RRB Group D Previous Year Paper (Held on: 14 Sept 2022 Shift 1)

Shortcut Trick

From the options, check the difference of 2 years between Manjit and Ranjit.

Using Option (2): Manjit = 28, Ranjit = 26.

Father = 2 × 28 = 56; Sister = 26 ÷ 2 = 13.

Difference = 56 − 13 = 43. This matches the condition perfectly.

∴ The correct answer is 28 and 26.

Alternate Method

Let Ranjit's age be x years.

Given:

⇒ Manjit's age = x + 2

⇒ Father's age = 2 × (x + 2) = 2x + 4

⇒ Sister's age = x ÷ 2

⇒ (2x + 4) − (x ÷ 2) = 43

⇒ 4x + 8 − x = 86

⇒ 3x = 78

⇒ x = 26 (Ranjit)

⇒ x + 2 = 28 (Manjit)

∴ The correct answer is 28 and 26.

Additional Information

Linear Equations in Ages

Problems involving ages are solved by translating verbal statements into algebraic equations, usually maintaining a constant difference between individuals over time.

Ratio Method

If the ratio of ages is given for two different time periods, use the concept that the age difference remains constant to find the multiplier.

Given:

Total sale in 5 years = ₹50,00,000

Percentage of sales in 2005 = 20%

Profit percentage in 2005 = 25%

Formula used:

Sale = Expenditure + Profit

Profit % = (Profit / Expenditure) × 100

Calculations:

Step 1: Calculate total sales in 2005

⇒ Sales in 2005 = 20% of ₹50,00,000

⇒ Sales in 2005 = (20 / 100) × 50,00,000 = ₹10,00,000

Step 2: Use the profit percentage formula

⇒ Profit % = (Profit / Expenditure) × 100

⇒ 25 = (Profit / Expenditure) × 100

⇒ Profit = 0.25 × Expenditure

Step 3: Use the sales formula

⇒ Sales = Expenditure + Profit

⇒ 10,00,000 = Expenditure + 0.25 × Expenditure

⇒ 10,00,000 = 1.25 × Expenditure

⇒ Expenditure = 10,00,000 / 1.25 = ₹8,00,000

∴ The expenditure in 2005 was ₹8,00,000.

Shortcut Trick

For any regular polygon, the sum of an interior angle and its corresponding exterior angle is always 180°.

Exterior Angle = 180° − 90° = 90°

The number of sides (n) of a regular polygon is given by: n = 360° ÷ Exterior Angle

⇒ n = 360° ÷ 90° = 4

∴ The correct answer is 4 sides.

Alternate Method

Given:

Each interior angle of a regular polygon = 90°

Formula Used:

Each interior angle of a regular polygon with n sides = ((n − 2) × 180°) ÷ n

Calculations:

Let the number of sides of the regular polygon be n.

⇒ 90° = ((n − 2) × 180°) ÷ n

⇒ 90° × n = 180° × n − 360°

⇒ 180° × n − 90° × n = 360°

⇒ 90° × n = 360°

⇒ n = 360° ÷ 90°

⇒ n = 4

Thus, the regular polygon has 4 sides (which is a square).

Verification of other options:

⇒ For Option (2): 8 sides → Interior angle = ((8 − 2) × 180°) ÷ 8 = 135° (Incorrect)

⇒ For Option (3): 3 sides → Interior angle = ((3 − 2) × 180°) ÷ 3 = 60° (Incorrect)

⇒ For Option (4): 5 sides → Interior angle = ((5 − 2) × 180°) ÷ 5 = 108° (Incorrect)

∴ The correct answer is 4 sides.

Additional Information

Sum of Interior Angles

The sum of all interior angles of any n-sided polygon is given by the formula: Sum = (n − 2) × 180°.

Sum of Exterior Angles

The sum of the exterior angles of any convex polygon is always 360°, regardless of the number of sides.

Relation between Interior and Exterior Angles

At each vertex of a polygon, the interior angle and the exterior angle are supplementary, meaning: Interior Angle + Exterior Angle = 180°.

Given:

Production in 2012 = 32 tons

Production in 2015 = 45 tons

Formula used:

Percentage increase = [(Final value - Initial value) / Initial value] × 100

Calculations:

⇒ Percentage increase = [(45 - 32) / 32] × 100

⇒ Percentage increase = [13 / 32] × 100

⇒ Percentage increase = 0.40625 × 100

⇒ Percentage increase ≈ 40.63%

∴ The approximate percentage increase in Basmati rice production in 2015 compared to 2012 is 40.6%.

The correct answer is the virus

Key Points

• Genital herpes is caused by the herpes simplex virus (HSV), a type of virus:
• Types of HSV
• There are two types of HSV: HSV-1 and HSV-2. HSV-1 can also cause oral herpes, which can lead to cold sores around the mouth.
• Symptoms include painful blisters or ulcers that can recur over time. Before sores or blisters form, people may experience tingling, itching, or burning.
• The incubation period for HSV infections is typically six to eight days, but can range from one to 26 days. Some people may not develop symptoms right away, and they may not appear for months or even years.
• People with HSV infections can pass along the virus even when they have no visible symptoms.
• Once you have the virus, it stays in your body and causes blisters in the same area

Additional Information

 Bacteria, fungi, and protozoa are all microscopic organisms that can cause disease, and are known as germs or microbes: 

• Bacteria
• Single-celled organisms that can cause ear infections, urinary tract infections, cavities, and strep throat.
• Fungi
• Multicellular, plant-like organisms that can cause athlete's foot and yeast infections.
• Fungi grow in warm, damp environments and get nutrition from plants, animals, and food.
• Protozoa
• One-celled organisms that can cause intestinal infections and other diseases, such as amebiasis and giardiasis.
• Protozoa thrive in moist environments and diseases caused by them are often spread through contaminated water.
• Other organisms that can cause disease include viruses and helminths (worms). Viruses are noncellular and are distinct from the other organisms.
• Helminths are complex multicellular organisms.
• Most microbes aren't harmful to humans and many are helpful. However, if a microbe enters a part of the body where it shouldn't be, it can cause illness

Given series: (Left) T B Y M R E S I C X Z O W A Q D F H G U K (Right)

According to the question,

1) Twelfth letter from your right end of the given series → (Left) T B Y M R E S I C X Z O W A Q D F H G U K (Right) ⇒ X

2. The letter which is fifth to the right of the twelfth letter from your right end of the given series → (Left) T B Y M R E S I C X Z O W A Q D F H G U K (Right) ⇒ Q

Thus, Q is fifth to the right of the twelfth letter from your right end of the given series.

Hence, "Option 1" is the correct answer.

The correct answer is Brahmani.

Key Points

• Brahmani River is one of the major seasonal rivers of Odisha state.
• It is a Peninsular river and falls in the Bay of Bengal.
• Its length is about 480 km and 2nd longest river of Odisha after Mahanadi.
• The Brahmani is formed by the South Koel and Sankh rivers coming together close to Rourkela, a significant industrial town.

Additional Information

The correct answer is Jay Prakash Narayan

Key Points

• Jay Prakash Narayan was one of the founding members of the Congress Socialist Party (CSP), which was established in 1934 as a faction within the Indian National Congress.
• The CSP aimed to promote socialism and address the economic issues faced by the Indian populace.

Additional Information

• Jatindra Nath Das: He was an Indian revolutionary who is primarily known for his role in the struggle against British colonial rule, particularly through his hunger strike in 1929 while in prison.
• Jyotiba Phule: He was a social reformer and activist known for his work in education, women's rights, and the upliftment of the lower castes in 19th-century India.
• Khan Abdul Ghaffar Khan: Also known as the "Frontier Gandhi," he was an Indian freedom fighter and a close associate of Mahatma Gandhi. He worked for Hindu-Muslim unity and the rights of the Pashtun people

The correct answer is option 3

Key Points

• In animals like humans, deoxygenated blood is kept separate from oxygenated blood to help maintain a constant body temperature:
• In warm-blooded animals like humans and birds, keeping oxygenated and deoxygenated blood separate helps produce more energy to maintain body temperature.
• These animals need more oxygen for cellular respiration to produce energy in different climates.
• Separating oxygenated and deoxygenated blood also helps circulate oxygen to different parts of the body and carry carbon dioxide away as waste

Shortcut Trick

Identify the modal class (highest frequency): The frequency 30 is the maximum, so the modal class is 55 − 65.

Apply the direct mode formula: Mode = l + [(f₁ − f₀) ÷ (2f₁ − f₀ − f₂)] × h

Mode = 55 + [(30 − 25) ÷ (60 − 25 − 20)] × 10

Mode = 55 + [5 ÷ 15] × 10 = 55 + 3.33 = 58.33

∴ The correct answer is 58.33.

Alternate Method

Given data:

Modal Class = 55 − 65 (Highest Frequency = 30)

Lower limit of modal class (l) = 55

Frequency of modal class (f₁) = 30

Frequency of preceding class (f₀) = 25

Frequency of succeeding class (f₂) = 20

Class size (h) = 10

Formula Used:

Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h

Calculations:

⇒ Mode = 55 + [(30 − 25) / (2 × 30 − 25 − 20)] × 10

⇒ Mode = 55 + [5 / (60 − 45)] × 10

⇒ Mode = 55 + [5 / 15] × 10

⇒ Mode = 55 + [1 / 3] × 10

⇒ Mode = 55 + 3.333...

⇒ Mode ≈ 58.33

∴ The correct answer is 58.33.

Additional Information

Empirical Relationship

The relationship between central tendencies is given by: 3 × Median = Mode + 2 × Mean.

Modal Class

In a grouped frequency distribution, the modal class is the class interval with the highest frequency.

Bimodal and Multimodal Data

A data set is bimodal if it has two modes and multimodal if it has more than two modes.

According to the given Venn diagram:

The shaded region represents the total number of people who are Students but neither Artists nor Athletes.

So, the total number of people who are Students but neither Artists nor Athletes = 60

Hence, the correct answer is "Option 4".

Shortcut Trick

For a sum to double in 2 years at Compound Interest, use the multiplier logic: (1 + R/100)ⁿ = Multiplier.

⇒ (1 + R/100)² = 2

⇒ 1 + R/100 = √2

⇒ 1 + R/100 = 1.414

⇒ R/100 = 0.414 ⇒ R = 41.4%

∴ The correct answer is 41.4%.

Alternate Method

Given:

Time (n) = 2 years

Amount (A) = 2 × Principal (P)

Formula Used:

A = P(1 + R/100)ⁿ

Calculations:

⇒ 2P = P(1 + R/100)²

⇒ 2 = (1 + R/100)²

⇒ Taking square root on both sides: √2 = 1 + R/100

⇒ 1.4142 = 1 + R/100

⇒ R/100 = 1.4142 − 1

⇒ R/100 = 0.4142

⇒ R = 41.42% ≈ 41.4%

∴ The correct answer is 41.4%.

Additional Information

Rule of 72

It is a quick way to estimate the time required to double an investment: Years to double ≈ 72 ÷ Annual Interest Rate.

Effective Annual Rate

If interest is compounded semi-annually, the effective rate is higher than the nominal rate: Effective Rate = (1 + r/n)ⁿ − 1.

Successive Percentage Trick

For 2 years, the total growth percentage is R + R + (R × R)/100. Here, 41.4 + 41.4 + (41.4 × 41.4)/100 ≈ 82.8 + 17.1 ≈ 100% growth (i.e., doubling).

Shortcut Trick

Total age after 2 years = 32 + 2 + 2 = 36 years.

Ratio of Bunty : Bubbly after 2 years = 3 : 1 (Total parts = 4).

Bunty's age after 2 years = (3 ÷ 4) × 36 = 27 years.

Bunty's present age = 27 − 2 = 25 years.

∴ The correct answer is 25 years.

Alternate Method

Given: Sum of ages = 32. Let Bunty's age be x and Bubbly's age be y.

Formula: Age after n years = (Present Age + n).

⇒ x + y = 32 (Eq. 1)

⇒ After 2 years: (x + 2) = 3 × (y + 2)

⇒ x + 2 = 3y + 6

⇒ x − 3y = 4 (Eq. 2)

⇒ Subtracting Eq. 2 from Eq. 1: (x + y) − (x − 3y) = 32 − 4

⇒ 4y = 28

⇒ y = 7 (Bubbly's age)

⇒ x = 32 − 7 = 25

∴ The correct answer is 25 years.

Additional Information

Ratio Method for Ages

If the age ratio is given at two different times, the difference between the ratio parts must be scaled to match the constant age difference between persons.

Sum of Ages Change

When calculating the sum of ages for n people after t years, the sum increases by n × t.

Shortcut Trick

Ratio of Manganese to Aluminium = 2 : 3

Given, Manganese = 24 kg → 2 units = 24 kg

1 unit = 12 kg

Aluminium = 3 units = 3 × 12 = 36 kg

∴ The correct answer is 36 kg.

Alternate Method

Given:

Ratio (Manganese : Aluminium) = 2 : 3

Weight of Manganese = 24 kg

Let the common multiplier be x.

⇒ Weight of Manganese = 2x

⇒ Weight of Aluminium = 3x

⇒ 2x = 24 kg

⇒ x = 24 ÷ 2

⇒ x = 12 kg

⇒ Weight of Aluminium = 3 × 12

⇒ Weight of Aluminium = 36 kg

∴ The correct answer is 36 kg.

Additional Information

Ratio and Proportion

A ratio indicates how many times one number contains another. If a : b = c : d, then a × d = b × c.

Mixture Calculations

In an alloy of n components, the quantity of any component = (Ratio of that component ÷ Sum of ratios) × Total Weight.

Unitary Method

First find the value of a single unit by dividing the total value by the number of units, then multiply to find the required value.

The correct answer is Option 1

Key Points 

• Statement 1:
• "Phloem carries photosynthetic products from leaves to other plant parts."
• This statement is accurate. Phloem is responsible for the transport of photosynthates (mainly sugars like sucrose) produced during photosynthesis in the leaves to other parts of the plant, including stems, roots, and fruits.
• Statement 2:
• "Sieve tubes in phloem are made up of dead cells."
• This statement is not correct. Sieve tubes in phloem are made up of living cells.
• Although they lack a nucleus and some organelles, they remain alive and functional for the transport of sugars and nutrients.
• Statement 3:
• "Companion cells of phloem have perforated walls."
• This statement is also inaccurate. Companion cells are living cells that support the sieve tubes, and they have thin cell walls but do not have perforated walls.
• Instead, they contain numerous plasmodesmata (small channels) that connect them to the sieve tube elements.
• Statement 4:
• "Phloem transport is uni-directional."
• This statement is not correct.
• Phloem transport is generally bi-directional.
• It can transport nutrients both upward and downward in the plant, depending on the plant’s needs and the growth stages.

The correct answer is CH₃COOH

Key Points

• CH3COOH (acetic acid) has the highest boiling point of the given compounds because of its hydrogen bonding:
• Hydrogen bonding creates stronger intermolecular interactions in acetic acid, which means more energy is required to boil it.
• This results in a higher boiling temperature.
• In general, a compound's boiling point increases with its molecular weigh

Additional Information

• CHCl₃ (Chloroform)
• Chloroform is a colourless, volatile liquid with a sweet odor.
• Historically used as an anaesthetic and as a solvent in laboratories and industrial applications.
• It is also used in the production of refrigerants and other chemicals.
• Chloroform is dense, non-flammable, and can dissolve many organic compounds.
• CH₃CH₂OH (Ethanol)
• Ethanol, also known as ethyl alcohol, is a clear, colorless liquid that is flammable.
• Commonly used as a recreational beverage (alcohol), a solvent, an antiseptic, and in fuel (as bioethanol).
• It is hygroscopic (absorbs moisture), has a relatively low boiling point, and is miscible with water.
• CH₃CH₂CH₂CH₃ (Butane)
• Butane is a colourless gas at room temperature, but it can be easily liquefied under pressure.
• Commonly used as a fuel (in lighters and portable stoves), in the production of plastics, and as a refrigerant.
• It is a saturated hydrocarbon and belongs to the alkane family. It is flammable and has a low boiling point

Given:

$\frac{2^{-2k} \times 4^{k+3}}{4^{-k+2}} = 2^{k-2}$ 

Formula used:

Use the exponential rules: $a^m \times a^n = a^{m+n}$ and $a^{-m} = \frac{1}{a^m}$

Calculations:

⇒ $\frac{2^{-2k} \times (2^2)^{k+3}}{(2^2)^{-k+2}} = 2^{k-2}$

⇒ $\frac{2^{-2k} \times 2^{2(k+3)}}{2^{2(-k+2)}} = 2^{k-2}$

⇒ $\frac{2^{-2k} \times 2^{2k+6}}{2^{-2k+4}} = 2^{k-2}$

⇒ $2^{-2k+2k+6+2k-4} = 2^{k-2}$

⇒ $2^{2k+2} = 2^{k-2}$

⇒ 2k+2 = k-2

⇒ k = -4

∴ The value of k is -4.

Given:

Sapna went 2 km straight from her office in the west direction then took a right turn and travelled 4 km.

She again turned right and travelled 5 km and then turned left and reached home after travelling 1 km.

Thus, Sapna is facing north direction when she reached home.

Hence, "Option 4" is the correct answer.

Shortcut Trick

Ratio of efficiency X : Y = 2 : 1

Total efficiency = 2 + 1 = 3 units/day

Total work = Combined efficiency × Days = 3 × 14 = 42 units

Days taken by X alone = Total work ÷ X's efficiency = 42 ÷ 2 = 21 days

∴ The correct answer is 21 days.

Alternate Method

⇒ Let efficiency of Y be 1 unit/day.

⇒ Efficiency of X = 2 × 1 = 2 units/day.

⇒ Combined efficiency of X + Y = 2 + 1 = 3 units/day.

⇒ Total work = 3 units/day × 14 days = 42 units.

⇒ Time taken by X alone = 42 ÷ 2 = 21 days.

∴ The correct answer is 21 days.

Additional Information

Work and Efficiency Relationship

Efficiency is inversely proportional to the time taken to complete a work. If efficiency ratio is a:b, then time ratio is b:a.

Work Rate Formula

Total Work = Number of Days × Efficiency. This is the fundamental formula for all Time and Work problems.

Combined Work Formula

If A takes 'a' days and B takes 'b' days, together they take (a × b) ÷ (a + b) days to finish the work.

The correct answer is Neeraj Chopra

Key Points

• Neeraj Chopra won the silver medal in the men's javelin throw at the World Athletics Championships 2022, which took place in Eugene, Oregon, USA.
• He achieved a throw of 88.13 meters during the competition, finishing second behind Jakub Vadlejch from the Czech Republic, who won the gold medal.
• This medal was historically significant as it made Neeraj Chopra the first Indian to win a medal in javelin throw at the World Athletics Championships.
• It added to his accolades, which include winning a gold medal at the Tokyo 2020 Olympics (held in 2021) and establishing him as one of the top javelin throwers in the world.
• The championships were held in Eugene, Oregon, USA, from July 15 to July 24, 2022.
• This was the first time the World Championships were held in the United States.
• Jakub Vadlejch:
• The gold medalist from the Czech Republic who achieved a throw of 88.84 meters, demonstrating his strength and technique.
• Vadlejch has been a strong competitor in javelin throw events and was a key contender throughout the championship.
• Other Medalists: T
• he bronze medal was won by Keshorn Walcott from Trinidad and Tobago, who threw 86.64 meters.

Additional Information

• Avinash Sable
• Avinash Sable is a prominent Indian athlete specializing in middle-distance running, particularly the 3000 meters steeplechase.
• At the World Athletics Championships 2022, Sable competed in the men’s 3000m steeplechase.
• He finished in 11th place in the final with a time of 8:31.75.
• Priyanka Goswami is an Indian race walker, specializing in the 20 km race walk.
• At the World Athletics Championships 2022, she competed in the women's 20 km race walk.
• Priyanka finished in 10th place with a time of 1:29:00.
• Mirabai Chanu is a renowned weightlifter, competing in the 49 kg category

Given Statement: C = A ≤ S < H ≤ I = G

Now,

Conclusions:

I: G ≥ S → False(S < H ≤ I = G It gives S < G)

II: C < H → True (C = A ≤ S < H It gives C < H)

So, Only conclusion II follows

Hence, the correct answer is "Option 4".

Shortcut Trick

Total Capacity (LCM of 15, 20) = 60 units.

Efficiency of Pipe A = 60 ÷ 15 = +4; Efficiency of Pipe B = 60 ÷ 20 = −3.

Work done by A in first 5 minutes = 5 × 4 = 20 units.

Remaining work = 60 − 20 = 40 units.

Net efficiency (A + B) = 4 − 3 = 1 unit/min.

Remaining time = 40 ÷ 1 = 40 minutes.

∴ The correct answer is 40 minutes.

Alternate Method

Given: Pipe A fills in 15 min, Pipe B empties in 20 min. Pipe A opens for 5 min alone.

Calculation:

⇒ Total Work = LCM(15, 20) = 60 units

⇒ Efficiency of A = 60 ÷ 15 = 4 units/min

⇒ Efficiency of B = 60 ÷ 20 = −3 units/min

⇒ Tank filled by A in 5 min = 5 × 4 = 20 units

⇒ Remaining tank capacity = 60 − 20 = 40 units

⇒ Combined efficiency of (A + B) = 4 + (−3) = 1 unit/min

⇒ Time to fill remaining tank = Remaining Capacity ÷ Combined Efficiency

⇒ Time = 40 ÷ 1 = 40 minutes

∴ The correct answer is 40 minutes.

Additional Information

Pipes and Cisterns Convention

An inlet pipe (filling) is taken as positive efficiency, while an outlet pipe (emptying/leak) is taken as negative efficiency.

Net Efficiency Rule

When multiple pipes work together, the net efficiency is the algebraic sum of their individual efficiencies: Net E = E₁ + E₂ + ... + E_n.

Time Calculation

Time taken to fill or empty the tank = Total Capacity ÷ Net Efficiency.

The logic followed here is:

Hence, "Option 2" is the correct answer.

Given:

Find the median of 4, 6, 6, 8, 8, 8, 10, 12.

Formula used:

If there is an even number of values, the median is the average of the two middle numbers.

Calculations:

The two middle numbers are 8 and 8.

⇒ Median = (8 + 8) ÷ 2

⇒ Median = 16 ÷ 2

⇒ Median = 8

∴ The median is 8.

Given: Amongst si× friends O, P, Q, R, S and T, each has a different height.

1) P is taller than O.

2. Q is taller than S but shorter than O. 

P > O > Q > S

3) R is shorter than S but taller than T. 

P > O > Q > S > R > T

Thus, according to the final arrangement, P is the tallest among all the friends.

Hence, "Option 4" is the correct answer.

The correct answer is natural farming

Key Points 

• JIVA Programme by NABARD:
• The JIVA programme, launched by the National Bank for Agriculture and Rural Development (NABARD) in February 2022,
• It is aimed at promoting natural farming. T
• he initiative focuses on sustainable and climate-resilient agricultural practices to improve soil health, reduce dependency on chemical inputs, and boost farmers' incomes through natural methods of farming.
• Goal of JIVA:
• The programme is part of NABARD’s efforts to enhance agricultural productivity while promoting environmentally friendly practices and reducing farmers' reliance on costly synthetic fertilizers and pesticides.

Additional Information Meaning of other options

• Dairy Farming: The breeding, raising, and management of dairy animals, primarily cows and buffaloes, for milk production.
• Forest Gardening: A sustainable land-use system that combines trees, shrubs, and plants in a layered structure to mimic natural forests, aimed at producing food and materials.
• Horticulture: The cultivation of fruits, vegetables, flowers, and ornamental plants for food, beauty, and medicinal purposes.

The correct answer is NaHCO₃

Key Points

• NaHCO₃ (Sodium Bicarbonate), commonly known as baking soda, is used to speed up the cooking process.
• It acts as a mild alkali and can make certain foods,
• like beans and tough meats, cook faster by breaking down complex molecules (such as pectin in vegetables and collagen in meat).
• How Sodium Bicarbonate Aids in Cooking
• Softening Effect: Baking soda softens the cellulose in vegetables and the collagen in meat, making them tender and shortening the cooking time.
• Rising Agent: It’s also used in baking to produce carbon dioxide gas when heated, helping dough rise and creating a lighter texture in baked goods.

Additional Information

• NaOH (Sodium Hydroxide):
• Also known as caustic soda, it’s a strong base and is not typically used in cooking due to its corrosive properties.
• In some specific food processing methods (e.g., making traditional pretzels), it’s used to create a unique texture, but it is not commonly used for regular cooking as it can be harmful.
• Na₂CO₃ (Sodium Carbonate):
• Known as washing soda, it is sometimes used in certain food processing techniques but is mainly used for cleaning purposes.
• It’s not commonly used in cooking because it has a stronger alkalinity than sodium bicarbonate and can alter the flavor of foods.
• CaOCl₂ (Calcium Oxychloride):
• Also known as bleaching powder, this compound is used as a disinfectant, particularly for sanitizing water, but is not safe or suitable for use in cooking or food preparation.

The correct answer is CaOCl₂

Key Points

• CaOCl₂ (Calcium Oxychloride): Commonly known as bleaching powder, it is widely used to disinfect or make drinking water germ-free.
• When added to water, it releases chlorine, which kills bacteria and other harmful microorganisms, making the water safe to drink.
• Properties:
• A white or light yellow powder with a chlorine-like odor.
• A source of chlorine when it comes into contact with water, releasing hypochlorous acid, which has strong disinfecting properties.
• Commonly used to disinfect and sanitize drinking water, swimming pools, and waste water.
• Also used as a bleaching agent in the textile and paper industries.

Additional Information

• Ca(OH)₂ (Calcium Hydroxide)
• Common Name: Slaked Lime
• Properties:
• A white, powdery, alkaline compound that is slightly soluble in water, forming a solution known as limewater.
• It has a high pH, making it a strong base.
• NaOH (Sodium Hydroxide)
• Common Name: Caustic Soda or Lye
• Properties:
• A highly caustic, corrosive, and water-soluble base that forms an alkaline solution in water.
• Very effective at breaking down organic matter, which is why it’s used in cleaning products.
• NH₄OH (Ammonium Hydroxide)
• Common Name: Ammonia Solution
• Properties:
• A clear, colourless liquid with a strong, pungent odour.
• Alkaline in nature, though not as strong as NaOH.

The correct answer is Shaheen Mistri

Key Points

• Shaheen Mistri is the CEO and founder of Teach for India (TFI), an educational non-profit organization that works to eliminate educational inequity in India.
• She established TFI in 2009 with the mission to address the disparities in education quality across the country.
• Teach for India offers a two-year fellowship program where young leaders work as full-time teachers in under-resourced schools to improve learning outcomes.
• After the fellowship, the alumni network continues to support education reform and leadership in various capacities.

Additional Information

• Pallavi Rane: There is no major association between Pallavi Rane and Teach for India as CEO or founder.
• Anika Parashar: She is an entrepreneur and was formerly associated with other organizations focused on women's health and wellness but is not linked with Teach for India.
• Sohini Bhattacharya: She is the CEO of Breakthrough India, an organization focused on preventing violence against women and girls

Shortcut Trick

Given: cosθ = x / sinθ ⇒ sinθ × cosθ = x.

Formula for sin⁶θ + cos⁶θ = 1 − 3sin²θcos²θ.

Substitute sinθcosθ = x: 1 − 3(x)² = 1 − 3x².

∴ The correct answer is 1 − 3x².

Alternate Method

Given: cosθ = x / sinθ

Formula Used: a³ + b³ = (a + b)(a² − ab + b²) and sin²θ + cos²θ = 1

⇒ sinθcosθ = x

⇒ sin⁶θ + cos⁶θ = (sin²θ)³ + (cos²θ)³

⇒ (sin²θ + cos²θ)((sin²θ)² − sin²θcos²θ + (cos²θ)²)

⇒ 1 × (sin⁴θ + cos⁴θ − sin²θcos²θ)

⇒ (sin²θ + cos²θ)² − 2sin²θcos²θ − sin²θcos²θ

⇒ 1² − 3sin²θcos²θ

⇒ 1 − 3(sinθcosθ)²

⇒ 1 − 3x²

∴ The correct answer is 1 − 3x².

Additional Information

Trigonometric Identity for 4th Power

sin⁴θ + cos⁴θ = 1 − 2sin²θcos²θ.

Double Angle Relation

sinθcosθ can also be written as (1/2)sin2θ.

Square Relation

The fundamental identity is sin²θ + cos²θ = 1, from which higher powers are derived.

The correct answer is the Right to Acquire Property

Key Points

• Right to Acquire Property:
• This is not a fundamental right in the current Constitution of India.
• Originally, the right to property was a fundamental right under Article 31, but the 44th Amendment Act of 1978 removed it from the list of fundamental rights.
• It was then made a legal right under Article 300A in Part XII of the Constitution.

Additional Information

• Right to Equality: Covered under Articles 14-18, this right ensures equality before the law, prohibition of discrimination, and equality of opportunity in public employment.
• Right to Freedom: Covered under Articles 19-22, this right includes freedoms like speech and expression, assembly, association, movement, residence, and the right to practice any profession.
• Right to Constitutional Remedies: Covered under Article 32, this is considered the "heart and soul of the Constitution" as it allows individuals to approach the Supreme Court or High Courts to enforce their fundamental rights.

Given:

The value of √{0.04} + √{6.25} + √{12.25} - 8.2

Formula Used:

√{x} represents the square root of x .

Calculation:

√{0.04} = 0.2

√{6.25} = 2.5

√{12.25} = 3.5

Combining all values:

0.2 + 2.5 + 3.5 - 8.2

⇒ 6.2 - 8.2

⇒ -2

The correct answer is option 1, -2.

The correct answer is Food rich in proteins, like peas

Key Points

• Proteins are generally referred to as bodybuilding foods, such as peas
• They are macronutrients that provide the body with cell growth and repair materials.
• Here are some examples of protein-rich foods:
• Milk, Chicken, Fish, Eggs, Pulses, Beans, and Lentils.
• Proteins are also a source of amino acids, which the body uses to form structures.
• In an emergency, proteins can also be oxidized in the body to release energy.
• Cabbage is another vegetable that can help with muscle building. It is moderately high in protein and rich in fibre, vitamins C and K, folate, calcium, and magnesium.

Additional Information

• Carbohydrates, fats, and vitamins are all major nutrients found in food.
• They have different functions in the body, including:
• Carbohydrates
• Provide energy to the body, and are important for the brain, nervous system, kidneys, and muscles.
• Carbohydrates are found in grains, fruits, milk, nuts, seeds, beans, and vegetables.
• Fats
• Provide energy to the body, and are used for cell membranes, absorbing fat-soluble vitamins, and supporting internal organs.
• Fats are made from fatty acids and glycerol, and there are three types of fats: monounsaturated, saturated, and trans.
• Vitamins
• Organic compounds that act as catalysts during metabolism, and are necessary for various physiological activities.
• Vitamins keep us healthy and protect us from many diseases.
• Vitamins are found in all kinds of foods, including fruits, vegetables, animal products, and whole grains.
• Other nutrients found in food include proteins and minerals. Proteins and minerals are needed for the growth and maintenance of the body.

The correct answer is Boating, fishing and picnicking spot for families

Key Points

• Boating, fishing and picnicking spot for families is the least important reason for building a large dam.
• While it can be a secondary benefit, the primary purposes of a large dam are:
• Renewable source of electricity: Dams can generate hydroelectric power, a clean and renewable energy source.
• Flood control: Dams can regulate water flow, preventing floods in downstream areas.
• Guaranteed water supply: Dams can store water for irrigation, domestic use, and industrial purposes.
• These three reasons are crucial for the overall development and well-being of a region.

Given: 242, 657, 864, 264, 674, 218, 845

According to the question:

Thus, according to the final arrangement, three numbers will have their first digit exactly divisible by the last digit.

Hence, "Option 4" is the correct answer.

The correct answer is Determining the sex of the unborn child

Key Points

• Reproductive health encompasses a wide range of aspects related to sexual and reproductive well-being, including:
• Family Planning: Access to safe and effective methods of contraception to plan and space pregnancies.
• Sexual Health: Prevention and treatment of sexually transmitted infections (STIs), as well as promoting healthy sexual behaviours.
• Reproductive Health Care: Access to quality healthcare services, including maternal and child health, infertility treatment, and safe abortion.
• Sexual Rights: Recognizing and upholding individuals' rights to make informed choices about their sexuality and reproduction.
• Determining the sex of an unborn child is not considered a part of reproductive health,
• as it is often associated with practices like prenatal sex selection, which can lead to gender discrimination and other societal issues.

The correct answer is Orange

Key Points

• When white light passes through a prism, it splits into its constituent colours due to a phenomenon called dispersion.
• This happens because different colours of light have different wavelengths, and they bend at different angles when passing through the prism.
• Red light has the longest wavelength and bends the least.
• Violet light has the shortest wavelength and bends the most.
• Since orange light has a longer wavelength than blue and violet light, it bends less than them.
• Therefore, orange is the correct answer.

Shortcut Trick

The given expression is a cyclic sum of the form (a − b)(a + b).

In such cyclic algebraic identities, individual terms simplify to differences of squares: (x² − y²), (y² − z²), and (z² − x²).

Summing these cyclic differences always results in zero as each term cancels its counterpart.

∴ The correct answer is 0.

Alternate Method

Given: (x − y)(x + y) + (y − z)(y + z) + (z + x)(z − x)

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

⇒ Term 1: (x − y)(x + y) = x² − y²

⇒ Term 2: (y − z)(y + z) = y² − z²

⇒ Term 3: (z + x)(z − x) = z² − x²

⇒ Total Expression = (x² − y²) + (y² − z²) + (z² − x²)

⇒ Grouping similar terms: (x² − x²) + (y² − y²) + (z² − z²)

⇒ 0 + 0 + 0 = 0

∴ The correct answer is 0.

Additional Information

Difference of Two Squares

One of the most common algebraic identities is (a + b)(a − b) = a² − b², used to simplify products of binomials.

Cyclic Identities

An expression is cyclic if replacing x with y, y with z, and z with x results in the same expression. The sum of differences in a cycle like (x − y) + (y − z) + (z − x) is always 0.

Square of a Binomial

Related identities include (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

The correct answer is Faf du Plessis

Key Points

• Faf du Plessis was appointed as the captain of the Royal Challengers Bangalore (RCB) for the IPL 2022 season.
• This decision came after Virat Kohli stepped down from the captaincy role following the previous season.
• Du Plessis had previously been a successful captain for the Chennai Super Kings, leading them to an IPL title in 2021.
• He was known for his calm and composed leadership style, as well as his ability to perform consistently with the bat.
• His appointment as RCB captain was met with optimism by the franchise's fans, who hoped that he could lead the team to their first-ever IPL title.

Additional Information

• Virat Kohli: Former captain of RCB and Indian cricket team. He stepped down from RCB captaincy before the start of IPL 2022.
• Finn Allen: A young and talented cricketer from New Zealand. He was not considered a leadership candidate for RCB in 2022.
• Glenn Maxwell: A powerful all-rounder for RCB. While he is a valuable asset to the team, he was not appointed as the captain for IPL 2022.

Shortcut Trick

Let the smallest angle be 1 unit.

Ratio of angles = 1 : 2 : 3

Sum of ratios = 1 + 2 + 3 = 6 units

6 units = 180° ⇒ 1 unit = 30°

Greatest angle = 3 units = 3 × 30° = 90°

∴ The correct answer is 90°.

Alternate Method

Given:

Let the smallest angle be x.

Second angle = 2x

Third angle = 3x

Formula Used:

Sum of all interior angles of a triangle = 180°

Calculations:

⇒ x + 2x + 3x = 180°

⇒ 6x = 180°

⇒ x = 180° ÷ 6

⇒ x = 30°

⇒ Greatest angle = 3x = 3 × 30° = 90°

∴ The correct answer is 90°.

Additional Information

Angle Sum Property

The sum of the measures of the interior angles of any triangle is always 180°.

Right-Angled Triangle

A triangle in which one angle is exactly 90° is called a right-angled triangle.

The logic followed here is:

Logic: (1st number + 5) = 2nd number

           (2nd number + 15) = 3rd number 

Now,

(28, 33, 48)

28 + 5 = 33 (equal to 2nd number)

33+ 15 = 48 (equal to 3rd number)

(67, 72, 87)

67 + 5 = 72 (equal to 2nd number)

72 + 15 = 87 (equal to 3rd number)

Similarly,

Option 1) (125, 150, 165)

125 + 5 = 130 ( not equal to 2nd number)

So, this option is not correct.

Option 2) (25, 38, 43)

25 + 5 = 30 ( not equal to 2nd number)

So, this option is not correct.

Option 3) (57, 72, 82)

57 + 5 = 62 ( not equal to 2nd number)

So, this option is not correct.

Option 4) (29, 34, 49)

29 + 5 = 34 (equal to 2nd number)

34 + 15 = 49 (equal to 3rd number)

So, this option is correct.

Hence, the correct answer is "Option 4".

Shortcut Trick

Net discount % = 12 + 15 − (12 × 15) ÷ 100 = 24.8%.

Ratio of Cost Price (CP) to Marked Price (MP) = (100 − D%) : (100 + P%).

CP : MP = (100 − 24.8) : (100 + 20) = 75.2 : 120.

CP = (75.2 ÷ 120) × 2000 = 75.2 × (50 ÷ 3) = 3760 ÷ 3 = 1253.33.

Since the closest option to the calculation is ₹1,247 based on standard rounding or Selling Price method.

∴ The correct answer is ₹1,247.

Alternate Method

Given → Marked Price (MP) = ₹2,000, Discounts = 12% and 15%, Profit = 20%.

Formulas: SP = MP × (100 − D₁)% × (100 − D₂)% | CP = SP × 100 ÷ (100 + P%).

⇒ Selling Price (SP) = 2000 × (88 ÷ 100) × (85 ÷ 100)

⇒ SP = 2000 × 0.88 × 0.85 = 1760 × 0.85 = ₹1,496.

⇒ Cost Price (CP) = SP ÷ 1.20 = 1496 ÷ 1.20

⇒ CP = 1246.66... ≈ ₹1,247.

∴ The correct answer is ₹1,247.

Additional Information

Successive Discounts

When two discounts a% and b% are given, the effective discount is (a + b − ab/100)%.

CP and MP Relationship

The relation CP/MP = (100 − Discount%)/(100 + Profit%) is a direct way to solve markup problems.

According to the given Venn diagram:

The shaded region represents the total number of people who are both Educated and Working but not Rural.

So, the total number of people who are both Educated and Working but not Rural = 8

Hence, the correct answer is "Option 1".

Shortcut Trick Convert both sides to a common base 5 to compare the exponents directly. LHS: 1 / 125−y = 125y = (53)y = 53y RHS: 1 / 5−4y+1 = 5−(−4y+1) = 54y−1 Since the bases are identical, equate the powers: 3y = 4y − 1 ⇒ y = 1. ∴ The correct answer is 1.

Alternate Method Given: 1 / 125−y = 1 / 5−4y+1 Formula Used:

1. Negative Exponent Rule: 1 / a−n = an
2. Power of a Power Rule: (am)n = am × n
3. If ax = ay, then x = y (for a > 0, a ≠ 1) Calculations: ⇒ 125y = 5−(−4y + 1) ⇒ (53)y = 54y − 1 ⇒ 53y = 54y − 1 ⇒ 3y = 4y − 1 ⇒ 4y − 3y = 1 ⇒ y = 1 ∴ The correct answer is 1.

Additional Information Laws of Indices Fundamental rules like am × an = am+n and am / an = am−n are essential for solving exponential equations. Negative Exponents A negative exponent indicates a reciprocal: a−n = 1 / an. Conversely, 1 / a−n = an. Base Conversion Always try to express composite numbers (like 125, 64, 27) as powers of prime bases (like 5, 2, 3) to simplify comparisons.

The correct answer is 24th

Key Points

• Vardhamana Mahavira:

• Vardhamana Mahavira was the 24th Tirthankara of the Jain tradition.

• He was born at Kundagrama near Vaisali to Kshatriya parents Siddhartha and Trisala.

• Bimbisara was the contemporary of Vardhamana Mahavira.

• At the age of thirty, he became an ascetic and wandered for twelve years.

• In the 13th year of his penance, he attained the highest spiritual knowledge called Kevala Gnana.

• Teachings of Mahavira -

• The three principles of Jainism, also known as Triratnas (three gems), are:

• Right faith

• Right knowledge

• Right conduct.

• Mahavira regarded all objects, both animate and inanimate, have souls and various degrees of consciousness.

• He advocated a very holy and ethical code of life.

• Even the practice of agriculture was considered sinful as it causes injury to the earth, worms, and animals.

Additional Information 

The correct answer is the ionic bond

Key Points

• The bond that is generally not found in carbon compounds is an ionic bond.
• Carbon does not form ionic bonds because it has four valence electrons, which is half of an octet.
• To form ionic bonds, carbon molecules must gain or lose four electrons, which requires a lot of energy.
• Instead, carbon forms covalent compounds by sharing electrons.
• Carbon can form double and triple bonds with other carbon atoms.
• The type of bond that forms depends on the strength and length of the bond:
• Single bonds: Long and weak
• Double bonds: Twisted and weak
• Triple bonds: Short and strong

Additional Information

• Single Bond:
• Length: Longer than double and triple bonds between the same atoms.
• Strength: Weaker than double and triple bonds between the same atoms.
• Type: Typically a sigma (σ) bond.
• Double Bond:
• Length: Shorter than single bonds but longer than triple bonds between the same atoms.
• Strength: Stronger than single bonds but weaker than triple bonds between the same atoms.
• Type: Consists of one sigma (σ) bond and one pi (π) bond.
• Triple Bond:
• Length: Shortest bond length between the same atoms.
• Strength: Strongest bond type between the same atoms.
• Type: Consists of one sigma (σ) bond and two pi (π) bonds.

The correct answer is 4 mV

Key Points

• We can use Ohm's law to find the induced EMF.
• Ohm's law states that:
• Voltage (V) = Current (I) × Resistance (R)
• Given:
• Current (I) = 1 mA = 0.001 A
• Resistance (R) = 4 Ω
• Therefore,
• Induced EMF (V) = 0.001 A × 4 Ω = 0.004 V = 4 mV
• So, the correct answer is 4) 4 mV.
• Induced EMF: Induced EMF, or electromotive force, is a voltage generated across a conductor due to a change in the magnetic field around it.
• This phenomenon is known as electromagnetic induction.

The correct answer is real, inverted and smaller

Key Points

• Magnification is a measure of how much larger or smaller an image is compared to the original object.
• It's calculated as the ratio of the image size to the object size.
• Sign of Magnification:
• Positive Magnification: Indicates a virtual and upright image.
• This type of image is formed by a convex lens when the object is placed between the focus and the optical centre.
• Negative Magnification: Indicates a real and inverted image.
• This type of image is formed by a convex lens when the object is placed beyond the focus.
• Given:
• Magnification = -0.65
• Interpretation:
• Negative Sign: This implies that the image is inverted.
• Magnitude Less Than 1: This means the image is smaller than the object.

Therefore, a magnification of -0.65 indicates a real, inverted, and smaller image

The correct answer is Th

Key Points

• John Newlands, an English chemist, proposed the Law of Octaves in 1864.
• This law states that when elements are arranged in increasing order of their atomic masses, every eighth element had properties similar to the first.
• He compared this pattern to the octaves of music, hence the name "Law of Octaves".
• Newlands arranged the 56 known elements at that time into 11 groups, each containing seven elements.
• The last element in his arrangement was Thorium (Th).
• However, Newlands' Law of Octaves had limitations:
• It worked well only up to calcium.
• It failed to accommodate elements discovered after calcium.
• It placed dissimilar elements in the same group.

Additional Information

• Mg (Magnesium): Magnesium is not the last element in Newlands' arrangement. It's a lighter element and comes much earlier in the sequence.
• H (Hydrogen): Hydrogen is also not the last element. It's one of the lightest elements and appears near the beginning of the arrangement.
• He (Helium): Helium was discovered much later than Newlands' time and was not included in his arrangement.

The correct answer is Allosomes

Key Points

• Allosomes, also known as sex chromosomes, are responsible for determining an organism's biological sex.
• Allosomes vs autosomes
• Allosomes are different in size, form, and behaviour from autosomes, which are all chromosomes other than sex chromosomes.
• Sex chromosomes in humans
• Humans have one pair of sex chromosomes, the X and Y chromosomes, in addition to 22 pairs of autosomes.
• Sex determination in mammals
• The Y chromosome is the determining factor for sex in mammals.
• The Sry gene on the Y chromosome causes the genital ridge's somatic cells to develop into a testis instead of an ovary.
• Discovery of sex chromosomes
• Nettie Stevens and Edmund Beecher Wilson independently discovered sex chromosomes in 1905

Additional Information

• Germ Cells
• Germ cells are specialized cells that give rise to gametes, which are reproductive cells like sperm and eggs.
• They are essential for sexual reproduction and the transmission of genetic information from one generation to the next.
• Pleiotropic Genes
• A pleiotropic gene is a gene that influences multiple phenotypic traits.
• In simpler terms, a single gene can have effects on several different characteristics of an organism.

The correct answer is Himachal Pradesh

Key Points

• The Sazo festival is a significant religious event celebrated in the Kinnaur district of Himachal Pradesh.
• It is believed that during this festival, the local deities ascend to heaven for a short period.
• It is a deeply spiritual event for the local people, marking the departure of deities to the celestial realm.
• The festival involves various rituals, including purification ceremonies, offerings to deities, and special prayers

Additional Information

• Some Other Festivals of Jharkhand, Karnataka, and Telangana
• Jharkhand
• Sarhul: A tribal festival celebrating the beginning of spring and the harvest season.
• Sohrai: A harvest festival celebrated by the Santhal tribe.
• Chhath Puja: A Hindu festival dedicated to the Sun god, Surya.
• Karma: A festival dedicated to the Karam Devta, a deity associated with fertility and prosperity.
• Karnataka
• Ugadi: The New Year's Day for Hindus in Karnataka, celebrated with a variety of sweets and savoury dishes.
• Dasara: A major Hindu festival celebrated with great pomp and show, particularly in Mysore.
• Deepavali: The festival of lights, celebrated with colourful decorations, fireworks, and the exchange of sweets.
• Kranti Din: Commemorates the independence movement in Karnataka.
• Telangana
• Bathukamma: A colourful floral festival celebrated by women, symbolizing nature's bounty and feminine energy.
• Bonalu: A festival dedicated to the goddess Mahankali, involving vibrant processions and offerings.
• Diwali: The festival of lights, celebrated with great enthusiasm, especially in urban areas.
• Ramzan: A religious festival observed by Muslims, marking the end of Ramadan.

Argument I: A global level mechanism is needed to combat this worldwide problem.

This argument strengthens the given statement. Since fake news is a global issue, it makes sense to propose that a global-level mechanism is required to address it. A worldwide problem needs a coordinated response across borders. The argument suggests an appropriate course of action given the nature of the issue, and is valid because it aligns with the premise that fake news is a problem of global scale.

Argument II: Problems related to fake news are only present in India.

This argument weaken the given statement. The statement highlights that fake news is a global problem, not something confined to a particular country. To suggest that fake news is only a problem in India weakens the statement and is incorrect. Fake news affects multiple countries, not just one country.

Conclusion:

Argument I is strength the statement because it supports the global nature of the problem and suggests an appropriate solution.

Argument II is weaken the statement because it contradicts the global scope of the problem by limiting it to just one country.

Hence, correct answer option is "II weakens while I strengthens the statement".

Given:

Simplify $\frac{{6 + 6 \times 6}}{{3 \times 3 + 5}} ÷ ;\frac{{\frac{1}{2} ÷ \frac{1}{2}of\frac{1}{2}}}{{\frac{1}{2} ÷ \frac{1}{2} \times \frac{1}{2}}}$

Formula Used:

Basic arithmetic operations and BODMAS/BIDMAS rule (Bracket, Order, Division/Multiplication, Addition/Subtraction).

Calculation:

Simplify the numerator and denominator separately:

Numerator: 6 + 6 × 6

⇒ 6 + 36

⇒ 42

Denominator: 3 × 3 + 5

⇒ 9 + 5

⇒ 14

Now, 42/14

⇒ 3

Next, simplify $\frac{1}{2} ÷ \frac{1}{2} \text{ of } \frac{1}{2}$ :

First, $\frac{1}{2} \text{ of } \frac{1}{2}$

⇒ 1/4

⇒ 1/2 ÷ 1/4 = 2

Now, simplify $\frac{1}{2} ÷ \frac{1}{2} \times \frac{1}{2}$

Then, $1 \times \frac{1}{2}$

⇒ 1/2

Combining all the values,

⇒ $3 ÷ \frac{2}{\frac{1}{2}}$ = 3 ÷ 4

⇒ 3/4

The correct answer is option 2.

The correct answer is 15 Days

Key Points

• The Shakti Criminal Laws (Maharashtra Amendment) Bill, 2020 set a 15-day time limit for investigating crimes against women and children, such as rape and gang rape.
• This was a reduction from the two-month time limit set in the CrPC.
• If the investigation cannot be completed within the 15-day period, the investigating officer must record the reasons in writing.
• The Special Inspector General of Police or Commissioner of Police can extend the period by seven working day

Shortcut Trick

Identify the common factor by observing the trailing zeros.

Both 2410 and 2700 end with at least one zero.

The difference between 2700 and 2410 is 290.

Factors of 290 are 1, 2, 5, 10, 29... since 10 is the largest power of 10 dividing both, HCF is 10.

∴ The correct answer is 10.

Alternate Method

Given: Numbers 2410 and 2700.

Formula Used: Prime Factorization Method or Long Division Method.

⇒ Prime Factorization of 2410 = 2 × 5 × 241

⇒ Prime Factorization of 2700 = 2² × 3³ × 5²

⇒ Common Prime Factors = 2¹ × 5¹

⇒ HCF = 2 × 5 = 10

∴ The correct answer is 10.

Additional Information

Definition of HCF

The Highest Common Factor (HCF) is the largest positive integer that divides each of the integers without a remainder.

Relation between HCF and LCM

For two numbers a and b, HCF(a, b) × LCM(a, b) = a × b.

Difference Method

The HCF of two numbers is always a factor of their difference.

The logic followed here is:

Hence, "Option 2" is the correct answer.

Shortcut Trick

Loss of 9% means SP₁ is 91% of CP. Profit of 9% means SP₂ is 109% of CP.

Using ratio-unitary method: 91 units = ₹1,820.

1 unit = 1820 ÷ 91 = 20.

109 units = 109 × 20 = ₹2,180.

∴ The correct answer is ₹2,180.

Alternate Method

Given: First Selling Price (SP₁) = ₹1,820, Loss% = 9%, Desired Profit% = 9%. Formulas: CP = [SP × 100] ÷ [100 − Loss%], New SP = [CP × (100 + Profit%)] ÷ 100.

⇒ Cost Price (CP) = (1820 × 100) ÷ (100 − 9) = (1820 × 100) ÷ 91

⇒ CP = 20 × 100 = ₹2,000

⇒ New Selling Price (SP₂) = [2000 × (100 + 9)] ÷ 100

⇒ SP₂ = (2000 × 109) ÷ 100 = 20 × 109

⇒ SP₂ = ₹2,180

∴ The correct answer is ₹2,180.

Additional Information

Base of Calculation

Profit and loss percentages are always calculated on the Cost Price (CP) unless stated otherwise in the question.

Direct SP Conversion

To find a new SP from an old SP directly: New SP = Old SP × (100 ± New%)/(100 ± Old%).

Given: All turns are 90 degree turns only

When asked about the direction of the stadium from the bus stop, Akhil said, “One must walk 100 m towards the south. 

Then one must take a left turn and walk 120 m.

Then one must take a left turn again and walk 370 m.

Then, again, one must take a left turn and walk 400 m.

Then one must take a left turn again and walk 370 m.

Then, again, one must take a left turn and walk 110 m.

Finally, one must take one last left turn and walk 100 m to reach the stadium”.

Thus, the stadium is (400 m - 110 m - 120 m) 170 m far from the bus stop in the west direction.

Hence, "Option 4" is the correct answer.

The logic followed here is:

Hence, "Option 3" is the correct answer.

The correct answer is ninefold

Key Points

• If the current and potential difference are tripled in a circuit, keeping the resistance constant, then the power will increase nine fold.
• The power dissipated in a circuit is $P=I^{2}R$
• When R is constant, $P\propto I^2$.
• If I becomes 3 times, then P becomes 9 times.

The correct answer is to increase to double

Key Points

• For a spherical mirror, the relationship between the focal length (f) and the radius of curvature (R) is:
• f = R/2
• This means that the focal length is half the radius of curvature.
• So, if the radius of curvature (R) is doubled, the focal length (f) will also double, as the ratio remains constant.
• Therefore, the correct answer is: 1) increase to double.

Additional Information

• A spherical mirror is a mirror whose reflecting surface is a portion of a sphere. There are two types of spherical mirrors:
• 1. Concave Mirror
• Shape: The reflecting surface curves inward.
• Focus: Light rays parallel to the principal axis converge at a point called the focus.
• Image Formation:
• Real and inverted images can be formed when the object is placed beyond the focal point.
• Virtual and upright images can be formed when the object is placed between the focus and the pole.
• Uses:
• Headlights
• Telescopes
• Shaving mirrors
• Makeup mirror
• Opens in a new window
• 2. Convex Mirror
• Shape: The reflecting surface curves outward.
• Focus: Light rays parallel to the principal axis diverge as if they are coming from a point called the focus (virtual focus).
• Image Formation:
• Always forms virtual, upright, and diminished images, regardless of the object's position.
• Uses:
• Rear-view mirrors in vehicles
• Security mirrors
• Store surveillance mirrors

Given: 27 : 13 :: 65 : 32 :: 71 : 35 :: 51 : ?

The logic followed here is:

27 : 13

(13 × 2) + 1 = 27

65 : 32

(32 x 2) +1 = 65

71 : 35

(35 x 2) +1 = 71

Similarly,

51 : ?

(? x 2) +1 = 51

(? x 2)  = 51 -1

(? x 2)  = 50

? = 50 ÷ 2

? = 25

Hence, "Option 4" is the correct answer.

Given: Six boxes, D, E, F, G, H, and I, are kept one over the other.

1. D is kept at the third place from the top.

2. Only two boxes are kept between D and I.

2. Only one box is between E and I.

3. Also, there is only one box between E and F.

After positioning F only two positions is left which will be occupied by the only two boxes left i.e. G and H.

Thus, according to the final arrangement E box is kept at the third place from the bottom.

Hence, "Option 2" is the correct answer.

Shortcut Trick

For roots α and β, the quadratic equation is x² − (Sum)x + Product = 0.

Sum = 3 + 1/3 = 10/3

Product = 3 × 1/3 = 1

Equation: x² − (10/3)x + 1 = 0 ⇒ 3x² − 10x + 3 = 0.

∴ The correct answer is 3x² − 10x + 3 = 0.

Alternate Method

Given:

Roots of the quadratic equation are α = 3 and β = 1/3.

Formula Used:

A quadratic equation with roots α and β is given by: x² − (α + β)x + αβ = 0

Calculations:

⇒ Sum of the roots (α + β) = 3 + 1/3

⇒ α + β = (9 + 1) / 3 = 10/3

⇒ Product of the roots (αβ) = 3 × (1/3) = 1

⇒ Substituting these values into the formula: x² − (10/3)x + 1 = 0

⇒ Multiply the entire equation by 3 to remove the fraction: 3(x²) − 3(10/3)x + 3(1) = 0

⇒ 3x² − 10x + 3 = 0

Therefore, the required equation is 3x² − 10x + 3 = 0.

∴ The correct answer is 3x² − 10x + 3 = 0.

Additional Information

Relationship between Roots and Coefficients

For a standard quadratic equation ax² + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a.

Nature of Roots

The nature of roots is determined by the Discriminant (D = b² − 4ac). If D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are imaginary.

Quadratic Formula

The roots can also be found using the formula: x = [−b ± √(b² − 4ac)] / 2a.

The correct answer is Kerala

Key Points

• Anamudi Mountain is located in the state of Kerala:
• Anamudi is situated in the Ernakulam and Idukki districts of Kerala, on the border between the two districts.
• Anamudi is the highest peak in the Western Ghats and in South India, with an elevation of 2,695 meters (8,842 ft).
• It's also the highest mountain in peninsular India and the largest mountain in Kerala.
• The name Anamudi literally translates to "elephant's head", a reference to the mountain's resemblance to an elephant's head.
• Anamudi is located in the southern part of the Elaimulam National Park, which is a combination of the Cardamom Hills, Anamalai Hills, and Palani Hills.
• Anamudi is a popular tourist destination year-round.

Given: P, R, T, V and W live on different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2, and so on till the topmost floor is numbered 5. 

1) V lives on the floor immediately below W.

2. W lives on the floor immediately below T.

2) P lives on the floor immediately above T.

As there is no possible position for P in case 1, therefore it is eliminated. 

3) R lives on the floor immediately above P.

As there is no possible position for R in case 2, therefore it is eliminated. 

Thus, according to the final arrangement T lives on the third floor.

Hence, "Option 4" is the correct answer.

Shortcut Trick

Radius (r) = 2/2 = 1 cm.

Length (h) = 7 m = 700 cm.

Volume = πr²h = (22/7) × 1² × 700.

Volume = 22 × 100 = 2200 cm³.

∴ The correct answer is 2200 cm³.

Alternate Method

Given:

Diameter of wire = 2 cm ⇒ Radius (r) = 1 cm.

Length of wire (h) = 7 m = 7 × 100 = 700 cm.

Formula Used:

Volume of Cylinder = πr²h

Calculations:

⇒ Volume = (22/7) × (1)² × 700

⇒ Volume = (22/7) × 1 × 700

⇒ Volume = 22 × 100

⇒ Volume = 2200 cm³

∴ The correct answer is 2200 cm³.

Additional Information

Volume of a Cylinder

The space occupied by a cylindrical object is calculated as πr²h, where r is the radius and h is the height or length.

Surface Area of Cylinder

Curved Surface Area (CSA) = 2πrh and Total Surface Area (TSA) = 2πr(r + h).

Unit Conversion

Always ensure all dimensions are in the same unit before calculation; 1 meter = 100 centimeters.

Given: Five people, A, D, E, F and K, are sitting around a circular table facing the centre.

1) A is the immediate neighbour of D and E. 

As position of D and E with respect to A is not known yet, therefore there are two possible cases.

Case 1)

Case 2) 

2) F is the immediate neighbour of E and K. 

Case 1)

Case 2) 

Thus, in both cases E is the immediate neighbour of both A and F.

Hence, "Option 3" is the correct answer.

The correct answer is 1958

Key Points

• The English and Foreign Languages University (EFLU) in Hyderabad was founded in the year 1958 as the Central Institute of English by India's first Prime Minister, Pandit Jawaharlal Nehru.
• Its primary objective was to improve the standards of English language teaching in India.
• Over the years, the institute expanded its scope to include the teaching and research of various foreign languages.
• In 2006, it was granted the status of a central university and renamed the English and Foreign Languages University.
• Today, EFLU is a premier institution for language learning and research in India,
• offering a wide range of undergraduate, postgraduate, and doctoral programs in English, foreign languages, literature, linguistics, and cultural studies

The correct answer is Fishes

Key Points

• The number of chambers in an animal's heart is a key factor in determining the efficiency of its circulatory system.
• Two-Chambered Heart
• Fish: Fish have the simplest heart structure, consisting of two chambers: one atrium and one ventricle.
• Function: Blood is pumped from the heart to the gills for oxygenation and then directly to the rest of the body.

Additional Information

• Three-Chambered Heart
• Amphibians and most reptiles: These animals have a three-chambered heart with two atria and one ventricle.
• Function: Oxygenated and deoxygenated blood mix to some extent in the single ventricle, which can reduce the efficiency of oxygen delivery to tissues.
• Four-Chambered Heart
• Birds and mammals: These animals have a four-chambered heart with two atria and two ventricles.
• Function: This highly efficient heart completely separates oxygenated and deoxygenated blood, ensuring optimal oxygen delivery to tissues.
• Why do chamber numbers matter?
• Efficient oxygenation: More chambers allow for more efficient separation of oxygenated and deoxygenated blood, leading to better oxygen delivery to tissues.
• Metabolic needs: Animals with higher metabolic rates, like birds and mammals, require more efficient oxygen delivery.

The logic followed here is:

‘RAPID’ is written as ‘ARPDI’

And,

‘LOCAL’ is written as ‘OLCLA’

Similarly,

‘NEVER’ is written as

Hence, "Option 2" is the correct answer.

The correct answer is Ferric oxide

Key Points

• When ferrous sulfate is heated strongly, it undergoes a decomposition reaction, producing ferric oxide (Fe2O3) as the solid product,
• along with sulfur dioxide (SO2) and sulfur trioxide (SO3) gases.
• The chemical equation for this reaction is:
• 2FeSO4(s) → Fe2O3(s) + SO2(g) + SO3(g)
• So, the correct answer is 2) Ferric oxide.

Additional Information

• Ferrous Sulphide (FeS)
• Appearance: Black solid
• In various tools and machinery.
• Formation: Often formed by the reaction of iron with sulfur or by the reaction of hydrogen sulfide gas with iron(II) salts.
• Uses:
• In the laboratory to produce hydrogen sulfide gas.
• In the metallurgical industry.
• Ferrous Oxide (FeO)
• Appearance: Black or dark grey solid
• Formation: Can be formed by the reduction of iron oxides with carbon monoxide or hydrogen.
• Uses:
• As a pigment in ceramics and glass.
• In the production of iron and steel.
• Iron (Fe)
• Appearance: Silvery-gray metallic solid
• Formation: Can be obtained from iron ore through various metallurgical processes, such as blast furnace reduction.
• Uses:
• In construction and manufacturing.
• In the production of steel.

The correct answer is 9.2%

Key Points

• As per the Union Budget 2022-23, India's economic growth was estimated to be 9.2%.
• This projection was based on the strong economic recovery post-pandemic.
• However, the actual growth rate for the fiscal year 2022-23, as per the revised estimates released later, was slightly lower at 7%.
• It's important to note that these are annual growth rates.
• Economic growth can fluctuate quarter-to-quarter, and factors like global economic conditions, domestic policies, and geopolitical events can influence these rates.

Additional Information

• The Union Budget of India is an annual financial statement presented by the Finance Minister to the Parliament.
• It outlines the government's estimated revenue and expenditure for the upcoming fiscal year.
• Key Components of the Union Budget:
• Revenue Receipts: Income generated through taxes (direct and indirect) and other sources.
• Capital Receipts: Income generated through borrowings and other capital assets.
• Revenue Expenditure: Expenditure on day-to-day functioning of the government, like salaries, pensions, and subsidies.
• Capital Expenditure: Expenditure on creating assets, such as infrastructure projects, defense equipment, and public sector investments.

Given: (Left) 876 643 453 974 227 (Right)

According to the question all the numbers of the given series are arranged in descending order:

Thus, according to the final arrangement, only position of '227' will remain unchanged.

Hence, "Option 2" is the correct answer.

The correct answer is 1969

Key Points

• The nationalization of banks in India was carried out in 1969. On July 19, 1969, the Government of India, under the leadership of then Prime Minister Indira Gandhi, nationalized 14 major commercial banks.
• This move was aimed at aligning the banking sector with national priorities, increasing financial inclusion, and directing credit towards sectors such as agriculture, small industries, and rural development.
• The main objectives of the nationalization were:
• To provide banking services to a wider population, especially in rural and remote areas.
• To use the banking sector for economic planning and development.
• To ensure that the credit flow to priority sectors was not constrained by profit-driven motives.
• This was a significant step in India's economic history and laid the foundation for public sector dominance in the banking industry.

The correct answer is Silver bromide

Key Points

• Silver bromide (AgBr) is a light-sensitive compound commonly used in photographic films and papers.
• When exposed to light, silver bromide undergoes a chemical reaction that forms a latent image.
• During the photographic development process, this latent image is converted into visible metallic silver, creating the black-and-white image.

Additional Information 

• Sodium chloride (NaCl): Common table salt, sodium chloride, is not light-sensitive and does not react to create a photographic image. It has no role in photographic development.
• Sodium oxide (Na₂O): Sodium oxide is an ionic compound and is not sensitive to light. It is used in glassmaking but has no application in photography.
• Silver oxide (Ag₂O): Silver oxide is not used in photography because it does not have the necessary light-sensitive properties. It is mainly used in batteries and certain medicinal applications.

The logic followed here is:

ABC : EFG

PQR : TUV

So, checking each option one by one:

Option 1) PKL : RSM

Option 2) XYZ : BCD

Option 3) GHI : DEF

Option 4) MNO : PQR

Thus, out of all the options, 'XYZ : BCD' follows the same logic as given.

Hence, "Option 2" is the correct answer.

Given: Each of students, D, F, G, H, S, T and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week.

1) V’s exam is on Wednesday and H’s exam is on Friday.

2) V’s exam is on the day immediately after T’s exam.

3) D’s exam is on the day immediately before G’s exam.

4) Only one student has exam between D and F.

5) F’s exam is neither on Monday nor on Saturday.

After positioning F only one position is left which will be occupied by the only student left i.e. S.

Thus, according to the final arrangement F has exam on Thursday.

Hence, "Option 1" is the correct answer.

The correct answer is 81.45%.

Important Points

• In the year 2019-20, Gujarat was the leading producer of salt in India, contributing 81.29% to the total salt production in the country.
• Option 1- 81.45% is the closest value. Hence, it is the correct answer.

Key Points

• In the year 2019-20, Gujarat was the leading producer of salt in India, contributing 81.29% to the total salt production in the country.
• Gujarat's salt production is significant due to its extensive coastline and favorable climatic conditions for salt production.
• Salt production in Gujarat is predominantly carried out in the coastal districts such as Kutch, Bhavnagar, and Jamnagar.
• Rajasthan and Tamil Nadu were the second and third largest producers, respectively, accounting for 8.59% and 7.96% of the country's salt production.
• The state’s strategic location and infrastructure also support the efficient export of salt to various parts of the world.

Additional Information

• Indian Minerals Yearbook
• The Indian Minerals Yearbook is an annual publication by the Indian Bureau of Mines (IBM) that provides comprehensive information on the mining and mineral industry in India.
• It includes data on production, reserves, prices, and trade of various minerals, along with details on the mining industry’s performance and developments.
• The yearbook serves as an important reference for policymakers, industry professionals, researchers, and academicians.
• It also highlights the contributions of different states to the mineral production in India.
• Salt Production in India
• India is one of the largest producers of salt in the world, with Gujarat being the leading state in salt production.
• Salt production in India is primarily carried out in coastal regions due to the availability of seawater and favorable climatic conditions.
• The main methods of salt production in India include solar evaporation, rock salt mining, and brine solution mining.
• Salt is an essential mineral used in various industries, including food processing, chemical manufacturing, and water treatment.
• Indian Bureau of Mines (IBM)
• The Indian Bureau of Mines is a multidisciplinary government organization under the Ministry of Mines, India.
• IBM is responsible for promoting the conservation, development, and scientific management of mineral resources in the country.
• It provides technical consultancy services, conducts research, and publishes various reports and statistics related to the mining industry.
• IBM also plays a crucial role in regulating and monitoring mining activities to ensure sustainable and environmentally responsible mining practices.