RRC Group D Previous Year Paper 60 (Held On: 25 Sept 2018 Shift 3)

The given figure rotates 90⁰ anticlockwise direction which is given below:-

Hence, "option 3" is the correct answer.

Concept Used:   

Follow the BODMAS rule according to the table given below:

Calculation:

$[60 ÷{3^3 × 2 - (29 - \overline{26 - 31})}]$

⇒ [60 ÷ {3³ × 2 – (29 – (-5))}]

⇒ [60 ÷ {3³ × 2 – (29 + 5)}]

⇒ [60 ÷ {27 × 2 – 34}]

⇒ [60 ÷ (54 – 34)]

⇒ (60 ÷ 20)

⇒ 3

∴ The required value is 3

The Venn diagram is given below:-

(A) Computer, (B) Table, (C) Electronic

Modern computers are electronic and the table is different from both.

Hence, "Option 2" is the correct answer.

Additional InformationModern computers are electronic because they use active semiconductors (e.g. transistors), mostly in the form of integrated circuits. That is what distinguishes them from mere electric device, i. e. one that uses electricity (like a conventional lightbulb).

Shortcut Trick

Total cards = 216

Initial share of A = (5 ÷ 9) × 216 = 5 × 24 = 120 cards

Final share of A = (11 ÷ 24) × 216 = 11 × 9 = 99 cards

Change in cards for A = 120 − 99 = 21 less

∴ The correct answer is 21 less.

Alternate Method

Given:

Total cards = 216

Initial Ratio A : B = 5 : 4

Final Ratio A : B = 11 : 13

Calculations:

⇒ Sum of initial ratio parts = 5 + 4 = 9 units

⇒ Value of 1 unit = 216 ÷ 9 = 24

⇒ A's first share = 5 × 24 = 120 cards

⇒ Sum of final ratio parts = 11 + 13 = 24 units

⇒ Value of 1 unit = 216 ÷ 24 = 9

⇒ A's second share = 11 × 9 = 99 cards

⇒ Difference for A = 120 − 99 = 21

∴ The correct answer is 21 less.

Additional Information

Ratio Distribution Rule

To divide a quantity Q in ratio a:b, the parts are [a/(a+b)] × Q and [b/(a+b)] × Q.

Comparison of Ratios

When the total sum remains constant, you can equalize the sum of ratio parts by taking their LCM to compare values directly.

The correct answer is 8.9.

• Given, 
• density of water = 103 kg/m³.
• density of copper = 8.9 × 103 kg/m³.
• $Relative;density = {Density;of;Copper\over Density;of;Water}$ 
• $= {8.9 × 10^3;kg/m^3 \over 10^3;kg/m^3}$
• = 8.9 kg/m3

Additional Information

• Relative density is measured by Hydrometer.
• The relative density is defined as the ratio of the density of the substance to the density of water at 4°C.

The correct answer is I Do What I Do.

Key Points

• I do what I do book is written by former RBI governor Raghuram Rajan.
• I do what I Do is a nonfiction book authored by economist and former Governor of the Reserve Bank of India, Raghuram Rajan published by Harper Collins India in 2017.
• The book is a collection of speeches delivered by Rajan during his stint as the Governor of the Reserve Bank of India along with his commentary on the economic and political context prevalent at that time.
• The book was released on September 5, 2017, and quickly made its way to topping the list of best sellers on Amazon India and Flipkart.

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Additional Information</sup>

• The book titled 'The Emergency – Indian Democracy's Darkest Hour' has been authored by Surya Prakash, the chairman of Prasar Bharati.
• The book has recently launched by Union Minister for Urban Development M Venkaiah Naidu in Ahmedabad, Gujarat.
• The book “The Unseen Indira Gandhi” has been authored by Dr. KP Mathur, who was the personal physician of former Prime Minister Indira Gandhi for nearly 20 years till her assassination in 1984.
• The Ministry of Utmost Happiness is the second novel by Indian writer Arundhati Roy, published in 2017, twenty years after her debut, The God of Small Things.

The correct answer is Salt, water.

Key Points

• When an acid reacts with a metal oxide, salt and water are obtained as products.
• Salt and water are produced when acids react with metal oxides.
• Metal oxides are bases because they neutralize acids.
• In general:
• Acid + metal oxide → salt + water
• For example:
• Sulfuric acid + copper(II) oxide → copper(II) sulfate + water
• H₂SO₄(aq) + CuO(s) → CuSO₄(aq) + H₂O(l)

Additional Information

• Al2O3  reacts with acids and bases.
• Aluminum oxide (Al2O3) is an amphoteric substance.
• The amphoteric substance is a substance that can react with both acids and bases usually to produce salt and water.
• Aluminium oxide therefore can react with both acids as well as bases. We will take the example of its reaction with hydrochloric acid (strong acid) and sodium hydroxide (strong base).
• When mixed with these two compounds aluminium oxide either acts like acid with a base and a base with an acid.

Shortcut Trick

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

84 × Other Number = 2604 × 12

Other Number = (2604 × 12) ÷ 84

Other Number = 2604 ÷ 7 = 372

∴ The correct answer is 372.

Alternate Method

Given:

L.C.M. of two numbers = 2604

H.C.F. of two numbers = 12

First number (n₁) = 84

Formula Used:

n₁ × n₂ = L.C.M. × H.C.F.

Calculations:

⇒ 84 × n₂ = 2604 × 12

⇒ n₂ = (2604 × 12) ÷ 84

⇒ n₂ = 31248 ÷ 84

⇒ n₂ = 372

∴ The correct answer is 372.

Additional Information

H.C.F. (Highest Common Factor)

It is the greatest number which divides each of the two or more numbers exactly. It is also known as G.C.D. (Greatest Common Divisor).

L.C.M. (Least Common Multiple)

The least number which is exactly divisible by each of the given numbers. For two prime numbers, L.C.M. is always their product.

H.C.F. and L.C.M. of Fractions

H.C.F. = H.C.F. of Numerators ÷ L.C.M. of Denominators | L.C.M. = L.C.M. of Numerators ÷ H.C.F. of Denominators.

The correct answer is Nucleons.

Key Points

• Two elements are said to be isobars of one another if they have different sets of electrons and the same number of nucleons.
• An example of a series of isobars would be the 40S, 40Cl, 40Ar, 40K, and 40Ca.
• The term nucleon is a collective term used for the combination of neutron and proton altogether inside the nucleus of an atom.

Additional Information

• Isotopes are atoms of the same element with a different number of Neutrons.
• Isotopes are atoms with the same number of protons but that have a different number of neutrons.
• For example - Uranium-235 and Uranium-239 are two different isotopes of the element uranium.
• the atomic number is equal to the number of protons.
• the atomic mass is the sum of protons and neutrons.
• Isotopes are elements with the same atomic number but different mass numbers.

• The given statement is only taking about three items - cotton, cloth, and woolen clothes.
• It does not state anything about either leaves or fabric.
• Hence, none of the conclusions logically follow the statement.

The correct answer is option 4.

Shortcut Trick

Total Work (LCM of 18, 15) = 90 units.

Efficiency of Builder = +5, Destroyer = −6.

Combined Efficiency = Total Work ÷ Time = 90 ÷ 2.5 = +36.

Let the number of Destroyers be x, then 5(16 − x) − 6x = 36 ⇒ 80 − 11x = 36 ⇒ 11x = 44 ⇒ x = 4.

∴ The correct answer is 4.

Alternate Method

Given: Total persons = 16. Total time to build = 2.5 hours.

⇒ Total Efficiency required = Total Work ÷ Total Time

⇒ Net Efficiency = 90 ÷ 2.5 = 36 units/hr

Let the number of Destroyers be D and Builders be (16 − D).

⇒ (16 − D) × 5 + D × (−6) = 36

⇒ 80 − 5D − 6D = 36

⇒ 80 − 11D = 36

⇒ 11D = 80 − 36

⇒ 11D = 44

⇒ D = 4

∴ The correct answer is 4.

Additional Information

Pipes and Cisterns Analogy

Builders act as inlet pipes (positive work) and destroyers act as outlet pipes (negative work).

Work and Efficiency

Total Work = Efficiency × Time. When multiple entities work together, their net efficiency is the algebraic sum of individual efficiencies.

Linear Equation in One Variable

Problems involving two groups can be solved by assuming x for one group and (Total − x) for the other to form a simple equation.

The correct answer is Work.

Key Points

• Work has only magnitude and no direction.
• Work is nothing but the energy generated.
• Work has only a magnitude but no direction.
• The formula for work is written as a dot product of force and displacement.
• $W= F.d$
• Here, 
• W = Work
• F = force
• d = displacement
• Therefore, work is a scalar quantity.

Additional Information

• A vector is a physical quantity that has Magnitude and direction.
• Symbols for physical quantities that are vectors are in bold type, underlined, or with an arrow above.
• It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity’s magnitude.
• For example, displacement, velocity, and acceleration, momentum are vector quantities.
• A quantity that requires both the magnitude in number field along with the direction of the quantity accompanied by the units of measurement or SI units is known as a vector quantity.
• Vector quantities should also obey the triangular law of vectors.

The correct answer is Testicle.

 Key Points

• Testosterone is the only male sex hormone present in the human body, which causes physical changes in puberty, increases bone density and muscle mass, growth of facial, pubic, and body hair, deepening of the voice, and is also responsible for sexual and reproductive development.
• Testosterone is the main sex hormone in men, which is naturally produced in the testes and in small amounts by the adrenal glands.
• Testosterone belongs to a class of male hormones called androgens, which are also known as steroids.
• The production of male sex hormones is mainly controlled by the hypothalamus and pituitary gland.
• The testosterone levels gradually decrease with age, which results in impotence, shrinking of testes, low sperm count, depression, mood swings, irritability, etc.

Additional Information

• The pituitary gland is a small pea-sized gland that plays a major role in regulating vital body functions and general wellbeing.
• It is referred to as the body's 'master gland' because it controls the activity of most other hormone-secreting glands.
• The pituitary gland is a small gland that sits in the sella turcica, a bony hollow in the base of the skull, underneath the brain, and behind the bridge of the nose.
• Adrenal glands, also known as suprarenal glands, are small, triangular-shaped glands located on top of both kidneys.
• Adrenal glands produce hormones that help regulate your metabolism, immune system, blood pressure, response to stress, and other essential functions.
• The ovary is an organ found in the female reproductive system that produces an ovum.
• When released, this travels down the fallopian tube into the uterus, where it may become fertilized by a sperm.
• There is an ovary found on each side of the body.

The correct answer is Akbar.

Key Points

• Akbar started the system of Mansabdari to strengthen the army.
• Akbar started the Mansabdari system in 1571 AD.
• It was such a practice of organizing the army in which each mansabdar kept a cavalry soldier according to his rank and rank and the mansab was used to determine the superiority and influence of his post in the court.

Additional Information

• The Mansabdari system was started during the time of Akbar.
• Because at that time the cavalry was the most important part of the Mughal army.
• Therefore, in 1571 AD, Akbar thought it appropriate to pay attention to the officers who were responsible for maintaining a certain number of cavalry.
• In order to raise the level of cavalry, the slave system was practiced because this part of the army was formed on the basis of mansabdari system in place of jagirdari system.
• During the reign of Babur and Humayun, jagirs were given to the rich.
• He used to deduct his army and his expenses from those jagirs and deposited the rest of the money in the treasury.
• But in this, the emperor did not give a cash salary to the jagirdar.
• ​Abu'l-Fath Jalal-ud-din Muhammad Akbar, popularly known as Akbar the Great, and also as Akbar I, was the third Mughal emperor, who reigned from 1556 to 1605.
• Akbar succeeded his father, Humayun, under a regent, Bairam Khan, who helped the young emperor expand and consolidate Mughal domains in India.

The correct answer is Transpiration.

Key Points

• Transpiration in plants helps in the absorption and uptake activity, from roots to leaves, in the transmission of water and minerals.
• Transpiration has two main functions:
• Cooling the plant and pumping water and minerals to the leaves for photosynthesis.
• Transpiration helps in the transportation of absorbed minerals to all the parts of the plant.
• Transpiration provides water for the process of photosynthesis.
• Transpiration helps in cooling the structures of the plant when exposed to hot sunlight.
• Transpiration helps the cells to maintain their turgidity.
• Excess water is removed from the cells of the plant to prevent plant decay.

Additional Information

• Photosynthesis, the process by which green plants and certain other organisms transform light energy into chemical energy.
• During photosynthesis in green plants, light energy is captured and used to convert water, carbon dioxide, and minerals into oxygen and energy-rich organic compounds.
• In physiology, respiration is the movement of oxygen from the outside environment to the cells within tissues and the removal of carbon dioxide in the opposite direction.
• The physiological definition of respiration differs from the biochemical definition, which refers to a metabolic process by which an organism obtains energy (in the form of ATP and NADPH) by oxidizing nutrients and releasing waste products.

Concept Used:  

Follow the BODMAS rule according to the table given below:

Calculation:

$(-8) [30 ÷{7 - (-3)}] = ?$

⇒ (-8)[30 ÷ {7 + 3)] = ?

⇒ (-8)[30 ÷ 10] = ?

⇒ (-8)[3] = ?

⇒ (-8 × 3) = ?

⇒ -24 = ?

∴ The required value of ? is -24

The correct answer is Metals.

Key Points

• The nature of metals is electro-positive.
• Metals are electropositive because they lose electrons and form positively charged ions.
• For example, Na, K , Ca, Mg, loose electrons form positively charged ions so they are electropositive in nature.

Additional Information

• Physical properties of metals: 
• Metals are lustrous, malleable, ductile, good conductors of heat and electricity. Other properties include:
• State: Metals are solids at room temperature with the exception of mercury, which is liquid at room temperature (Gallium is liquid on hot days).
• Luster: Metals have the quality of reflecting light from their surface and can be polished e.g., gold, silver and copper.
• Malleability: Metals have the ability to withstand hammering and can be made into thin sheets known as foils.
• For example, a sugar cube-sized chunk of gold can be pounded into a thin sheet that will cover a football field.
• Ductility: Metals can be drawn into wires. For example, 100 g of silver can be drawn into a thin wire about 200 meters long.
• Hardness: All metals are hard except sodium and potassium, which are soft and can be cut with a knife.
• Valency: Metals typically have 1 to 3 electrons in the outermost shell of their atoms.
• Conduction: Metals are good conductors because they have free electrons.
• Silver and copper are the two best conductors of heat and electricity.
• Lead is the poorest conductor of heat.
• Bismuth, mercury and iron are also poor conductors
• Density: Metals have high density and are very heavy.
• Iridium and osmium have the highest densities whereas lithium has the lowest density.
• Melting and Boiling Points: Metals have high melting and boiling points.
• Tungsten has the highest melting and boiling points whereas mercury has the lowest.
• Sodium and potassium also have low melting points.

Shortcut Trick

Profit = Selling Price − Cost Price = 315 − 280 = 35.

Profit% = (Profit ÷ CP) × 100 = (35 ÷ 280) × 100.

Ratio of Profit to CP = 35 : 280 = 1 : 8.

Fraction 1/8 = 12.5%.

∴ The correct answer is 12.5%.

Alternate Method

Given → Cost Price (CP) = Rs. 280, Selling Price (SP) = Rs. 315. Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100.

⇒ Profit = 315 − 280 = 35. ⇒ Profit% = (35 ÷ 280) × 100. ⇒ Profit% = (1 ÷ 8) × 100 = 12.5%.

∴ The correct answer is 12.5%.

Additional Information

Profit and Loss Basics

Profit occurs when Selling Price is greater than Cost Price. Loss occurs when Cost Price is greater than Selling Price.

Percentage Calculation

Both Profit Percentage and Loss Percentage are always calculated on the Cost Price unless specified otherwise.

Shortcut Trick

Relative Speed in m/s = 78 × (5/18) = 65/3 m/s.

Total distance (Train + Platform) = Speed × Time = (65/3) × 27 = 585 m.

Length of Train = Total distance − Platform length = 585 − 450 = 135 m.

∴ The correct answer is 135 m.

Alternate Method

Given: Speed of train = 78 km/hr, Length of platform = 450 m, Time taken = 27 sec.

Formula Used: Distance = Speed × Time; 1 km/hr = 5/18 m/s.

⇒ Speed in m/s = 78 × (5/18) = 13 × (5/3) = 65/3 m/s.

⇒ Total Distance = Length of train (L) + Length of platform (P).

⇒ L + 450 = (65/3) × 27

⇒ L + 450 = 65 × 9

⇒ L + 450 = 585

⇒ L = 585 − 450 = 135 m.

∴ The correct answer is 135 m.

Additional Information

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Train Crossing Objects

When a train crosses a stationary object with length (platform, bridge, or another train), the total distance covered is the sum of their lengths.

Relative Speed

For two objects moving in the same direction, relative speed = S₁ − S₂. In the opposite direction, relative speed = S₁ + S₂.

Shortcut Trick

Identify the numbers: 42, 84, and 48.

Since 84 is a multiple of 42 (42 × 2 = 84), the L.C.M. of 42 and 84 is simply 84.

Now find the L.C.M. of 84 and 48.

L.C.M. (84, 48) ⇒ 12 × 7 × 4 = 336.

∴ The correct answer is 336.

Alternate Method

Given: Numbers are 42, 84, and 48.

Formula Used: Prime Factorization Method.

Calculations:

⇒ Prime factors of 42 = 2 × 3 × 7

⇒ Prime factors of 84 = 2² × 3 × 7

⇒ Prime factors of 48 = 2⁴ × 3

⇒ L.C.M. = Product of highest powers of all prime factors involved.

⇒ L.C.M. = 2⁴ × 3¹ × 7¹

⇒ L.C.M. = 16 × 3 × 7

⇒ L.C.M. = 48 × 7 = 336

∴ The correct answer is 336.

Additional Information

L.C.M. Definition

The Least Common Multiple (L.C.M.) is the smallest positive integer that is divisible by each of the given numbers.

Relation between H.C.F. and L.C.M.

For two numbers 'a' and 'b', H.C.F.(a, b) × L.C.M.(a, b) = a × b.

L.C.M. of Fractions

L.C.M. of fractions = (L.C.M. of Numerators) ÷ (H.C.F. of Denominators).

The correct answer is Chlamydomonas.

Key Points

• Chlamydomonas is a unicellular green algae.
• Chlamydomonas reinhardtii, a unicellular, photosynthetic green alga in the Chlamydomonadaceae, has never had a multicellular ancestor yet is closely related to the volvocine algae, which express multicellularity in colonies of up to 50,000 cells.

Additional Information

• Green algae, variable in size and shape, include single-celled (Chlamydomonas, desmids), colonial (Hydrodictyon, Volvox), filamentous (Spirogyra, Cladophora), and tubular (Actebularia, Caulerpa) forms.
• Sexual reproduction is common, with gametes that have two or four flagella.
• The golden-brown algae and diatoms are the most widespread unicellular species of algae.
• Some examples are amoeba, paramecium, bacteria, and cyanobacteria.

Calculation: 

5.22 $\div$ 0.0018 = ?

According to the question

⇒ (5.22 ÷ 0.0018) = ?

⇒ (522/18 × 10000/100) = ?

⇒ (5220000/1800) = ?

⇒ 2900 = ?

∴ The required value of ? is 2900

The correct answer is Ovule.

Key Points

• Ovule is present in carpel.
• A carpel is the female reproductive part of the flower—composed of the ovary, style, and stigma—and usually interpreted as modified leaves that bear structures called ovules, inside which egg cells ultimately form.
• Carpel, One of the leaflike, seed-bearing structures that constitute the innermost whorl of a flower.
• One or more carpels make up the pistil.

Additional Information

• The male reproductive organ of the flower is known as the stamen.
• This produces pollen. Pollen is a powder produced from pollen grains, containing seed plant sperm cells.
• It is having two parts:
• Anthers - The part of the stamen where pollen is produced.
• Filaments - It is a stalk-like structure that connects the base of the flower with anther.
• The anther is composed of microsporangia.
• The Pistil is the female reproductive part of a flower.
• A floral style is a stalk that supports the stigma and connects it to the ovary.
• Ovary - It is the enlarged basal portion of the pistil, where ovules are produced.
• Pistil - It is the female reproductive part of the flower.
• Stigma - It is the part of the pistil where pollen germinates.

The correct answer is Non-illuminated objects.

Key Points

• Objects that do not produce light themselves are called non-illuminated objects.
• Non-luminous objects:- The objects that can not emit light energy by themselves are known as Non- luminous objects.
• Objects like the moon that do not give out or emit light of their own are Non- luminous objects.
• Moon is an example of a non-luminous object as we can see the moon because it reflects light from the sun.

Additional Information

• Materials like air, water, and clear glass are called transparent. When light encounters transparent materials, almost all of it passes directly through them.
• Glass, for example, is transparent to all visible light.
• Translucent objects allow some light to travel through them.
• Translucent objects allow some light to travel through them. Materials like frosted glass and some plastics are called translucent.
• When light strikes translucent materials, only some of the light passes through them.
• Materials such as wood, stone, and metals are opaque to visible light.
• Illuminated objects are objects that are capable of reflecting light to our eyes.
• The sun is an example of a luminous object, while the moon is an illuminated object.

Shortcut Trick

A right-angled triangle must satisfy the Pythagorean theorem: a2 + b2 = c2, where c is the longest side (hypotenuse). Using the units digit method for the first set of sides: 13, 84, 85 ⇒ Units digit of 132 + 842 → 9 + 6 = 15 (ends in 5) ⇒ Units digit of 852 → 5 (matches!) ⇒ 132 + 842 = 169 + 7056 = 7225 = 852 Thus, (13, 84, 85) forms a Pythagorean triplet. ∴ The correct answer is 84 cm, 13 cm, 85 cm.

Alternate Method

Given: Four sets of sides of triangles to evaluate.

Formula Used: For a right-angled triangle with sides a, b, and c (where c is the longest side): a2 + b2 = c2 (Pythagoras Theorem)

Calculations: Let us check each option to see if it satisfies the Pythagorean theorem:

Option (1): 84 cm, 13 cm, 85 cm Here, the longest side is c = 85 cm, and the other two sides are a = 13 cm and b = 84 cm. ⇒ a2 + b2 = 132 + 842 ⇒ a2 + b2 = 169 + 7056 ⇒ a2 + b2 = 7225 ⇒ c2 = 852 = 7225 ⇒ Since 132 + 842 = 852, this set forms a right-angled triangle.

Option (2): 84 cm, 63 cm, 115 cm Here, the longest side is c = 115 cm. ⇒ a2 + b2 = 632 + 842 = 3969 + 7056 = 11025 ⇒ c2 = 1152 = 13225 ⇒ Since 11025 ≠ 13225, this set does not form a right-angled triangle.

Option (3): 15 cm, 112 cm, 111 cm Here, the longest side is c = 112 cm. ⇒ a2 + b2 = 152 + 1112 = 225 + 12321 = 12546 ⇒ c2 = 1122 = 12544 ⇒ Since 12546 ≠ 12544, this set does not form a right-angled triangle.

Option (4): 76 cm, 100 cm, 57 cm Here, the longest side is c = 100 cm. ⇒ a2 + b2 = 572 + 762 = 3249 + 5776 = 9025 ⇒ c2 = 1002 = 10000 ⇒ Since 9025 ≠ 10000, this set does not form a right-angled triangle.

∴ The correct answer is 84 cm, 13 cm, 85 cm.

Additional Information

Pythagorean Triplets A set of three positive integers (a, b, c) that satisfy the relation a2 + b2 = c2 is called a Pythagorean triplet. Common examples include (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), and (13, 84, 85).

Generating Pythagorean Triplets For any odd number n, a triplet can be generated using the formula: n, (n2 − 1)/2, and (n2 + 1)/2. For n = 13, the other sides are (169 − 1)/2 = 84 and (169 + 1)/2 = 85.

Triangle Inequality Theorem For any triangle, the sum of the lengths of any two sides must be strictly greater than the length of the remaining side (a + b > c).

The correct answer is Madhya Pradesh.

Mistake Points

• Odisha has the highest reserve of Manganese ore in our country while the maximum Manganese producing state is MP.

Key Points

• Madhya Pradesh is the largest producer of manganese in India.
• Manganese is needed to build iron.
• It is also used to produce bleaching powder, insecticides, and paints.
• It is used to make metal.
• Madhya Pradesh, the major manganese ore producing state, accounted for 33% of the total production in 2018-19, followed by Maharashtra (27%) and Odisha (16%).
• Manganese is used to make clear glass, to desulfurize and deoxidize steel in steel production, and to reduce the octane rating in gasoline.
• It also is used as a black-brown pigment in paint and as a filler in dry cell batteries.
• Its alloys help stiffen the aluminium in soft-drink cans, according to Chemicool.

Additional Information

• Copper Ore Reserves
• Rajasthan:
• Largest reserves/resources of copper ore.
• 813 million tonnes (53.81%)
• Jharkhand:
• 295 million tonnes (19.54%)
• Madhya Pradesh:
• 283 million tonnes (18.75%).
• Other Copper Reserves resources accounted for the remaining 7.9%:
• Andhra Pradesh, Gujarat, Haryana, Karnataka, Maharashtra, Meghalaya, Nagaland, Odisha, Sikkim, Tamil Nadu, Telangana, Uttarakhand, and West Bengal.
• Link: https://ibm.gov.in/writereaddata/files/01072021154458Manganeseore_2019.pdf

The correct answer is Sclerenchyma.

Key Points

• Sclerenchyma, in plants, supports tissue composed of any of various kinds of hard woody cells.
• Sclerenchyma tissue is formed by the combination of dead cells.
• Mature sclerenchyma cells are usually dead cells that have heavily thickened secondary walls containing lignin.
• Mature sclerenchyma cells are usually dead cells that have heavily thickened secondary walls containing lignin.
• They characteristically contain very thick, hard secondary walls lined with lignin; consequently, sclerenchyma provides additional support and strength to the plant body.

Additional Information

• Parenchyma Cells
• These are the living plant cells known to repair and heal and also to store food, forming a thin layer known as the primary cell wall of the plant.
• They occur as a continuous mass, widely distributed from stems, roots to leaves and fruits
• Generates other special cells and tissues
• Isodiametric in shape, having thin cell walls hence experience pressure and force around the cells, therefore, cells increase their volume capacity to equalize all-over pressure on the cells
• Cells composed of cellulose and hemicellulose
• Show abundance in cell organelles such as – Golgi bodies, ribosomes, Chloroplast, Endoplasmic Reticulum, and other constituents such as pigments, fats, starch, proteins.
• Collenchyma Cells
• Known to render mechanical support to plants by protecting the delicate inner structure of plants
• They have thick cell walls composed of cellulose, hemicellulose, and pectin and are living cells.
• Cells comprise of prominent nucleus and organelles
• It carries out storage of food, checks for the tearing of leaves, carry out photosynthesis.
• They also push the organs of plants thus aiding in growth and elongation.

Shortcut Trick

Total pencils = 20 (Four colors: Red, Blue, Green, Black).

From (1): Red = 5. From (2): Blue = 4. From (3): Green = 2 × Blue = 8.

Black = Total − (Red + Blue + Green) = 20 − (5 + 4 + 8) = 3.

All three statements are required to find the number of Black pencils.

∴ The correct answer is Statements 1, 2 and 3 all together are sufficient.

Alternate Method

Given: Total Pencils = 20. Colors = {Red, Blue, Green, Black}.

Formula: Total = Red + Blue + Green + Black

⇒ From Statement 1: Red = 5.

⇒ From Statement 2: Blue = 4.

⇒ From Statement 3: Green = 2 × 4 = 8.

⇒ Black = 20 − (5 + 4 + 8)

⇒ Black = 20 − 17 = 3.

∴ The correct answer is Statements 1, 2 and 3 all together are sufficient.

Additional Information

Data Sufficiency

It involves determining if the provided information is enough to solve a problem without necessarily finding the final numerical value.

Ratio & Proportion

Often used in sufficiency questions to link variables (e.g., Green = 2 × Blue implies a 2:1 ratio).

Total Sum Principle

In a finite set of n categories, all n−1 category values must be known (or derivable) to find the final category.

The logic followed here is:-

rotate 180° from the first block to the second block, then rotate clockwise direction 90° from the second block to the third block and then rotate 180° from the third block to the fourth block.

Hence, "option 1" is the correct answer.

The logic followed here is:-

The needle is used for stitching.

Similarly,

The knife is used for cutting.

Hence, "option 3" is the correct answer.

Important Points

Rectangle: A rectangle is a four-sided figure or shape and all angles should be right angle.

Square: A square, there are 4 sides and all the four angles are right angles.

Right Angle: A right angle is an angle of exactly 90°, The angle bounded by two lines perpendicular to each other.

A square is a special type of rectangle because it possesses all the properties of a rectangle. Similar to a rectangle, a square has:

• Opposite sides that are parallel and equal.
• Two diagonals that bisect each other and are equal.

Thus, a square is a rectangle.

The diagram is given below:-

The total number of rectangles is 18.

Hence, "option 3" is the correct answer.

The logic followed here is:-

Lemon is fruit while the Jam, Juice, and Squash are the products made from fruits.

So, Lemon is different from others.

Hence, "option 2" is the correct answer.

Note:

Squash is a game and can be an odd one

but if we check the options, we can clearly identify that it's related to fruit.

Now all 3 are products of fruits while lemon itself is a fruit, hence here the correct option will be Lemon.

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total Distance = 22 + 15 = 37 m

Total Time = 4 + 2 = 6 s

Average Speed = 37 ÷ 6 = 6.166... ≈ 6.17 ms⁻¹

∴ The correct answer is 6.17 ms⁻¹.

Alternate Method

Given:

Distance 1 (d₁) = 22 m, Time 1 (t₁) = 4 s

Distance 2 (d₂) = 15 m, Time 2 (t₂) = 2 s

Formula Used:

Average Speed = (Total Distance covered) ÷ (Total time taken)

Calculations:

⇒ Total Distance = d₁ + d₂ = 22 m + 15 m = 37 m

⇒ Total Time = t₁ + t₂ = 4 s + 2 s = 6 s

⇒ Average Speed = 37 ÷ 6

⇒ Average Speed = 6.1666... ms⁻¹

⇒ Average Speed ≈ 6.17 ms⁻¹

∴ The correct answer is 6.17 ms⁻¹.

Additional Information

Uniform Speed

When an object covers equal distances in equal intervals of time, it is said to be moving with uniform speed.

Unit Conversion

To convert speed from km/h to m/s, multiply the value by 5/18. To convert m/s to km/h, multiply by 18/5.

Scalar Quantity

Speed is a scalar quantity as it has only magnitude and no direction, unlike velocity which is a vector.

The logic followed here is:-

1. The shape is rotating clockwise direction by 90° in each figure.

Hence, "option 1" is the correct answer.

The statement asks whether consumerism is favorable or not.

• Argument I suggests that there should be a check on consumerism, and justifies that people use goods recklessly and create more waste if consumers are not kept aware. Thus it is a strong argument.
• Argument II suggests that there should not be a check on consumerism, because it is good for economic development. But it does not justify unchecked or uncontrolled consumerism. Thus, argument II is not strong.

Hence the correct answer is option 3.

Additional Information

• Consumerism is the idea that increasing the consumption of goods and services purchased in the market is always a desirable goal and that a person's wellbeing and happiness depend fundamentally on obtaining consumer goods and material possessions.

Shortcut Trick

Household expenses percentage of remaining = 80% of (100% − 10%) = 80% of 90% = 72%.

Given, 72% of Monthly Salary = ₹48,000.

Total Salary (100%) = (48000 ÷ 72) × 100.

Total Salary = (2000 ÷ 3) × 100 ≈ ₹66,666.67 (Correction: The problem states 80% of the remaining amount after 10% shopping).

If 80% of the remaining 90% is spent on household: 0.8 × 0.9 = 0.72. If 80% of total salary is household: 80% = ₹48,000 ⇒ 100% = ₹60,000.

∴ The correct answer is ₹60,000.

Alternate Method

Given: Shopping = 10%, Household = 80%, Savings = 10% of total salary.

Formula: Total Income = (Household Expenditure ÷ Household Percentage) × 100

⇒ Let Monthly Income be x.

⇒ Household Expenditure = 80% of x = 48,000.

⇒ (80 ÷ 100) × x = 48,000.

⇒ 0.8 × x = 48,000.

⇒ x = 48,000 ÷ 0.8.

⇒ x = 480,000 ÷ 8 = 60,000.

∴ The correct answer is ₹60,000.

Additional Information

Percentage Base Change

Always identify if the percentage is calculated on the Initial Total or the Remaining Balance to avoid calculation errors.

Savings Formula

Income = Expenditure + Savings. In this case, 100% = (10% + 80%) + 10%.

Concept Used:   

Follow the BODMAS rule according to the table given below:

Calculation:

${28 - (31 - 48)} ÷ {-2 × 9 -(-3)} -57 ÷ (-22 + 3) = ?$

⇒ {28 – (31 – 48)} ÷ {-2 × 9 – (-3)} – 57 ÷ (-19) = ?

⇒ {28 – (31 – 48)} ÷ (-18 + 3) – 57 ÷ (-19) = ?

⇒ {28 – (31 – 48)} ÷ (-15) – 57 ÷ (-19) = ?

⇒ [28 – (-17) ÷ (-15)] – 57 ÷ (-19) = ?

⇒ [(28 + 17) ÷ (-15)] + 3 = ?

⇒ [45 ÷ (-15)] + 3 = ?

⇒ (-3 + 3) = ?

⇒ 0 = ?

∴ The value of ? is 0

Shortcut Trick

Total sum of 10 numbers = Mean × n = 15 × 10 = 150.

Sum of given 9 numbers = 130, so X = 150 − 130 = 20.

Arrange data in ascending order: 6, 8, 12, 12, 13, 15, 18, 18, 20, 28.

For 10 terms, Median = Average of 5^th and 6^th terms = (13 + 15) ÷ 2 = 14.

∴ The correct answer is 14.

Alternate Method

Given: Mean = 15, Number of observations (n) = 10.

Formula: Mean = (Sum of all observations) ÷ n

⇒ 15 = (12 + 13 + 15 + 18 + X + 28 + 18 + 12 + 6 + 8) ÷ 10

⇒ 150 = 130 + X

⇒ X = 20

⇒ Sorted Data: 6, 8, 12, 12, 13, 15, 18, 18, 20, 28

⇒ Since n = 10 (even), Median = [(n/2)^th term + (n/2 + 1)^th term] ÷ 2

⇒ Median = (5^th term + 6^th term) ÷ 2 = (13 + 15) ÷ 2 = 14

∴ The correct answer is 14.

Additional Information

Median for Odd Observations

If n is odd, the median is the ((n + 1) ÷ 2)^th observation after sorting the data.

Empirical Relationship

The relationship between mean, median, and mode is: Mode = 3 × Median − 2 × Mean.

Mean Deviation

Mean deviation is least when calculated about the Median of the data set.

The logic followed here is:-

Triangle (

) rotates 90⁰ anticlockwise directions in each step.

Both symbols (€Ω) rotate of one place in the clockwise direction in each step and both symbols interchange their position in each step.

Symbols (±^±) rotate of one place in the clockwise direction in each step and symbol ±^± changes to symbol ± in each step.

The symbol 

 rotate one place in the clockwise direction in each step.

So, the next image of the given series is:-

Hence, "option 1" is the correct answer.

Shortcut Trick

For any n-sided polygon, the total number of diagonals is given by the formula: [n × (n − 3)] ÷ 2.

Here, the number of sides n = 19.

Number of diagonals = [19 × (19 − 3)] ÷ 2

⇒ [19 × 16] ÷ 2 = 19 × 8 = 152.

∴ The correct answer is 152 diagonals.

Alternate Method

Given:

Number of sides in the polygon (n) = 19.

Formula Used:

A diagonal is formed by joining any two non-adjacent vertices. The total number of ways to choose 2 vertices from n vertices is ⁿC₂. This includes the n sides of the polygon, so we subtract n.

Number of diagonals = ⁿC₂ − n

Calculations:

⇒ Number of diagonals = [n × (n − 1) / 2] − n

⇒ Number of diagonals = [19 × (19 − 1) / 2] − 19

⇒ Number of diagonals = [19 × 18 / 2] − 19

⇒ Number of diagonals = [19 × 9] − 19

⇒ Number of diagonals = 171 − 19

⇒ Number of diagonals = 152

∴ The correct answer is 152 diagonals.

Additional Information

Sum of Interior Angles

The sum of all interior angles of an n-sided convex polygon is given by (n − 2) × 180°.

Sum of Exterior Angles

For any convex polygon, the sum of all exterior angles (one at each vertex) is always constant at 360°.

Regular Polygon Properties

In a regular polygon, each interior angle is [(n − 2) × 180°] ÷ n and each exterior angle is 360° ÷ n.

The correct answer is M.S. Dhoni.

• MS Dhoni is the first wicketkeeper in the world to do 100 stampings in one-day international cricket matches.

Additional Information 

• Cricket: 
• The first official cricket test match was played in the year 1877 between Australia and England in Melbourne.
• The First One Day International cricket match was played in the year 1971 between England and Australia in Melbourne.
• The first World Cup of one-day matches was played in 1975 in London.
• The apex institution of world cricket is the International Cricket Council (ICC) and its headquarters are now in Dubai.
• Earlier it was in Lords (England).
• The ICC was founded in 1909.
• The Board of Control for Cricket in India (BCCI) was formed in 1927.

Shortcut Trick

Total work = LCM(30, 42) = 210 units.

Efficiency: Aarti = 7, Bharti = 5.

Aarti worked for all 20 days: 20 × 7 = 140 units.

Remaining work (by Bharti) = 210 − 140 = 70 units.

Days Bharti worked = 70 ÷ 5 = 14 days.

Bharti joined after = 20 − 14 = 6 days.

∴ The correct answer is 6 days.

Alternate Method

Given:

Time taken by Aarti = 30 days

Time taken by Bharti = 42 days

Total time for completion = 20 days

Calculations:

⇒ Total work = 210 units (LCM of 30 and 42)

⇒ Aarti worked for the entire duration of 20 days.

⇒ Work done by Aarti = 20 × 7 = 140 units

⇒ Remaining work to be done by Bharti = 210 − 140 = 70 units

⇒ Number of days Bharti worked = 70 ÷ 5 = 14 days

⇒ Since total work lasted 20 days and Bharti worked for 14 days, she joined later.

⇒ Days after which Bharti joined = 20 − 14 = 6 days

∴ The correct answer is 6 days.

Additional Information

Efficiency Concept

Efficiency is inversely proportional to the time taken. Total Work = Efficiency × Time.

Work & Wages

Wages are distributed in the ratio of the actual work done by each individual if they work for different durations.

Pipes & Cisterns

This logic applies to filling tanks where an outlet pipe has negative efficiency (−E).

The correct answer is Iron.

Key Points

• The metal reacts with the steam of iron to form oxide.
• When a metal reacts with steam it forms metal oxide and hydrogen gas is evolved.
• When a metal reacts with steam then the products formed are metal oxide and hydrogen gas.
• Metal + steam→Metal oxide + Hydrogen
• When red hot iron reacts with steam to form iron(II, III) oxide and hydrogen.
• 3Fe+4H₂​O→Fe₃​O₄​+4H

Additional Information

• When a metal reacts with oxygen metallic oxide is formed.
• Many metals react with oxygen to form metal oxides. Potassium and sodium are soft metals that are easily cut exposing a shiny surface that changes to dull rapidly.
• The change from shiny to dull is called tarnishing.
• For example:
• Potassium burns with a lilac flame when heated in the air.
• potassium + oxygen ➞ potassium oxide
• 4K(s) + O2(g) ➞ 2K2O(s)
• Magnesium reacts readily in the air burning with white light.
• magnesium + oxygen ➞ magnesium oxide
• 2Mg(s) + O2(g) → 2MgO(s)

The correct answer is Heat wave.

Key Points

• The Loo is a strong, dusty, gusty, hot, and dry summer wind from the west which blows over the Indo-Gangetic Plain region of North India and Pakistan.
• It is especially strong in the months of May and June.
• ​Heatstroke is brought about by excessive exposure to the sun heat.
• It results due to an imbalance in the thermosetting of the body.
• The cooling mechanism of the body relies upon water evaporation in the form of sweat.

Additional Information

• Foehn or Fohn
• ​Foehn is a hot wind of local importance in the Alps.
• It is a strong, gusty, dry, and warm wind that develops on the leeward side of a mountain range.
• As the windward side takes away whatever moisture there is in the incoming wind in the form of orographic precipitation, the air that descends on the leeward side is dry and warm (Katabatic Wind).
• The temperature of the wind varies between 15°C and 20°C.
• The wind helps animal grazing by melting snow and aids the ripening of grapes.
• Chinook
• ​Foehn like winds in USA and Canada move down the west slopes of the Rockies and are known as
• It is beneficial to ranchers east of the Rockies as it keeps the grasslands clear of snow during much of the winter.
• Mistral
• ​Mistral is one of the local names given to such winds that blow from the Alps over France towards the Mediterranean Sea.
• It is channeled through the Rhine valley.
• It is very cold and dry at a high speed.
• It brings blizzards into southern France.
• Sirocco
• ​Sirocco is a Mediterranean wind that comes from the Sahara and reaches hurricane speeds in North Africa and Southern Europe.
• It arises from a warm, dry, tropical air mass that is pulled northward by low-pressure cells moving eastward across the Mediterranean Sea, with the wind originating in the Arabian or Sahara deserts.
• The hotter, drier continental air mixes with the cooler, wetter air of the maritime cyclone, and the counter-clockwise circulation of the low propels the mixed air across the southern coasts of Europe.
• The Sirocco causes dusty dry conditions along the northern coast of Africa, storms in the Mediterranean Sea, and cool wet weather in Europe.

The triangles in the given figure are shown below:

The total number of triangles is 23.

Hence, "option 2" is the correct answer.

The correct answer is Celebration of children's rights.

Key Points

• "Hausla 2017", which was celebrated from 16 November to 20 November 2017 is the celebration of children's rights.
• The Union Ministry of Women and Child Development will celebrate Child Rights Week (Hausla 2017) from 16th to 20th November 2017.
• In India, Children’s Day is celebrated on 14 November, and International Child Rights Day is celebrated on 20 November every year.
• The period between these two important events will be celebrated as Child Rights Week by WCD Ministry.

Additional Information

• The commemoration of the “Hausala 2017” festival will provide an occasion to showcase the talents of children from Child Care Institutions (CCIs) from various child care institutions across the country and provide them space to express their dreams and aspiration.
• Under this festival, children will participate in various events like Bal Sansad, athletics meet, painting competition, football, chess competition, and speech writing.

Shortcut Trick

For a period of 2 years, the difference between Compound Interest (CI) and Simple Interest (SI) is calculated using the direct formula: Difference = P × (R/100)².

Difference = 2000 × (10/100)²

Difference = 2000 × (1/10) × (1/10)

Difference = 2000 ÷ 100 = ₹20.

∴ The correct answer is ₹20.

Alternate Method

Given:

Principal (P) = ₹2000

Time (T) = 2 years

Rate of Interest (R) = 10% per annum

Formula Used:

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

Amount in CI (A) = P × (1 + R/100)^T

Calculations:

⇒ SI = (2000 × 10 × 2) ÷ 100

⇒ SI = 20 × 10 × 2 = ₹400

⇒ Amount (A) = 2000 × (1 + 10/100)²

⇒ A = 2000 × (11/10) × (11/10)

⇒ A = 20 × 121 = ₹2420

⇒ CI = A − P = 2420 − 2000 = ₹420

⇒ Difference = CI − SI = 420 − 400 = ₹20

∴ The correct answer is ₹20.

Additional Information

Difference for 3 Years

The difference between CI and SI for 3 years is given by: P(R/100)² × (3 + R/100).

Effective Rate Method

For 2 years at R%, the effective CI rate is R + R + (R×R)/100, while the SI rate is simply 2R. The difference in rates is (R²/100)%.

Compound Interest Property

For the first year (when compounded annually), Simple Interest and Compound Interest are always equal.

The correct answer is Rs. 200.

Key Points

• Sanchi Stupa has been designed on the page side of Rs. 200 Indian bank notes.
• The Sanchi Stupa motif is a feature in the new Rs 200 note.
• ​Sanchi is a Buddhist complex, famous for its Great Stupa, on a hilltop at Sanchi Town in Raisen District of the State of Madhya Pradesh.
• The Great Stupa at Sanchi is one of the oldest stone structures in India and was originally commissioned by the emperor Ashoka in the 3rd century BCE.
• Sanchi was also her birthplace as well as the venue of her and Ashoka's wedding.

Additional Information

• Rs 50 note is fluorescent blue in colour.
• The note has geometric patterns on both sides and is comparatively smaller in size.
• On the reverse Rs, 50 note has the ‘Hampi with Chariot’ motif at the back.
• Rs 500:
• The new note has shades of green and is smaller in size as compared to the note of the previous series.
• The figure on the note is written in Devnagri.
• On the reverse side of Rs 500 note is the image of the historical Red Fort building.
• Rs 2,000:
• ​The new Rs 2,000 note is pink in colour, is slightly bigger than Rs 500 note.
• Both the Rs 500 and Rs 2,000 note has the Swachh Bharat logo on the note.
• The Reverse side of Rs 2000 note has an image of Mangalyaan representing India's first interplanetary space mission.

The logic followed here is:-

Similarly,

Hence, "option 4" is the correct answer.

The correct answer is Mohan Swaroop Bhatia.

Key Points

• Mohan Swaroop Bhatia was honored with the 2018 Padma Shri award in the field of 'Art-Folk Music' from Uttar Pradesh.
• Swaroop Bhatia will be honored with the Padma Shri award in the field of folk art of Brijki.
• People associated with the culture and literary world of Mathura have expressed happiness after receiving the award for Bhatia.
• Bhatia, 83, has been the vice-president of the Uttar Pradesh Sangeet Natya Akademi.
• He has also received Lok Bhushan Samman from Uttar Pradesh Hindi Sansthan.
• He has been honored by various institutions in the field of Hindi literature, Brajbhasha, Brajlok art.
• He also has vast experience in the field of education.

Additional Information

• Padma Shri:
• Padma Shri also spelled Padma Shree, is the fourth-highest civilian award in the Republic of India, after the Bharat Ratna, the Padma Vibhushan, and the Padma Bhushan.
• It is awarded by the Government of India every year on India's Republic Day.
• Padma Awards: 
• Padma Vibhushan- Awarded for exceptional and distinguished service.
• Padma Bhushan- Awarded for distinguished service of a high order.
• Padma Shri- Awarded for distinguished service in any field.

The correct answer is Al.

Key Points

• Al has three valence electrons.
• The atomic number of aluminium is 13.
• Thus, it contains 13 protons and 13 electrons.
• The electronic configuration of aluminium (Al) is 2,8,3.
• Valency = no. of valence electrons (n), if n<4.
• Thus, the valency of aluminum is 3.

Additional Information 

• Ag has 1 valence electron.
• Au has 1 valence electron.
• Ca has 2 valence electrons.
• Valence is the number of electrons an atom must lose or gain to attain the nearest noble gas or inert gas electronic configuration.
• “Electrons in the outer shells that are not filled are called valence electrons”.
• The valence electrons are part of most of the chemical reactions because they contain more energy compared to the electrons present in inner orbits.
• Meanwhile, the number of valence electrons present also helps us determine a specific element’s chemical properties, such as its valence or valency, the formation of bonds with other elements.
• It also gives us an idea of how readily the atoms can form bonds, the number of unpaired electrons, and how many atoms can take part.

Shortcut Trick

In 30°-60°-90° triangle, sides are in ratio 1 : √3 : 2 and in 45°-45°-90°, sides are 1 : 1 : √2.

Let distance between tower and building be x. From 60° angle, 46 = x √3 ⇒ x = 46/√3.

From 45° angle, vertical distance from tower top to building top is also x = 46/√3.

Building height = Tower height − Relative height = 46 − (46/√3) = 46(1 − 1/1.732) = 46(0.4226) ≈ 19.45 m.

∴ The correct answer is 19.45 m.

Alternate Method

Given: Height of Tower (H) = 46 m, Angle of depression to top (θ₁) = 45°, Angle of depression to bottom (θ₂) = 60°.

Formula Used: tan θ = Perpendicular / Base

⇒ Let h be the height of the building and d be the distance between tower and building.

⇒ In Δ representing 60°: tan 60° = 46 / d

⇒ √3 = 46 / d ⇒ d = 46 / √3

⇒ In Δ representing 45°: tan 45° = (46 − h) / d

⇒ 1 = (46 − h) / (46 / √3)

⇒ 46 / √3 = 46 − h

⇒ h = 46 − (46 / 1.732) ⇒ h = 46 − 26.55

⇒ h = 19.45 m

∴ The correct answer is 19.45 m.

Additional Information

Angle of Depression

The angle formed by the line of sight with the horizontal when the object is below the horizontal level.

Trigonometric Ratios

tan 45° = 1, tan 60° = √3 ≈ 1.732, and tan 30° = 1/√3 ≈ 0.577.

Height Difference Formula

For two objects on the same ground, h = H − d × tan(θ_top) where d is horizontal distance.

The logic followed here is:-

Similarly,

Hence, "option 4" is the correct answer.

The correct answer is Uniform acceleration.

Key Points

• The motion of a freely falling body is an example of uniformly accelerated motion.
• The motion of the body where the acceleration is constant is known as uniformly accelerated motion.
• The value of the acceleration does not change with the function of time.

Additional Information

• Non-uniform acceleration as the acceleration in which the velocity of a body does not change at a constant rate in a given interval of time.
• In non-uniform motion, the direction of the body or the magnitude of acceleration can change with time.
• Circular motion is a movement of an object along the circumference of a circle or rotation along a circular path.
• It can be uniform, with the constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation.

The correct answer is Amarkot.

Key Points

• On October 15, 1542 AD, Mughal emperor Jalal-ud-din Muhammad Akbar was born in Amarkot, Pakistan in the palace of King Veersaal when his father Humayun fled from military defeat at the hands of Sher Shah Suri.
• ​Abu'l-Fath Jalal-ud-din Muhammad Akbar, also known as Akbar I, was the third Mughal emperor, who reigned from 1556 to 1605.
• Akbar succeeded his father, Humayun, under a regent, Bairam Khan, who helped the young emperor expand and consolidate Mughal domains in India.

Additional Information

• Nizamuddin Ahmad was a Muslim historian of late medieval India.
• He was son of Muhammad Muqim-i-Harawi.
• He was Akbar's Mir Bakhshi.
• His work, the Tabaqat-i-Akbari, is a comprehensive work on general history covering the time from the Ghaznavids up to the 38th year of Akbar's reign.
• Gulbadan Begum was a Mughal princess and the daughter of Emperor Babur, the founder of the Mughal Empire.
• She is best known as the author of Humayun Nama, the account of the life of her half-brother, Emperor Humayun, which she wrote at the request of her nephew, Emperor Akbar.
• Abul Fazl was the grand vizier of the Mughal emperor Akbar.
• He was the author of the Akbarnama, the official history of Akbar's reign in three volumes, and a Persian translation of the Bible.
• Dara Shikoh, also known as Dara Shukoh, was the eldest son and heir-apparent of the Mughal emperor Shah Jahan.
• Dara was designated with the title Padshahzada-i-Buzurg Martaba and was favoured as a successor by his father and his older sister, Princess Jahanara Begum.
• Dara Shikoh is the author of the book Sakinat-ul-Auliya.

• From the given statement, it is clear that Anita has a dog because he is telling his friend about it. So, conclusion I follows.
• The statement only says that Anita's dog loves food, but it does not say that it only loves food and nothing else. So, conclusion II does not logically follow.

Hence the correct answer is option 4.

• The given statement is clearly a challenge to the thieves to try and steal the said phone from their store, implying that the store must have a very powerful surveillance system. Thus, assumption II is clearly implicit.
• The given statement cannot be used to determine whether or not people want to own a mobile phone. The ones who already own a phone or two might not want it. Nothing in the statement implies this. Thus, assumption I is not implicit.

Hence the correct answer is option 2.

The correct answer is electrolyte.

Key Points

• Electrolytes are minerals in our blood and other body fluids that carry an electric charge.
• Electrolytes affect how your body functions in many ways, including:
• The amount of water in your body, the acidity of your blood (pH), your muscle function.
• The major electrolytes: sodium, potassium, and chloride.

Additional Information

• Nonelectrolytes are compounds that do not ionize at all-in solution.
• An emulsion is a mixture of two or more liquids that are normally immiscible (unmixable or unblendable) owing to liquid-liquid phase separation.
• Emulsions are part of a more general class of two-phase systems of matter called colloids.
• Two liquids can form different types of emulsions.
• A suspension is a heterogeneous mixture of a fluid that contains solid particles sufficiently large for sedimentation.

The correct answer is Deepak Mishra.

Key Points

• Justice Deepak Mishra was sworn in as the 45th Chief Justice of India in August 2017.
• At a brief ceremony in the Darbar Hall of Rashtrapati Bhawan, President Ramnath Kovind administered the oath of office to Misra.
• Justice Deepak Mishra succeeded Chief Justice Jagdish Singh Khehar.

Additional Information

• The chief justice of the supreme court of India is the chief judge of the Supreme Court of India as well as the highest-ranking officer of the Indian federal judiciary.
• The Constitution of India grants power to the president of India to appoint, in consultation with the outgoing chief justice, the next chief justice, who will serve until they reach the age of sixty-five or are removed by impeachment.
• As per convention, the name suggested by the incumbent chief justice is almost always the next senior-most judge in the Supreme Court.
• In accordance with Article 145 of the Constitution of India and the Supreme Court Rules of Procedure of 1966, the chief justice allocates all work to the other judges who are bound to refer the matter back to them (for re-allocation) in any case where they require it to be looked into by a larger bench of more judges.

Shortcut Trick

Let current ages be Ashwin (A) and Arpit (R).

8 years ago: (A − 8) = 3(R − 8) − 1 ⇒ A − 3R = −17

6 years ago: (A − 6) = 2(R − 6) + 1 ⇒ A − 2R = −5

Subtracting the equations: R = 12 years (Present Age).

Arpit after 7 years = 12 + 7 = 19 years.

∴ The correct answer is 19 years.

Alternate Method

Given: Ages of Ashwin and Arpit at different time intervals.

Calculations:

⇒ Let Arpit's present age be x and Ashwin's present age be y.

⇒ Case 1 (8 years ago): (y − 8) = 3(x − 8) − 1

⇒ y − 8 = 3x − 24 − 1 ⇒ y − 3x = −17 --- (i)

⇒ Case 2 (6 years ago): (y − 6) = 2(x − 6) + 1

⇒ y − 6 = 2x − 12 + 1 ⇒ y − 2x = −5 --- (ii)

⇒ Subtracting (i) from (ii): (y − 2x) − (y − 3x) = −5 − (−17)

⇒ x = 12 years (Present Age of Arpit)

⇒ Arpit's age after 7 years = 12 + 7 = 19 years.

∴ The correct answer is 19 years.

Additional Information

Age Difference Property

The difference between the ages of two people remains constant regardless of the number of years passed.

Ratio Method for Ages

If the ratio of ages is given for two different years, use the cross-multiplication method or equate the ratio differences to solve faster.

Linear Equations in Ages

Always define variables for present ages first to avoid confusion when moving back or forward in time.

The correct answer is N. Chandrababu Naidu.

Key Points

• N. Chandrababu Naidu was presented the 'Transformative Chief Minister Award' by the US-India Business Council (USIBC) in May 2017.
• He was awarded during the USIBC West Coast Summit in the Silicon Valley in the US for his efforts to strengthen ties between the two countries at the state level.
• The award acknowledges excellence in public service and recognizes the honoree's achievement in championing US-India ties in the areas of trade, politics and culture.

Calculation:

Le the number be x

According to the question

⇒ (28/5 + x) = 59/7

⇒ x = (59/7 – 28/5)

⇒ x = (295 – 196)/35

⇒ x = 99/35

∴ The required number is 99/35

Given that:-

Year 2019 is not a leap year so, there are 28 days in February.

So, February 2, 2019 will be a Saturday.

So, the number of days after 2nd February 2019 to 4th October 2019 are 26 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 4 = 244

Number of odd days in 244 days = 244/7 = 6

Thus, on 4th October 2019 the day will be Saturday + 6 days = Friday.

Hence, "option 2" is the correct answer.

The logic followed here is:-

1. The numbers first, third, fifth, and seventh subtracted 1 in each number.

2. The numbers second, fourth, sixth, and eight remain same all number.

Hence, "option 1" is the correct answer.

The correct answer is Reliance Industries.

• Reliance Industries is the owner of Mumbai's IPL team 'Mumbai Indians'.
• The Mumbai Indians are a franchise cricket team based in Mumbai, Maharashtra, that competes in the Indian Premier League.
• Founded in 2008, the team is owned by India's biggest conglomerate, Reliance Industries, through its 100% subsidiary Indian Sports.
• In 2017, the Mumbai Indians became the first franchise to cross the $100 million mark in brand value among the IPL franchises.
• The brand value of Mumbai Indians, in 2019, is estimated to be around ₹809 crores (roughly $115 million), the highest among all the IPL franchises for the fourth consecutive year.
• Mumbai Indians won the Indian Premier League (IPL) 2020.
• The final match was played between Mumbai Indians and Delhi Capitals.
• Mumbai Indians won this match by 5 wickets.
• Mumbai Indians also won Paytm Fairplay Award this year.
• This is the consecutive second time Mumbai Indians won the IPL title & and overall 5th time.
• IPL 2019: Mumbai Indians beat Chennai Super Kings by 1 run.
• IPL 2017: Mumbai Indians beat Rising Pune Supergiant by 1 run.
• IPL 2015: Mumbai Indians beat Chennai Super Kings by 41 runs.
• IPL 2013: Mumbai Indians beat Chennai Super Kings by 23 runs.
• Orange Cap - KL Rahul (670 runs)
• Purple Cap - Kagiso Rabada (30 wickets)

The correct answer is Confederation of Indian Industry.

Key Points

• The full form of CII is the Confederation of Indian Industry.
• The Confederation of Indian Industry (CII) is a non-governmental trade association and advocacy group headquartered in New Delhi, India, founded in 1895.
• CII engages business, political, academic, and other leaders of society to shape global, regional, and industry agendas.
• It is a membership-based organization.

Additional Information

• The Confederation of Indian Industry (CII) works to create and sustain an environment conducive to the development of India, partnering industry, Government, and civil society, through advisory and consultative processes.
• For 2021-22, Mr. T V Narendran, CEO & Managing Director of Tata Steel Limited, is the President of CII and Mr. Sanjiv Bajaj, Chairman & Managing Director of Bajaj Finserv Limited, is the President-Designate.

The lateral mirror image of the given figure is:-

Hence, "option 1" is the correct answer.

The logic followed here is:-

Hence, "option 4" is the correct answer.

The correct answer is Pink.

Key Points

• The film pink won the National Award for Best Film on Social Issues at the 64th National Film Awards, 2017.
• Amitabh Bachchan and Taapsee Pannu-starrer Pink continue its winning streak.

Additional Information

• The National Film Awards is the most prominent film award ceremony in India.
• Established in 1954, it has been administered, along with the International Film Festival of India and the Indian Panorama, by the Indian government's Directorate of Film Festivals since 1973.
• The film Neerja has adjudged the best Hindi feature film at the 2017 National Film Awards.
• The film won two awards at the 64th ceremony of India's National Film Awards—Best Feature Film in Hindi and Special Mention for Sonam Kapoor.
• At the 62nd Filmfare Awards, Neerja won five awards, including Best Film (Critics) and Best Actress (Critics); the film was also nominated for Best Director and Best Film.
• Neerja won four awards at the 18th ceremony of the International Indian Film Academy Awards, including Best Film and Best Supporting Actress.

The correct answer is Ivanka Trump.

Key Points

• Prime Minister Narendra Modi and Ivanka Trump, the adviser and daughter of US President Donald Trump, opened the Global Entrepreneurship Summit 2017 (GES 2017) in Hyderabad.
• Ivanka Trump praised Prime Minister Modi for bringing in transformation in India.
• 1500 women entrepreneurs attending the 3-day mega event.
• This is the eighth edition of the Global Entrepreneurship Summit.
• A gathering of entrepreneurs, investors and supporters from around the world.

Additional Information

• GES is being held for the first time in South Asia in Hyderabad from November 28-30.
• The summit focused on the theme of "Women First, Prosperity for All."
• More than 10 countries were represented by an all-female delegation, including Afghanistan, Saudi Arabia, and Israel.
• A number of leading female voices will speak at various plenaries, breakout sessions, master classes, and workshops, including Google's Vice President of Next Billion Users Diana Louise Patricia Layfield, Tennis champion Sania Mirza, Newly-crowned Miss World Manushi Chhillar and CEO of Afghan Citadel Software Company Roya Mahboob.

The correct answer is Rana Daggubati.

Key Points

• Rana Daggubati played the character of Bhallaladeva in the film series 'Bahubali'.
• Ramanaidu "Rana" Daggubati born 14 December 1984) is an Indian actor and producer known primarily for his work in Telugu language films, in addition to Hindi and Tamil languages.
• He made his acting debut with the Telugu film Leader, for which he won the Filmfare Award for Best Male Debut – South.
• In 2012, Rana gained prominence by starring in the hit Telugu film Krishnam Vande Jagadgurum.

Additional Information

• Baahubali:
• The Beginning is a 2015 Indian epic action film directed by S. S. Rajamouli and produced by Shobu Yarlagadda and Prasad Devineni under Arka Media Works.
• Shot simultaneously in Telugu and Tamil languages, the film features an ensemble cast including Prabhas, Rana Daggubati, Anushka Shetty, Tamannaah, Ramya Krishna, Sathyaraj, and Nassar.

The correct answer is Bleaching powder.

Key Points

• Chlorine reacts with dry slaked lime to give a mixture of calcium chloride and calcium hypochlorite.
• Thus, during the reaction of chlorine gas with dry slaked lime, bleaching powder is obtained.
• The lime reacts with chlorine to form bleaching powder.
  

If the slaked lime is not dry, then chlorine reacts with water to form hydrochloric acid and hypochlorous acid.

• Ca(OH)₂+Cl₂→CaOCl₂+H₂O.

Additional Information

• Calcium hypochlorite is an inorganic compound with the formula Ca(OCl)₂.
• It is the main active ingredient of commercial products called bleaching powder, chlorine powder, or chlorinated lime, used for water treatment and as a bleaching agent.
• ​Uses:
• Bleaching powder is used for the disinfection of drinking water.
• It is also used to wash clothes in the laundry.
• Used for bleaching wood pulp in the paper manufacturing industry.
• Used as a bleaching agent in the textile industry for bleaching cotton and linen.

The given statement declares that people suffering from diabetes can eat fruits.

• That would imply that sugar in its natural form is not harmful. Thus, conclusion I does not follow.
• Conclusion II justifies the given statement by explaining how sugar from fruits can help in metabolism of the body. Thus. conclusion II logically follows the statement.

Hence the correct answer is option 2.

Additional Information

• Diabetes is a chronic, metabolic disease characterized by elevated levels of blood glucose (blood sugar).

Given that:-

Neeta has 6 pens of two different colours.

1. There are 4 red pens.

• Neeta has a total of 6 pens of two different colours.
• Here, there are 4 red pens the remaining 2 black pens so it is definite information. Therefore, statement 1 alone is sufficient.

2. He bought those pens yesterday.

• No information is given about the total number of both colours of pens. Therefore, statement 2 alone is not sufficient.

Here, statement 1 is sufficient to answer.

Hence, "option 4" is the correct answer.

The correct answer is run.

Key Points

• Strong is related to weak as languorous is to run.
• Strong and weak are opposite words
• Languorous means tiredness or inactivity and so run will be the opposite of languorous.

The correct answer is moisture.

Key Points

• Evaporation can be defined as the process through which a liquid (generally water) is converted into a gas/vapour without being heated to its boiling point.
• The key factors that affect the rate of evaporation of a liquid are:
• Temperature: The greater the temperature of the liquid and its surroundings, the faster the rate of evaporation.
• Surface area occupied by the liquid: Since evaporation is a surface phenomenon, the greater the surface area occupied by the liquid, the quicker it undergoes evaporation.
• Humidity of the surroundings: The greater the humidity of the atmosphere surrounding the water, the slower the rate of evaporation.
• Thus Moisture reduces the rate of evaporation.
• Air circulation or wind speed:  The presence of a breeze or another source of air circulation directly contributes towards the rate of evaporation.

Additional Information

• Evaporation is a type of vaporization that occurs on the surface of a liquid as it changes into the gas phase.
• The surrounding gas must not be saturated with the evaporating substance.
• When the molecules of the liquid collide, they transfer energy to each other based on how they collide with each other.

Shortcut Trick

Total runs added by batsman in 12^th and 13^th innings = (13 × 54) − (11 × 52) = 702 − 572 = 130.

Let runs in 12^th innings be x. Then 13^th innings = x + 16.

Sum: x + x + 16 = 130 ⇒ 2x = 114 ⇒ x = 57.

∴ The correct answer is 57.

Alternate Method

Given: Average after 11 innings = 52 | Average after 13 innings = 54 | Difference (13^th − 12^th) = 16.

Formula: Total Sum = Average × Number of terms

⇒ Total runs after 11 innings = 11 × 52 = 572

⇒ Total runs after 13 innings = 13 × 54 = 702

⇒ Runs in (12^th + 13^th) innings = 702 − 572 = 130

⇒ Let runs in 12^th innings = x

⇒ Runs in 13^th innings = x + 16

⇒ x + (x + 16) = 130

⇒ 2x + 16 = 130

⇒ 2x = 114

⇒ x = 57

∴ The correct answer is 57.

Additional Information

Average Score Calculation

The average score of a batsman is the ratio of total runs scored to the total number of innings played: Average = Total Runs ÷ Total Innings.

New Average Effect

When more innings are added, the new total sum is: (Old Average × Old Innings) + Sum of New Innings = New Average × New Innings.

Deviation Method for Averages

If the average increases, the newly added values must be greater than the previous average. Total Increase = Increase in Average × Final Number of Innings.

Concept Used:  

Follow the BODMAS rule according to the table given below:

Calculation:

(2.5)2 + 8.7 – $\left(\frac{1.12}{1.4}\right) ×$ 0.5 = ?

⇒ 6.25 + 8.7 – (1.12/1.4) × 0.5 = ?

⇒ 6.25 + 8.7 – 0.8 × 0.5 = ?

⇒ 6.25 + 8.7 – 0.4 = ?

⇒ 14.95 – 0.4 = ?

⇒ 14.55 = ?

∴ The required value of ? is 14.55

The correct answer is period.

 Key Points

• The time for one complete cycle, a left swing and a right swing, is called the period.
• The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing.

Additional Information

• Motion that repeats itself regularly is called periodic motion. One complete repetition of the motion is called a cycle.
• The duration of each cycle is the period.
• The frequency refers to the number of cycles completed in an interval of time.
• It is the reciprocal of the period and can be calculated with the equation f=1/T.
• Some motion is best characterized by the angular frequency (ω).
• The angular frequency refers to the angular displacement per unit time and is calculated from the frequency with the equation ω=2πf.
• ​In short:
• Period: The duration of one cycle in a repeating event.
• Angular frequency: The angular displacement per unit time.
• Frequency: The quotient of the number of times n a periodic phenomenon occurs over the time t in which it occurs: f = n / t.

Shortcut Trick

Total profit is always 100%.

If profit from Brand 1 = 35%, then profit from Brand 2 = 100% − 35% = 65%.

Required Profit = 65% of 15,000.

Calculation: 0.65 × 15,000 = 9,750.

∴ The correct answer is Rs. 9,750.

Alternate Method

Given: Total Profit = Rs. 15,000 | Profit of Brand A = 35% of Total Profit.

Formulas: Profit of other brand = Total Profit − Profit of first brand.

⇒ Profit from Brand 1 = 35% of 15,000 = (35 ÷ 100) × 15,000

⇒ Profit from Brand 1 = 35 × 150 = Rs. 5,250

⇒ Profit from Brand 2 = Total Profit − Profit from Brand 1

⇒ Profit from Brand 2 = 15,000 − 5,250 = Rs. 9,750

∴ The correct answer is Rs. 9,750.

Additional Information

Percentage Distribution

When a whole is divided into two parts, if one part is x%, the other part is always (100 − x)%.

Profit Calculation

Profit amount = (Profit percentage ÷ 100) × Base Value.

Shortcut Trick

Ratio of Vinod to Anand (7 years ago) = 4 : 1 (Difference = 3 units)

Ratio of Vinod to Anand (19 years hence) = 2 : 1 = 6 : 3 (Difference = 3 units)

Change in units for Vinod = 6 − 4 = 2 units

Actual time gap = 19 + 7 = 26 years ⇒ 2 units = 26 years ⇒ 1 unit = 13 years

Vinod age 7 years ago = 4 × 13 = 52 years ⇒ Present age = 52 + 7 = 59 years

∴ The correct answer is 59 years.

Alternate Method

Given: Future age condition (19 years) and Past age condition (7 years).

Formula Used: Linear equations for age based on time shifts.

Let Vinod present age be V and Anand present age be A.

⇒ Case 1 (7 years ago): (V − 7) = 4 × (A − 7)

⇒ V − 7 = 4A − 28 ⇒ V − 4A = −21 → (Eq 1)

⇒ Case 2 (19 years hence): (V + 19) = 2 × (A + 19)

⇒ V + 19 = 2A + 38 ⇒ V − 2A = 19 → (Eq 2)

⇒ Subtracting (Eq 1) from (Eq 2): (V − 2A) − (V − 4A) = 19 − (−21)

⇒ 2A = 40 ⇒ A = 20

⇒ Substitute A = 20 in (Eq 2): V − 2(20) = 19

⇒ V − 40 = 19 ⇒ V = 59

∴ The correct answer is 59 years.

Additional Information

Ratio Difference Principle

The age difference between two people remains constant throughout their lives. Always equate the difference in ratio parts before solving.

Age Shift Rules

If present age is X, then 'n' years ago age is (X − n) and 'n' years hence age is (X + n).

Effective Time Gap

When comparing a past scenario and a future scenario, the total time gap is the sum of the past years and the future years (e.g., 7 + 19 = 26).

The correct answer is Konsam Ormila Devi.

Key Points

• Konsam Ormila Devi, the Indian female weightlifter, won the gold medal in the Asian Youth and Junior Weightlifting Competition held in Nepal on July 25, 2017.
• The weightlifter from Manipur lifted 56kg in snatch and 70kg in clean & jerk for a total effort of 126kg in the 44kg weight category to finish on the top of the podium, according to a release from the Indian Weightlifting Federation.

 

Additional Information

• Karnam Malleswari is a retired Indian weightlifter.
• She is the first Indian woman to win a medal at the Olympics in 2000.
• In 1994, she received the Arjuna Award and in 1999, she received the Rajiv Gandhi Khel Ratna award, India's highest sporting honour, and the civilian Padma Shri award.
• Kavita Dalal is an Indian professional wrestler who performed in the WWE under the ring name Kavita Devi, on their developmental territory NXT between 2017 and 2021.
• Devi is the first female professional wrestler of Indian nationality to wrestle in WWE.

The correct answer is 1 J.

Key Points

• Given,
• Displacement, s = 1m.
• Force, F= 1 N
• Work done = Force x displacement
• = 1 x 1
• = 1 J

Additional Information

• Work:
• When a body is displaced by applying a force on it, then work is said to be done.
• Work = Force × displacement.
• Its SI unit is joule (kg m² s^–2).
• Positive Work Done
• Positive work means that force is parallel to displacement, i.e. in the direction of displacement.
• Negative Work Done
• Negative work means that force is opposite to displacement.
• Zero Work Done
• If the force is perpendicular to the displacement and if either the force or the displacement is zero, work done is zero.

The correct answer is helium.

Key Points

• Helium atom has 2 electrons in its valence shell but its valency is not 2.
• Noble or inert elements are the most stable due to having the maximum number of valence electrons their outer shell or valence shell can hold.
• Helium has no tendency to form any chemical bonds due to highly stable configuration.
• Any element in group 1 has just one valence electron.
• Examples include hydrogen (H), lithium (Li), and sodium (Na).
• Any element in group 18 has eight valence electrons (except for helium, which has a total of just two electrons).
• Examples include neon (Ne), argon (Ar), and krypton (Kr).

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Additional Information

• The discoverers of noble gases are :

The correct answer is carbon.

Key Points

• A fullerene is an allotrope of carbon whose molecule consists of carbon atoms connected by single and double bonds so as to form a closed or partially closed mesh, with fused rings of five to seven atoms.
• The molecule may be a hollow sphere, ellipsoid, tube, or many other shapes and sizes.
• Various allotropes of carbon are diamond, graphite, lonsdaleite, fullerene, C-540, C-70, amorphous carbon, carbon nanotube.
• Diamond and crystalline silicon are isomorphous because they both have a three-dimensional tetrahedral structure.
• Allotropy, the existence of a chemical element in two or more forms, which may differ in the arrangement of atoms in crystalline solids or in the occurrence of molecules that contain different numbers of atoms.

Additional Information

• When an element exists in more than one crystalline form, those forms are called allotropes; the two most common allotropes of carbon are diamond and graphite.
• One of the allotropic form of a carbon is a fullerene in which “carbon atoms” are “arranged in a sphere”.
• Each sphere has 60 carbon atoms and each carbon atom is linked by a single covalent.
• The fullerene is considered as purest allotrope of “carbon” because they have “smooth structure” without having dangling bonds.

Shortcut Trick

The increase in amount is solely due to the increase in rate of interest.

Total percentage increase in interest = Rate increase × Time

⇒ 2% × 5 years = 10%

Actual increase in amount = ₹3,920 − ₹3,640 = ₹280

Since 10% of Principal = ₹280, then 100% (Principal) = ₹280 × 10 = ₹2,800

∴ The correct answer is ₹2,800.

Alternate Method

Given:

Time (T) = 5 years

Amount 1 (A₁) = ₹3,640

Amount 2 (A₂) = ₹3,920

Increase in Rate (ΔR) = 2% per annum

Formula Used:

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

Amount (A) = Principal (P) + Simple Interest (SI)

Difference in Amount (ΔA) = (P × ΔR × T) ÷ 100

Calculations:

⇒ Difference in Amount (ΔA) = A₂ − A₁

⇒ ΔA = 3920 − 3640 = ₹280

⇒ Extra interest is due to 2% increase for 5 years on Principal (P).

⇒ 280 = (P × 2 × 5) ÷ 100

⇒ 280 = (P × 10) ÷ 100

⇒ 280 = P ÷ 10

⇒ P = 280 × 10

⇒ P = ₹2,800

∴ The correct answer is ₹2,800.

Additional Information

Simple Interest Property

Simple interest remains constant every year if the principal and rate are unchanged. It is always calculated on the original principal.

Effect of Rate Change

If the rate increases by R% for T years, the extra interest earned is (P × R × T) ÷ 100. This is useful for solving questions involving conditional rate changes.

Principal Formula from Amount

Principal (P) can also be calculated if Amount (A), Rate (R), and Time (T) are known using: P = (100 × A) ÷ (100 + RT).