1. In a row of 28 students, Jamuna was 12th from the extreme left end.

• This implies that Jamuna was 17th from the extreme right end.

2. Ganga was 19th from the extreme right end.
3. If Sarasvati was seated exactly between them.

Clearly, Sarasvati is 18th from the right end.

Hence, ‘18th’ is the correct answer.

Six identical boxes of different colours, Purple, Black, Yellow, Green, Cyan and Magenta, are arranged one over the other in the following manner:

1. The Yellow box is kept at the bottom-most position.

2. Only three boxes are kept between the Cyan and Purple boxes.

3. Only the Black colour box is kept between the Magenta and Green colour boxes.

Clearly, Black coloured box is kept at the third position from the top.

Hence, ‘Black’ is the correct answer.

The correct answer is Kerala.

Key Points

• On May 17, 1998, former Prime Minister Atal Bihari Vajpayee officially launched Kudumbashree, the Kerala State Poverty Eradication Mission.
• Under the direction of Local Self Governments established and given authority by the 73rd and 74th Amendments to the Indian Constitution, the Mission aspires to remove absolute poverty within a set time frame of ten years.
• By putting the impoverished in community-based groups, the Mission established by the State Government with the active assistance of the Government of India and NABARD has adopted a novel approach to combating poverty.
• Instead of using a project-based strategy, the Mission uses a process approach.
• Bringing together women from all walks of life to fight for their rights or for empowerment, Kudumbashree, a community organisation of Neighborhood Groups (NHGs) of women in Kerala, has been recognised as a successful method for the empowerment of women in rural as well as urban regions.

Important Points

• Kerala: (As of 2022)
• Governor: Arif Mohammad Khan
• Capital: Thiruvananthapuram
• Chief Minister: Pinarayi Vijayan

A, B, C, D, E, F, G and H are sitting around a square table facing the centre of the table.

Four of them are sitting at each of the corners, while the other four are sitting at the exact centre of each of the sides.

1. G sits in the middle of one of the sides of the table.

2. E is an immediate neighbour of G.

3. E sits third to the left of F.

   

4. Only three people sit between F and H.

The above condition cannot be satisfied in Case I, so it is eliminated.

5. B sits to the immediate left of H.

6. C sits third to the right of A.

Only one position is vacant and only D is left, so the vacant position will be occupied by D.

Clearly, H sits third to the right of D.

Hence, ‘H’ is the correct answer.

The correct answer is 241.

Key Points

• Article 241
• Deals with high courts for union territories.

Additional Information

• Article 221 of the Indian Constitution makes laws for the salaries to be provided to the judges of each High court.
• Article 189
• Voting in Houses, power of Houses to act notwithstanding vacancies and quorum.
• Article 263 - Provisions with respect to an inter-State Council If any time it appears to the President that the public interests would be served by the establishment of a Council charged with the duty of
• Inquiring into and advising upon disputes which may have arisen between States;
• Investigating and discussing subjects in which some or all of the States, or the Union and one or more of the States, have a common interest; or
• Making recommendations upon any such subject and, in particular, recommendations for the better coordination of policy and action with respect to that subject, it shall be lawful for the President by order to establish such a Council, and to define the nature of the duties to be performed by it and its organisation and procedure.

The correct answer is Rudra Veena.

Key Points

• Ustad Mohi Bahauddin Dagar is the son of renowned North Indian musician Zia Mohiuddin Dagar, he plays the Rudra veena.
• He performs Dagarbani-style Rudra veena.
• Referring to Nayak Haridas Dagar of the 16th century, he represents the 20th generation of the Dagar dynasty.
• He received the highest honour for performing artists in 2012 when the Sangeet Natak Akademi, India's National Academy for Music, Dance, and Drama, presented him with the Sangeet Natak Akademi Award.

Important Points

• Large plucked string instruments, such as the Rudra veena, are employed in Hindustani classical music, particularly dhrupad.
• It is one of the main veena varieties used in Indian classical music and is distinguished by its powerful bottom resonance.
• The Rudra veena achieved great importance among Mughal court musicians, and it is documented in court records as early as Zain-ul Abidin's (1418–1470) reign.

The correct answer is If the market of a particular commodity consists of more than one seller, but the number of sellers is few, the market structure has termed an oligopoly.

Key Points

• A market with an oligopoly has a small number of businesses that are aware of their interdependence in terms of price and production strategies.
• Each company has a certain amount of market power due to the small number of enterprises.
• Oligopoly differs from perfect competition in that each firm must consider its interconnectedness, from monopolistic competition in that firms have some control over pricing, and from monopoly, in that, a monopolist has no competitors.
• The implications of mutual dependency among firms in pricing and output decisions are generally the focus of oligopoly study.​

Additional Information

• A market with a monopoly has just one producer, a duopoly has two businesses, and an oligopoly has three or more businesses.
• A monopoly is a market system where there is only one seller and there are enough barriers to entry for any other sellers.

The correct answer is PRASHAD scheme.

In News 

• According to a release by the PMO, the Somnath Promenade has been developed under the PRASHAD (Pilgrimage Rejuvenation and Spiritual, Heritage Augmentation Drive) Scheme at a cost of over Rs 47 crore.

Additional Information

• ​PRASAD scheme was launched in the year 2014-2015 under the Ministry of Tourism.
• This scheme focuses on developing and identifying pilgrimage sites across India for enriching the religious tourism experience.
• It aims to integrate pilgrimage destinations in a prioritised, planned and sustainable manner to provide a complete religious tourism experience.

Given:

From $\frac{3}{4}$ of a number P, Ramakrishna subtracts $\frac{2}{3}$ of another number Q and obtain $\frac{5}{8}$ as the difference.

Calculation:

$\frac{3}{4}$ of a number P = $\frac{3P}{4}$

$\frac{2}{3}$ of number Q = $\frac{2Q}{3}$

According to the question,

$\frac{3P}{4}$ - $\frac{2Q}{3}$ = $\frac{5}{8}$

⇒ ${(9P\ -\ 8Q) \over 12} = {5 \over 8}$

⇒ ${(9P\ -\ 8Q) \over 3} = {5 \over 2}$

⇒ 9P - 8Q = ${5 \times 3} \over 2$

⇒ 9P - 8Q = ${15} \over 2$

∴ The answer Ramakrishna should obtain is ${15} \over 2$ if he subtracts eight times of Q from nine times of P.

Given:

Amount (A) = ₹3,400

Rate of interest (R) = 12% p.a.

Time (T) = 3 years.

Concept used:

Simple Interest, SI = (P × R × T)/100

Amount = P + SI

where

P = Principal amount

R = Rate of interest per year

T = Time in years

Calculation:

Let the principal amount be ₹P.

According to the concept,

P + (P × 12 × 3)/100 = 3400

⇒ (100P + 36P)/100 = 3400

⇒ 136P = 340000

⇒ P = 340000/136

⇒ P = 2500

∴ The sum is ₹2500.

Shortcut TrickLet Principal be 100%

The total interest after 3 years = 12% × 3 = 36%

⇒ P + Interest = Amount

⇒ 136% = Rs. 3,400

⇒ 100% = (3400/136) × 100 = Rs. 2,500

Shortcut Trick

Principal = 100%

 As per question,

2% = 26.50

Principal = 100% = (26.50/2) × 100 = 1325

Interest = Amount - Principal = 1484 - 1325 = 159

∴ The interest that was paid on the sum invested at the original rate is ₹159.

Given:

The amount payable on maturity of a certain sum invested at a certain rate of simple interest per annum for one year was ₹1,484.

If the rate of interest had been 2% higher, the amount would have been ₹26.50 more.

Concept used:

Simple Interest, SI = (P × R × T)/100

Amount = P + SI

where

P = Principal amount

R = Rate of interest per year

T = Time in years

Calculation:

Let the principal sum and rate of interest be ₹P and R% respectively.

According to the question,

P + (P × R × 1)/100 = 1484

⇒ P(100 + R) = 1484 × 100

⇒ P(100 + R) = 148400      ....(1)

P + {P × (R + 2) × 1}/100 = 1484 + 26.50

⇒ P(100 + R + 2) = 1510.5 × 100

⇒ P(102 + R) = 151050      ....(2)

Now (2) ÷ (1),

P(102 + R)/P(100 + R) = 151050/148400

⇒ (102 + R)/(100 + R) = 57/56

⇒ ${(102 + R)\ +\ (100 + R)} \over {(102 + R)\ -\ (100 + R)}$ = ${57\ +\ 56} \over {57\ -\ 56}$

⇒ ${202\ +\ 2R} \over {2}$ = ${113 \over 1}$

⇒ 202 + 2R = 113 × 2

⇒ 202 + 2R = 226

⇒ 2R = 226 - 202

⇒ R = 24/2

⇒ R = 12

Putting R = 12 in (1),

P(100 + 12) = 148400

⇒ P = 148400/112

⇒ P = 1325

Now, the interest that was paid on the sum invested at the original rate

⇒ 1484 - 1325

⇒ 159

∴ The interest that was paid on the sum invested at the original rate is ₹159.

The correct answer is Tamil Nadu​.

Key Points 

• Kanyakumari is located at the southern tip of the Cardamom Hills in Tamil Nadu.
• Cape means the land infiltrated into the sea and Comorin is the former ame of the Kanyakumari.
• During the British Rule, sailors and traders used the word Cape to mention the identical landmark of Comorin.

Important Points

• The north-south extent from Indira Col in Kashmir to Kanyakumari is 3,214 km.
• The east-west width from the Rann of Kutch to Arunachal Pradesh is 2,933 km.
• With an area of 32,87,263 sq km, India is the seventh-largest country in the world.
• India accounts for about 2.4 per cent of the total surface area of the world.

Additional Information 

• Extreme points of India:

Shortcut Trick

Find total days for A and B: A = 30 × (100/75) = 40 days, B = 18 × (100/50) = 36 days.

Combined 1-day work fraction = (A + B) ÷ (A × B)

Combined 1-day work = (40 + 36) ÷ (40 × 36) = 76 ÷ 1440 = 19/360.

∴ The correct answer is 19/360.

Alternate Method

Given:

A does 75% (3/4) work in 30 days.

B does 50% (1/2) work in 18 days.

Calculations:

⇒ Time taken by A to complete 100% work = 30 × (4/3) = 40 days

⇒ Time taken by B to complete 100% work = 18 × 2 = 36 days

⇒ Let Total Work be the LCM of 40 and 36.

⇒ Combined Efficiency of (A + B) = 9 + 10 = 19 units/day

⇒ Fraction of work done in 1 day = Combined Efficiency ÷ Total Work

⇒ Fraction = 19 ÷ 360 = 19/360

∴ The correct answer is 19/360.

Additional Information

Efficiency and Time Relationship

The Efficiency of a person is inversely proportional to the Time taken to complete the work (Efficiency = 1 ÷ Time).

Combined Work Formula

If A can do a piece of work in 'x' days and B can do it in 'y' days, then together they can finish it in (x × y) ÷ (x + y) days.

Work Fraction

If a person completes a work in n days, the part of work done in 1 day is 1/n.

The correct answer is 69.

Key Points

• Madhava Nidana, written by Madhavacharya in the 12th century, has 69 chapters that are dedicated solely to sickness diagnosis (Nidana).
• It is the first work of its kind in Ayurveda to concentrate solely on one subject, diagnosis.
• It is interesting to observe that not a single sutra makes any reference to how to treat an illness.
• For the first time, comprehensive descriptions of Amavata (Rheumatism) and Amlapitta (Acid-peptic diseases) are provided.
• The details of Vatavyadhi (Neurological disorders) are pretty detailed.

Important Points

• Madhvacharya, also known as Purna Prajna and Nanda Tirtha, was a prominent advocate of the Dvaita (dualism) school of Vedanta and an Indian philosopher and theologian.
• Madhva's philosophy was known as Tattvavda, which translates as "Arguments from a realist viewpoint."

Given:

15, 2, 7, 8, 11, 5 and 14

Concept used:

Median is defined as the middle value of a sorted list of numbers.

Calculation:

The distribution in sorted form,

2, 5, 7, 8, 11, 14, 15.

Now, the median of the distribution = 8

∴ 8 is the median of 15, 2, 7, 8, 11, 5, and 14.

The correct answer is Monpa.

Key Points

• In Arunachal Pradesh, the Losar Festivals are observed. People of the Monpa Tribe, who are thought to reside in Arunachal Pradesh, celebrate it.
• Tawang celebrates the three-day Losar festival with a lot of fanfare.
• The celebration is observed to ward off bad spirits and greet the new year, which is meant to be prosperous and happy.
• The state of Nagaland in North-East India is home to a sizable Naga ethnic minority known as the Angamis.

Important Points

• The Angami Nagas are a recognised ethnic group in the state of Manipur and are primarily concentrated in the Nagaland districts of Kohima, Chümoukedima, and Dimapur.
• A group of Central Asian tribes that crossed the Khyber Pass into the Indian subcontinent towards the close of the fifth or beginning of the sixth century were known as the Hunas by the ancient Indians.
• In the Lower Subansiri district of Arunachal Pradesh, India, in the Ziro valley, there is a tribe known as the Apatani.

The correct answer is metamorphosis.

Key Points

• Metamorphosis process: The transformation of the larva into an adult through drastic changes is called metamorphosis. It is a biological process that involves sudden and abrupt changes in the body structure of the animal by cell growth and differentiation. It is generally observed in amphibians and insects. Examples: frogs and butterflies.

Important Points

• Metamorphosis of a butterfly
• There are four stages in the process of the Metamorphosis of a butterfly.
• The first stage is the egg.
• The Butterfly eggs are laid on the plants by the female Butterfly.
• The second stage is the larva stage in which the butterfly exists in the form of a caterpillar.
• The Third stage is Pupa which is the transitional phase in which the Caterpillar changes into Butterfly.
• The fourth stage is the Adult stage in which a full-grown adult butterfly comes out of the pupa.

Additional Information

• Complete metamorphosis is seen in butterflies.
• Complete metamorphosis consists of a very active, ravenously eating larval stage and an inactive pupa stage while the incomplete metamorphosis has a nymph, which very closely resembles the adult
• Examples of insects showing Complete metamorphosis -  wasps, ants, butterflies, and fleas
• Examples of insects showing Incomplete metamorphosis - are termites, praying mantis, and cockroaches

The correct answer is Net Worth = Assets - Liabilities.

Key Points

• The book value of the equity held by shareholders of a corporation is referred to as "Net worth."
• It can also be thought of as the net worth of a corporation that its shareholders would be able to claim in the event that all of its assets were liquidated and all of its obligations were paid off.
• To put it another way, it is the sum of assets that remain after all liabilities have been settled.
• Stockholder's equity and shareholder's equity are other names for a company's net worth.
• By deducting the subject company's total liabilities from its total assets, one can arrive at the formula for net worth.

Important Points

• Although equity and net worth are sometimes used interchangeably, they are occasionally employed in different circumstances.
• The net worth calculation takes into account both assets and liabilities.
• The following are the two things to keep in mind when thinking about net worth:
• If net worth is more than zero, it can pay off debt and has strong financial growth.
• If net worth is zero, the company cannot pay its debts and has negative financial growth.

1. All 80 students in a class are standing in a straight row facing north.
2. Ravali is 30th from the extreme right end.
3. Kiriti is 26th from the extreme left end.

Number of students standing between Ravali and Kiriti = 80 - (30 + 26)

= 80 - 56

= 24

Hence, ‘24’ is the correct answer.

The least possible Venn diagram is: 

Conclusions:

I. Some ponds are round. → False (it is possible but not definite)

II. Some mountains are square. → True (Some ponds are mountains and All ponds are square → Some mountains are square)

III. Some ponds are both mountains and round. → False (it is possible but not definite)

IV. Some stools are square. → False (it is possible but not definite)

Hence, only conclusion II follows.

Given: 

Rate of interest = 60%

Time (n) = 2 years

Interest = ₹11,700

Concept used:

Compound interest, CI = P(1 + R/100)ⁿ - P

where

P = Principal amount

R = Rate of interest per year

N = Time in years

Calculation:

Let the initial investment (Principal amount) be P.

According to the question,

P(1 + 60/100)² - P= 11700

⇒ P × 1.6² - P = 11700

⇒ P × 2.56 - P = 11700

⇒ P (2.56 - 1) = 11700

⇒ P × 1.56 = 11700

⇒ P = 11700/1.56

⇒ P = 7500

∴ He initially invested ₹7,500.

Shortcut Trick

Identify the Radius: Base area πr² = 144π ⇒ r = 12 cm.

Use the Pythagorean Triplet (5, 12, 13) where radius r = 12 and slant height l = 13.

∴ Height (h) of the cone = 5 cm.

Volume = (1/3) × Base Area × h = (1/3) × 144π × 5 = 48π × 5 = 240π cm³.

∴ The correct answer is 240π cm³.

Alternate Method

Given:

Slant height (l) = 13 cm

Base Area (πr²) = 144π cm²

Formula Used:

1. Volume of cone = (1/3) × πr²h
2. Slant height relation: l² = r² + h²

Calculations:

⇒ Base Area = πr² = 144π

⇒ r² = 144 ⇒ r = 12 cm

⇒ Using l² = r² + h²

⇒ 13² = 12² + h²

⇒ 169 = 144 + h²

⇒ h² = 169 − 144 = 25

⇒ h = √25 = 5 cm

⇒ Volume = (1/3) × 144π × 5

⇒ Volume = 48π × 5 = 240π cm³

∴ The correct answer is 240π cm³.

Additional Information

Curved Surface Area (CSA) of a Cone

The lateral or curved surface area is given by the formula CSA = π × r × l, where l is the slant height.

Total Surface Area (TSA) of a Cone

The total surface area includes the base area and the CSA: TSA = πr(r + l).

Relation between Cone and Cylinder Volume

The volume of a cone is exactly one-third of the volume of a cylinder with the same radius and height: V_cone = (1/3) × V_cylinder.

Pythagorean Relation

In any right circular cone, the height (h), radius (r), and slant height (l) always satisfy l² = h² + r².

The correct answer is Acetic acid.

Key Points

• Because it partially dissociates into its constituent ions when acetic acid is dissolved in water, Acetic acid is a weak acid.
• It is well known that this weak acid can mix miscible with water. In an aqueous solution, an acid called acetic acid ionises just marginally.
• A particularly popular weak acid is acetic acid, which is present in vinegar.
• Acetic acid, commonly known as ethanolic acid, is a liquid organic chemical that is colourless.
• The amount of the original acid that has been ionised in the solution is represented by the acid ionisation.
• As a result, the numerical value of Ka represents the acid's strength. Stronger acids than weaker acids with relatively lower Ka values include weak acids with substantially higher Ka values.

Important Points

• Fluorine-containing chemical compounds include hydrogen fluoride.
• It can exist as a colourless vapour, seething liquid, or as a substance that has been dissolved in water.
• Hydrofluoric acid is what hydrogen fluoride is known as when it dissolves in water.
• The inorganic substance nitric acid has the formula HNO₃.
• This mineral acid is extremely corrosive.
• One of the many industrial uses for hydrochloric acid (HCl), a colourless, potent mineral acid, is the creation of the hydrochloride salt when it is combined with an organic base.

Shortcut Trick

Ratio of parts = 7 : 11

Smaller part (7 units) = 77 cm

1 unit = 77 ÷ 7 = 11 cm

Total length = (7 + 11) units = 18 units

Total length = 18 × 11 = 198 cm = 1.98 m

∴ The correct answer is 1.98 m.

Alternate Method

Given: Ratio of parts = 7 : 11; Smaller part = 77 cm.

Formula Used: Total Length = Part 1 + Part 2

7 units 11 units Smaller = 77 cm Larger = ?

Total Unbroken Stick

⇒ Let the two parts be 7x and 11x.

⇒ According to the question, 7x = 77 cm

⇒ x = 77 ÷ 7 = 11 cm

⇒ Length of the larger part = 11x = 11 × 11 = 121 cm

⇒ Total length of the unbroken stick = 77 + 121 = 198 cm

⇒ Conversion to meters: 198 ÷ 100 = 1.98 m

∴ The correct answer is 1.98 m.

Additional Information

Ratio and Proportion

Ratio is the comparison of two quantities of the same unit. If a : b is given and the value of one part is k, the actual values are ak and bk.

Total from Ratios

If parts are in ratio a : b, the total is proportional to (a + b). Total = (Sum of ratio parts) × (Value of one unit).

Unit Conversion

1 meter (m) = 100 centimeters (cm). To convert cm to m, divide the value by 100.

Difference between Parts

The difference between the parts is proportional to |a − b|. Here, difference = (11 − 7) units = 4 units = 44 cm.

Given:

The person walks 825 m in 3 minutes.

Concept used:

1m/s = 18/5 km/h

Time × Speed = Distance

Calculation:

3 minutes = 180 seconds

According to the concept, his speed

⇒ 825 ÷ 180

⇒ 55/12 m/s

⇒ (55/12 × 18/5) km/h

⇒ 33/2 km/h

⇒ 16.5 km/h

∴ His speed is 16.5 km/h.

The correct answer is Calcutta.

Key Points

• In 1856, the kingdom of Awadh was formally annexed to the British Empire and the conquest happened in stages.
• The Subsidiary Alliance had been imposed on Awadh in 1801; by the terms of this alliance, the Nawab had to disband his military force, allow the British to position their troops within the kingdom, and act in accordance with the advice of the British Resident who was now to be attached to the court.
• Deprived of his armed forces, the Nawab became increasingly dependent on the British to maintain law and order within the kingdom and he could no longer assert control over the rebellious chiefs and taluqdars.
• In the meantime, the British became increasingly interested in acquiring the territory of Awadh as they felt that the soil there was good for producing indigo and cotton, and the region was ideally located to be developed into the principal market of Upper India.
• By the early 1850s, moreover, all the major areas of India had been conquered: the Maratha lands, the Doab, the Carnatic, the Punjab and Bengal & the takeover of Awadh in 1856 was expected to complete a process of territorial annexation that had begun with the conquest of Bengal almost a century earlier.
• Nawab Wajid Ali Shah was dethroned and exiled to Calcutta on the plea that the region was being misgoverned.
• The British government also wrongly assumed that Wajid Ali Shah was an unpopular ruler, on the contrary, he was widely loved, and when he left his beloved Lucknow, there were many who followed him all the way to Kanpur singing songs of lament.

The correct answer is stagflation.

Key Points

• An economy that is suffering both rising inflation and stagnant economic output is said to be in stagflation.
• Stagflation was initially identified in the 1970s when an oil shock caused high unemployment and rapid inflation in many industrialised nations.
• Slow economic development and relatively high unemployment, sometimes known as economic stagnation, are the hallmarks of stagflation, which is also characterised by rising prices (i.e., inflation).
• An alternative definition of stagflation is a time when there is both inflation and a fall in the GDP.

Important Points

• A needed return's inflation risk compensation is represented by the inflation premium component.
• The difference between the actual gross domestic product (GDP) at the present and the GDP that would be present if an economy were experiencing full employment is known as the inflationary gap, a macroeconomic concept.
• Policies to boost the economy and fight deflation are referred to as reflation.

The correct answer is Maharashtra.

Key Points

• Tarapur Atomic Power station is located in Tarapur, Maharashtra.
• It was the first commercial atomic power station of India commissioned on 28th October 1969.
• It was commissioned under 123 agreements signed between India, the United States, and International Atomic Energy Agency.
• The station is operated by the National power corporation of India.

Additional Information 

Other important Atomic Power stations in India - 

Given:

A solid metallic cone of diameter 36 cm and height 12 cm is melted and made into identical solid spheres each of radius 3 cm. 

Concept used:

Since the metallic cone is melted and made into identical solid spheres, the volume of the metallic cone and the total sum of the volumes of the solid spheres must be equal.

Volume of a sphere = ${4\pi R^3 \over 3}$

Where R is the radius

Volume of a cone = (π × R2 × H)/3

where R = Radius of the base, H = Height

Calculation:

Radius of the base of the cone = 36/2 = 18 cm

Now, the volume of the cone

⇒ (π × 18² × 12)/3 cm²

Let N number of spheres can be made.

According to the concept,

N × ${4\pi 3^3 \over 3}$  = (π × 182 × 12)/3

⇒ N = (18² × 12)/(4 × 3³)

⇒ N = 36

∴ 36 spheres can be made.

The correct answer is income effect.

Key Points

• The change in demand for a commodity or service brought on by a shift in a consumer's purchasing power as a result of a change in real income is known as the income effect in microeconomics.
• This adjustment may be brought about by an increase in salaries, for example, or by the release of funds from an existing income due to a drop in the cost of the item being purchased.
• The income effect is an expression of how changes in relative market prices and incomes impact consumption patterns for consumer goods and services.
• Consumer choice theory links preferences to consumption expenditures and consumer demand curves.
• When real consumer income increases, consumers will desire more of the typical economic items to buy.

Important Points

• The substitution effect is the decline in sales of a product that results from customers switching to less expensive substitutes when the price of the product increases.
• The change in output that results from using one extra unit of a certain input, given that the quantities of other inputs are held constant, is known as the marginal product or marginal physical productivity of an input (factor of production).
• The set of all conceivable consumption bundles that a customer may afford, given the prices of the commodities they have access to and their income, is known in economics as a budget set or the opportunity set facing a consumer.

The correct answer is Africa.

Key Points

• Negroid (also known as Congoid) is a defunct racial category that includes a variety of people who are native to Southern Africa.
• It extends from the southern Sahara desert in the west to the African Great Lakes in the southeast, as well as to isolated regions of South and Southeast Asia (Negritos).
• The phrase comes from outdated ideas of race as a biological category.
• Members of the Göttingen School of History first proposed the idea of categorising people into three races in the 1780s; it was later developed by Western academics in the context of "racist ideologies" during the colonial era under the names Caucasoid, Mongoloid, and Negroid (originally called "Ethiopian").

Important Points

• A person from Sub-Saharan Africa was referred to as a negroid.
• These people were referred to as the "Negroid race."
• Humans used to categorise people into one of three races.
• Negroid, Mongoloid, and Caucasoid were the names given to these races.
• There is just one human race, according to modern science.

Given:

Measures of the diagonals of the rhombus are 8 cm and 16 cm.

Area of the square = Area of the rhombus

Concept used:

Area of a rhombus = Product of two diagonals ÷ 2

Area of a square = side²

Perimeter of a square = 4 × side

Calculation:

 

Area of the rhombus = (8 × 16)/2 = 64 cm²

According to the question,

Area of the square = 64 cm2

The measure of each side of the square = $\sqrt {64}$ = 8 cm

Now, the perimeter of the square = 4 × 8 = 32 cm

∴ The perimeter of the square is 32 cm.

The correct answer is Madhya Pradesh.

Key Points

• The total forest cover of MP is 77,414 sq km.
• In terms of area, Madhya Pradesh has the largest forest cover in the country followed by Arunachal Pradesh, Chhattisgarh, Odisha, and Maharashtra.

Additional Information 

• In terms of forest cover as a percentage of their total geographical area, the top five states are
• Mizoram (85.41 per cent)
• Arunachal Pradesh (79.63 per cent)
• Meghalaya (76.33 per cent)
• Manipur (75.46 per cent)
• Nagaland (75.31 per cent).

The least possible Venn diagram is: 

Conclusions:

I. Some goods are costly. → False (it is possible but not definite)

II. All costly are beautiful. → False (it is possible but not definite)

Hence, neither conclusion I nor conclusion II follows.

The correct answer is Pushyabhuti dynasty.

Key Points

• Harshavardhana belonged to the Pushyabhuti dynasty.
• Pushpabhuti dynasty is also known as Vardhana Dynasty.
• It was founded by Naravardhana close to the 5th or beginning of the 6th century A.D.
• The dynasty flourished under Prabhakarvardhana (father of Harshavardhana).
• He assumed the title of Maharajadhiraja.
• Harshavardhana succeeded the throne in 606 A.D.
• Harsha was also known as Sakalottarapathanatha.
• He conquered Magadha.
• He established his capital at Kannauj.
• His empire extended from Punjab to northern Orissa and from the Himalayas to the bank of Narmada.
• The period of Harsha is well documented in Harshacharitra written by Banabhatta.
• Chinese scholar Hiuen-Tsang visited Harsha's court in 631 A.D.
• The empire came to an end along with the death of Harshavardhana in 647 A.D.
• Harshavardhan wrote three Sanskrit plays viz. Nagananda, Ratnavali and Priyadarshika.
• Hiuen-Tsang mentioned the grand assembly held at Kannauj in 643 A.D. which was attended by twenty kings, four thousand Buddhist monks and about three thousand Jains and Brahmans.
• He also organised Mahamoksha Harishad, a religious festival, at Prayaga (Allahabad).

Given:

Karisma has been spending ₹5,400 on the purchase of an item every year for the past three years.

She paid for the item in the first year, ₹24 in the second year and ₹14.40 in the third year. (per unit)

Concept used:

Total = Average × Number of entities

Calculation:

In the first year, she got 

⇒ 5400/9

⇒ 600 units of the item

In the second year, she got 

⇒ 5400/24

⇒ 225 units of the item

In the third year, she got 

⇒ 5400/14.4

⇒ 375 units of the item

Total units of item acquired by her = 600 + 225 + 375 = 1200 kg

Total price paid by her = 5400 × 3 = ₹16200

Now, the average per-unit price that she paid for this item in the three years

⇒ 16200/1200

⇒ ₹13.50

∴ The average per-unit price that she paid for this item in the three years was ₹13.50.

Shortcut Trick

Find the HCF of 24 and 18 by checking the largest number dividing both: 6.

Find the LCM using the ratio method: 24 : 18 → 4 : 3. LCM = 24 × 3 = 72.

Required Difference = LCM − HCF = 72 − 6 = 66.

∴ The correct answer is 66.

Alternate Method

Given: The numbers are 24 and 18.

Formula Used: Difference = LCM(a, b) − HCF(a, b)

⇒ Prime factorization of 24 = 2 × 2 × 2 × 3 = 2³ × 3¹

⇒ Prime factorization of 18 = 2 × 3 × 3 = 2¹ × 3²

⇒ Highest Common Factor (HCF) = 2¹ × 3¹ = 6

⇒ Least Common Multiple (LCM) = 2³ × 3² = 8 × 9 = 72

⇒ Required Difference = 72 − 6 = 66

∴ The correct answer is 66.

Additional Information

Product Rule of LCM and HCF

The product of two numbers is always equal to the product of their LCM and HCF (a × b = LCM × HCF).

Co-prime Numbers

For any two co-prime numbers, the HCF is always 1 and the LCM is the product of the two numbers.

HCF and LCM Relation

The HCF of any group of numbers is always a factor of their LCM.

Amit's birthday on 16th April 2020 was on Thursday.

Number of odd days from 17th April 2020 to 2nd June 2020 = 14 + 3 + 2 = 19

• This implies that 16th April 2020 + 19 odd days = 2nd June 2020

(Note: A month with 31 days has 3 odd days and a month with 30 days has 2 odd days. May has 31 days so it has 3 odd days)

19 when divided by 7, leaves 5 as remainder.

• Thursday + 5 odd days = Tuesday

So, it was Tuesday on 2nd June 2020.

Hence, ‘Tuesday’ is the correct answer.

The correct answer is Chandigarh.

Key Points

• Le Corbusier, a renowned architect, created the Palace of Assembly, a legislative building in Chandigarh, India.
• The Legislative Assembly, Secretariat, and High Court are three of the structures that make up The Capitol Complex.
• Punjab had to find a new capital after being separated in 1947 as a result of India's independence because Lahore was now part of Pakistan.
• As a result, Jawaharlal Nehru, the first prime minister of India, hired Le Corbusier to design the new city of Chandigarh.
• A city "unbound by the traditions of the past, a symbol of the nation's faith in the future" was to be created, according to the design brief.

Important Points

• Le Corbusier was a French-Swiss architect, designer, painter, writer, and advocate of modern architecture.
• Having been born in Switzerland, he acquired French citizenship in 1930.
• In the five decades of his work, he designed structures in North and South America, Europe, Japan, and India.
• The architectural work of Le Corbusier, an Outstanding Contribution to the Modern Movement, was inscribed as one of 17 Le Corbusier projects across seven nations on the UNESCO World Heritage List on July 17, 2016.

Given:

The total surface area of a solid hemisphere is 1848 cm2. 

Concept used:

Total surface area of a hemisphere = 3πR2 

where R is the radius of the hemisphere

Diameter = 2 × Radius

Calculation:

Let the radius of the hemisphere be R.

According to the concept,

3πR² = 1848

⇒ R² = 1848/3π

⇒ R² = 1848/(3 × 22/7)

⇒ R² = (1848 × 7)/66

⇒ R² = 196

⇒ R² = 14²

⇒ R = 14 (∵ Radius can't be negative)

Now, the diameter of the flat surface of the hemisphere

⇒ 2 × 14

⇒ 28 cm

∴ The diameter of the flat surface of the hemisphere is 28 cm.

The logic followed here is:

Hence, ‘5255’ is the correct answer.

The logic/pattern followed here is:

1. 22 ∶ 485 → 22² + 1 = 484 + 1 = 485 2. 20 ∶ 401 → 202 + 1 = 400 + 1 = 401 3. 14 ∶ 198 → 142 + 1 = 196 + 1 = 197 ≠ 198 4. 18 ∶ 325 → 182 + 1 = 324 + 1 = 325

Hence, '14 ∶ 198' is the odd one out.

Shortcut Trick

Loss of 30% means the Selling Price is 70% of the Cost Price (CP).

⇒ 70% = ₹1,729

To make a gain of 16%, the required Selling Price should be 116% of CP.

⇒ Required SP = (1,729 ÷ 70) × 116

⇒ Required SP = 24.7 × 116 = ₹2,865.20

∴ The correct answer is ₹2,865.20.

Alternate Method

Given:

First Selling Price (SP₁) = ₹1,729

Loss Percentage = 30%

Desired Gain Percentage = 16%

Step 1: Find the Cost Price (CP)

⇒ CP = (SP₁ × 100) ÷ (100 − Loss%)

⇒ CP = (1,729 × 100) ÷ (100 − 30)

⇒ CP = (1,729 × 100) ÷ 70

⇒ CP = 24.7 × 100 = ₹2,470

Step 2: Find the new Selling Price (SP₂)

⇒ SP₂ = CP × (100 + Gain%) ÷ 100

⇒ SP₂ = 2,470 × (100 + 16) ÷ 100

⇒ SP₂ = 2,470 × (116 ÷ 100)

⇒ SP₂ = 2,470 × 1.16

⇒ SP₂ = ₹2,865.20

∴ The correct answer is ₹2,865.20.

Additional Information

Basic Profit and Loss Formulas

Profit = SP − CP; Loss = CP − SP. Profit % = (Profit ÷ CP) × 100; Loss % = (Loss ÷ CP) × 100.

Marked Price (MP) and Discount

Selling Price = Marked Price − Discount. Discount % = (Discount ÷ MP) × 100.

Effective Rate for Successive Changes

For two successive changes of a% and b%, the effective change is [a + b + (ab ÷ 100)]%.

Given:

27 × 3 × 896 ÷ $\sqrt {3136}$ = y + 640

Concept used:

Calculation:

27 × 3 × 896 ÷ $\sqrt {3136}$ = y + 640

⇒ 27 × 3 × 896 ÷ 56 = y + 640

⇒ 27 × 3 × 16 = y + 640

⇒ 1296 = y + 640

⇒ y = 1296 - 640

⇒ y = 656

∴ The value of y is 656.

The correct answer is Ranchi.

Key Points

• The ninth edition of the National Open Race Walking Championships, a qualifying event for the 2022 year’s World Championships, was held in Ranchi, Jharkhand.
• The championships will have 35km and 20km race walk events for men and 20km events for women.
• There will also be 10km events for both U-10 men and women.
• The championships will also be a qualifying event for the World Championships to be held in Eugene, USA, from July 15-24.

Given:

A certain sum was invested at 40% p.a. compound interest for two years. (compounded annually)

When the interest was compounded half-yearly, the amount payable on maturity after two years would have been ₹4,544 more.

Concept used:

Compound interest, CI = P(1 + R/100)^N - P

where

P = Principal amount

R = Rate of interest per year

N = Time in years

Calculation:

Let the sum invested be P.

The amount becomes according to the initial conditions = P(1 + 40/100)2

When the interest compounded half-yearly,

Rate of interest (R) = 40 ÷ 2 = 20%

Time (N) = 2 × 2 = 4

According to the concept,

P(1 + 20/100)⁴ = P(1 + 40/100)2 + 4544

⇒ P × 1.2⁴ - P × 1.4² = 4544

⇒ P × 2.0736 - P × 1.96 = 4544

⇒ P(2.0736 - 1.96) = 4544

⇒ P × 0.1136 = 4544

⇒ P = 4544/0.1136

⇒ P = 40,000

∴ The sum invested was ₹40,000.

The correct answer is Red sea.

Key Points

• The Red Sea is a confined body of water that stretches 1,930 kilometres southeast from Suez, Egypt, to the Bab el-Mandeb Strait, where it joins the Gulf of Aden and, ultimately, the Arabian Sea.
• The Gulf of Aqaba (Elat) and the Gulf of Suez must be viewed geologically as the northern extension of the same structure.
• The coasts of Saudi Arabia and Yemen are to the east, while those of Egypt, Sudan, and Eritrea are to the west.
• It has a maximum width of 190 miles, a maximum depth of 3,040 metres (9,974 ft), and an area of over 174,000 miles (450,000 square km). Some of the world's saltiest and hottest waters can be found in the Red Sea.
• It is one of the busiest waterways in the world, bringing maritime traffic between Europe and Asia and connecting to the Mediterranean Sea via the Suez Canal.
• Its name comes from the colour shifts in its waters that have been noticed.

Important Points

• The North and Central European Plain, Denmark, Estonia, Finland, Germany, Latvia, Lithuania, Poland, Russia, and Sweden all enclose the Baltic Sea, which is a branch of the Atlantic Ocean.
• The Sulu Archipelago, Sulu Sea, and Mindanao Island in the Philippines, the Sangihe Islands series, Sulawesi's Minahasa Peninsula, northern Kalimantan in Indonesia, and the western Pacific Ocean's Celebes Sea all abut the sea on the Celebes Sea's northern and western edges, respectively.
• A peripheral Mediterranean sea of the Atlantic Ocean, the Black Sea is located between Europe and Asia, east of the Balkans, south of the East European Plain, west of the Caucasus, and north of Anatolia.

Shortcut Trick

Initial Average of 2 numbers = 46

New Average after adding the 3rd number = 43

Change in Average = 43 − 46 = −3

Third Number = New Average + (Initial Count × Change)

⇒ 43 + (2 × (−3)) = 43 − 6 = 37

∴ The correct answer is 37.

Alternate Method

Given: Average of 2 numbers = 46, Combined average of 3 numbers = 43.

Formula Used: Sum of observations = Average × Number of observations

⇒ Sum of the first 2 numbers = 46 × 2 = 92

⇒ Sum of all 3 numbers = 43 × 3 = 129

⇒ Third number = (Sum of 3 numbers) − (Sum of 2 numbers)

⇒ Third number = 129 − 92

⇒ Third number = 37

∴ The correct answer is 37.

Additional Information

Arithmetic Mean

The average is the sum of all elements divided by the total count: Average = (∑x) ÷ n.

Weighted Average

If two groups have averages A₁ and A₂ with n₁ and n₂ terms, the combined average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Effect of Change

If a constant k is added to every number in a set, the average also increases by k. If multiplied by k, the average is multiplied by k.

Given:

The length and the width of a rectangular plot of land are 10.5 m and 8 m, respectively. 

Concept used:

Area of a rectangle = Length × Width

Calculation:

Area of the rectangular plot = 10.5 × 8 = 84 m²

Cost of laying grass in the entire plot

⇒ 84 × 15.25

⇒ ₹1,281

∴ The cost of grass in the entire plot is ₹1,281.

Given:

Sunidhi earned an average of ₹6,250 per month during the past 12 months.

During the first 10 months, her average earnings per month were ₹5,800.

Concept used:

Total = Average × Number of entities

Calculation:

Sum of the earnings received by her during the entire year

⇒ 6250 × 12

⇒ ₹75000

Sum of the earnings received by her in the first 10 months

⇒ 5800 × 10

⇒ ₹58000

Sum of the earnings received by her in the last 2 months

⇒ 75000 - 58000

⇒ 17000

Average earnings received by her in the last 2 months

⇒ 17000/2

⇒ ₹8500

∴ Sunidhi's average earnings per month during the last two months of the period was ₹8500.

The pattern followed here is:

Similarly,

Hence, ‘FBESUM’ is the correct answer.

Shortcut Trick

In a circle, angles subtended by the same arc at the circumference are equal. ∴ ∠ABD = ∠ACD = 35°.

Since AB is the diameter, the angle in the semicircle ∠ADB = 90°.

In right-angled ΔADB, the sum of acute angles is 90°.

∠BAD = 90° − ∠ABD ⇒ 90° − 35° = 55°.

∴ The correct answer is 55°.

Alternate Method

Given: ABCD is a cyclic quadrilateral with diameter AB and ∠ACD = 35°.

Formula Used: Angle in a semicircle is 90°; Angles in the same segment are equal; Sum of angles in a triangle = 180°.

⇒ In the circle, ∠ACD and ∠ABD are subtended by the same arc AD.

⇒ ∴ ∠ABD = ∠ACD = 35°

⇒ Since AB is the diameter, the angle subtended at the circumference is 90°.

⇒ ∴ ∠ADB = 90°

⇒ In ΔADB, sum of angles = 180°

⇒ ∠BAD + ∠ADB + ∠ABD = 180°

⇒ ∠BAD + 90° + 35° = 180°

⇒ ∠BAD = 180° − 125°

⇒ ∠BAD = 55°

∴ The correct answer is 55°.

Additional Information

Angle in a Semicircle

Any angle subtended by the diameter at any point on the circumference of the circle is always a right angle (90°).

Angles in the Same Segment

Angles subtended by the same arc or chord at any point on the remaining part of the circle are equal.

Cyclic Quadrilateral Property

In a cyclic quadrilateral, the sum of each pair of opposite angles is 180° (∠A + ∠C = 180° and ∠B + ∠D = 180°).

The correct answer is Brazil.

Key Points

• PSLV-C51 is the Indian Polar Satellite Launch Vehicle (PSLV) program's 53rd mission.
• On February 28, 2021, the Polar Satellite Launch Vehicle (PSLV)-C51 was launched with the main payload from Brazil, INPE's Amazônia-1, and 18 smaller ride-sharing tiny satellites.
• NSIL is launching its first focused commercial product.
• The PSLV-C51 was launched from the Satish Dhawan Space Centre's First Launch Pad in Sriharikota, Andhra Pradesh.
• The PSLV-C51/Amazonia-1 was NewSpace India Limited's (NSIL), a government of India company under the Department of Space, first dedicated commercial mission.
• PSLV has now launched 342 client spacecraft from 34 countries into orbit, bringing the total number of customer satellites launched by PSLV to 342 from 34 countries.

The code for each word is shown below:

Code for:

money - io

bank - km

Hence, ‘km io’ is the correct answer.

The least possible Venn diagram is: 

Conclusions:

I. At least some mobiles are computers. → False (it is possible but not definite)

II. At least some phones are laptops. → False (As no laptop is a computer and all phones are computers → No phone is laptop)

Hence, neither conclusion I nor II follows.

Statement:

W = H ≤ G < C ≥ T = L > M

Conclusions:

I. W < T → False (As W = H ≤ G < C ≥ T → a definite relation between W and T cannot be determined)

II. C > M → True (As C ≥ T = L > M → C > M)

Hence, only conclusion II is true.

The correct answer is Muhammad Tughluq.

Key Points

• Muhammad Tughluq had the Begumpuri mosque constructed as the primary mosque for Jahanpanah, the "Sanctuary of the World," his new city in Delhi.
• One of the biggest mosques in the city is called Begampuri Masjid, and it is situated close to Aurobindo Ashram on Sri Aurobindo road in Begampur, close to Delhi.
• Khan-i-Jahan, the son of Muqbal Khan, the Prime Minister of Firuz Shah, constructed it in the 12th century.
• Muhammad bin Tughlaq (1325–51), the Delhi Sultan, founded the fourth mediaeval city of Delhi in the years 1326-1327.

Important Points

• From February 1325 until his death, Muhammad ibn Tughlaq served as the Delhi Sultanate's eighteenth ruler.
• He was Ghiyath al-Din Tughluq's (the Tughlaq dynasty's founder) eldest son.
• Ghiyas-ud-din Tughlaq, who ruled the Sultanate of Delhi from 1320 to 1325, was the founder of the Tughluq dynasty in India.
• Tughluqabad was the city he founded.
• The ninth ruler of Delhi's Mamluk dynasty was Ghiyas ud din Balban.
• The Ghurid monarch Muhammad Ghori's general was Qutb ud-Din Aibak.

Four students - Ravindra, Shiva, Triveni and Nagesh, who want to be selected in the basketball team.

1. Nagesh is shorter than Ravindra but taller than Triveni.

Ravindra > Nagesh > Triveni

2. Shiva is shorter than Nagesh but taller than Triveni.

Nagesh > Shiva > Triveni

From 1 and 2, we get:

Ravindra > Nagesh > Shiva > Triveni

If the coach wants to select the tallest student among them, then Ravindra will be selected.

Hence, ‘Ravindra’ is the correct answer.

Given:

The LCM of the two numbers is 35 times their HCF. The LCM and HCF differ by 238

The difference between the numbers is 14.

Concept used:

LCM × HCF = The Product of two numbers

(A + B)2 = (A - B)2 + 4AB

Calculation:

Let the HCF and LCM be H & L respectively.

According to the question,

L = 35 × H      ....(1)

L - H = 238      ....(2)

⇒ 35H - H = 238 (From 1)

⇒ 34H = 238

⇒ H = 238/34

⇒ H = 7

Now, L = 35 × 7

⇒ L = 245

So, the product of HCF and LCM = 245 × 7 = 1715

Let the aforementioned numbers be P and Q (P > Q).

Sum of the two numbers = (P + Q)

According to the concept,

PQ = 1715

According to the question,

P - Q = 14

⇒ (P - Q)2 = 142

⇒ (P - Q)2 + 4PQ = 142 + 4PQ (Adding 4PQ on both side)

⇒ (P - Q)2 + 4PQ = 142 + 4 × 1715 (∵ PQ = 1715)

⇒ (P + Q)2 = 7056

⇒ (P + Q)² = 84²

⇒ (P + Q) = 84 (∵ Here, the sum of the numbers can't be negative)

∴ The sum of the numbers is 84.

The correct answer is Palagummi Sainath.

Key Points

• The Fukuoka Grand Prize for 2021 has been given to journalist Palagummi Sainath.
• He is a dedicated journalist who has persisted in looking into India's poor farming villages and documenting the reality of the people who live there.
• The Fukuoka City International Foundation and the Japanese city of Fukuoka established the prize, which is granted to people and organisations who seek to preserve Asian culture.
• There are two other award categories in addition to the Grand Prize: academics and culture.
• Professor Kishimoto Mio, a Japanese historian with expertise in the socio-economic history of China during the Ming-Qing dynasty, received the Academics Prize.​

Important Points

• Born in Chennai, Palagummi Sainath has held positions as vice-editor of the political magazine Blitz and editor of The Hindu.
• The journalist received the 1995 Lorenzo Natali Prize for Journalism from the European Commission and the 2000 Amnesty International Global Human Rights Journalism Prize.
• In 2001, he was awarded the Boerma Prize by the Food and Agriculture Organization of the United Nations, and in 2007, he was given the Ramon Magsaysay Award for distinguished service to Asian media.

Additional Information

• Indian historian Romila Thapar specialises in ancient Indian history, a field in which she is a leader.
• Ramachandra "Ram" Guha is an Indian historian, environmentalist, author, and public intellectual whose areas of interest include economics, the social and political history of cricket, and historical and present issues related to the environment.
• Ustad Amjad Ali Khan, an Indian classical sarod player who was born on October 9, 1945, is most renowned for his crisp and quick ekhara taans.

The correct answer is 40.

Key Points

• For Assembly elections (February - March 2022) in Uttar Pradesh, Uttarakhand and Punjab, the expenditure limit for legislative assembly candidates was revised to ₹40 lakh in January 2022.
• According to a notification from the Law Ministry, the increased value of Rs. 40 lakh would be applicable in Uttar Pradesh, Uttarakhand, and Punjab and Rs. 28 lakh in Goa and Manipur.
• The most recent significant change to candidate spending caps was made in 2014, with the exception of a 10% increase in response to the COVID-19 pandemic in 2020.
• In 2020, the EC established a committee to investigate the spending cap.
• Political parties, key election officials, and election observers were invited to provide comments by the committee.
• The committee discovered a significant rise in the number of voters and the Cost Inflation Index during 2014.
• It also had a role in the evolving campaigning strategies, which eventually moved toward virtual campaigns.

Important Points

• In order to elect all 403 members of the 18th Uttar Pradesh Legislative Assembly, elections for the assembly were held in seven phases from 10 February to 7 March 2022.
• In order to choose the 70 members of the Uttarakhand Legislative Assembly, elections were held on February 14, 2022.
• Punjab held its legislative assembly elections on February 20, 2022, to choose the 117 members of the province's 16th assembly.

Given:

The price of item A was $\frac{2}{3}$ of the price of item B, while the price of item C was $\frac{3}{4}$ of the price of item B.

The price of item A was ₹88

Calculation:

Let the price of item B be Q.

The price of item A = 2Q/3

The price of item C = 3Q/4

According to the question,

2Q/3 = 88

⇒ Q = (88 × 3)/2

⇒ Q = 132

Now,

3Q/4 = (3 × 132)/4

⇒ 99

∴ The price of item C was ₹99.

The correct answer is Deepika Kumari.

Key Points

• Deepika Kumari won the gold medal in the women's individual recurve event at the Archery World Cup Stage 3 held in Paris in June 2021.
• At the Archery World Cup Stage 3 competition in Paris, the talented Indian archer Deepika Kumari set a new world record by winning three consecutive gold medals.
• With four gold medals, India took first place in the medal count.
• Abhishek Verma won the fourth gold medal for the compound section's men's solo event.
• Indian professional archer Deepika Kumari competes in the archery event and is now rated No. 1 in the world.
• She won the women's individual recurve gold medal at the 2010 Commonwealth Games.

Important Points

• The World Archery Federation has ranked Ankita Bhakat, an Indian recurve archer, as the 20th best in the world.
• Since joining the national recurve squad in 2007, Bombayla Devi Laishram has competed internationally for India as an archer.
• She has won four gold, five silver, and four bronze medals at different Archery World Cup competitions, as well as a silver medal at the World Archery Championships.
• Dola Banerjee is an Indian sportswoman who competes in archery.

Given:

A and B can do a piece of work together in 48 days.

B alone can do the work in 60 days.

The duo starts working together, but B leaves 15 days before the work gets over.

Concept used:

Total work = Work done per day × Total time taken 

Calculation:

LCM (48, 60) = 240

Let the total work be the individual time taken by the workers.

Now, the total work = 240 units

B does a day = 240/60 = 4 units of work

A and B together do a day = 240/48 = 5 units of work

⇒ A does a day = (5 - 4) units of work

⇒ A does a day = 1 unit of work

Let the total work be completed in K days.

So, A and B will work for K and (K - 15) days.

According to the question,

1 × K + 4 × (K - 15) = 240

⇒ K + 4K - 60 = 240

⇒ 5K = 240 + 60

⇒ 5K = 300

⇒ K = 300/5

⇒ K = 60

Now, the duo worked together for

⇒ (K - 15) days

⇒ (60 - 15) days

⇒ 45 days

∴ 45 days A and B worked together.

The correct answer is It requires decreasing inputs over time.

Key Points

• The introduction of new, high-yielding varieties into emerging countries starting in the middle of the 20th century, led to a significant increase in the production of food grains (particularly wheat and rice).
• Mexico and the Indian subcontinent saw their first stunning successes.
• In order to achieve their high yields, the new types need to use significant quantities of chemical fertilisers and pesticides, which raises concerns about the expense and potential negative impacts on the environment.

Important Points

• The collection of research and technology transfer programmes known as the "Green Revolution" took place between 1950 and the late 1960s and significantly enhanced agricultural production throughout much of the world.
• High-yielding varieties (HYVs) of cereals, particularly dwarf wheat and rice, were adopted as a result of the initiatives.
• It was connected to mechanised farming, artificial fertilisers, agrochemicals, controlled water supply (typically using irrigation), and innovative farming techniques.
• These were all considered to be part of a "bundle of activities" that would replace "conventional" technology and be adopted as a whole.

According to given conditions,

Clearly, Point X is to the South-East of Point K.

Hence, ‘South-East’ is the correct answer.

The correct answer is Pradhan Mantri Kaushal Vikas Yojana 3.0.

Key Points

• A pilot initiative was started by the Ministry of Skill Development and Entrepreneurship to bring Kashmir's Namda craft back to life.
• The Pradhan Mantri Kaushal Vikas Yojana 3.0 saw the launch of the Namda Craft Pilot Project.
• 25 batches are required for implementation. Three training cycles are required for these 25 batches.
• Three and a half months will be allocated to each training cycle.
• 2,250 persons will gain from the project.
• Through Recognition of Prior Learning, the project will improve people's learning (a component of Pradhan Mantri Kaushal Vikas Yojana).

Important Points

• A sheepskin rug is known as a Namda.
• The craft uses a felting technique rather than the standard weaving procedure.
• The majority of floor pieces made using Namda craft are for floors.
• Additionally, mattresses and bed covers are made from it.
• There is a tradition of sitting on the floor in every Kashmiri household, regardless of wealth. In the winter, the floor gets very chilly.
• Because of this, Namda craft evolved in Kashmir.

Additional Information

• The capacity development scheme is an ongoing MoSPI (Ministry of Data & Programme Implementation) central sector programme with the general goal of increasing infrastructural, technical, and human resources in order to make reliable and timely official statistics available.
• The Pradhan Mantri Vaya Vandana Yojana is a pension-insurance programme that offers security to senior folks.
• A Rozgar Mela is a gathering of businesses and job seekers where applications and interviews are conducted for open positions.

Given: 

Vimal secured 46% marks in the exam and failed to qualify in the exam by 10 marks.

If he secured 52% marks, he would have secured 8 marks more than what was the minimum qualifying marks.

Calculation:

Let the total marks in the exam be Q.

Vimal scored = 46% × Q = 0.46Q

Minimum passing marks = 0.46Q + 10

According to the question,

0.46Q + 10 = 52% × Q - 8

⇒ 0.46Q + 10 = 0.52Q - 8

⇒ 0.52Q - 0.46Q = 10 + 8

⇒ 0.06Q = 18

⇒ Q = 18/0.06

⇒ Q = 300

Now, the passing marks in the exam

⇒ 0.46 × 300 + 10

⇒ 148

∴ The minimum marks one had to score to qualify in the exam were 148.

1. R > U → True (As, R > T ≥ N > U → R > U) 2. N < Z → False (As, N > U = S ≤ Z → No definite relation between N and Z can be determined) 3. V < T → False (As, T ≥ N > U = S ≤ Z < V → No definite relation between V and T can be determined) 4. T = S → False (As, T ≥ N > U = S → T > S)

Hence, ‘R > U’ is the correct answer.

The correct answer is 1000.100.10.1.

Key Points

• A network interface on a system is uniquely identified by its 32-bit IPv4 address.
• The format of an IPv4 address is typically four 8-bit fields separated by periods, printed in decimal digits.
• A byte of the IPv4 address is represented by each 8-bit field.
• Dotted-decimal format is a common name for this way of expressing the bytes of an IPv4 address.
• The network component and the host part are the additional divisions made in the IPv4 address's bytes.
• Each octet in IPv4 address can have a value from 0 to 255, but in option 4 the first octet value is 1000 which is not valid. Consequently, it can not be a valid IPv4 address.

Important Points

• The unique number allocated to the network is specified in the network component.
• The allocated class of the network is also identified by the network component.
• The portion of the IPv4 address that you give to each host is known as the host part.
• This machine on your network is identified by the host part specifically.

The correct answer is Andhra Pradesh.

Key Points

• Jawahar Lal Nehru announced the formation of Andhra Pradesh as a separate state in 1952.
• In 1953, the first linguistic state of Andhra for Telugu-speaking people was formed.
• Constituent Assembly in 1948 appointed Linguistic Provinces Commission to enquire into the desirability of linguistic provinces.
• It was headed by Justice S. K. Dhar.
• The Commission advised against the organisation of states on a linguistic basis at that time because it might harm national unity and also it is administratively inconvenient.
• It recommended reorganization on the basis of administrative convenience rather than on a Linguistic basis.
• In 1953, Nehru appointed States Reorganisation Commission to examine the reorganization of the states of the Union.
• Members: Justice Fazl Ali, KM Panikkar & H Kunzru.
• States Reorganization Act 1956:
• It provided for 14 states and 6 centrally administered territories although opposed to the disintegration of Bombay & Punjab.

Given:

5 is added to one-third of the number, the sum is 59.

Calculation:

Let the number be Q.

One-third of Q = Q/3

According to the question,

5 + Q/3 = 59

⇒ Q/3 = 59 - 5

⇒ Q/3 = 54

⇒ Q = 54 × 3

⇒ Q = 162

∴ The number is 162.

According to given conditions, 

Clearly, point A is 12 km to the West of point F.

Hence, ‘12 km, west’ is the correct answer.

The pattern followed here is:

Hence, ‘QXJ’ is the correct answer.

Given:

(3/4) of a number is subtracted from (6/7) of 126

Calculation:

Let the number be X

According to question,

(6/7) × 126 - (3/4) × X = 33

108 - 33 = (3/4) × X

75 = (3/4) × X

X = 100

∴ The number is 100.

The correct answer is Assam.

Key Points

• The first-ever Bihu "Husori troupe" is stealing the show in Dibrugarh's Moran area since this is the first time young girls will be playing the Dhol, Pepa, Gagana, and Taal, which are typically played by men when performing Husori.
• The only Husori Troupe for girls in Assam and the first. Husori is typically performed by boys, however, girls can also do it.
• Lahori is also performed by boys.
• A crucial component of Rongali Bihu, "Husori" is sung on Cow Bihu, the first day of the festival.
• On this day, young men sing a Bihu song called "Husori" door to door while being guided by the elders.

Important Points

• Assam: (As of June 2022) 
• Statehood: 26 January 1950
• Largest city: Guwahati
• Capital: Dispur
• Districts: 35
• ​Governor: Jagdish Mukhi
• Chief Minister: Himanta Biswa Sarma (BJP)

The correct answer is SoftWorthy.

Key Points

• The coveted National Science Foundation Innovation-Corps (NSF I-Corps) Teams Award has been given to SoftWorthy in the US.
• The award-winning project of SoftWorthy, which was established in 2020, is dedicated to creating cutting-edge computational techniques for "stochastic modelling, design simulation, and sensitivity analysis of electronic devices like printed-circuit-boards (PCBs), which are essential for the development of cutting-edge technological applications like driverless cars and energy-efficient smart buildings.
• The business has been working to create cutting-edge software technology for carrying out engineering analysis.
• It is run by a group of Indian engineers who received their training at the Massachusetts Institute of Technology and Harvard University.

Important Points

• Zenefits has all the HR tools you need to manage your workforce effectively, including performance appraisals, org charts, and easy PTO tracking, among many other features.
• San Jose, California serves as the home base for the publicly traded Bloom Energy.
• It produces and sells on-site electricity-generating solid oxide fuel cells.
• An American business called Instacart provides grocery delivery and pickup services in both the US and Canada.

If

• 'Autumn' is called 'Winter'
• 'Winter' is called 'Summer'
• 'Summer' is called 'Rainy'
• 'Rainy' is called 'Cloudy'

In winter season we definitely wear woollen garments and 'Winter' is called 'Summer'.

Therefore, in 'Summer' season we definitely wear woollen garments.

Hence, ‘Summer’ is the correct answer.

Varun, Kashyap, Anil, Johnson, Samson and Prasad are sitting in a row facing north but not necessarily in the same order.

1. Varun and Kashyap sit at the extreme ends.

2. Anil is sitting to the immediate left of Varun.

The above condition cannot be satisfied in Case I, so it is elimianted.

3. Only one person sits between Anil and Samson. 

4. Johnson is not an immediate neighbour of Kashyap.

Johnson is sitting between Samson and Anil, as it is the only possible position for Johnson to occupy.

Remaining person Prasad is sitting to the immediate right of Kashyap as it is the only possible position for Prasad to occupy.

Therefore, the final arrangement will be as shown below:

Prasad is sitting to the immediate right of Kashyap.

Hence, ‘Prasad’ is the correct answer.

The correct answer is 1988.

Key Points

• In India, the National Consumer Disputes Redressal Commission (NCDRC) was established in 1988 in accordance with the Consumer Protection Act of 1986.
• In New Delhi, it has its headquarters. A Supreme Court of India judge who is now sitting or has retired is in charge of the commission.
• Justice R K Agrawal, a former Supreme Court of India judge, is currently in charge of the commission.
• According to Section 21 of the Consumer Protection Act of 1986, the National Consumer must have the authority to hear complaints worth more than one crore as well as to appeal and review decisions made by State Commissions or District Fora, as the case may be.

Important Points

• To safeguard the interests of Indian consumers, the Indian Parliament passed the Consumer Protection Act, 1986 (COPRA).
• The Consumer Protection Act of 2019 took its place.
• It was created to facilitate the creation of consumer councils and other institutions for the resolution of consumer complaints and issues related to them.
• The law was passed by the Assembly in October 1986, and it became effective on December 24 of the same year.
• The law to the right was created prior to the COPRA act.

There are seven members, H, I, J, K, L, M and N, in a family.

1. H is K's mother's mother.
2. J and L are the only two children of H and M.
3. J is the only daughter of M.
4. N is the son of L and I.

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

M is the grandfather of N, or we can say that M is N's father's father.

Hence, ‘Father's father’ is the correct answer.

Given sequence: a_ bca _ _ ca _ b _ _ abc

1. aaacba → aabc - aaac - acbb - aabc
2. bacaaa → abbc - aacc -aaba - aabc
3. abacaa → aabc - abac - acba - aabc
4. aabaca → aabc - aabc - aabc - aabc

• Here, aabc is repeated

Hence, ‘aabaca’ is the correct answer.

The correct answer is the Citizenship of India.

Key Points

• Articles 5 to 11 of the Indian Constitution relate to the Citizenship of India.
• Citizenship comes under Part II of the Indian Constitution.
• It is borrowed from Britain's Constitution.
• The Indian constitution prohibits Dual citizenship.

Important Points 

• Methods to acquire citizenship:

1. By Birth
2. By Descent
3. By Registration
4. By Naturalisation
5. By Incorporation of Territory.

• Methods to lose citizenship:

1. By Renunciation
2. By Termination
3. By Deprivation

Additional Information

• Fundamental Duties are defined in Part IV-A of the Indian Constitution.
• Fundamental Duties are the moral obligations of all the citizens of India.
• There are 11 Fundamental duties.
• Fundamental Duties were added to the Constitution by 42nd Amendment of the Constitution in the year 1976.​
• Part III of the Indian Constitution deals with the fundamental rights given to the citizens of India
• These rights are enshrined in Articles 12 to 35 of the Indian Constitution.

Given:

(162 ÷ 9) ÷ 3 - (343 ÷ 49) ÷ 7

Concept used:

Calculation:

(162 ÷ 9) ÷ 3 - (343 ÷ 49) ÷ 7

⇒ 18 ÷ 3 - 7 ÷ 7

⇒ 6 - 1

⇒ 5

∴ The value of (162 ÷ 9) ÷ 3 - (343 ÷ 49) ÷ 7 is 5.

The logic followed here is:

Similarly,

Hence, ‘EGLTDR’ is the correct answer.

Shortcut Trick

Usual time = 9:46 am − 7:40 am = 126 minutes.

New time = [Usual Time × (1/4) × (7/6)] + [Usual Time × (3/4) × (5/6)]

New time = [126 × 7/24] + [126 × 15/24] = 126 × (22/24) = 115.5 minutes.

115.5 minutes = 1 hour 55 minutes 30 seconds.

Arrival time = 7:40 am + 1 hr 55 min 30 sec = 9:35:30 am.

∴ The correct answer is 9:35:30 am.

Alternate Method

Given: Departure = 7:40 am, Usual Arrival = 9:46 am.

Formula Used: Time = Distance ÷ Speed

⇒ Usual Time (T) = 9:46 − 7:40 = 2 hours 6 minutes = 126 minutes.

⇒ Let usual distance be D and usual speed be S. T = D/S = 126.

⇒ New Time (T_n) = [(1/4)D ÷ (6/7)S] + [(3/4)D ÷ (6/5)S]

⇒ T_n = [(1/4) × (7/6) × (D/S)] + [(3/4) × (5/6) × (D/S)]

⇒ T_n = (D/S) × [(7/24) + (15/24)] = 126 × (22/24)

⇒ T_n = 126 × (11/12) = 10.5 × 11 = 115.5 minutes.

⇒ 115.5 minutes = 1 hour 55 minutes 30 seconds.

⇒ New Arrival = 7:40:00 + 1:55:30 = 9:35:30 am.

∴ The correct answer is 9:35:30 am.

Additional Information

Inverse Proportion of Speed and Time

When distance is constant, Speed is inversely proportional to Time (S ∝ 1/T). If speed becomes x/y of usual, time becomes y/x of usual.

Average Speed for Different Portions

Total Time = ∑(Distance_i ÷ Speed_i). Always convert total time into minutes or seconds for easier calculation in clock-based problems.