RRB Group D Previous Year Paper (Held on: 15 Sept 2022 Shift 3)

Given: 

Sumit starts from Point F and drives 5 km towards the east.

He then takes a left turn, drives 10 km, turns left and drives 8 km.

He then takes a left turn and drives 3 km.

He takes a final left turn, drives 3 km and stops at Point G.

So, Point F is '7 km towards the south' from Point G.

Hence, the correct answer is "Option 4".

Shortcut Trick

Ratio of x : y is 4 : 3.

Value of 3 units (y share) = ₹2,400.

⇒ 1 unit = 2,400 ÷ 3 = ₹800.

Total amount (4 + 3 units) = 7 units × 800 = ₹5,600.

∴ The correct answer is ₹5,600.

Alternate Method

Given: Ratio of x : y = 4 : 3, y share = ₹2,400.

Formula: Total Amount = (Sum of Ratios ÷ Specific Ratio Part) × Specific Share

⇒ Let the shares of x and y be 4k and 3k.

⇒ 3k = 2,400

⇒ k = 2,400 ÷ 3 = 800

⇒ Total Amount = 4k + 3k = 7k

⇒ Total Amount = 7 × 800 = 5,600

∴ The correct answer is ₹5,600.

Additional Information

Ratio and Proportion

If a total quantity Q is divided in the ratio a : b, then the first part is Q × [a/(a+b)] and the second part is Q × [b/(a+b)].

Invertendo and Dividendo

Properties used to manipulate ratios where if a/b = c/d, then b/a = d/c (Invertendo) and (a+b)/b = (c+d)/d (Componendo).

Shortcut Trick

Perimeter (Circumference) of a circle is calculated as 2 × π × radius.

Given radius = 15 cm.

Perimeter = 2 × π × 15 = 30π cm.

∴ The correct answer is 30 π cm.

Alternate Method

Given:

Radius (r) of the circle = 15 cm

Formula Used:

Perimeter (C) = 2πr

Calculations:

⇒ Perimeter = 2 × π × 15

⇒ Perimeter = 30π cm

∴ The correct answer is 30 π cm.

Additional Information

Area of a Circle

The total space occupied by a circle is given by Area = πr².

Diameter of a Circle

The diameter (d) is the longest chord and is equal to twice the radius, d = 2r.

Semicircle Perimeter

The perimeter of a semicircle including the diameter base is πr + 2r.

Shortcut Trick Given: Area = 225 cm2 and Length (x) = 4y + 4. ⇒ y = (x − 4) / 4. Substitute in Area = x × y ⇒ x × (x − 4) / 4 = 225. ⇒ x2 − 4x = 900 ⇒ x2 − 4x − 900 = 0. ∴ The correct answer is x2 − 4x − 900 = 0.

Alternate Method Given: Area of rectangle = 225 cm2 Length = x Breadth = y Relation: x = 4y + 4

Formula Used: Area of Rectangle = Length × Breadth Calculations: ⇒ Area = x × y = 225 ⇒ From relation: 4y = x − 4 ⇒ y = (x − 4) / 4 ⇒ x × [(x − 4) / 4] = 225 ⇒ (x2 − 4x) / 4 = 225 ⇒ x2 − 4x = 225 × 4 ⇒ x2 − 4x = 900 ⇒ x2 − 4x − 900 = 0 ∴ The correct answer is x2 − 4x − 900 = 0.

Additional Information Quadratic Equation Form A standard quadratic equation is represented as ax2 + bx + c = 0, where x is the variable and a, b, c are constants. Area and Perimeter of Rectangle Area = L × B and Perimeter = 2(L + B). These relationships are often used to form algebraic equations in geometry problems. Nature of Roots The nature of roots for ax2 + bx + c = 0 depends on the discriminant (D = b2 − 4ac). If D > 0, the roots are real and distinct.

The logic followed here is:

So, 'FKSNI' will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

The logic followed here is:​

So, '58' will replace the question mark in the given series.

Hence, the correct answer is "Option 2".

The correct answer is 34, 51, 53, 84.

Key Points

• Tellurium's symbol is Te and atomic number is 52.
• It is a rare metalloid found in ores like gold and silver tellurides.
• Used in thermoelectric devices, semiconductors, and alloys.
• It appears silvery-white, brittle, and metallic.
• Tellurium compounds have a garlic-like odor and are toxic.

Additional Information

• In the modern periodic table metals, metalloids and nonmetals are found in the p-block which is on the right-hand side of the chart.
• Metalloids are those elements possessing properties between nonmetals and metals.
• These are also known as semi-metals.
• They have a metallic appearance with the brittle property of non-metals.
• They show average conductance and most of their chemical properties resemble the non-metals.
• The elements which are metalloids in the periodic table are boron, silicon, arsenic, antimony, polonium, and carbon.
• Metalloids are semiconductors.

Given Statements:

1. Some cats are pets.
2. All pets are snakes.
3. Some snakes are cats.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some snakes are pets - True (Because, All pets are snakes implies that some snakes are pets).

II. All cats are snakes - False (Because, Some snakes are definitely cats, but All cats are snakes can be possible only).

III. No snake is a cat - False (Because, Some snakes are cats).

So, Only conclusions I follows.

Hence, the correct answer is "Option 1".

The correct answer is uniform inside the solenoid.

Key Points

• A solenoid is a long coil of wire tightly wound in a helix shape.
• The magnetic field inside a long solenoid is uniform and parallel to the axis of the solenoid.
• Outside the solenoid, the magnetic field is weak and dispersed.
• The strength of the magnetic field inside the solenoid depends on the current through the wire and the number of turns per unit length of the solenoid.

Additional Information

• Magnetic Field:
• A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.
• It is represented by magnetic field lines that show the direction and strength of the field.
• The SI unit of magnetic field strength is the Tesla (T).
• Solenoid:
• A solenoid is a type of electromagnet, the purpose of which is to generate a controlled magnetic field.
• It consists of a coil of wire, and when an electric current is passed through it, a magnetic field is created.
• Solenoids are commonly used in electromechanical devices such as relays, valves, and actuators.
• Electromagnetism:
• Electromagnetism is a branch of physics that deals with the study of electromagnetic forces, which occur between electrically charged particles.
• It encompasses various phenomena like electric fields, magnetic fields, and light.
• Electromagnetic forces are one of the four fundamental forces of nature.

Given: Each of six students, A, B, C, D, E and F, have their class monitor duties on six different days of a week starting from Monday and ending on Saturday of the same week, but not necessarily in the same order.

1. B’s monitor duties are on Saturday.

2. F’s monitor duties are on Wednesday.

3. D’s monitor duties are on the day immediately before E, but it is not on Monday.

4. A’s monitor duties are on the day immediately after C.

So, monitor 'A' duties on Tuesday.

Hence, the correct answer is "Option 4".

The logic followed here is:

For, ‘YOUTH' is written as ‘DUBBQ’,

For, 'AGENT’ is written as ‘FMLVC',

Similarly, for 'CURVE'

So, 'CURVE' will be written as 'HAYDN'.

Hence, the correct answer is "Option 3".

Given:

Adding 1 to the numerator and subtracting 1 from the denominator of a given fraction makes it 1.

Adding 1 to the denominator while leaving the numerator unchanged makes the fraction 2/3.

Calculation:

Let the original fraction be (x/y).

From condition 1: ((x + 1)/(y - 1) = 1)

From condition 2: (x/(y + 1) = 2/3)

From condition 1:

⇒ (x + 1 = y - 1)

⇒ (x - y = -2) ......(I)

From condition 2:

⇒ (3x = 2(y + 1))

⇒ (3x = 2y + 2)

⇒ (3x - 2y = 2) ......(ii)

Solving equations (i) and (ii) together:

From (i) (x = y - 2), substitute in (ii):

⇒ (3(y - 2) - 2y = 2)

⇒ (3y - 6 - 2y = 2)

⇒ (y - 6 = 2)

⇒ (y = 8)

Substitute (y = 8) in (x = y - 2):

⇒ (x = 8 - 2)

⇒ (x = 6)

The original fraction is 6/8.

Shortcut Trick

Since n || m, angles a and b form a linear pair, so a + b = 180°.

Given ratio a : b = 2 : 3 ⇒ 5 units = 180° ⇒ 1 unit = 36°.

⇒ b = 3 × 36° = 108°.

By parallel line properties, ∠b and ∠h are alternate exterior angles, so ∠h = ∠b.

∴ The correct answer is 108°.

Alternate Method

Given:

Lines n || m intersected by a transversal.

Ratio of angles m∠a : m∠b = 2 : 3.

Formula Used:

1. Linear Pair Axiom: Sum of adjacent angles on a straight line is 180°.
2. Alternate Exterior Angles Theorem: When two parallel lines are cut by a transversal, the alternate exterior angles are equal.

Calculations:

Let m∠a = 2x and m∠b = 3x.

Since ∠a and ∠b lie on the straight line n:

⇒ m∠a + m∠b = 180°

⇒ 2x + 3x = 180°

⇒ 5x = 180°

⇒ x = 36°

⇒ m∠b = 3 × 36° = 108°

Since n || m, ∠b and ∠h are alternate exterior angles:

⇒ m∠h = m∠b

⇒ m∠h = 108°

∴ The correct answer is 108°.

The correct answer is H2.

Key Points

• Hydrogen's symbol is H and atomic number is 1.
• It is the lightest element and most abundant in the universe.
• It is found in water (H₂O) and most organic compounds.
• It is used as a fuel in rockets and clean energy systems.
• It exists in diatomic form (H₂) under normal conditions.

Additional Information

• Brine can be obtained from industrial facilities, salt mining operations, or the waste stream of reverse osmosis (RO) desalination plants, and can be processed to produce useful chemicals like sodium hydroxide (NaOH) or hydrochloric acid (HCl).
• Due to their efficiency as conductors and the quantity of free electrons they have available for transfer, carbon electrodes are utilised in electrolysis.
• Carbon not only has a high melting point but is also a good conductor of electricity, which means that it can facilitate a variety of reactions.
• Salt hydroxide, hydrogen, and chlorine are produced during the electrolysis of brine.
• Hydrogen is a byproduct regularly burned with chlorine in the traditional chlor-alkali business to create hydrochloric acid.​

Given word: 'CONVERTS'

Now, checking the pairs in both forward and backward directions:

The pairs in forward direction are: OT and NS.

And, The pairs in backward direction are: ON and TS.

So, Total 'Four' pairs are formed from the given word.

Hence, the correct answer is "Option 3".

Shortcut Trick

Given 2tan θ = 3 ⇒ tan θ = 3/2.

Expression: (sec θ + (tan θ − 1))(sec θ − (tan θ − 1)) = sec² θ − (tan θ − 1)².

Using sec² θ = 1 + tan² θ: (1 + tan² θ) − (tan² θ − 2tan θ + 1).

Simplifying: 1 + tan² θ − tan² θ + 2tan θ − 1 = 2tan θ.

Result = 2 × (3/2) = 3.

∴ The correct answer is 3.

Alternate Method

Given: 2tan θ = 3 ⇒ tan θ = 3/2 (Perpendicular/Base).

Formula Used: (a + b)(a − b) = a² − b² and sec² θ − tan² θ = 1.

Let the expression be E = (sec θ + tan θ − 1)(sec θ − tan θ + 1).

⇒ E = [sec θ + (tan θ − 1)] [sec θ − (tan θ − 1)].

⇒ E = sec² θ − (tan θ − 1)².

⇒ E = sec² θ − (tan² θ + 1 − 2tan θ).

⇒ E = (sec² θ − tan² θ) − 1 + 2tan θ.

⇒ E = 1 − 1 + 2tan θ.

⇒ E = 2tan θ.

⇒ E = 2 × (3/2) = 3.

∴ The correct answer is 3.

Additional Information

Trigonometric Identities

Fundamental identities include sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Pythagorean Triplets

In a right-angled triangle, P² + B² = H². Common triplets include (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Reciprocal Relations

sec θ = 1/cos θ, cosec θ = 1/sin θ, and cot θ = 1/tan θ.

The correct answer is 0.9 W.

Key Points

• Two 5 Ω bulbs in series give total resistance: R_total = 5+5 = 10 Ω.
• Current from a 3 V source: I = V/R = 3/10 = 0.3 A (Ohm’s law V = IR).
• Total power drawn: P = V²/R = 3²/10 = 0.9 W (equivalently P = VI).
• Each bulb dissipates P_bulb = I²R = (0.3)² × 5 = 0.45 W; sum of bulb powers equals 0.9 W.

Additional Information

• Series vs. Parallel: In series, the same current flows through all elements; in parallel, the same voltage appears across each branch.
• Equivalent Resistance: Series resistances add (R_s = ΣR); in parallel, 1/R_p = Σ(1/R).
• Power Identities: P = VI = I²R = V²/R (from combining power with Ohm’s law).
• What if parallel? Two 5 Ω bulbs in parallel → R = 2.5 Ω; P = V²/R = 9/2.5 = 3.6 W (greater than series).
• SI Units: ampere (A) for current, ohm (Ω) for resistance, watt (W) for power (SI-defined).

Given: (Left) 478 775 357 183 246 (Right)

Now, 

The third digit of the largest number is: 5 (775)

The second digit of the smallest number is: 8 (183)

And, the sum of the third digit of the largest number and the second digit of the smallest number is: 5 + 8 = 13.

Hence, the correct answer is "Option 4".

Given: Six boxes, red, green, yellow, pink, blue, and orange, are kept vertically, one over the other (but not necessarily in the same order).

1. The red box is placed at an odd number position when counted from the bottom but it is not in the fifth position.

2. The red box is placed immediately above the yellow box.

3. Only two boxes are placed between the yellow box and the orange box.

4. Only two boxes are placed between the blue box and the pink box and only one box is placed between the blue box and the green box.

So, 'Blue' box is placed third from the top.

Hence, the correct answer is "Option 2".

Shortcut Trick

Apply the Empirical formula: 2 × Mean = 3 × Median − Mode

2 × Mean = 3 × 35 − 27

2 × Mean = 105 − 27 = 78

Mean = 78 ÷ 2 = 39

∴ The correct answer is 39.

Alternate Method

Given:

Mode = 27

Median = 35

Formula Used:

In a moderately skewed distribution, the relationship between Mean, Median, and Mode is:

Mean − Mode = 3 × (Mean − Median)

Calculations:

⇒ Let Mean be x.

⇒ x − 27 = 3 × (x − 35)

⇒ x − 27 = 3x − 105

⇒ 3x − x = 105 − 27

⇒ 2x = 78

⇒ x = 78 ÷ 2

⇒ x = 39

∴ The correct answer is 39.

Additional Information

Karl Pearson's Empirical Relation

For moderately asymmetrical distributions, Mode ≈ 3 Median − 2 Mean.

Symmetrical Distribution

In a perfectly symmetrical distribution, the values of Mean, Median, and Mode are equal (Mean = Median = Mode).

Skewness of Distribution

If Mean > Median > Mode, the distribution is positively skewed. If Mode > Median > Mean, the distribution is negatively skewed.

Calculation:

$1\over{4\over5}+ {3\over7}$ ÷ $8\over35$

⇒ $1\over{28+15\over35}$ ÷ $8\over35$ 

⇒ $\frac{35}{43} \times \frac{35}{8}$

⇒ $\frac{1225}{344}$

⇒ $3{193\over344}$

∴ Option 3 is the correct answer.

The correct answer is hydrogen.

Key Points

• Scientists at the Centre for Nano and Soft Matter Sciences (CeNS) have designed an electrocatalyst system for the energy-efficient production of hydrogen.
• This production of hydrogen is achieved through the electrolysis of urea, which is more energy-efficient compared to water electrolysis.
• Hydrogen is a clean fuel and has the potential to be a significant part of the renewable energy landscape.
• The development of efficient and cost-effective methods for hydrogen production is crucial for the advancement of hydrogen energy technologies.

Additional Information

• Hydrogen:
• Hydrogen is the most abundant element in the universe and is considered a potential clean energy carrier for the future.
• It can be used in fuel cells to generate electricity, with water as the only byproduct, making it environmentally friendly.
• Hydrogen can be produced from various sources, including natural gas, biomass, and water, through different processes such as steam methane reforming, gasification, and electrolysis.
• Research and development in hydrogen production aim to make the process more efficient and cost-effective to promote its use as a sustainable energy source.
• Electrolysis of Urea:
• Urea electrolysis is a process that involves the decomposition of urea into hydrogen, nitrogen, and carbon dioxide using an electric current.
• This process is more energy-efficient compared to water electrolysis because urea has a lower thermodynamic potential for decomposition.
• Urea is commonly available as a waste product in agricultural and industrial processes, making it a cost-effective feedstock for hydrogen production.
• The development of effective electrocatalysts for urea electrolysis is crucial for enhancing the efficiency and feasibility of this method.
• Centre for Nano and Soft Matter Sciences (CeNS):
• CeNS is an autonomous research institute under the Department of Science and Technology (DST), Government of India.
• The institute focuses on research in the areas of nano and soft matter sciences, including the development of novel materials and technologies.
• CeNS aims to address scientific and technological challenges through innovative research and collaboration with academic and industrial partners.
• The development of the electrocatalyst system for hydrogen production is one of the many significant contributions of CeNS in the field of renewable energy.

The correct answer is is parallel to the principal axis.

Key Points

• An incident ray that passes through the focus of a concave mirror will reflect parallel to the principal axis.
• This is due to the property of concave mirrors where rays passing through the focus reflect parallel to the principal axis.
• The principal axis is the line that passes through the center of curvature and the focus, extending to infinity on both sides.
• This property is used in various optical devices to direct light in a specific direction.

Additional Information

• Concave Mirror:
• A concave mirror is a spherical mirror with a reflecting surface that curves inward.
• It is also known as a converging mirror because it converges light to a point.
• Principal Axis:
• The principal axis is a straight line that passes through the pole (the midpoint of the mirror) and the center of curvature of the mirror.
• Focus (Focal Point):
• The focus of a concave mirror is the point where parallel rays of light either converge or appear to converge after reflecting off the mirror.
• Center of Curvature:
• The center of curvature is the center of the sphere of which the concave mirror is a part.

The shaded part represents the Schools are Colleges and Universities but NOT Gurukuls .

The number of Schools who are Colleges and Universities but NOT Gurukuls  =  22

Hence, ‘22’ is the correct answer.

Shortcut Trick

Sum of supplementary angles = 180°

Difference between angles = 36°

Smaller angle = (Sum − Difference) ÷ 2

Smaller angle = (180° − 36°) ÷ 2 = 144° ÷ 2 = 72°

∴ The correct answer is 72°.

Alternate Method

Given: Sum of supplementary angles = 180°, Difference = 36°.

Formula: Let the smaller angle be x and the larger angle be y. Then x + y = 180°.

Calculations:

⇒ y = x + 36°

⇒ x + (x + 36°) = 180°

⇒ 2x + 36° = 180°

⇒ 2x = 180° − 36°

⇒ 2x = 144°

⇒ x = 72°

∴ The correct answer is 72°.

Additional Information

Supplementary Angles

Two angles are called **supplementary

Given Series: (Left) F $ 3 & 4 P W S 8 # T * A 2 F 5 M 2 6 $ Y 9 K (Right)

Letters immediately preceded by a letter and also immediately followed by a number,

So, the pattern needed is: Letter - Letter - Number

Now,

So, there are 'One' pairs i.e.: 'WS8'.

Hence, the correct answer is "Option 1".

The correct answer is Loo.

Key Points

• Loo refers to the strong, gusty, hot, dry winds that blow during the day over the north and northwestern parts of India during the summer season.
• These winds are extremely hot and can cause severe heat waves, leading to heatstroke and other health issues.
• They typically blow from the west or northwest and are particularly prevalent in the states of Rajasthan, Haryana, Punjab, and Uttar Pradesh.
• The temperature of Loo winds can often exceed 45°C, significantly raising the ambient temperature and creating harsh living conditions.

Additional Information

• Mango Winds
• Mango winds are pre-monsoon showers in the coastal regions of Kerala and Karnataka in India.
• These winds are named so because they help in the ripening of mangoes in these regions.
• Kaal Baishakhi
• Kaal Baishakhi refers to the violent thunderstorms that occur in the eastern parts of India, particularly in West Bengal and Assam, during the pre-monsoon months of April and May.
• These storms are characterized by strong winds, heavy rains, and lightning, often causing significant damage to property and crops.
• Trade Winds
• Trade winds are steady winds that blow from east to west just north and south of the equator.
• They are part of the Earth's atmospheric circulation system and play a crucial role in maritime navigation and weather patterns across tropical regions.

The correct answer is Udaan.

Key Points

• The Udaan scheme was launched by the Government of Rajasthan in collaboration with 'IPE Global'.
• The aim of the scheme is to provide scholarships to rural girls to encourage their enrollment at the secondary level of education.
• This initiative is part of the broader efforts to improve female education and reduce gender disparity in education in rural areas.
• By providing financial support, the scheme aims to reduce the dropout rates of girls at the secondary level and promote higher education among rural girls.

Additional Information

• Begum Hazrat Scholarship:
• Begum Hazrat Mahal National Scholarship is a scheme for meritorious girl students belonging to minority communities.
• It aims to provide financial assistance to girls in the minority community to reduce their dropout rate and promote higher education.
• This scholarship is provided by the Ministry of Minority Affairs, Government of India.
• Beti Bachao, Beti Padhao:
• Beti Bachao, Beti Padhao (BBBP) is a national campaign to save and educate the girl child.
• It was launched by the Government of India to address the declining child sex ratio and promote the education of girls.
• BBBP focuses on changing mindsets and creating awareness about the importance of girls' education and their rights.
• Yuvika:
• Yuvika, also known as the Young Scientist Programme, is an initiative by ISRO to impart basic knowledge on space technology and its applications to school students.
• It aims to create interest in space activities among young students and encourage them to pursue careers in space science and technology.

Shortcut Trick

When three numbers are in continued proportion a : b :: b : c, then b is the mean proportional.

Direct formula: y = √(a × c)

y = √(361 × 121)

y = 19 × 11 = 209

∴ The correct answer is 209.

Alternate Method

Given: 361 : y :: y : 121

Formula Used: Product of means = Product of extremes (y² = a × c)

⇒ 361 / y = y / 121

⇒ y² = 361 × 121

⇒ y = √(361 × 121)

⇒ y = √(19² × 11²)

⇒ y = 19 × 11

⇒ y = 209

∴ The correct answer is 209.

Additional Information

Mean Proportional

For two numbers a and b, the mean proportional x is defined such that a:x = x:b, which gives x = √(ab).

Third Proportional

If a : b :: b : c, then c is called the third proportional to a and b, calculated as c = b²/a.

Fourth Proportional

If a : b :: c : d, then d is the fourth proportional, calculated as d = (b × c)/a.

The correct answer is 175.

Key Points

• Consumption Function: C = 50 + 0.6Y, where 50 is autonomous consumption and 0.6 is the marginal propensity to consume (MPC).
• Investment: The given investment value is  I=20 (autonomous and constant).
• Equilibrium Condition: = C + IY=C+I, meaning total income equals the sum of consumption and investment.
• Calculation: Solving the equation Y = 50 + 0.6Y + 20 , we get Y = 175

Additional Information

• Equilibrium Income Concept: Equilibrium income occurs where total demand (consumption + investment) equals total output or income in an economy.
• Keynesian Model: Keynesian economics, emphasizes the role of aggregate demand in determining income and employment levels.
• Real-World Applications: Understanding equilibrium income helps policymakers predict the impact of fiscal policies, such as government spending or tax changes, on national income.
• Autonomous Components: Both autonomous consumption and investment are independent of income and represent fixed expenditures regardless of income levels.
• Economic Multiplier: Changes in autonomous investment (like ΔI) have a multiplied effect on equilibrium income, influencing GDP growth significantly.

The correct answer is inversely proportional to the wavelength.

Key Points

• When white light passes through a prism, it splits into its constituent colors due to dispersion.
• The angle of deviation for each color depends on its wavelength.
• The angle of deviation is inversely proportional to the wavelength of the light.
• This means that light with a shorter wavelength (e.g., violet) deviates more than light with a longer wavelength (e.g., red).

Additional Information

• Dispersion of Light
• Dispersion occurs when light separates into its component colors due to different degrees of refraction for different wavelengths.
• The refractive index of the material of the prism varies with wavelength, causing different colors to bend by different amounts.
• Wavelength and Frequency
• Wavelength is the distance between successive crests of a wave, typically measured in meters.
• Frequency is the number of waves that pass a point in one second, measured in Hertz (Hz).
• The speed of light (c) is the product of its wavelength (λ) and frequency (f): c = λf.
• Prism
• A prism is a transparent optical element with flat, polished surfaces that refract light.
• The most common type of prism is a triangular prism, used to disperse light into a spectrum of colors.

The correct answer is Covalent bonds.

Key Points

• Covalent bonds are formed by the sharing of electrons between atoms, which allows each atom to attain the electron configuration of a noble gas.
• Carbon atoms form covalent bonds in hydrocarbons due to their ability to form four bonds, satisfying their valence electron requirement.
• Hydrocarbons are organic compounds consisting entirely of hydrogen and carbon, and their structures are stabilized through covalent bonding.
• Covalent bonds result in the formation of molecules with specific geometries and properties, important for the diverse range of hydrocarbon compounds.

Additional Information

• Ionic Bonds
• Ionic bonds are formed through the transfer of electrons from one atom to another, resulting in the creation of positively and negatively charged ions.
• These bonds are typically found in compounds formed between metals and non-metals, such as sodium chloride (NaCl).
• Coordination Covalent Bonds
• Coordination covalent bonds, also known as dative bonds, occur when one atom provides both electrons for a shared pair in a bond.
• These bonds are common in complex ions and coordination compounds, such as in metal-ligand complexes.
• Hydrogen Bonds
• Hydrogen bonds are weak interactions that occur between a hydrogen atom covalently bonded to a highly electronegative atom (like oxygen, nitrogen, or fluorine) and another electronegative atom.
• These bonds are essential for the properties of water and the structure of biological molecules like DNA.
• Covalent Bonds
• Covalent bonds involve the sharing of electron pairs between atoms, leading to the formation of molecules.
• These bonds can be single, double, or triple, depending on the number of shared electron pairs.
• Covalent bonding is fundamental to organic chemistry, forming the basis of the structures of hydrocarbons and other organic molecules.

The correct answer is Wardha.

Key Points

• Mahatma Gandhi Antarrashtriya Hindi VishwaVidyalaya is located in Wardha, Maharashtra.
• The university was established to promote and develop the Hindi language.
• Wardha is a city in the state of Maharashtra, which has historical significance due to its association with Mahatma Gandhi.
• The university aims to provide higher education and advanced research opportunities in the field of Hindi language and literature.

Additional Information

• Mahatma Gandhi Antarrashtriya Hindi VishwaVidyalaya
• It was established by an Act of Parliament in 1997.
• The primary objective of the university is to promote and spread the knowledge of Hindi language and literature at national and international levels.
• It offers various undergraduate, postgraduate, and doctoral programs in Hindi and related fields.
• The university also conducts research in Hindi language, literature, and culture.
• Wardha
• Wardha is a city in Maharashtra known for its connection with Mahatma Gandhi and the Indian independence movement.
• It is the location of Sevagram Ashram, where Mahatma Gandhi lived for several years.
• The city is also known for its educational institutions and contribution to the promotion of Hindi and Gandhian studies.

Shortcut Trick

Identify the expression as the difference of squares: (a + b)(a − b) = a² − b².

Here, a = 6 and b = 2√3.

Product = 6² − (2√3)² = 36 − 12 = 24.

Positive square root = √24 = √(4 × 6) = 2√6.

∴ The correct answer is 2√6.

Alternate Method

Given: The expression is (6 + 2√3)(6 − 2√3).

Formula Used: (a + b)(a − b) = a² − b² and √(x × y) = √x × √y

⇒ First, simplify the product inside the square root:

⇒ (6 + 2√3)(6 − 2√3) = (6)² − (2√3)²

⇒ = 36 − (4 × 3)

⇒ = 36 − 12 = 24

⇒ Required positive square root = √24

⇒ √24 = √(4 × 6) = √4 × √6

⇒ = 2√6

∴ The correct answer is 2√6.

Additional Information

Difference of Squares

The identity (a + b)(a − b) = a² − b² is a core algebraic property used to simplify conjugate pairs of surds.

Simplification of Radicals

To simplify a square root, factor out the largest perfect square. For example, √24 = √(4 × 6) = 2√6.

Surd Squaring Rule

When squaring a term like (x√y), the result is x² × y. In this case, (2√3)² = 4 × 3 = 12.

The correct answer is 1) Cells are long, cylindrical, unbranched and uninucleate..

Key Points

• Voluntary muscles are also known as skeletal muscles because they are usually attached to bones and can be consciously controlled.
• These muscles are characterized by their striated appearance, showing alternate light and dark bands.
• Cells of voluntary muscles are long, cylindrical, and typically multinucleate, not uninucleate.
• These muscles play a crucial role in movements and locomotion of the body.

Additional Information

• Voluntary Muscles
• These muscles are under conscious control, meaning they can be voluntarily moved.
• Skeletal muscles are attached to bones by tendons and are responsible for movement.
• The structure of these muscles includes muscle fibers that are long and cylindrical, containing multiple nuclei (multinucleate).
• The striated appearance of these muscles is due to the arrangement of actin and myosin filaments within the muscle cells.
• Involuntary Muscles
• These muscles are not under conscious control and function automatically.
• Examples include smooth muscles found in the walls of internal organs and blood vessels, and cardiac muscles found in the heart.
• Smooth muscles are spindle-shaped, unstriated, and uninucleate.
• Cardiac muscles are striated like skeletal muscles but are branched and typically uninucleate.

Shortcut Trick

For a period of 2 years, the difference between CI and SI is given by the formula:

Difference (D) = P × (R/100)²

D = 10,000 × (5/100)²

D = 10,000 × (25/10,000)

D = 25

∴ The correct answer is Rs. 25.

Alternate Method

Given: Principal (P) = Rs. 10,000, Rate (R) = 5% per annum, Time (T) = 2 years.

Formula Used: SI = (P × R × T) ÷ 100; CI = P[(1 + R/100)^T − 1]

⇒ Simple Interest (SI) = (10,000 × 5 × 2) ÷ 100 = 1,00,000 ÷ 100 = Rs. 1,000

⇒ Compound Interest (CI) = 10,000 × [(1 + 5/100)² − 1]

⇒ CI = 10,000 × [(1.05)² − 1] = 10,000 × [1.1025 − 1]

⇒ CI = 10,000 × 0.1025 = Rs. 1,025

⇒ Difference = CI − SI = 1,025 − 1,000 = Rs. 25

∴ The correct answer is Rs. 25.

Additional Information

Difference for 3 Years

For 3 years, the difference between CI and SI is P × (R/100)² × (3 + R/100).

Successive Percentage Change

The effective rate for CI for 2 years can be calculated as x + y + (xy/100), where x = y = R%.

Simple Interest Property

Simple interest remains constant for every year if the principal and rate do not change.

The correct answer is Prime Minister.

Key Points

• The Prime Minister of India is the head of the Council of Ministers.
• The Prime Minister is appointed by the President of India.
• The Prime Minister is usually the leader of the majority party in the Lok Sabha.
• As the head of the Council of Ministers, the Prime Minister plays a key role in the executive branch of the Government of India.

Additional Information

• Prime Minister: The Prime Minister is the head of the government in India and leads the executive branch. The Prime Minister is responsible for running the government and implementing policies.
• Speaker of Lok Sabha: The Speaker is the presiding officer of the Lok Sabha, the lower house of the Parliament of India. The Speaker's role is to maintain order during debates and ensure that parliamentary procedures are followed.
• President: The President of India is the ceremonial head of state and the supreme commander of the Indian Armed Forces. The President's role is largely ceremonial, with executive powers being exercised by the Prime Minister and the Council of Ministers.
• Vice President: The Vice President of India is the second-highest constitutional office in the country. The Vice President also serves as the Chairman of the Rajya Sabha, the upper house of the Parliament of India.

The correct answer is One.

Key Points

• Each Gram Panchayat is typically represented by one Sarpanch.
• The Sarpanch is the elected head of the Gram Panchayat.
• The Sarpanch plays a crucial role in local governance and administration in rural areas.
• The position of Sarpanch is a cornerstone of the Panchayati Raj system in India.

Additional Information

• Gram Panchayat
• A Gram Panchayat is the basic unit of local administration in India, functioning at the village level.
• It consists of members elected by the village residents, with the Sarpanch serving as the head.
• The Gram Panchayat is responsible for implementing government schemes and addressing local issues.
• Panchayati Raj System
• The Panchayati Raj system is a decentralized form of government where each village or group of villages is governed by a Gram Panchayat.
• This system was formalized in India by the 73rd Constitutional Amendment Act of 1992.
• The goal of the Panchayati Raj is to empower local communities and promote participatory governance.
• Role of the Sarpanch
• The Sarpanch is responsible for calling and presiding over Gram Panchayat meetings.
• The Sarpanch ensures the execution of developmental projects and government schemes at the village level.
• The Sarpanch acts as a liaison between the village residents and higher levels of government.

Given:

Statement:

The impact of social media is very much visible in every sphere of society.

Arguments:

I. Today, people are connected across different countries though social media - Strong Argument (Because, it does not necessarily demonstrate a widespread impact of social media across every sphere of society. It only highlights one specific aspect of social media's influence)

Il. Different cultures have been explored by people through social media - Strong Argument (Because, this statement focuses on a specific aspect of social media's impact. While it is true that social media can expose people to different cultures, it does not necessarily translate to a significant impact across all spheres of society.)

So, Both I and II strengthen the statement. 

Hence, the correct answer is "Option 1".

Calculation:

932

⇒ 93 × 93

⇒ 8649

∴ Option 4 is the correct answer.

Given: Five persons are sitting around a circular table facing the centre.

1) Akash sits second to the left of Aman.

2) Ansh sits second to the right of Aman.

3. Akash is an immediate neighbour of both Ansu and Ansh.

4. Aman is an immediate neighbour of both Ansu and Ajit.

So, 'Ansh' is an immediate neighbour of both Ajit and Akash.

Hence, the correct answer is "Option 2".

Calculation:

Difference between the production of two companies in 2001 = 139 - 119 = 20

Difference between the production of two companies in 2002 = 120 - 99 = 21

Difference between the production of two companies in 2003 = 141 - 100 = 41

Difference between the production of two companies in 2004 = 128 - 78 = 50

Difference between the production of two companies in 2005 = 120 - 107 = 13

Difference between the production of two companies in 2006 = 159 - 148 = 11

∴ Difference between the production of two companies was maximum in 2004.

The correct answer is Kannad Plain.

Key Points

• The Kannad Plain is located on the western coast of India, between the Western Ghats and the Arabian Sea.
• This plain is part of the larger Western Coastal Plains, which stretch from Gujarat in the north to Kerala in the south.
• The Western Coastal Plains are known for their fertile soil and significant agricultural activities.
• The Kannad Plain, in particular, is characterized by its flat terrain and is a prominent feature of the Karnataka coast.

Additional Information

• Uttkal Plain:
• The Uttkal Plain is located in the eastern part of India, in the state of Odisha.
• It is known for its rich cultural heritage and historical significance.
• Rohilkhand Plain:
• The Rohilkhand Plain is located in the northern part of India, primarily in the state of Uttar Pradesh.
• It is named after the Rohilla Pathans who settled in the region.
• Barind Tract:
• The Barind Tract is located in the eastern part of the Indian subcontinent, primarily in Bangladesh and parts of West Bengal, India.
• It is characterized by its older alluvial soil and is an important agricultural region.

The correct answer is Cs (Cesium).

Key Points

• Cesium (Cs) is located in Group 1 (alkali metals) and Period 6 of the periodic table.
• It has the lowest ionization energy among the elements listed, making it the most metallic.
• Cesium is highly reactive and readily loses its single valence electron to form positive ions.
• It is characterized by its large atomic radius and low electronegativity.

Additional Information

• Metallic Character:
• Metallic character refers to the level of reactivity of a metal.
• Metals tend to lose electrons and form positive ions (cations).
• The metallic character increases as we move down a group in the periodic table.
• This is due to the increase in atomic size and the decreasing attraction between the nucleus and the valence electrons.
• Periodic Table Trends:
• The periodic table is arranged in such a way that elements with similar properties fall into the same groups or columns.
• Group 1 elements, also known as alkali metals, are highly reactive and have a single valence electron.
• Reactivity and metallic character increase as we move down the group from lithium (Li) to cesium (Cs).
• Ionization Energy:
• Ionization energy is the energy required to remove an electron from an atom in its gaseous state.
• Elements with low ionization energies lose electrons more easily and exhibit higher metallic character.
• In alkali metals, ionization energy decreases down the group, making cesium the most metallic among the options provided.

Given:

( a = 984, b = 16 )

Formula:

( a² - b² = (a+b) (a-b) )

Calculation:

⇒ ( (984 + 16) × (984 - 16) )

⇒ ( 1000 × 968 )

⇒ ( 968000 )

∴ Option 2 is the correct answer.

The correct answer is Shooting.

Key Points

• Abhishek Verma is an Indian sport shooter who has earned significant accolades in the sport of shooting.
• He has competed in the 10-meter air pistol events and has won numerous medals in international competitions.
• In recognition of his outstanding achievements in shooting, he was awarded the Arjuna Award in 2021.
• The Arjuna Award is one of the highest honors given by the Indian government to athletes for their exceptional performance in national sports.

Additional Information

• Arjuna Award:
• The Arjuna Award was instituted in 1961 by the Government of India to recognize outstanding achievements in national sports.
• The award includes a bronze statuette of Arjuna, a certificate, ceremonial dress, and a cash prize.
• It aims to encourage and motivate athletes to achieve higher levels of performance.
• The selection committee considers athletes' performance over a period of four years and other factors such as leadership qualities, discipline, and sportsmanship.
• Shooting Sport:
• Shooting is a competitive sport involving tests of proficiency (accuracy and speed) using various types of guns such as firearms and airguns.
• In India, shooting has become increasingly popular, with Indian shooters excelling in various international competitions, including the Olympics.
• Some of the prominent shooting events include 10m air pistol, 10m air rifle, and 50m rifle events, among others.
• The National Rifle Association of India (NRAI) is the governing body for shooting sports in India.

The correct answer is Double Displacement Reaction.

Key PointsPb(NO3)2 + 2KI → PbI2 +2KNO3

• In the given equation, Pb(NO3)2 reacts with 2KI to produce PbI2 and 2KNO3.
• In a double displacement reaction, elements from two different compounds displace each other to create new compounds. This is exactly what is happening in the equation.
• The lead ion (Pb2+) in lead nitrate displaces the potassium ion (K+) in potassium iodide, and the potassium ion (K+) in potassium iodide displaces the lead ion (Pb2+) in lead nitrate.
• As a result, lead ends up with iodide to form lead iodide (PbI2) and potassium ends up with nitrate to form potassium nitrate (2KNO3).

Additional Information

• Combination:
• A combination reaction is a type of reaction in which two or more substances (elements or compounds) combine to form a single product.
• However, in this provided equation, we have two reactants and two products. Hence, it is not a combination reaction.
• Decomposition:
• A decomposition reaction is characterized by a single compound breaking down into two or more smaller compounds or elements.
• The given chemical equation does not depict this type of reaction as we start with two reactants which form two new products.

The correct answer is electrical energy into mechanical energy.

Key Points

• An electric motor is a device that converts electrical energy into mechanical energy.
• It operates on the principle of electromagnetic induction.
• Electric motors are widely used in industrial, commercial, and residential applications.
• Common examples include fans, pumps, electric vehicles, and household appliances.

Additional Information

• Electromagnetic Induction: The process by which a conductor placed in a changing magnetic field causes the production of a voltage across the conductor.
• Types of Electric Motors: There are various types of electric motors including DC motors, AC motors, synchronous motors, and induction motors.
• Applications of Electric Motors: Electric motors are used in various applications such as home appliances (refrigerators, washing machines), industrial machinery (conveyors, pumps), and transportation (electric vehicles, trains).
• Maintenance of Electric Motors: Regular maintenance of electric motors includes checking for wear and tear, lubrication of moving parts, and ensuring proper electrical connections to ensure optimal performance and longevity.

Shortcut Trick

Successive ratio method: Price Ratio × Weight Ratio = Profit Ratio.

Price Ratio = 18 : 20 = 9 : 10.

Weight Ratio (Inversely proportional to quantity) = 900 : 1000 = 9 : 10.

Overall Ratio = (9 × 9) : (10 × 10) = 81 : 100.

Profit% = (19 ÷ 81) × 100 = 23.456...% ≈ 23.45%.

∴ The correct answer is 23.45 %.

Alternate Method

Given → CP = Rs. 18/kg, SP = Rs. 20/kg, Actual weight given = 900 gm. Formulas: Profit% = (Total SP − Total CP) ÷ Total CP × 100.

⇒ Effective CP for 900 gm = (18 ÷ 1000) × 900 = Rs. 16.2. ⇒ SP for the same 900 gm = Rs. 20. ⇒ Profit = 20 − 16.2 = Rs. 3.8. ⇒ Profit% = (3.8 ÷ 16.2) × 100. ⇒ Profit% = 3800 ÷ 162 = 23.456...% ≈ 23.45%.

∴ The correct answer is 23.45 %.

Additional Information

Dishonest Dealer Concept

When a dealer sells goods at cost price but uses less weight, Profit% = [Error ÷ (True Value − Error)] × 100.

Combined Profit

If there is a price markup and weight manipulation, the net profit is calculated by multiplying the respective ratios of SP/CP for each transaction.

Given: A music school has classes for teaching six different musical instruments - flute, harmonium, guitar, sitar, drum and violin - each on a different day of a week starting from Monday and ending on Saturday of the same week, but not necessarily in the same order.

1. Drum class is scheduled on Monday.

2. Flute class is on Friday.

3. Sitar class is on the day immediately after flute class.

4. Only three classes are scheduled between Guitar and Sitar classes.

5. Only Violin class is scheduled between Flute and Harmonium classes.

So, Harmonium class is scheduled at 'Wednesday'.

Hence, the correct answer is "Option 2".

The correct answer is Brahmaputra.

Key Points

• Majuli is the world's largest river island and is located in the Brahmaputra River in Assam, India.
• The Brahmaputra River is one of the major rivers of the Indian subcontinent, originating from the Angsi Glacier in Tibet.
• Majuli has been the cultural capital of Assam since the 16th century and is known for its satras (Vaishnavite monasteries).
• The island is prone to erosion and flooding due to its location within the dynamic Brahmaputra basin.

Additional Information

• Brahmaputra River
• The Brahmaputra River flows through Tibet, India, and Bangladesh, covering a total distance of about 2,900 km.
• In Tibet, it is known as the Yarlung Tsangpo River, and in Bangladesh, it is called the Jamuna River.
• The river is crucial for the irrigation, transportation, and power generation in the regions it flows through.
• The Brahmaputra basin is subject to seasonal flooding, which affects agriculture and settlements in the area.
• Majuli Island
• Majuli was declared a district in Assam in 2016, making it India's first island district.
• The island is home to a diverse range of flora and fauna, including many migratory birds.
• It is also a significant center for the Neo-Vaishnavism culture and has around 22 satras that preserve ancient practices, art, and culture.
• The island faces environmental challenges such as erosion and flooding, leading to a reduction in its size over the years.

Shortcut Trick

The sum of exterior angles of any convex polygon, including a triangle, is always 360°.

Regardless of the number of sides, if you traverse around the boundary, you complete one full rotation.

Total rotation = 360°.

∴ The correct answer is 360°.

Alternate Method

Given: A triangle with three interior angles.

Formula Used:

1. Linear Pair Postulate: Interior angle + Exterior angle = 180°
2. Angle Sum Property: Sum of interior angles of a triangle = 180°

Calculations:

Let the interior angles be α, β, and γ.

⇒ α + β + γ = 180°

Let the corresponding exterior angles be E₁, E₂, and E₃.

⇒ E₁ = 180° − α

⇒ E₂ = 180° − β

⇒ E₃ = 180° − γ

⇒ Sum = E₁ + E₂ + E₃

⇒ Sum = (180° − α) + (180° − β) + (180° − γ)

⇒ Sum = 540° − (α + β + γ)

⇒ Sum = 540° − 180°

⇒ Sum = 360°

∴ The correct answer is 360°.

Additional Information

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Polygon Exterior Angle Sum

For any n-sided convex polygon, the sum of the exterior angles (one at each vertex) is always constant and equal to 360°.

Interior Angle Sum Formula

The sum of the interior angles of a polygon with n sides is given by (n − 2) × 180°.

The correct answer is Fifth Five-Year Plan.

Key Points

• The Fifth Five-Year Plan (1974-1978) aimed at removing poverty and attaining self-reliance through the promotion of economic growth, social justice, and self-reliance.
• This plan was formulated and launched under the guidance of D.P. Dhar and was approved during the tenure of Prime Minister Indira Gandhi.
• The plan focused on increasing the income levels of the poor and providing employment opportunities to reduce poverty.
• It emphasized the reduction of inequalities in income and wealth distribution, and the expansion of the agriculture sector to ensure food security.

Additional Information

• Five-Year Plans in India
• The Five-Year Plans were centralized and integrated national economic programs. Initially, they were implemented by the Planning Commission of India.
• The First Five-Year Plan (1951-1956) focused on the agricultural sector, aiming to increase food production and improve the living standards of the rural population.
• The Second Five-Year Plan (1956-1961) prioritized industrialization, especially heavy industries and the public sector.
• Each subsequent plan aimed at addressing specific economic challenges faced by the country, with a long-term vision for balanced and sustainable growth.
• Poverty Alleviation Programs in India
• Various poverty alleviation programs have been launched in India, such as the Integrated Rural Development Program (IRDP), National Rural Employment Guarantee Act (NREGA), and the Public Distribution System (PDS).
• The Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) provides legal guarantees for at least 100 days of wage employment in a year to every household whose adult members volunteer to do unskilled manual work.
• These programs aim to provide direct assistance to the poor and promote economic development through job creation and social support.

Shortcut Trick

Convert the interest rate to a ratio: 10% = 1/10. For Compound Interest, the amount grows from 10 to 11 units each year.

For 3 years, the growth factor is the cube of the ratio: (10)³ → (11)³.

Principal (1000 units) → Amount (1331 units).

Given Principal = ₹1,000 (which is 1000 units), so Amount = 1331 units = ₹1331.

∴ The correct answer is ₹1331.

Alternate Method

Given:

Principal (P) = ₹1,000

Rate (R) = 10% per annum

Time (n) = 3 years

Formula Used:

Amount (A) = P × (1 + R/100)ⁿ

Calculations:

⇒ A = 1000 × (1 + 10/100)³

⇒ A = 1000 × (1 + 0.1)³

⇒ A = 1000 × (1.1)³

⇒ A = 1000 × (1.1 × 1.1 × 1.1)

⇒ A = 1000 × 1.331

⇒ A = 1331

∴ The correct answer is ₹1331.

Additional Information

Effective Rate of Interest

For a 10% rate compounded annually for 3 years, the Effective Percentage Rate is 33.1%. Net Amount = P × (100 + 33.1)%.

CI vs SI Difference for 3 Years

The difference (D) between Compound Interest and Simple Interest for 3 years is given by: D = P(R/100)² × (3 + R/100).

Compounding Half-Yearly

If interest is compounded half-yearly, the rate becomes R/2 and the time period becomes 2n.

The correct answer is Article 51A.

Key Points

• The 42nd Constitutional Amendment Act of 1976 added a new part IV-A to the Indian Constitution, which enshrines the Fundamental Duties of citizens.
• Article 51A, specifically, lists ten Fundamental Duties for every citizen of India.
• These duties include respecting the Constitution, the national flag, and the national anthem; cherishing the noble ideals of the freedom struggle; and upholding and protecting the sovereignty, unity, and integrity of India.
• Other duties involve promoting harmony, safeguarding public property, protecting the environment, and striving towards excellence in all spheres of individual and collective activity.

Additional Information

• Constitutional Amendments:
• Constitutional amendments are changes made to the Constitution to address issues or update its provisions. The Constitution of India provides a detailed process for amendments under Article 368.
• The 42nd Amendment, enacted in 1976, is one of the most significant amendments as it brought about extensive changes, including the addition of the Fundamental Duties.
• Part IV-A of the Indian Constitution:
• Part IV-A was added to the Constitution through the 42nd Amendment and it deals with Fundamental Duties. This part aims to remind citizens that while they enjoy their rights, they also have certain duties to perform.
• The Fundamental Duties are inspired by the Constitution of the erstwhile USSR. They are non-justiciable, which means they are not enforceable by the courts for their violation.
• Importance of Fundamental Duties:
• The inclusion of Fundamental Duties was intended to serve as a constant reminder to citizens that they should be conscious of their duties towards their country, society, and fellow citizens.
• These duties help in promoting a sense of discipline and commitment among citizens, which is essential for the unity and integrity of the nation.

Shortcut Trick For two numbers with sum (S) and difference (D), the ratio of the larger number to the smaller number is (S + D) : (S − D). Given Sum = 20 and Difference = 16. Ratio = (20 + 16) : (20 − 16) = 36 : 4 = 9 : 1. ∴ The correct answer is 9 : 1. Alternate Method Given: Sum of numbers = 20, Difference of numbers = 16. Formula Used: Larger number (L) = (Sum + Difference) ÷ 2; Smaller number (S) = (Sum − Difference) ÷ 2.

⇒ Let the numbers be x and y (where x > y). ⇒ x + y = 20 ⇒ x − y = 16 ⇒ Adding both equations: 2x = 36 ⇒ x = 18 ⇒ Subtracting both equations: 2y = 4 ⇒ y = 2 ⇒ Required Ratio = x : y = 18 : 2 ⇒ Ratio = 9 : 1 ∴ The correct answer is 9 : 1. Additional Information Linear Equations in Two Variables To find two quantities when their sum and difference are known, the values are (S+D)/2 and (S-D)/2 respectively. Ratio Simplification A ratio is always expressed in its simplest form by dividing both terms by their Highest Common Factor (HCF).

The correct answer is Sunil Chhetri.

Key Points

• Sunil Chhetri is an Indian professional footballer who plays as a forward and captains both the Indian Super League side Bengaluru FC and the Indian national team.
• As of June 2021, Sunil Chhetri surpassed Lionel Messi to become the second-highest active international goal-scorer, with 74 goals.
• Sunil Chhetri is considered one of the greatest footballers in Indian history and has received numerous accolades for his contributions to Indian football.
• He has been awarded the AIFF Player of the Year a record six times and has been instrumental in India's performance in international tournaments.

Additional Information

• Lionel Messi:
• He is an Argentine professional footballer who plays as a forward for Paris Saint-Germain and the Argentina national team.
• Messi is widely regarded as one of the greatest footballers of all time.
• He has won the Ballon d'Or award seven times, which is the most by any player in history.
• Cristiano Ronaldo:
• He is a Portuguese professional footballer who plays as a forward for Al Nassr and the Portugal national team.
• As of June 2021, Cristiano Ronaldo is the highest active international goal-scorer.
• Ronaldo has won the Ballon d'Or award five times.
• AIFF (All India Football Federation):
• It is the governing body of football in India under the jurisdiction of the Ministry of Youth Affairs and Sports, Government of India.
• The AIFF is responsible for the development and promotion of football in India.
• It organizes various leagues and tournaments, including the Indian Super League and I-League.
• International Goals:
• International goals refer to the goals scored by a footballer in matches representing their national team.
• These matches include official tournaments like the FIFA World Cup, continental championships, and international friendlies.
• Scoring international goals is considered a significant achievement and contributes to a player's legacy in the sport.

The correct answer is Ethanoic acid.

Key Points

• When ethanol (C2H5OH) reacts with potassium dichromate (K2Cr2O7) in an acidic medium, it undergoes oxidation.
• Potassium dichromate in the presence of acid acts as a strong oxidizing agent.
• The primary alcohol ethanol is first oxidized to ethanal (acetaldehyde), which is further oxidized to ethanoic acid (acetic acid).
• This two-step oxidation process results in the formation of ethanoic acid as the major product.

Additional Information

• Ethanol (C2H5OH):
• Ethanol, commonly known as alcohol, is a volatile, flammable, colorless liquid with a slight characteristic odor.
• It is used in alcoholic beverages, as a solvent, and as a fuel.
• Potassium Dichromate (K2Cr2O7):
• Potassium dichromate is a common inorganic chemical reagent, mostly used as an oxidizing agent in various laboratory and industrial applications.
• In the presence of acid, it acts as a strong oxidizing agent and can oxidize primary alcohols to carboxylic acids.
• Oxidation Reactions:
• Oxidation involves the loss of electrons or an increase in the oxidation state of a molecule, atom, or ion.
• In organic chemistry, oxidation often involves the addition of oxygen to a compound or the removal of hydrogen.
• Ethanoic Acid (CH3COOH):
• Ethanoic acid, also known as acetic acid, is a colorless liquid organic compound with the chemical formula CH3COOH.
• It is the main component of vinegar and has a distinctive sour taste and pungent smell.
• Ethanoic acid is widely used in the production of synthetic fibers, plastics, food additives, and as a chemical reagent in laboratories.

The correct answer is Option 2.

The correct answer is Orange.

Key Points

• Orange light has a lower refractive index compared to indigo, green, and yellow lights.
• The refractive index of a color decreases as the wavelength of the light increases. Orange light has a longer wavelength compared to indigo, green, and yellow.
• Refractive index is inversely related to the speed of light in the medium. Orange light, having a lower refractive index, travels faster in a medium compared to indigo, green, and yellow lights.
• Therefore, among the given options, orange light bends the least when passing through a prism, indicating it has the lowest refractive index.

Additional Information

• Refractive Index:
• The refractive index of a material is a measure of how much the speed of light is reduced inside the material compared to the speed of light in a vacuum.
• It is a dimensionless number, typically greater than 1, and is denoted by the letter 'n'.
• The refractive index can be calculated using the formula n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the material.
• Dispersion of Light:
• When light passes through a prism, it is separated into its constituent colors, a process known as dispersion.
• Different colors of light bend by different amounts due to their varying refractive indices.
• Violet and indigo light, having shorter wavelengths, bend more than red and orange light, which have longer wavelengths.
• Wavelength and Frequency:
• The wavelength of light is the distance between successive peaks of the electromagnetic waves.
• Frequency is the number of wave cycles that pass a point per unit time, typically measured in hertz (Hz).
• There is an inverse relationship between wavelength and frequency: λ = c/f, where λ is the wavelength, c is the speed of light, and f is the frequency.
• Prisms and Light Bending:
• A prism is a transparent optical element with flat, polished surfaces that refract light.
• The angle at which light enters and exits the prism affects how much it bends and how it is dispersed into its constituent colors.
• Prisms are commonly used in spectrometers to analyze light and determine the wavelengths present in a light source.

The correct answer is Option 2.

The correct answer is Calcutta.

Key Points

• The Black Hole of Calcutta was a small prison or dungeon in Fort William, Calcutta, where British soldiers and Indian sepoys were held by the Nawab of Bengal, Siraj-ud-Daulah.
• The incident took place on the night of June 20, 1756, when troops of Siraj-ud-Daulah captured Fort William.
• It is alleged that 146 prisoners were confined in a room measuring 14 by 18 feet, and by morning only 23 survived due to suffocation and heat exhaustion.
• The event was used by the British to justify their subsequent military actions in India, leading to the Battle of Plassey in 1757.

Additional Information

• Siraj-ud-Daulah
• Siraj-ud-Daulah was the last independent Nawab of Bengal, Bihar, and Orissa.
• He succeeded his grandfather, Alivardi Khan, in April 1756 and immediately faced challenges from the British East India Company.
• His attack on Fort William was a response to British military fortifications in Bengal without his permission.
• After his defeat at the Battle of Plassey, he was overthrown and executed.
• Fort William
• Fort William is a fort built in Calcutta in 1696 during the early years of British East India Company rule in India.
• The fort was named after King William III of England.
• It served as the British stronghold in Bengal and was the site of significant events in the early colonial history of India.
• After the Black Hole incident, the fort was extensively rebuilt and expanded.
• Battle of Plassey
• The Battle of Plassey was fought on June 23, 1757, between the forces of the British East India Company, led by Robert Clive, and the Nawab of Bengal, Siraj-ud-Daulah.
• It was a decisive victory for the British, largely due to the betrayal of Siraj-ud-Daulah's key general, Mir Jafar.
• The battle marked the beginning of British political control over India.
• It led to the establishment of the British East India Company's rule in Bengal and eventually all of India.

The correct answer is Option 2.

The correct answer is Vacuoles.

Key Points

• Vacuoles are membrane-bound organelles present in plant cells.
• They play a crucial role in storing nutrients, waste products, and maintaining turgor pressure within the cell.
• The vacuole in a plant cell is large and centrally located, occupying a significant portion of the cell's volume.
• Besides waste storage, vacuoles also store essential compounds such as ions, sugars, and amino acids.

Additional Information

• Mitochondria
• They are known as the powerhouse of the cell because they generate most of the cell's supply of ATP, used as a source of chemical energy.
• Mitochondria are not involved in storing waste products.
• Golgi Bodies
• Also known as the Golgi apparatus, they are involved in modifying, sorting, and packaging proteins and lipids for secretion or for use within the cell.
• Golgi bodies do not play a role in storing waste products.
• Lysosomes
• They are membrane-bound organelles that contain enzymes to break down waste materials and cellular debris.
• While lysosomes do help in waste processing, they do not store waste products.

The correct answer is Option 2.

The correct answer is PARAM Ganga.

Key Points

• The supercomputer PARAM Ganga was designed and installed by the Centre for Development of Advanced Computing (CDAC).
• It was installed at IIT Roorkee as part of Phase II of the National Supercomputing Mission (NSM) in March 2022.
• The installation of PARAM Ganga is aimed at boosting research and innovation in various scientific fields.
• The National Supercomputing Mission (NSM) is an initiative by the Indian government to enhance the computing capabilities in academic and research institutions.

Additional Information

• Centre for Development of Advanced Computing (CDAC)
• CDAC is an organization established in 1988 by the Indian government to carry out research and development in IT, Electronics, and associated areas.
• It is known for its high-performance computing and grid computing capabilities.
• CDAC has played a significant role in the development of the PARAM series of supercomputers.
• National Supercomputing Mission (NSM)
• Launched in 2015, NSM is a joint initiative of the Department of Science and Technology (DST) and the Ministry of Electronics and Information Technology (MeitY).
• The mission aims to enhance the research capacities and capabilities of the country by setting up a network of supercomputers.
• It involves the installation of more than 70 high-performance computing facilities across India.
• The mission also focuses on the development of indigenous supercomputing capabilities and applications.
• Supercomputing Applications
• Supercomputers are used for complex simulations, scientific research, weather forecasting, drug discovery, and various other fields that require high computational power.
• They play a crucial role in solving large-scale problems in physics, chemistry, biology, and engineering.

The correct answer is Option 2.

The logic followed here is:

Logic: 1st number × 3rd number × 3 = 2nd number.

For, (10, 300, 10)

⇒ 10 × 10 × 3 = 300.

For, (11, 165, 5) 

⇒ 11 × 5 × 3 = 165.

Similarly, for (9, 243, 9) 

⇒ 9 × 9 × 3 = 243.

Hence, the correct option is "Option 4".

BODMAS Table: 

Given equation: 13 - 7 + 8 ÷ 2 × 10 

Now, if ‘×’ and ‘-’ are interchanged, then:

⇒ 13 × 7 + 8 ÷ 2 - 10 

⇒ 13 × 7 + 4 - 10 

⇒ 91 + 4 - 10 

⇒ 95 - 10 = 85.

Hence, the correct answer is "Option 4".

Given: Amongst six friends A, B, C, D, E and F, each has a different height.

1. A is taller than only two other friends.

__ > __ > __ > A > __ > __

2. C is shorter than only one friend.

__ > C > __ > A > __ > __

3. E is shorter than A but taller than B.

__ > C > __ > A > E > B

4. F is shorter than D.

D > C > F > A > E > B

So, 'D' is the tallest among all the friends.

Hence, the correct answer is "Option 4".

Shortcut Trick

Ramesh's selling price (SP) = 4,000 × (110 ÷ 100) = 4,400.

Mohan's total cost price = 4,400 + 500 = 4,900.

Ritwik's cost price = 4,900 × (112 ÷ 100) = 49 × 112.

Multiplier method: 4,900 × 1.12 = 5,488.

∴ The correct answer is Rs. 5,488.

Alternate Method

Given → CP of Ramesh = Rs. 4,000 | Profit% Ramesh = 10% | Repairs = Rs. 500 | Profit% Mohan = 12%. Formulas: SP = CP × (100 + Profit%) ÷ 100 | Total CP = Purchase Price + Overheads.

⇒ Selling Price of Ramesh = 4,000 + (10 ÷ 100 × 4,000) = 4,000 + 400 = Rs. 4,400. ⇒ Cost Price for Mohan = Rs. 4,400. ⇒ Total effective CP for Mohan = Purchase Price + Repairs = 4,400 + 500 = Rs. 4,900. ⇒ Selling Price of Mohan (CP for Ritwik) = 4,900 × (112 ÷ 100). ⇒ CP for Ritwik = 49 × 112 = Rs. 5,488.

∴ The correct answer is Rs. 5,488.

Additional Information

Effective Cost Price

Any additional expenditure like repairs, transportation, or installation is always added to the purchase price to calculate the total Cost Price (CP) before calculating profit or loss.

Successive Transactions

In a chain of sales, the Selling Price (SP) of the previous seller becomes the Cost Price (CP) for the next buyer.

The correct answer is Goa.

Key Points

• Konsachem Fest is a traditional harvest festival celebrated in the state of Goa.
• It is also known as the Harvest feast, a thanksgiving ritual wherein farmers pray for continued blessings from the gods.
• The festival is marked by various rituals and ceremonies to honor the agricultural bounty.
• During the Konsachem Fest, farmers bring the first sheaves of paddy to the church as an offering and thanksgiving for a good harvest.

Additional Information

• Harvest Festivals in India
• Harvest festivals are celebrated across India with great enthusiasm, each region having its unique customs and traditions.
• Some of the prominent harvest festivals include Pongal in Tamil Nadu, Makar Sankranti in various parts of India, Baisakhi in Punjab, and Onam in Kerala.
• These festivals are a way to thank nature and gods for a bountiful harvest and are often marked by feasting, dancing, and various cultural activities.
• Goa's Cultural Festivities
• Goa is known for its vibrant and diverse cultural heritage, with numerous festivals celebrated throughout the year.
• Some of the key festivals include Carnival, Shigmo, Sao Joao, and Christmas, reflecting the state's unique blend of Indian and Portuguese influences.
• These festivals often involve colorful parades, music, dance, and traditional rituals, showcasing Goa's rich cultural tapestry.

The correct answer is Option 2.

The correct answer is Option 1: Exothermic reaction.

Key Points

• Exothermic reactions are chemical reactions that release energy by light or heat.
• In an exothermic reaction, the energy released in the form of heat is greater than the energy absorbed during the reaction.
• Common examples of exothermic reactions include combustion reactions, such as burning wood or fossil fuels, and many oxidation reactions.
• These reactions are characterized by a negative change in enthalpy (ΔH < 0), indicating that energy is being released.

Additional Information

• Endothermic Reaction
• An endothermic reaction is a chemical reaction that absorbs energy from its surroundings, usually in the form of heat.
• These reactions are characterized by a positive change in enthalpy (ΔH > 0), indicating that energy is being absorbed.
• An example of an endothermic reaction is the process of photosynthesis in plants.
• Sigma Tropic Reactions
• Sigma tropic reactions are a class of pericyclic reactions where a sigma bond adjacent to one or more pi systems shifts to a new position in the molecule, resulting in a new sigma bond.
• These reactions are typically involved in organic transformations and are governed by the Woodward-Hoffmann rules.
• Rearrangement Reactions
• Rearrangement reactions involve the reorganization of the structure of a molecule, leading to a different isomer.
• These reactions can involve shifts of atoms or groups within a molecule and often occur via a series of intermediate steps.
• Examples include the Wagner-Meerwein rearrangement and the Beckmann rearrangement.

The correct answer is Option 2: Both the statements (I) and (II) are not related..

Shortcut Trick

When a sum of money doubles itself, the Simple Interest (SI) earned is exactly 100% of the Principal.

Shortcut Formula: Rate (R) = 100 ÷ Time (T)

R = 100 ÷ 10

R = 10%

∴ The correct answer is 10%.

Alternate Method

Given:

Let Principal (P) = ₹100

Since the sum doubles, Amount (A) = ₹200

Time (T) = 10 years

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ SI = Amount − Principal

⇒ SI = 200 − 100 = ₹100

⇒ 100 = (100 × R × 10) ÷ 100

⇒ 100 = 10 × R

⇒ R = 100 ÷ 10

⇒ R = 10%

∴ The correct answer is 10%.

Additional Information

General Formula for 'n' times

If a sum becomes n times itself in T years at Simple Interest, then the Rate (R) = [(n − 1) × 100] ÷ T.

Simple Interest vs Compound Interest

In Simple Interest, the interest remains constant every year as it is always calculated on the original principal.

Time to Triple

To find the time (T) required for a sum to triple (n=3) at a given rate (R): T = 200 ÷ R.

Given equation: 21 + 7 - 3 ÷ 20 × 5 = ?  

Decoding the given information :

Now, replacing the sign from left to right and using BODMAS rule, we get :

New equation : 21 - 7 × 3 + 20 ÷ 5 = ?  

Calculation :

⇒ 21 - 7 × 3 + 20 ÷ 5 = ? 

⇒ 21 - 7 × 3 + 4 = ? 

⇒ 21 - 21 + 4 = ? 

⇒ 25 - 21 = 4.

Hence, the correct answer is "Option 4".

Shortcut Trick

A Prime Number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Numbers list: 1 (neither prime nor composite), 2 (first prime), 3 (second prime), 4 (composite)...

The smallest prime number is 2, which is also the only even prime number.

∴ The correct answer is 2.

Alternate Method

Given: A set of natural numbers to identify the smallest prime.

Definition: Prime numbers must have exactly two distinct factors: 1 and the number itself.

⇒ Number 1: Factors are {1}. Only 1 factor, so it is not prime.

⇒ Number 2: Factors are {1, 2}. Exactly 2 factors, so it is prime.

⇒ Number 3: Factors are {1, 3}. Exactly 2 factors, so it is prime.

⇒ Comparing 2 and 3, 2 is the smallest value.

∴ The correct answer is 2.

Additional Information

Even Prime Number

The number 2 is the only even prime number in the entire number system; all other prime numbers are odd.

Co-prime Numbers

Two numbers are called co-prime if their Highest Common Factor (HCF) is 1. They do not necessarily have to be prime individually.

Composite Numbers

Numbers with more than two factors are called composite numbers. The smallest composite number is 4.

The Number 1

The number 1 is a unique number that is neither prime nor composite.

The logic followed here is:

Logic: (1st number × 2) - 1 = 2nd number.

For, 58 : 115

⇒ (58 × 2) - 1 

⇒ 116 - 1 = 115.

For, 47 : 93

⇒ (47 × 2) - 1 

⇒ 94 - 1 = 93.

Similarly, for 67 : ?

⇒ (67 × 2) - 1 

⇒ 134 - 1 = 133.

Hence, the correct option is "Option 3"

The correct answer is 750 W.

Key Points

• Given Values:
• Heat produced (Q) = 60 kJ = 60000 J
• Time Taken: The given time is 1 minute and 20 seconds, which equals 80 seconds.
• Formula for Power:
• Power is calculated as the total heat divided by time.
• Power (P) = Q / t
• Substitute the Values:
• P = 60000 / 80
• Calculating the Power:
• P = 750 W

Additional Information

• Power is the rate at which energy is transferred or converted and is measured in watts (W).
• Heat is a form of energy, and its rate of transfer determines the power of the system.
• The SI unit of power is the watt (W), where 1 watt equals 1 joule per second.
• The heat generated in devices like heaters depends on current, resistance, and voltage.
• Power ratings of electrical appliances help determine their energy consumption and operational efficiency.
• Understanding power and heat transfer is crucial in designing efficient heating systems and optimizing energy usage.

Given: 167, 876, 567, 187, 873 

Now, 11 is subtracted from each of the following numbers:

167 - 11 = 156,

876 - 11 = 865,

567 - 11 = 556,

187 - 11 = 176,

873 - 11 = 862,

If the digits of each number are written in reverse order:

And now, the numbers are arranged in ascending order:

So, the position of 'one' numbers will NOT change.

The correct answer is "Option 4".

The logic followed here is:

For, HP : MS

For, DL : IO

Similarly, for AL : FO

Hence, the correct answer is "Option 3".

The correct answer is Option 3: appear to diverge from a point at a distance 1 m behind the mirror.

Key Points

• A convex mirror is also known as a diverging mirror.
• When parallel rays of light strike a convex mirror, they appear to diverge from a single point behind the mirror.
• This point is called the focal point, and the distance from the mirror's surface to this point is called the focal length (f).
• For a convex mirror, the focal length is considered positive, and the focal point is virtual as the light rays do not actually converge there.

Additional Information

• Convex Mirror:
• A convex mirror is a spherical mirror in which the reflective surface bulges outwards.
• It is used in various applications like vehicle rearview mirrors and in surveillance.
• Focal Length (f):
• The focal length is the distance between the mirror's surface and the focal point.
• For a convex mirror, the focal length is positive and virtual.
• Virtual Image:
• A virtual image is formed when the reflected rays appear to diverge from a point behind the mirror.
• Virtual images cannot be projected on a screen as the light rays do not actually meet.
• Diverging Mirror:
• Convex mirrors are also known as diverging mirrors because they spread out light rays that are initially parallel when they reflect off the mirror.

The correct answer is Option 2: Both the statements (I) and (II) are not related..

The correct answer is Condom.

Key Points

• Condoms are a barrier method of contraception that can prevent both unwanted pregnancies and sexually transmitted diseases (STDs).
• They work by preventing sperm from entering the vagina, thereby preventing fertilization.
• Condoms also act as a barrier to viruses and bacteria that cause STDs, including HIV.
• They are available for both males and females and are one of the most accessible and cost-effective methods of contraception.

Additional Information

• Oral Pills:
• Oral contraceptive pills are taken by women to prevent pregnancy.
• They contain hormones that inhibit ovulation and thicken cervical mucus to prevent sperm from reaching an egg.
• While effective in preventing pregnancy, they do not offer any protection against STDs.
• Surgical Method:
• Surgical methods such as vasectomy in men and tubal ligation in women are permanent methods of contraception.
• These procedures involve cutting or sealing the reproductive tubes to prevent sperm and egg from meeting.
• They do not offer protection against STDs.
• Copper-T:
• Copper-T is a type of intrauterine device (IUD) used by women to prevent pregnancy.
• It is a small T-shaped device inserted into the uterus that releases copper to prevent fertilization and implantation of an egg.
• It does not provide protection against STDs.

The correct answer is Both the statements (I) and (II) are not related.

Shortcut Trick

Total Work (LCM of 14, 18) = 126 units.

Efficiency of A = 9 units/day, Efficiency of B = 7 units/day.

A works for 6 days: 9 × 6 = 54 units done.

Remaining work: 126 − 54 = 72 units.

Days for B = 72 ÷ 7 = 10 2/7 days.

∴ The correct answer is 10 2/7 days.

Alternate Method

Given: Time taken by A = 14 days, Time taken by B = 18 days.

Formula Used: Total Work = Efficiency × Time; Remaining Work = Total Work − Completed Work.

Calculations:

⇒ Work completed by A in 6 days = 9 × 6 = 54 units

⇒ Remaining Job = 126 − 54 = 72 units

⇒ Days required by B to complete remaining work = 72 ÷ 7

⇒ Time = 10 2/7 days

∴ The correct answer is 10 2/7 days.

Additional Information

Work-Efficiency Relationship

Efficiency is inversely proportional to the time taken to complete a job. If A is twice as efficient as B, A will take half the time of B.

Fractional Work Method

If a person completes a job in 'D' days, work done in 1 day = 1/D. Total work is always considered as 1 unit.

Pipes & Cisterns Analogy

This concept is identical to inlet pipes filling a tank, where work done is equivalent to the volume of the tank.

The correct answer is Substances that are not broken down by biological processes.

Key Points

• Non-biodegradable substances are materials that cannot be decomposed by natural biological processes.
• These substances tend to persist in the environment for a long time, often causing pollution.
• Common examples include plastics, synthetic chemicals, and certain types of metals.
• Managing non-biodegradable waste is crucial for environmental protection and sustainability.

Additional Information

• Biodegradable Substances:
• These are materials that can be broken down by microorganisms into simpler, non-toxic substances.
• Common examples include food scraps, paper, and natural fibers like cotton and wool.
• Biodegradation is a crucial process in the natural recycling of organic matter.
• Proper waste management of biodegradable substances helps reduce landfill use and greenhouse gas emissions.
• Environmental Impact of Non-Biodegradable Substances:
• Non-biodegradable waste contributes significantly to environmental pollution.
• Plastics, in particular, can cause harm to wildlife and marine life.
• These substances often accumulate in landfills, leading to soil and water contamination.
• Efforts to reduce the use of non-biodegradable materials include recycling, using alternative materials, and promoting sustainable practices.
• Recycling and Waste Management:
• Recycling is the process of converting waste materials into new materials and objects.
• Effective waste management involves reducing, reusing, and recycling materials to minimize environmental impact.
• Governments and organizations are increasingly promoting recycling programs to manage non-biodegradable waste effectively.
• Public awareness and participation are essential for the success of recycling and waste management initiatives.

The correct answer is revenue receipt.

Key Points

• Revenue receipts are the income that the government receives from its normal, day-to-day activities.
• These include tax revenues such as income tax, corporate tax, excise duty, and non-tax revenues such as interest receipts, dividends, and profits from public sector enterprises.
• Cash Grant-in-Aid from foreign countries and international organizations are considered as non-tax revenues under revenue receipts.
• Revenue receipts do not create any liability or lead to a reduction in assets.

Additional Information

• Non-Planned Revenue Receipt
• Non-planned revenue receipts are those which are not included in the planned revenue receipts of the government.
• These include items like interest receipts, dividends and profits from public sector enterprises, and other non-tax revenues.
• Planned Revenue Income
• Planned revenue income refers to the income that is expected to be received as per the budgetary plans of the government.
• It includes both tax and non-tax revenues that have been planned for in the budget.
• Capital Receipt
• Capital receipts are the income received by the government that either creates liabilities or reduces the assets of the government.
• Examples include loans from the public, foreign governments, or international organizations, and disinvestment proceeds.

The correct answer is a renewable resource.

Key Points

• The Chipko Andolan, or Chipko Movement, was primarily an environmental movement in India.
• The movement was aimed at protecting trees from being cut down by contractors and loggers.
• Women played a significant role in this movement, emphasizing the conservation of forests as a renewable resource.
• Forests are considered a renewable resource because they can regrow and provide ecological benefits over time if managed sustainably.

Additional Information

• Chipko Movement:
• Started in the early 1970s in the Garhwal Himalayas of Uttarakhand, India.
• The name "Chipko" means "to hug" or "to cling to," reflecting the method of protest where villagers, especially women, hugged trees to prevent them from being cut down.
• The movement led to a ban on the felling of trees in the Himalayan regions for 15 years, allowing the forests to regenerate.
• Renewable Resources:
• Resources that can be replenished naturally over short periods of time.
• Examples include sunlight, wind, water, and biomass.
• Renewable resources are crucial for sustainable development as they reduce dependency on non-renewable resources, which can be depleted.
• Importance of Forests:
• Forests play a critical role in maintaining ecological balance and supporting biodiversity.
• They act as carbon sinks, absorbing CO2 from the atmosphere and mitigating climate change.
• Forests provide livelihood to millions of people, especially in rural areas, through resources like timber, fruits, and medicinal plants.

Given: P, Q, R, S, T, X, Y and Z are sitting around a square table facing the centre of the table (but not necessarily in the same order).

Some of them are sitting at the corners while some are sitting at the exact centre of the sides.

If S, T, Y and Z are sitting at the exact center of the sides of the table,

1) Z who is to the immediate left of R, has P as immediate neighbours.

2. S is the immediate neighbor of Q and X .

3. Y does not have X and P as his immediate neighbours. 

And, T sits at the remaining place.

So, 'T' is sitting to the immediate right of X.

Hence, the correct answer is "Option 3".

The correct answer is starch.

Key Points

• Salivary amylase is an enzyme found in the saliva of humans and some other animals.
• It begins the process of digesting starch, breaking it down into simpler sugars such as maltose and dextrin.
• Starch digestion by salivary amylase starts in the mouth and continues until the enzyme is inactivated by stomach acid.
• Salivary amylase is produced by the salivary glands, including the parotid, submandibular, and sublingual glands.

Additional Information

• Enzyme: A protein that acts as a catalyst to speed up chemical reactions in the body, including digestion.
• Starch: A complex carbohydrate found in foods like potatoes, rice, and bread that is broken down into glucose by enzymes like amylase for energy.
• Maltose: A disaccharide sugar produced by the breakdown of starch by amylase; consists of two glucose units.
• Dextrin: Intermediate products of the breakdown of starch by amylase, consisting of varying lengths of glucose chains.