MP Police Constable : (27 Nov 2025, Shift 2) Memory-Based Paper (Previous Year Paper)

Pietra Dura is a fine inlay work with semi-precious stones.

Important Points

• Pietra Dura is an elaborate architectural technique introduced by Shah Jahan during his reign.
• His reign is known as the Golden Age of the Mughal Architecture who built some of the extraordinary buildings and forts like the Taj Mahal, the Red Fort, Jama Masjid, and Shalimar Bagh.
• His buildings include Persian styles, fine white marbles, domes, symmetrical designs, curved lines, etc.
• One of the distinctive features of his building is Petra Dura or Parchin Kari where semi-precious stones like lapis lazuli, topaz, and onyx were carved into the fine marble to create different floral images.
• Pietra Dura inlays were prominent in the Red Fort at Delhi where a series of Pietra Dura were inlaid behind the emperor's throne.

Hence, we can conclude that Pietra Dura is a floral design embedded into marbles.

Confusion Points

• Pietra Dura Coloured, hard stones placed in depressions carved into marble or sandstone create beautiful, ornate patterns with precious stones adorning the walls with flowers.

The correct answer is Ajinomoto.

Key Points

CONCEPT:

• Paracetamol: It is a non-narcotic analgesic drug with a chemical name 4-Acetamidophenol.
• Analgesic drugs are drugs that relieve pain without causing impairment to consciousness, mental confusion.
• Antiseptics are chemicals which either kill or prevent the growth of microorganisms,
• Dettol is a commonly used antiseptic
• It is a mixture of chloroxylenol and terpineol.
• Washing soda: Sodium carbonate is known as washing soda.
• It is used as a cleansing agent.
• It makes water soft and allows the detergent to absorb properly into fibers.

EXPLANATION:

• Monosodium Glutamate is commonly known as Ajinomoto.
• It is the sodium salt of glutamic acid

​

• Chemical formula: C₅H₈NO₄Na
• It is an artificial flavoring substance.
• MSG was first prepared in 1908 by Japanese biochemist Kikunae Ikeda.

The given statement is: Due to the failure of the main grid, power supply to many parts of the city was affected.

Assumptions:

I. The main grid is responsible for transmission of power to different parts of the city → True (Because due to the failure of the main grid, power supply to many parts of the city was affected).

II. Most people have backup power installations at their homes to manage during times when power supply is disrupted → False (Because nothing related to this has been mentioned in the statement).

Hence, the correct answer is "Only assumption I is implicit".

Given:

A = Rs. 1440, T = 4 years, R = 5%

Formula Used:

A = P + (P × R × T)/100

Calculation:

According to the question,

1440 = P + [(P × 5 × 4)/100]

⇒ 1440 = P + P/5

⇒ 6P/5 = 1440

⇒ P = 1440 × 5/6

⇒ P = 1200

Shortcut Trick

Let the sum be 100%

Simple interest for 4 years = 4 × 5 = 20%

⇒ 120% = 1440

⇒ 100% = 1200

The correct answer is Acquired Immuno-Deficiency Syndrome

Key Point

• AIDS:
• AIDS stands for Acquired immune deficiency syndrome.
• It is a syndrome caused by a virus termed HIV (human immunodeficiency virus).
• This virus affects the immune system in humans and makes them much more vulnerable to infections and diseases.
• It is a disease that progressed initially foar a long period without any symptoms.
• When the HIV virus attacks the T-cells in the immune system, it makes your body weak symptoms like a headache, fever, sore joints, and muscles, etc start appearing. When AIDS remains unattended, it leads to death.

The correct answer is Pulmonary Veins.

Key Points

• The veins that carry oxygenated blood from the lungs to the heart are known as the pulmonary veins.
• The four primary pulmonary veins—two from each lung—that empty into the left atrium of the heart are the largest pulmonary veins.
• The pulmonary veins are part of the pulmonary circulation.
• The main pulmonary veins receive blood from three or four feeding veins in each lung, and drain into the left atrium.
• The peripheral feeding veins do not follow the bronchial tree.
• They run between the pulmonary segments from which they drain the blood.

Additional Information

• Cardiac vein:
• The cardiac veins returns deoxygenated blood from the myocardium to the right atrium.
• Pulmonary arteries:
• These are blood vessels that carry oxygen-poor blood from the right side of your heart to your lungs.
• Cardiac artery:
• These are the arterial blood vessels of coronary circulation, which transport oxygenated blood to the heart muscle.

​

The pattern followed here is,

Similarly,

Hence, option 1 is the correct answer.

Given:

An article was sold at 65% of its marked price

There was a gain = 30%

Calculation:

Let the Cost price be 100 and Marked price be x

According to the question

An article was sold at 65% of its marked price = (65% of x)

And there was a gain = (130% of 100)

Now,

⇒ (65/100 × x) = (130/100 × 100)

⇒ 13x/20 = 130

⇒ 13x = (130 × 20)

⇒ x = (130 × 20)/13

⇒ x = 200

Now,

The ratio of the marked price to cost price = (200 : 100)

⇒ 2 : 1

∴ The required ratio is 2 : 1

The correct answer is Ohm.

Key Points

• Impedance is the total sum of resistance and reactance.
• The SI Unit of Impedance(Z), resistance(R), and reactance(X) is Ohm(Ω).
• Reactance is a kind of imaginary resistance offered by electrical components like Capacitance and Inductor.
• Reactance offered by the Inductor is called Inductive reactance, given as X_L = 2πfL.
• Reactance offered by the Capacitor is called Capacitor reactance, given as \(X_{C}=\frac{1}{2\pi fC}\).
• Where 'f' - frequency of the source, 'L' - Inductance, and 'C' - Capacitance.

Additional Information

The correct answer is Conversion of sugar into alcohol.

Key Points

• Fermentation is the process by which molecules such as glucose are broken down anaerobically.
• Through the process of fermentation, the sugars are converted into alcohol.
• The enzymes like pyruvic acid decarboxylase and alcohol dehydrogenase catalyze these reactions.
• It normally occurs in yeast cells bacteria and in the muscles of animals.
• It is a method of extracting energy from molecules.
• Fermentation accounts for only a partial breakdown of glucose.
• In fermentation, there is a net gain of only two molecules of ATP for each molecule of glucose degraded to pyruvic acid.
• Wine and beer are produced by fermentation.
• No ATP would be produced without fermentation.

Given:

So, 156 will be next in series.

Hence, the correct answer is "Option 4".

Given:

Average of 5 consecutive odd natural numbers is 27.

Formula:

Sum of n terms in AP (Arithmetic Progression) =  \(n(a + l )\over 2\)

Where-

n = number of terms

a = starting term

l = last term

Calculations:

Let the first integer be “n”

⇒ Consecutive odd integers = (n + 2), (n + 4), (n + 6), and (n + 8)

These terms would be in Arithmetic progression with the common difference being 2.

Sum of 5 terms = \(5 × ( n + n + 8)\over 2\)

Average of 5 terms =  \(5 × ( n + n + 8)\over 2× 5\) =  \( 2n + 8\over 2\) = n + 4

According to the question, average = 27

⇒ n + 4 = 27

⇒ n = 27 - 4 = 23

∴ Fifth number = n + 8 = 23 + 8 = 31

⇒ Product of first and fifth number = 23 × 31 = 713

∴ The product is 713.

The Correct answer is Edwin Hubble.

Key Points 

• 'Expanding Universe'
• Edwin Hubble, an American astronomer, and was the first to prove that the universe is expanding.
• According to Expanding Universe theory, the universe is presently expanding.
• Hubble proved that there is a direct relationship between the speeds of distant galaxies and their distances from Earth.
• This is now known as Hubble’s Law.

Additional Information

• Black Hole
• It refers to a point in space where the matter is so compressed as to create a gravity field from which even light cannot escape.
• The concept was theorized by Albert Einstein in 1915 and the term ‘black hole’ was coined in the mid-1960s by American physicist John Archibald Wheeler.
• Usually, the black holes belong to two categories:
• One category ranges between a few solar masses and tens of solar masses. These are thought to form when massive stars die.
• The other category is supermassive black holes.
• These range from hundreds of thousands to billions of times that of the sun from the Solar system to which Earth belongs.
• In April 2019, the scientists at the Event Horizon Telescope Project released the first-ever image of a Black Hole (more precisely, of its shadow).
• The Event Horizon Telescope is a group of 8 radio telescopes (used to detect radio waves from space) located in different parts of the world.
• Gravitational waves are created when two black holes orbit each other and merge.

The correct answer is Lactobacillus Acidophilus.

Key Points

Explanation:

• This is a species of Gram-positive bacteria in the genus Lactobacillus.
• L. acidophilus is a homofermentative, microaerophilic species, fermenting sugars into lactic acid, and grows readily at rather low pH values (below pH 5.0).
• It has an optimum growth temperature of around 37 °C (99 °F).
• L. acidophilus is found in the human and animal gastrointestinal tract and mouth.

Additional Information

Microorganism:  A microorganism is a living thing that is too small to be seen with the naked eye.

• Microorganisms are classified into four major groups. These groups are bacteria, fungi, protozoa and some algae.
• The effect of microorganisms in our daily lives are so much, some are beneficial for human beings but some of the microorganisms are very harmful to the living and in extreme cases may lead to death.

Friendly microorganism:

• Curd contains several microorganisms. Of these, the bacterium, Lactobacillus promotes the formation of curd. It multiplies in milk and converts it into curd.
• Bacteria and yeast are also helpful for the fermentation of rice.
• Penicillin also contains microorganism that acts as antibiotics and help us to fight diseases.
• Some bacteria are able to fix nitrogen from the atmosphere to enrich the soil with nitrogen and increase its fertility. The Nitrogen-fixing cyanobacteria (blue-green algae) and Rhizobium.

Harmful microorganism:

Disease-causing microorganisms are called pathogens.

Since the problem of shortage of water is so rampant everywhere the people in these states have taken steps sincerely. Thus option 1 is the correct answer.

Concept used:

Follow BODMAS rule to solve this question, as per the order given below,

Now,

Calculation:

Expression : 2 – [6 – {3 + (–4 + 5 + 1) × 8} + 12]

⇒ 2 – [6 – {3 + (2 × 8)} + 12]

⇒ 2 – [6 – 19 + 12]

⇒ 2 – [– 1]

⇒ 2 + 1 = 3

∴ The required value is 3

Characteristics of Intensive Farming:

• Intensive farming is an agricultural intensification and mechanization system that aims to maximize yields from available land through various means, such as heavy use of pesticides and chemical fertilizers.
• Three major characteristics of intensive farming are as follows, 
• Low fallow ratio
• Labour and capital intensive
• Higher crop yields per unit land area.
• Executive use of mechanization found.
• It is a labour-intensive farming method.
• This farming produces cheaper food per hectare to feed the rising population.
• Created multiple cropping systems.
• High productivity using modern inputs.
• It also involves intensive livestock farming.
• It is a common practice in the fertile areas of south-east Asia, China, India (Punjab, parts of Rajasthan, Madhya Pradesh, etc.), etc.

Therefore, '3' is the correct option here.

The correct answer is Limestone.

• Limestone is a form of calcium carbonate.
• Other Different forms of calcium carbonate are Chalk and Marble.
• Calcium carbonate is a chemical compound with the formula CaCO₃.
• It is a common substance found in rocks as the minerals calcite and aragonite (most notably as limestone, which is a type of sedimentary rock consisting mainly of calcite) and is the main component of eggshells, snail shells, sea shells, and pearls.

Additional Information

Properties of Calcium Carbonate:

• Molar mass - 100.0869 g/mol.
• Odor - odorless.
• Appearance - Fine white powder; chalky taste.
• pH value - 9

The correct answer is Option 2.

Conclusion I generalizes the fact of lightning strikes with one incident given in the statement. Therefore it is incorrect.

The statement uses the words such that  which help us conclude that the lightning strike injured the thief which helped the police to catch him. Hence Conclusion II follows.

Given: 

Principal (P) = Rs. 12500

Rate of Interest = 12%

Concept used:

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

where

P = Principal amount

R = Rate of interest per year

N = Time in years

Calculation:

Since interest is compounded half-yearly, time (N) = 2

Thus, the principal becomes = 12500 × (1 + (12 ÷ 2)/100)² = Rs. 14045

Hence, compound interest incurred = 14045 - 12500 = Rs. 1545

∴ The compound interest incurred is Rs. 1545.

Shortcut TrickRate of interest when calculated half-yearly = 12/2 = 6%

Simple interest for each six-month term on the sum of Rs. 12500 = (12500 × 6 × 1) ÷ 100 = Rs. 750

Interest on the first Rs. 750 = (750 × 6 × 1) ÷ 100 = Rs. 45

Hence, total interest incurred = 750 × 2 + 45 = Rs. 1545

∴ The compound interest incurred is Rs. 1545.

The correct answer is Marina Beach.

• Marina Beach is the longest beach in India.
• Marina beach is located in Chennai, Tamil Nadu.
• It lies along the Bay of Bengal.
• Marina Beach is also the world’s second-longest beach.
• The beach was renovated by Governor Mountstuart Elphinstone Grant Duff in the 1880s.
• Two prominent statues of Mahatma Gandhi is situated on the Marina beach.
• Marina Beach is one of the most crowded beaches in India.

Additional Information

• Juhu Beach is located in Mumbai in Maharashtra.
• Dandi Beach is located in Dandi village, Gujarat.
• Puri Beach is located in Puri, Odisha.

The correct answer is Pascal's law.

• The Pascal's law states that in a fluid which is at rest in a container, the pressure applied to one part of the fluid is uniformly transmitted to all the parts of the fluid.

Key Points

• A hydraulic lift employs this principle to lift heavy objects.
• When pressure is applied to a fluid through one piston, it results in an equivalent pressure on another piston in the system which is then able to lift objects.
• With the increase in the area of the second piston, the force exerted by it also increases thus enabling lifting of heavier objects.

Additional Information

• Hooke's law states that force needed to extend or compress a spring by some distance is directly proportional to that distance.
• Newton's first law of motion - A body at rest remains at rest, or if in motion, remains in motion at constant velocity unless acted on by a net external force.
• Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.

In an ordinary year, there are 365 days and on dividing 365 by 7 we get remainder = 1 so this extra one day is taken as an odd day.

Similarly, in a leap year, there are 366 days and on dividing 366 by 7 we get remainder = 2 so these extra 2 days are taken as the odd days.

Thus, the remainder which we get after dividing a number of days by 7 is considered as odd days.

Now, we have to calculate the odd days from Feb 10, 2004 - Feb09, 2006.

May07, 1986 - May06, 1987 = 365 days = 1 odd day

May 07, 1987 - May06, 1988 = 366 days = 2 odd days (as 1988 is the leap year and 29^th Feb is included in this period).

Total odd days = 3

Thus, May 07, 1986 is 3 days (of the week) beyond the day of May 07, 1988.

May 07, 1986(Wednesday) → May 07, 1988(Saturday)

Hence, it was Saturday on May07, 1988.

Calculation:

Given that

⇒ \(\frac{A}{B} = \frac{5}{7}\)       -----(1)

⇒ \(\frac{B}{C} = \frac{9}{11}\)     ------(2)

Multiply both equations, 

⇒  \(\frac{A}{C} = \frac{A}{B}\times \frac{B}{C}\) 

⇒ \(\frac{A}{C} = \frac{5}{7}\times \frac{9}{11}=\frac{45}{77}\) 

∴ A : C = 45 : 77

CONCEPT:

Storage of Sodium

• Sodium is a highly reactive alkali metal.
• It reacts vigorously with oxygen and moisture present in air, forming sodium oxide and sodium hydroxide.
• This reaction can lead to the ignition of sodium, as it generates heat and hydrogen gas, which is flammable.

EXPLANATION:

• To prevent sodium from reacting with air or moisture, it is stored under a non-reactive liquid like kerosene.
• Kerosene acts as a protective barrier, isolating sodium from air and water, thereby preventing unwanted reactions.

Additional Information

• Absolute alcohol can react with sodium, forming hydrogen gas and sodium alkoxide.
• Petrol is highly volatile and flammable, which increases the risk of fire when combined with sodium.
• CHCl₃ (chloroform) is not commonly used for sodium storage and may not effectively isolate sodium from air and moisture.

Therefore, sodium is usually kept in kerosene to ensure its safe storage and prevent reactions with air and moisture.

The correct answer is Newton’s third law of motion.

Key Points

• When a ball drops on the floor it bounces.
• This is according to Newton’s third law of motion.

Additional Information

• Newton's third law implies that for every action there is a reaction.
• When a ball drops on to the floor it bounces because
• As Newton's third law implies that for every action there is a reaction.

Mistake Points

• The elasticity of the object/ball just gives the extra bounce, but the actual reason behind the bounce is the existence of 2 equal and opposite forces (Newton's third law).

According to the given information:

In a class of fifty students, Geeta's rank is thirty-two from the left end. 

Now,

Toatl student = Geeta's position from left + Geeta's position from right - 1

Geeta's position from right = Total student - Geeta's position from left + 1

= 50 - 32 + 1

= 18 + 1

= 19

Thus, Geeta's rank from the right end is '19'.

Hence, the correct answer is "19".

Given

The ratio of a fruit costing Rs. 20 per kg and Rs. 38 per kg = 5 : 4.

The cost of fruits = Rs. 20 per kg

The cost of fruits= Rs. 38 per kg

Formula used

Total value = Quantity × price

Solution

Let the two types of oil be 5x and 4x.

Total cost of the mixture = (5x × 20) + (4x × 38)

⇒ 100x + 152x = 252x

The cost per kg of the resulting mixture:

⇒ 252x/9x

⇒ 28

The answer is Rs. 28 per kg.

The Correct Answer is Masaki Kashiwara.

In News

• Japanese mathematician Masaki Kashiwara awarded the Abel Prize 2025.

Key Points

• Recipient of the 2025 Abel Prize: Masaki Kashiwara, a Japanese mathematician.
• Field of Contribution:
• Algebraic analysis
• Representation theory
• Development of D-modules
• Discovery of crystal bases.
• About the Abel Prize:
• Named after Niels Henrik Abel, a legendary Norwegian mathematician.
• Established by the Norwegian Parliament in 2002 to commemorate Abel's 200^th birth anniversary.
• First awarded in 2003.
• Often regarded as the Nobel Prize equivalent in mathematics.
• Awarded by a committee in consultation with the International Mathematical Union (IMU) and the European Mathematical Society (EMS).
• Includes a cash award and a glass plaque designed by Norwegian artist Henrik Haugan.

The correct answer is Lactobacillus.

Key Points

• Lactobacillus is a genus of Gram-positive, aerotolerant anaerobes or microaerophilic, rod-shaped, non-spore-forming bacteria.
• There are many species of lactobacillus.
• These are "friendly" bacteria that normally live in our digestive, urinary, and genital systems without causing disease.
• Curd contains a wide variety of bacteria like Lactobacillus, Lactococcus lactis, etc, whereas yogurt contains Streptococcus thermophilous and Lactobacillus bulgaricus.

Additional Information

• Salmonella is a type of bacteria that commonly causes diarrhea.
• Clostridium is a bacterium that can cause symptoms ranging from diarrhea to life-threatening inflammation of the colon.

Explanation: From the statement, it can be inferred that despite the presence of an interview panel, a candidate who does not meet the desired qualifications or values and attributes might still be selected.

Conclusion I: Having specialists (or any structured panel) does not ensure a perfect selection process, leading to the conclusion that the inclusion of specialists on the interview panel does not guarantee proper selection.

Conclusion II: The interview test has certain limitations in the matter of selection of candidates. In the statement, no mention of the limits in the personal interview.

Therefore, only conclusions I logically follow from the statement provided.

Hence, the correct answer is "Option (2)".

Shortcut Trick

Total decrease in weight = Total men × Decrease in average weight

Total decrease = 15 × 2 = 30 kg

Weight of new man = Weight of replaced man − Total decrease

Weight of new man = 70 − 30 = 40 kg

∴ The correct answer is 40 kg.

Alternate Method

Given:

Total number of men (n) = 15

Weight of the man replaced = 70 kg

Decrease in average weight = 2 kg

Formula Used:

Weight of new person = Weight of replaced person + (Total number of persons × Change in average)

Calculations:

⇒ Let the initial average weight be 'A' kg.

⇒ Total weight of 15 men = 15A

⇒ Let the weight of the new man be 'W' kg.

⇒ New total weight = 15A − 70 + W

⇒ New average = (15A − 70 + W) ÷ 15

⇒ New average = A − 2

⇒ (15A − 70 + W) ÷ 15 = A − 2

⇒ 15A − 70 + W = 15(A − 2)

⇒ 15A − 70 + W = 15A − 30

⇒ W = 70 − 30

⇒ W = 40 kg

∴ The correct answer is 40 kg.

Additional Information

Average Replacement Formula

When one person is replaced: New value = Old value + (Total number × Change in average). Use positive for increase and negative for decrease.

Average Inclusion

When a new person joins: New value = New average + (Old number × Change in average).

Average Exclusion

When a person leaves: Removed value = Old average + (New number × Change in average).

The correct answer is Baking Soda.

Key Points

• Baking soda, also known as sodium bicarbonate (NaHCO₃), is commonly used in cooking to create a crispy texture in fried foods like pakoras.
• When baking soda is mixed with water and acidic substances (like lemon juice or curd), it releases carbon dioxide gas, leading to a lighter and crispier texture in fried items.
• It acts as a leavening agent, helping the batter to rise and create air pockets, which result in a crunchy and airy texture upon frying.
• Baking soda is widely used in Indian kitchens for traditional recipes requiring a light and crispy coating, such as pakoras, bhaturas, and dhoklas.
• It is safe for consumption in small quantities when used for culinary purposes.

Additional Information

• Sodium Bicarbonate (Baking Soda):
• Chemical formula: NaHCO₃.
• It is a white crystalline powder that is mildly alkaline in nature.
• Commonly used in cooking, cleaning, and even as an antacid to neutralize stomach acidity.
• Difference Between Baking Soda and Baking Powder:
• Baking soda is pure sodium bicarbonate, whereas baking powder contains baking soda along with an acidic component and a drying agent (usually starch).
• Baking powder is used in recipes that do not contain acidic ingredients, while baking soda requires an acidic ingredient to activate.
• Other Culinary Uses of Baking Soda:
• Used to tenderize meats by breaking down proteins.
• Employed in recipes to neutralize overly acidic flavors.
• Health Considerations:
• Excessive consumption of baking soda can lead to alkalosis, a condition characterized by an excessively alkaline pH in the body.
• It should always be used in moderation in cooking and baking.

The correct answer is ​Anthocyanins.

Key Points

• Anthocyanins can be defined as a type of compound with an antioxidant effect.
• It is a type of flavonoid that give red, purple, and blue plant their rich coloring.
• The food processing plants are rich in anthocyanins include -

1. Blueberry
2. Raspberry
3. Black rice
4. Black Soybean
5. Cherry
6. Redcurrant
7. Nortan Grape
8. Red Cabbage

Important Points

• Anthocyanins are also used as Ph indicators because their color changes with Ph.
• They are red and pink in acidic solutions, purple in neutral solutions, and greenish in alkaline solution.

The pattern followed here is,

1357 → (12)³ + 1357 → (13)³ + 3085 → (14)³ + 5282 → (15)³ + 8026 → 11401

Thus, the next term in the series will be ‘11401’.

Given:

Curved surface area = 4,455 cm2

Diameter = 105 cm

π = 22/7

Formula:

Curved surface area of a cone = πrl

here:

r = radius of the cone

l = slant height of the cone

Solution:

First, we need to find the radius of the cone. We know that the diameter is 105 cm, so the radius is 105/2 = 52.5 cm.

4455 = (22/7) × 52.5 × l

l = 4455 × 7/(22 × 52.5)

l = 27 cm

Therefore, the slant height of the cone is 27 cm.

CONCEPT:

Tamarind and Its Acid Content

• Tamarind is a fruit known for its sour taste, which is primarily due to the presence of organic acids.
• The main acid found in tamarind is D-tartaric acid, which contributes to its characteristic tangy flavor.
• Other acids like lactic acid, oxalic acid, and acetic acid may be present in trace amounts, but D-tartaric acid is the dominant one.

EXPLANATION:

• D-tartaric acid is correct because tamarind contains significant quantities of this acid.
• Lactic acid is incorrect as it is not typically found in tamarind.
• Oxalic acid is incorrect, though it may be present in minute amounts in some fruits, it is not the main acid in tamarind.
• Acetic acid is incorrect as it is primarily associated with vinegar and not tamarind.

Conclusion: Tamarind contains D-tartaric acid, which is responsible for its sour taste.

The correct answer is Cobalamin.

Key Points

• Thiamin - Vitamin B1
• Riboflavin - Vitamin B2
• Niacin - Vitamin B3
• Ascorbic acid - Vitamin C
• Calciferol - Vitamin D
• Tocopherol - Vitamin E
• Phylloquinone - Vitamin K

Symbol representation:

The family tree diagram is shown below:

Hence, ‘Uncle’ is the correct answer.

As we know,

Sum of all three angles of a triangle is 180.

Ratio of three angles of a triangle = 2 : 3 : 4

2 + 3 + 4 = 9 unit

⇒ 9 unit = 180

⇒ 1 unit = 20

⇒ 2 unit = 20 × 2 = 40°

The correct answer is Speed is constant.

Key Points

• Circular motion is a movement of an object along the circumference of a circle or rotation along a circular path.
• The distance and displacement are different at every instance at any particular point of time.

Confusion Points

• While the speed is a scalar quantity, in uniform motion, it remains constant.
• As, Velocity is a vector quantity, and the direction of movement changes continuously, velocity changes continuously.
• Due to this, the object is in accelerated motion.

Important Points

About the Circular Motion:

• As the direction of the velocity changes at every instant, it is an accelerated motion.
• During the motion, the particle repeats it's paths along the same trajectory.
• Thus the motion is periodic.

Uniform Circular Motion:

• During circular motion, if the speed of the period remains constant, it is a Uniform Circular Motion. Hence option 4 is correct.

The correct answer is Watt.

Key Points

• The SI unit of electric power is watt (W).
• The rate at which electric energy is dissipated or consumed in an electric circuit is termed as electric power.
• The power P is given by, P = VI.
• The SI unit of electric power is watt (W). It is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V.

Additional Information

6 × 8 ÷ 32 + 64 – 11

After interchanging signs,

6 + 8 ÷ 32 × 64 – 11

6 + 16 – 11 = 22 – 11 = 11

Thus, the correct answer is “11”.

Shortcut Trick

Using VBODMAS, solve the Vinculum (bar) first: 15 − 21 = −6

Resolve Bracket: 27 − (−6) = 33

Evaluate 'Of': 5 × 33 = 165

Perform Division and Addition: 19/165 + 37 = (19 + 6105) / 165 = 6124/165

∴ The correct answer is 6124/165.

Alternate Method

Given:

19 ÷ 5 of (27 − 15 − 21) + 37

Formula Used:

VBODMAS Rule: Vinculum → Brackets → Of → Division → Multiplication → Addition → Subtraction

Calculations:

⇒ 19 ÷ 5 of (27 − 15 − 21) + 37

⇒ 19 ÷ 5 of (27 − (−6)) + 37

⇒ 19 ÷ 5 of (27 + 6) + 37

⇒ 19 ÷ 5 of 33 + 37

⇒ 19 ÷ 165 + 37

⇒ 19/165 + 37

⇒ (19 + 37 × 165) / 165

⇒ (19 + 6105) / 165

⇒ 6124 / 165

∴ The correct answer is 6124/165.

Additional Information

VBODMAS Rule

It dictates the order of mathematical operations: V (Vinculum/Bar), B (Brackets), O (Of), D (Division), M (Multiplication), A (Addition), and S (Subtraction).

Vinculum (Bar Bracket)

A horizontal line placed over an expression to indicate that it should be evaluated first, acting exactly like an innermost set of parentheses.

'Of' Operation

It represents multiplication but takes higher precedence over standard division and multiplication in the BODMAS sequence.

The correct answer is Diamond.

• Panna is famous for its diamond mines located in a belt of about 80 km across the town.
• Madhya Pradesh has the only diamond mine in the country.
• The National Mineral Development Corporation Ltd. is operating the only mechanized diamond mine at Majhgawan in the Panna district since 1958 is now producing 81000 carats of diamond annually. Besides this, about 400 carats is also being produced from the "shallow diamond mines" in Panna and part of Satna district.

• In terms of mineral production, Madhya Pradesh ranks third next only to Jharkhand and Chhattisgarh.

Additional Information

• Manganese - State is enriched with a good deposit of manganese ore mainly spread over in the Balaghat, Chhindwara, and Jhabua districts.
• The total reserves of 23.64 million tonnes of manganese ore is available in the State constituting 14.09% of total national reserve.
• The "Bharveli manganese mine" in Balaghat district is the largest underground mine operating in the Asian sub-continent.
• Marble Cutting and Polishing Industry - Katni is famous for it.
• Limestone - The total reserves of limestone is 3625.98 million tonnes spread over in districts of Damoh, Hoshangabad, Mandsaur, Narsinghpur, Rewa, Satna, Panna, Katni, Sagar, Dhar, Khargone, Jhabua, Balaghat, Sidhi, and Morena.
• Coal - Coal reserves of 16027.07 million tonnes are spread over in the district of Sidhi, Shahdol, Umaria, Betul, Chhindwara, and Narsinghpur.
• Bauxite - Reserves of 63.87 million tonnes of bauxite are spread over in Shahdol, Mandla, Balaghat, Rewa, Satna, and Katni districts.
• Copper-Ore - Malajkhand; the country's largest open cast copper ore mine, is situated in Balaghat district.
• Fire Clay - The fire clay deposits occurring mainly in Shahdol, Gwalior, Kanti, Jabalpur, and Sidhi districts.

Location of Minerals in Madhya Pradesh on Map

Concept:

• Nitrogen Cycle:
• The Nitrogen Cycle describes how Nitrogen moves between various components - plants, animals, bacteria, air, and soil.
• The various processes involved in the Nitrogen cycle are fixation, nitrification, assimilation, ammonification, and denitrification.

Explanation:

• The process of converting nitrates into nitrogen is called denitrification

Denitrification:

• Nitrification is the process of converting ammonium ions into nitrates or nitrites.
• However, certain denitrifying bacteria in soil, like Pseudomonas, convert some of the nitrates back into nitrogen gas. This process is called Denitrification.
• This process is the opposite of nitrification.
• This process is the last stage in the Nitrogen cycle and occurs in the absence of Oxygen.

Additional Information 

• Ammonification refers to the stage of the Nitrogen cycle where certain ammonifying bacteria during the decomposition of organic matter, convert organic nitrogen into inorganic forms like ammonia or ammonium ions.
• Nitrogen fixation is the chemical process by which atmospheric nitrogen is assimilated into organic compounds, especially by certain microorganisms as part of the nitrogen cycle.
• Atmospheric nitrogen is fixed by several methods like biological N2 fixation, Industrial N2 fixation & Electrical N2 fixation.

The given series is,

(Left) 2 5 4 3 7 8 6 7 9 4 3 7 8 6 2 3 4 8 9 4 8 7 6 4 3 7 2 8 9 7 5 3 2 4 5 9  (Right)

As per the question, after dropping the even numbers, the above series will reduce to,

(Left)  5 3 7 7 9 3 7 3 9 7 3 7 9 7 5 3 5 9  (Right)

So, the sixth element from the left is,

(Left)  5 3 7 7 9 3 7 3 9 7 3 7 9 7 5 3 5 9  (Right)

Hence, the correct answer is, '3'.

Shortcut Trick

Use the weighted average formula to find the overall pass percentage directly.

Total Pass % = (Boys % × Boys Pass Rate + Girls % × Girls Pass Rate) ÷ 100

Total Pass % = (40 × 40 + 60 × 60) ÷ 100

Total Pass % = (1600 + 3600) ÷ 100 = 5200 ÷ 100 = 52%

∴ The correct answer is 52%.

Alternate Method

Given:

⇒ Boys in class = 40%

⇒ Girls in class = 100% − 40% = 60%

⇒ Pass rate among boys = 40%

⇒ Pass rate among girls = 60%

Formula Used:

Number of Passed Students = (Pass % × Total Students) ÷ 100

Calculations:

Let the total number of students in the class be 100.

⇒ Total Boys = 40

⇒ Total Girls = 60

⇒ Boys who passed = 40% of 40 = (40 × 40) ÷ 100 = 16

⇒ Girls who passed = 60% of 60 = (60 × 60) ÷ 100 = 36

⇒ Total students passed = 16 + 36 = 52

⇒ Passed percentage = (52 ÷ 100) × 100 = 52%

∴ The correct answer is 52%.

Additional Information

Weighted Average

When groups of different sizes have different averages, the combined average is calculated as (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Percentage Basics

x% of y is calculated as (x × y) ÷ 100. It is always helpful to assume the total base as 100 for easy calculation.

Ratio Method

The ratio of boys to girls here is 40:60 or 2:3. Total pass percentage = (2 × 40 + 3 × 60) ÷ (2 + 3) = (80 + 180) ÷ 5 = 260 ÷ 5 = 52%.

The correct answer is Mahakoshal.

Key Points

Mahakoshal region 

• ​Mahakoshal is a region of central India.
• Mahakoshal lies in the upper or eastern reaches of the Narmada River valley in the Indian state of Madhya Pradesh.
• Jabalpur is the largest city in the region.
• This region includes districts of Jabalpur, Shahdol, Katni, Chhindwara, Narsinghpur, Mandla, Dindori, Seoni and Balaghat.
• Important dynasties that ruled over this area includes Gonds, Kalchuris, Satvahannas and Marathas.
• During the British rule in India it was part of Central provinces.
• After the Third Anglo-Maratha War, the British took control of the entire region.

All the sovereign states in the region became princely states of British India, governed by the Central India Agency.

• The Mahakoshal region became a British province: the Saugor and Nerbudda Territories.
• In 1861, the British merged the Nagpur Province with the Saugor and Nerbudda Territories to form the Central Provinces.

 Important PointsThird Anglo-Maratha War

• ​The third war (1817–18) was the result of an invasion of Maratha territory in the course of operations against Pindari robber bands by the British governor-general, Lord Hastings.
• The peshwa’s forces, followed by those of the Bhonsle and Holkar, rose against the British, but the Sindhia remained neutral.
• Defeat was swift, followed by the pensioning of the peshwa and the annexation of his territories, thus completing the supremacy of the British in India.
• The Treaty of Gwalior was signed in 1817 between Shinde and the British, even though he had not been involved in the war. As per this treaty, Shinde gave up Rajasthan to the British. The Rajas of Rajputana remained the Princely States till 1947 after accepting British sovereignty.
• The Treaty of Mandasor was signed between the British and the Holkar chief in 1818. An infant was placed on the throne under British guardianship.
• The Peshwa surrendered in 1818. He was dethroned and pensioned off to a small estate in Bithur. Most parts of his territory became part of the Bombay Presidency.

Concept:

• Biodiversity conservation refers to the protection, scientific management, and upliftment of the natural flora and fauna. It involves the conservation of various threatened plant and animal species.
• Biodiversity conservation can be done in two modes i.e. In-Situ and  Ex-Situ

Explanation:

• Ex-Situ Conservation: The mode of conservation includes the protective maintenance of threatened species outside the areas where they naturally occur.
• Examples of Ex-Situ conservation are botanical gardens, zoological gardens, gene banks, etc.
• In-Situ Conservation: The conservation method to protect the entire ecosystem in which the species are protected in their natural habitat.
• Examples of In-Situ conservation are national parks, wildlife sanctuaries, biosphere reserves &Sacred groves.

​

Additional Information

• There are more than 100 national parks in India covering an area of 40,564.00 km2. Some of the important National parks of India are Ranthambore National Park, Jim Corbett national park, Kaziranga national park
• There are about 553 Wildlife sanctuaries present in India.
• Sacred groves are the patches of protected forest areas that are home to different tribal people. Examples -Khasi and Jaintia Hills in Meghalaya and Aravalli Hills of Rajasthan

Given

Statement:

Recent marketing trends suggest that words like 'premium', ‘exquisite', 'priority' are considered prestigious by consumers of the middle income group and hence increase the chances of sale of any product advertised with these words.

Now,

Assumptions:

1. The products advertised with the said 'prestigious' words definitely cost higher than those which are not advertised with such words - Not Implicit (The statement does not provide information regarding the cost of the products. It only talks about the perception of these words by the middle income group and their effect on sales.) 2. Such prestigious words have no impact on sales among the lower income group - Not Implicit (The statement only discusses the impact on the middle income group and does not provide information about the lower income group.)

Here, Neither assumption I nor II is implicit.

Hence, the correct answer is "Option 4".

Formula used:

SI = (P × R × T)/100

where P = Principal, R = Rate of Interest, and T = Time period

Solution:

Let the principal be 100 then the amounts become 300

Interest = Amount - Principal

Interest = 300 - 100

Interest = 200

Putting these values in the formula

⇒ 200 = (100 × R × 17/2)/100

R = (200 × 100 × 2)/17 × 100

R = 23.52%

The correct answer is Mhow.

Key Points

• Dr Bhimrao Ramji Ambedkar was born on 14 April 1891 in Mhow (now officially known as Dr Ambedkar Nagar) in Madhya Pradesh.
• He worked for the promotion of education among the depressed classes.
• He fought for the upliftment of Dalits & their rights in society along with equal rights for women.
• He founded the Scheduled Castes Federation in July 1942 & The Indian Labour Party.
• He stressed the reservations of Dalits in the civil services, and government jobs.
• He was appointed as the chairman of the Drafting Committee.
• He is referred to as the Father of the Indian Constitution.
• Some of his famous works are Annihilation of Caste, Who Were the Shudras?, The Buddha and His Dhamma.
• He was awarded the Bharat Ratna posthumously in 1990.

The correct answer is Kinetic.

• Kinetic energy: The kinetic energy of an object is the energy that it possesses due to its motion.
• The formula of kinetic energy KE = 1/2 mv²
• Kinetic energy is an example of the scalar quantity which means that the quantity has only magnitude and no direction.
• The unit of the kinetic energy is Joule. (J = kg m²/s²)
• An object of mass "m" places at a height "h" possess potential energy which is equal to "mgh", where g = 10 m/s² which is the acceleration due to gravity.

The logic follows here is:-

Each 1^st letter is increasing by 4.

Each 2^nd letter is increasing by 5.

And each 3^rd letter is increasing by 6.

Hence, the correct answer is "FLQ".

Shortcut Trick

Ratio of present ages (P : Q) = 5 : 4. Sum of ratios = 5 + 4 = 9 units.

The total age must be a multiple of 9.

Ratio 9 years ago: P − 9 = 2(Q − 9). Using units: (5x − 9) = 2(4x − 9).

5x − 9 = 8x − 18 ⇒ 3x = 9 ⇒ x = 3.

Sum of present ages = 9 × 3 = 27 years.

∴ The correct answer is 27 years.

Alternate Method

Given: Ratio of present ages of P and Q = 5 : 4. Time gap = 9 years.

Let present age of P = 5x and Q = 4x.

⇒ Age of P nine years ago = 5x − 9

⇒ Age of Q nine years ago = 4x − 9

⇒ According to question: (5x − 9) = 2 × (4x − 9)

⇒ 5x − 9 = 8x − 18

⇒ 18 − 9 = 8x − 5x

⇒ 9 = 3x ⇒ x = 3

⇒ Sum of present ages = 5x + 4x = 9x

⇒ 9 × 3 = 27 years.

∴ The correct answer is 27 years.

Additional Information

Age Ratio Concept

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

Sum of Ages Formula

If the ratio is a:b, then Total Sum = (a + b) × k, where k is the common constant of proportionality.

Future/Past Age Calculation

Age after 'n' years = Present age + n; Age 'n' years ago = Present age − n.

The correct answer is Pune.

Key Points

• National Institute of Virology
• It was established at Pune, Maharashtra in 1952 as Virus Research Centre (VRC).
• It was an outcome of the global programme of the Rockefeller Foundation (RF) of the USA for investigating the Arthropod-Borne viruses.
• The research activities of the Institute are coordinated by a Scientific Advisory Committee (SAC) consisting of eminent scientists.
• The Institute was designated as one of the collaborating laboratories of the World Health Organization (WHO) in 1967 and it started functioning as the regional centre of the WHO for South-East Asia for arbovirus studies from 1969.
• In 1995 it has been redesignated as the WHO Collaborating Centre for Arbovirus and Haemorrhagic Fever Reference and Research and Rapid Diagnosis of Viral Diseases.
• Director- Prof. Priya Abraham

The correct answer is Sodium Bicarbonate.

Key Points

• Sodium bicarbonate is an active ingredient of Antacids.
• It is also known as Sodium hydrogen carbonate (NaHCO3).
• Sodium bicarbonate reduces stomach acid.
• It is used as an antacid to treat heartburn, indigestion, and upset stomach.
• Sodium bicarbonate is a very quick-acting antacid.
• Sodium bicarbonate is a white solid that is crystalline.
• It has a slightly salty, alkaline taste.

Important Points

• The common name of Sodium Bicarbonate (NaHCO3) is baking soda.
• Baking soda is pure sodium bicarbonate.
• Baking powder or Sodium Hydrogen Carbonate NaHCO3.
• Baking powder is a mixture of several chemical compounds including sodium bicarbonate, an acidifying agent and a drying agent. Both baking powder and baking soda have the same formulae.

Additional Information

• Sodium Chloride is Common salt.
• Sodium Hydroxide is Caustic Soda.
• Sodium Carbonate is Washing Soda.

Nothing in the statement suggests that problems make one’s life interesting.

Therefore, conclusion I does not follow.

The statement emphasizes on the need to solve a problem to escape it. However, it does not suggest that the person facing the problem should always have a solution. A problem can be solved by seeking help/advice/suggestions from others. It is just that the final outcome should be the resolution of the problem.

Therefore, conclusion II does not follow.

Given:

Ratio of the incomes of A and B is 4 : 5

Ratio of their expenditures is 2 : 3

A and B saves ₹7,200 and ₹6,000 respectively

Concept Used:

Saving = Income - Expenditure

Calculation:

Let Income of A = 4x and income of B = 5x

According to question,

\(\frac{4x - 7200}{5x - 6000}\)= \(\frac{2}{3}\)

⇒ 12x - 21600 = 10x - 12000

⇒ 2x = 9600

⇒ x = 4800

Income of A = 4x

⇒ 4 × 4800

⇒ 19200.

∴  The income (in ₹) of A is 19,200.

The Correct answer is 212 ºF

Key Points

• The boiling point of water at sea level is 212 ºF, which is equivalent to 100 ºC.
• This boiling point is determined under standard atmospheric pressure, which is approximately 1 atmosphere (101.325 kPa).
• At this temperature, water transitions from the liquid phase to the gas phase, forming steam.
• The boiling point of water can change with variations in altitude and atmospheric pressure. For example, at higher altitudes, where the atmospheric pressure is lower, water boils at a temperature below 212 ºF.
• Boiling water is crucial in various scientific, industrial, and daily applications, such as cooking, sterilization, and generating steam for energy production.
• The boiling point of water is often used as a reference point in thermometry and other scientific measurements.

 Additional Information

• Altitude and Boiling Point Relationship
• As altitude increases, the atmospheric pressure decreases, which reduces the boiling point of water.
• For example, at an altitude of around 5,000 feet, water boils at approximately 203 ºF.
• This principle is significant in mountainous regions and affects cooking times for food preparation.
• Applications of Boiling Water
• Boiling water is widely used for purification and sterilization to kill harmful microbes.
• It is a key component in steam engines, which were historically significant in industrial development.
• Boiling water plays an essential role in scientific experiments and chemical processes.

In the first and second statements, the common code word are ‘ka’ and ýa’ and the common

words are ‘very’ and ‘intelligent’.

So, ‘ka’ and ‘ya’ stand for ‘very’ and ‘intelligent’.

In the first and third statements, the common code word is ‘pu’ and common word is ‘you’.

So, ‘pu’ stands for ‘you’.

Thus, ‘bi’ stands for ‘are’.

Given:

LCM = 648

Ratio = 8 : 9

Formula used:

LCM × HCF = 1^st number × 2^nd number

Calculation:

Let HCF of the number be x

LCM × HCF = 1^st number × 2^nd number

⇒ 648 × x = 8x × 9x

⇒ 648 = 72x

⇒ x = 648/72

⇒ x = 9

So, the numbers are 8x = 8 × 9 = 72 and 9x = 9 × 9 = 81

Difference = 81 – 72 

⇒ 9

∴ The difference between two number is 9

The correct answer is Banaras Hindu University.

• Mahatma Gandhi's first major public appearance in India after returning from South Africa was at the opening of the BHU(Banaras Hindu University) in February 1916.

Key Points

• Gopal Krishna Gokhale was Gandhiji’s acknowledged political mentor.
• On Gokhale’s advice, Gandhiji spent a year travelling around British India, getting to know the land and its people.
• On 4 February 1916, Gandhiji made his first public appearance after returning from South Africa to BHU.
• He addressed the audience in BHU, mostly consisting of impressionable youths, princes, bedecked and bejewelled, etc.

 Important Points

About Gandhiji:

• 1916 - 1^st public appearance --> Banaras Hindu University(BHU)
• 1917 - 1^st Civil Disobedience Movement  --> Champaran, Bihar
• 1918 - 1^st Hunger Strike --> Ahmedabad Mill Strike
• 1918 - 1^st Non Cooperation Movement(NCM) --> Kheda Satyagraha
• 1919 - 1^st mass strike --> Rowlatt Satyagraha
• 1919-1922 - Khilafat Movement & NCM

The pattern followed here is:

Hence, the correct answer is 210.

Given:

Ram can copy 60 pages in 15 hours.

Ram and Riya together can copy 180 pages in 30 hours

Formula Used:

Efficiency = Work done/Time Taken

Calculation:

By using the above formula

The efficiency of Ram is = 60/15= 4pages/hr

The efficiency of Ram and Riya = 180/30 = 6 pages/hr

The efficiency of Riya = 6 - 4 = 2 pages/hr

The time taken by Riya to copy 20 pages will be

⇒ 20/2= 10 hr

∴ The Time taken by Riya is 10 hours.

The correct answer is The Mughal Style.

Key Points

• The Tomb of Mohammed Ghaus is situated in the Gwalior district. The tomb is made in the Mughal style architecture.
• The Tomb was built in the sandstone mausoleum of the Ghaus Mohammed an Afghan prince. It is also designed on early Mughal lines style.
• In this tomb, the pierced stone technique was used which looks as delicate as lace. It is situated on the way to Gwalior fort near Hazira from the Main Railway Station of Gwalior.

Additional Information

• The Mughal architecture is a remarkably decorative and symmetrical amalgam of Turkish,  Indian, and Persian architecture.
• The architecture was first developed and flourished under the reign of The Mughal Emperor Akbar(1556–1605), where it was known for its extensive use of red sandstone as the main building material.

Given: 2^nd October 2003 was Thursday.

Now,

2003 to 2010 = 7 Years (5 Ordinary Year and 2 Leap Year).

So, 2 Leap Year has 4 odd days,

And, 5 Ordinary Year has 5 odd days.

Total odd days = 4 + 5 = 9.

9 odd days → 9/7 = 1 week and 2 odd days.

then, 2^nd October 2010 will be Thursday + 2 = Saturday.

Now, the number of days between 15^th July 2010 to 2^nd October 2010

= 16(July) + 31(August) + 30(September) + 2(October) = 79 days.

= 79days → 79/7 = 11 weeks and 2 odd days.

So, 15^th July 2010 will be Saturday - 2 = Thursday.

Hence, the correct answer is "Option 3".

Shortcut Trick

Total outcomes = 3 Red + 2 Black + 4 Pink = 9

Favorable outcomes (Pink balls) = 4

Probability = Favorable Outcomes ÷ Total Outcomes

P(Pink) = 4/9

∴ The correct answer is 4/9.

Alternate Method

Given:

Number of Red balls = 3

Number of Black balls = 2

Number of Pink balls = 4

Formula:

Probability P(E) = n(E) ÷ n(S)

Where n(E) is the number of favorable outcomes and n(S) is the total number of outcomes.

Calculations:

⇒ Total outcomes n(S) = 3 + 2 + 4

⇒ n(S) = 9

⇒ Favorable outcomes for drawing a Pink ball n(E) = 4

⇒ P(Pink) = 4 / 9

∴ The correct answer is 4/9.

Additional Information

Range of Probability

The probability of any event always lies between 0 and 1 (0 ≤ P(E) ≤ 1).

Sure and Impossible Events

An impossible event has a probability of 0, while a sure event has a probability of 1.

Complementary Events

The sum of the probability of an event and its complement is 1: P(E) + P(not E) = 1.

Narcolepsy is a condition characterized by an extreme tendency to fall asleep whenever in relaxing surroundings.

Debating culture gives an opportunity to school children to critically analyse a topic and argue in favour of what they believe in. It prepares them to put forward their ideas and consider the ideas of their opponents. This teaches them to respect and tolerate others’ opinions rather than creating a feeling of resentment. Argument I gives a vague reason as to why debates should not be conducted. Resentment can be caused due to several reasons and not just because of debating. Therefore, option 2 is the right answer.

Given:

There were two candidates in an election, 10% of voters did not vote and 48 votes were found invalid. The winning candidate got 53% of the total votes and won by 304 votes.

Concept used:

Percentage

Calculation:

Let the total number of voters be 100x

10% of voters did not vote 

Number of voters who vote = 100x - 10x = 90x

48 votes were found invalid

Valid votes = 90x - 48

Votes gained by the winning candidate = \(\frac{{53}}{{100}} \times 100x = 53x\)

Votes gained by the loosing candidate = 90x - 48 - 53x

⇒ 37x - 48

As per the question,

⇒ 53x - (37x - 48) = 304

⇒ 16x = 304 - 48

⇒ 16x = 256

⇒ x = 16

∴ Total number of voters = 100x = 1600

Alternate Method 

Let total number of votes be 100 units,

10% voters did not cast their vote

⇒ Votes polled = 90 units

The winning candidate got 53% of all the voters in the list and won by 304 votes,

⇒ Winning candidate got = 53 units votes

⇒ Other candidate got = 37 units votes

⇒ Difference in votes = 53 units votes - 37 units votes = 304 - 48 = 256 votes

⇒ 16 units = 256

∴ 100 units votes = 256/16 × 100 = 1600 votes

∴ Total number of voters = 1600.

The correct answer is Option 1: Li > Be > B > C > N > O​.

Key Points

• The atomic radius decreases across a period in the periodic table from left to right due to increasing nuclear charge and constant shielding effect.
• Elements in the order Li > Be > B > C > N > O show the correct decreasing trend based on their positions in the periodic table.
• Among these elements, lithium (Li) has the largest atomic radius as it is located at the beginning of the period.
• Oxygen (O), being the last element in the group mentioned, has the smallest atomic radius due to its high effective nuclear charge and strong electron attraction.
• Beryllium (Be) is slightly smaller than lithium due to increased nuclear charge but falls later in the order due to its placement in the second group.

Additional Information

• Atomic Radius: It is the distance from the nucleus of an atom to the outermost shell of electrons. It decreases across a period and increases down a group in the periodic table.
• Effective Nuclear Charge: The net positive charge experienced by an electron in a multi-electron atom. It increases across a period, causing atomic radii to shrink.
• Shielding Effect: Inner electrons shield the outer electrons from the full effect of the nuclear charge, influencing the atomic radius trends.
• Periodic Trends: Across a period, atomic radii decrease due to increased nuclear charge, while down a group, radii increase due to the addition of electron shells.
• Group and Period Placement: Lithium (Group 1), Beryllium (Group 2), and Oxygen (Group 16) showcase varying trends in atomic radii based on their specific positions and electron configurations.

Option 4 is the correct answer. As we see the statements, Both the statements are effects but of independent causes. The number of people establishing industries would have decreased due to the increase in tax last year. As a result of it, the Government is trying to attract the people to set up industries by giving the special package to them.