Search Previous Year Questions

The correct answer is 'I2R t' .

Key-points:

• Generally

​                 Energy produced = Power\(\times\) Time 

• Heat energy = Electrical Power \(\times\) time

                                = P \(\times\) t

                                = VI \(\times\) t

                             H = VIt

• By Ohm's law ( V = IR )we can write

                            H = IR\(\times\)It

                            H =  I2R t

 

Additional information:

• Ohm's Law
• ​Ohm’s law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperatures remain constant.
• V = IR

The correct answer is Ministry of Civil Aviation.

Key Points

• The Minister of Civil Aviation Shri Jyotiraditya M. Scindia launched National Air Sport Policy 2022 (NASP 2022).
• NASP 2022 lays out the vision of making India one of the top sports nations by 2030, by providing a safe, affordable, accessible, enjoyable and sustainable air sports ecosystem in India.
• The NASP 2022, is a step toward providing safe and affordable sustainable air sports.
• It has been drafted based on the inputs received from policymakers, air sports practitioners and the public at large and will ensure the establishment of good quality infrastructure, equipment, instructors and services.
• The main ministry in India for developing national policies and initiatives for the growth and regulation of civil aviation is the Ministry of Civil Aviation.
• It develops and puts into action plans for the country's civil aviation industry's orderly expansion.
• Its duties also include controlling airport infrastructure, managing air traffic, and transporting people and things by air.

Additional Information

• Ministry of Defence:
• India's defence, in its entirety, is the responsibility of the Indian government.
• The President has full authority over the armed forces.
• The Cabinet is in charge of overseeing national defence.
• This is done through the Ministry of Defence, which gives the Armed Forces the resources and the policy framework they need to carry out their duties in the context of national defence.
• The Ministry of Defence is led by the Defence Minister.
• The current Defence Minister of India is Rajnath Singh.
• ​Ministry of Culture:
• ​India's unique culture serves as a metaphor for the nation's diversity.
• The Ministry of Culture's mandate centres on tasks like protecting and promoting all forms of art and culture, both tangible and ethereal, as well as preserving and conserving our cultural legacy.
• The Ministry's job is to establish and maintain strategies for ensuring that people's aesthetic and creative sensitivities are alive and well.
• The current Minister of Culture is G. Kishan Reddy.
• Ministry of Youth Affairs and Sports:
• ​Throughout the year, the Minister of State (Independent Charge) for Youth Affairs & Sports provided overall leadership to the Ministry of Youth Affairs & Sports.
• The Department of Youth Affairs and the Department of Sports in India are both under the control of the Ministry of Youth Affairs and Sports, a division of the Indian government.
• The current Minister of Youth Affairs and Sports is Anurag Thakur, who is succeeded by Nisith Pramanik as his deputy.

The correct answer is 'Self-combining capacity to form a long chain of atoms' .

Key-points:

• Catenation:
• ​Catenation refers to the property of self–linking of atoms of an element.
• It depends upon bond energy, size, and bond length between the atoms of the same element.
• Thus, the element capable of forming stronger and shorter self – linking bonds will have the best catenation property.​

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**Additional information:**​

• Property of occurring as different allotropes
• The property of some metals and alloys that exhibit different crystalline lattices at different temperatures is called allotropy.
• ​Self-degeneration property
• ​Degeneracy is thus a relational property that requires comparing the behavior of two or more components.
• ​Property of carbon to give combustive nature to its compounds
• ​When carbon burns in the presence of oxygen, it produces heat and light.
• This process of burning carbon and its compounds to release energy is known as combustion.

The correct answer is Used to generate electricity in thermal plants and are cost effective.

Key Points

• Fossil Fuel:
• There are three major types of fossil fuels, they are coal, petroleum and natural gas.
• Coal is a hard substance which is black in colour and composed of carbon, hydrogen, nitrogen, oxygen and sulphur.

Additional Information

• Advantages of Fossil Fuel
• Fossil fuels have the ability to create a huge amount of electricity at a single location.
• Moreover, they are found easily and also cost-effective.
• Further, we can easily transport oil and gas through pipelines.
• Over time, they have become safer. Besides, most of our infrastructure is designed to operate through the use of fossil fuels.
• Finally, even though it is a finite resource, it is available in abundance.
• Disadvantages of Fossil Fuel
• They emit carbon dioxide, a major greenhouse gas, on burning, which is also a major source of pollution and contributes to global warming.
• When we burn coal and oil, it releases sulfur dioxide that can cause breathing problems and acid rain.
• Most importantly, we cannot replace them.
• Further, when we burn them, they make the environment more acidic due release of nitrogen and sulphur.
• Being nonrenewable energy resources, their limited supply means we will run out eventually.
• Moreover, harvesting them results in fatal diseases like coal miners suffer from Black Lung Disease sometimes and natural gas drillers are exposed to chemicals which is also dangerous health-wise.

Given:

3 - 6 ÷ 9 + 6 × 2 = 6 

Calculation:

By option Method:

Option I: After interchanging - and ×

⇒ 3 × 6 ÷ 9 + 6 - 2 = 6 

⇒ 2 + 6 - 2 = 6

⇒ 6 = 6

This is correct the equation.

Option II: After interchanging  ÷ and  +

⇒ 3 - 6 + 9 ÷ 6 × 2 = 6 

⇒ 3 - 6 + 3  = 6

⇒ 0 ≠ 6

This is not correct the equation.

Option III: After interchanging  + and × 

⇒ 3 - 6 ÷ 9 × 6 + 2 = 6 

⇒ 3 - 4 + 2 = 6

⇒ 1 ≠ 6

This is not correct the equation.

Option IV: After interchanging  ÷ and × 

⇒ 3 - 6 x 9 + 6 ÷ 2 = 6 

⇒ 3 - 0.66 + 3 = 6

⇒ 5.33 ≠ 6

This is not correct the equation.

∴ Interchanges (- , x) would make the given equation correct.

• The shaded part represents the people prefer salads but NOT stew.

 

• The number representing the people prefer salads but NOT stew = 29 + 12 = 41

Hence, ‘41’ is the correct answer.

Shortcut Trick

Sum of digits of the number = (Sum of number and its reverse) ÷ 11 = 99 ÷ 11 = 9.

Difference between the digits is given as 5.

Larger digit = (Sum + Difference) ÷ 2 = (9 + 5) ÷ 2 = 7.

Smaller digit = (Sum − Difference) ÷ 2 = (9 − 5) ÷ 2 = 2.

Possible two-digit numbers are 72 or 27.

∴ The correct answer is 27.

Alternate Method

Given: Sum of number and its reverse = 99, Difference between digits = 5.

Formula Used: Let the two-digit number be 10x + y, where x is the tens digit and y is the units digit.

⇒ (10x + y) + (10y + x) = 99

⇒ 11x + 11y = 99

⇒ 11(x + y) = 99

⇒ x + y = 9 ... (Eq. 1)

⇒ Case 1: x − y = 5 ... (Eq. 2)

⇒ Adding (Eq. 1) and (Eq. 2): 2x = 14 ⇒ x = 7, y = 2. Number = 72.

⇒ Case 2: y − x = 5 ... (Eq. 3)

⇒ Adding (Eq. 1) and (Eq. 3): 2y = 14 ⇒ y = 7, x = 2. Number = 27.

∴ The correct answer is 27.

Additional Information

Sum of Reversed Digits Rule

The sum of a 2-digit number and the number formed by reversing its digits is always 11 × (sum of its digits).

Difference of Reversed Digits Rule

The difference between a 2-digit number and the number formed by reversing its digits is always 9 × (difference of its digits).

Linear Equations for Digits

When the sum (S) and difference (D) of two values are known, the values are (S+D)÷2 and (S−D)÷2.

The correct answer is 'Electric fuse' .

 Key Points

• A fuse consists of a piece of wire made of a metal or an alloy of an appropriate melting point, for example, aluminum, copper, iron, lead etc.
• If a current larger than the specified value flows through the circuit, the temperature of the fuse wire increases.
• This melts the fuse wire and breaks the circuit.

​ 

Additional Information

• Loudspeaker
• Every amplifier (speaker) has an electrical current.
• When the current is changing, it produces a magnetic field.
• To make the cone (or panel) of the speaker move, magnets are used to create an opposing magnetic field which creates vibrations.
• These vibrations are the sound we hear.
• Ammeter and Voltmeter
• ​When an electric current passes through the coil, the electromagnetic field created around it reacts against the permanent magnetic field producing a deflecting torque that causes it to move.
• A pointer or needle attached to the coil indicates the amount of deflection.​

Shortcut Trick

Since 8 men + 6 women and 6 men + 8 women take the same 5 days, their total efficiency is equal.

Total persons in Case 1 = 8 + 6 = 14 persons | Total persons in Case 2 = 6 + 8 = 14 persons.

Since 14 persons take 5 days, then 7 men + 7 women (which is also 14 persons) will take the same time.

∴ The correct answer is 5 days.

Alternate Method

Given: Case 1 = (8M + 6W) × 5 | Case 2 = (6M + 8W) × 5

Formula Used: Total Work = Efficiency × Time

⇒ (8M + 6W) × 5 = (6M + 8W) × 5

⇒ 8M + 6W = 6M + 8W

⇒ 2M = 2W → 1 Man = 1 Woman

⇒ Total Work = (8M + 6M) × 5 = 14M × 5 = 70M units

⇒ Efficiency of (7M + 7W) = 7M + 7M = 14M units/day

⇒ Time required = 70M ÷ 14M = 5 days

∴ The correct answer is 5 days.

Additional Information

Man-Day Formula

M₁D₁H₁/W₁ = M₂D₂H₂/W₂, where M is number of workers, D is days, H is hours, and W is work done.

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a task. If efficiency doubles, time is halved.

Work & Wages

Wages are always distributed in the ratio of the work done by individuals, which is usually the ratio of their efficiencies.

Shortcut Trick

Convert the equation into standard form x² − 15x + 14 = 0.

Identify Sum of roots (−b/a) = 15 and Product of roots (c/a) = 14.

Check which option satisfies both conditions: 1 + 14 = 15 and 1 × 14 = 14.

Only the values 1 and 14 satisfy these conditions simultaneously.

∴ The correct answer is 1 and 14.

Alternate Method

Given: (x − 5)² = 5x + 11

Formula Used: (a − b)² = a² − 2ab + b²

⇒ (x − 5)² = 5x + 11

⇒ x² − 10x + 25 = 5x + 11

⇒ x² − 10x − 5x + 25 − 11 = 0

⇒ x² − 15x + 14 = 0

⇒ x² − 14x − x + 14 = 0

⇒ x(x − 14) − 1(x − 14) = 0

⇒ (x − 1)(x − 14) = 0

⇒ x = 1 or x = 14

∴ The correct answer is 1 and 14.

Additional Information

Quadratic Formula

For a quadratic equation ax² + bx + c = 0, the roots are given by x = [−b ± √(b² − 4ac)] / 2a.

Nature of Roots

The discriminant D = b² − 4ac determines the nature: if D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Relation between Roots and Coefficients

If α and β are the roots, then sum (α + β) = −b/a and product (αβ) = c/a.