, and Meesapulimala, it is the fourth-highest peak in South India.
• Two public telescopes are located in an observatory at the peak of Doddabetta.
• The Tamil Nadu Tourism Development Corporation (TTDC), which launched it on June 18, 1983, is in charge of running it.

Additional Information

• Armakonda
• Arma Konda, also known as Seethamma Konda, is the tallest mountain peak in the Godavari River basin and the state of Andhra Pradesh, standing 1,680 metres (5,510 feet) above sea level.
• It is the Eastern Ghats' tallest peak.
• Kalsubai
• The Kalsubai mountain of the Western Ghats lies in the Maharashtra region of India.
• The highest point in Maharashtra is located at its top, which is 1,646 metres above sea level.
• Anamudi 
• The Indian state of Kerala has a mountain called Anamudi that is situated in the Ernakulam and Idukki districts.
• Its elevation is 2,695 metres (8,842 feet), and it has a topographic prominence of 2,479 meters, making it the highest peak in both South India and the Western Ghats.
• Because of the mountain's similarity to an elephant's head, the name Anamudi is literally translated as "elephant's head."

Given

Percentage increase in the population = 10%

Present population = 6400

Formula used

$Pn=P(1+\frac{r}{100})^n$

where,

P_n = population after the n^th year

P = present population

r = rate of increase

n = no of years

Calculation

Population in 2 years = P₂

P = 6400

r = 10

n = 2

Substituting,

$Pn=6400(1+\frac{10}{100})^2=7744$

population  after 2 years will be 7744

Formula used

tan(180+x) = tan x

Calculation

2 sin (3x – 3)° = tan(180+60)°= tan(60)°

2 sin (3x – 3)° =$\sqrt{3}$

sin (3x – 3)°=$\frac{\sqrt{3}}{2}$.......(1)

sin 60° =$\frac{\sqrt{3}}{2}$.............(2)

equating (1) and (2)

so, (3x – 3)° = 60°

x = 21°

The value of x in the equation is 21°

The correct answer is Qatar.

Key Points

• FIFA World Cup, 2022
• The 2022 FIFA World Cup, a quadrennial international men's football championship played between the senior national teams of FIFA member countries, is set to take place for the 22^nd time in 2022.
• Qatar will host it from November 20 to December 18, 2022.
• After the event in South Korea and Japan in 2002, this will be the second World Cup wholly held in Asia and the first World Cup ever to be contested in the Arab world.
• The tournament will include 32 teams for the last time; the tournament in the United States, Mexico, and Canada in 2026 will have 48 teams instead.
• At Al Bayt Stadium in Al Khor, the opening game of the tournament will be played between Qatar and Ecuador.
• The final is scheduled for December 18, 2022, which also happens to be Qatar National Day.

Additional Information

• FIFA World Cup
• The senior men's national teams of the members of the Fédération Internationale de Football Association (FIFA), the world's governing organisation of association football, compete in the FIFA World Cup, commonly referred to as the World Cup.
• Since the first competition in 1930, the championship has been given out every four years, with the exception of 1942 and 1946, when it was postponed due to the Second World War.
• France is the reigning champion after taking home a second title from the 2018 competition in Russia.
• The qualification phase of the current format determines which teams advance to the tournament phase, and it occurs over the preceding three years.
• Over the course of around a month, 32 teams, including the host nation(s), which automatically qualify, compete for the championship in venues inside the host country(s).

Calculation:

$(1-\frac{1}{x + 1})(1-\frac{1}{x + 2})(1-\frac{1}{x + 3})$.....$(1-\frac{1}{2x})$

$(1-\frac{1}{x + 1})=\frac{x+1-1}{x+1}=\frac{x}{x+1}$

Similarly, the whole equation can be written as 

$(1-\frac{1}{x + 1})(1-\frac{1}{x + 2})(1-\frac{1}{x + 3})$...$(1-\frac{1}{2x})$ = $(\frac{x}{x+1})\times(\frac{x+1}{x+2})\times(\frac{x+2}{x+3})...(\frac{x+(x-1)}{x+x})$

by striking out all the equal terms we get

$(\frac{x}{{x+1}})\times(\frac{x+1}{x+2})\times(\frac{x+2}{x+3})...(\frac{x+(x-1)}{x+x})$ = $(\frac{x}{x+x})=\frac{x}{2x}=\frac{1}{2}$

Hence the product of the given question is $\frac{1}{2}$

The logic followed here is :-

Sum of alphabet positional values × 2 = Number code.

• W is coded as 46

= 23 × 2

= 46

And,

• CAT is coded as 48

= (3 + 1 + 20) × 2

= 24 × 2

= 48

Similarly,

• DOG will be coded as:

= (4 + 15 + 7) × 2

= 26 × 2

= 52

Hence, the correct answer is "52".