RRC Group D Previous Year Paper 26 (Held On: 22 Sept 2018 Shift 3)

• Vishwas Mandlik was the recipient of the Prime Minister’s Award for outstanding contribution to promotion and development of yoga in 2018.
• He was the founder of the "Yoga Vidya Dham".
• He has written many books and presented research papers in different International Yoga Conferences.
• 2019 Prime Minister's Award for outstanding contribution for promotion and development of Yoga-Antonietta Rozzi of Italy, Japan Yoga Niketan, Swami Rajarshi Muni of Life Mission, Gujarat, and Bihar School of Yoga, Munger.
• Tirumalai Krishnamacharya was also an Indian yoga teacher in the 20th century.
• K. Pattabhi Jois developed and popularized the vinyāsa style of yoga known as Ashtanga Yoga.
• B. K. S. Iyengar was an eminent yoga teacher. He regularly taught and popularized Hatha Yoga.

CONCEPT:

• Work: When a force is applied on a body and there is a displacement of the body in the direction of force then the work is said to be done by the force.

Work (W) = Force (F) × Displacement (S)

• The SI unit of work is Joule. 1 Joule (J) = 1 Nm
• Power: The rate of work done is power.

Power (P) = work (W) / time (t)   (P = W / t = J / s)

CALCULATION:

Given that:

Time (t) = 10 seconds and Power (P) = 20KW = 20,000 Watts. 

Work done (W) = Power (P) × Time (t) = 20,000 × 10 = 2,00,000 J = 200 KJ

• Hence, the amount of work done is 200 KJ. So option 2 is correct.

Shortcut Trick

Compare the two cases of work distribution:

Case 1: Arjun (2 days) + Bharath (9 days) = Total Work

Case 2: Arjun (3 days) + Bharath (6 days) = Total Work

Difference: 1 extra day of Arjun reduces 3 days of Bharath work.

∴ Work of 1 day of Arjun = Work of 3 days of Bharath. Efficiency Ratio (A:B) = 3 : 1.

Total work = (2 × 3) + (9 × 1) = 6 + 9 = 15 units. Arjun alone = 15 ÷ 3 = 5 days.

∴ The correct answer is 5 days.

Alternate Method

Let efficiency of Arjun be A and Bharath be B.

⇒ Total Work (TW) = 2A + 9B = 3A + 6B

⇒ 9B − 6B = 3A − 2A

⇒ 3B = 1A

⇒ A/B = 3/1 (Efficiency of Arjun = 3, Efficiency of Bharath = 1)

⇒ Total Work = (2 × 3) + (9 × 1) = 6 + 9 = 15 units

⇒ Days taken by Arjun alone = Total Work ÷ Efficiency of Arjun

⇒ Days = 15 ÷ 3 = 5 days

∴ The correct answer is 5 days.

Additional Information

Work-Efficiency Relationship

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

Work Equality Method

When the same task is performed by different combinations of people, equate the linear equations to find the ratio of their efficiencies.

Shortcut Trick

Total mean of 14 numbers is 17.

Mean of 6 numbers is 15, so deviation is 15 − 17 = −2 per number.

Total deviation for 6 numbers = 6 × (−2) = −12.

To balance the total deviation to zero, the remaining 8 numbers must provide a deviation of +12.

Average deviation for 8 largest numbers = +12 ÷ 8 = 1.5.

Required Mean = 17 + 1.5 = 18.5.

∴ The correct answer is 18.50.

Alternate Method

Given:

Number of smallest members (n₁) = 6, Mean (x₁) = 15

Total members (N) = 14, Total Mean (X) = 17

Remaining members (n₂) = 14 − 6 = 8

Formula used:

Total Sum = Mean × Number of items

Calculations:

⇒ Sum of all 14 members = 14 × 17

⇒ Sum of all 14 members = 238

⇒ Sum of 6 smallest numbers = 6 × 15 = 90

⇒ Sum of 8 largest numbers = Total Sum − Sum of 6 smallest

⇒ Sum of 8 largest numbers = 238 − 90 = 148

⇒ Mean of 8 largest numbers = 148 ÷ 8

⇒ Mean of 8 largest numbers = 18.5

∴ The correct answer is 18.50.

Additional Information

Weighted Average Formula

The combined mean of two groups is given by X = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂), where n is the number of items and x is the mean.

Properties of Arithmetic Mean

The sum of the deviations of a set of values from their arithmetic mean is always zero (Σ(x − X) = 0).

Effect of Constant on Mean

If every number in a dataset is increased or decreased by a constant value 'k', the mean also increases or decreases by the same constant 'k'.

Given:

Concept:

Firstly we have to calculate the number of days and then the time followed by it.

For Calculate Number of Days, we have to find the exact days i.e., from 11 May 2023 to 12 May 2024 (as Time period for 13^th May 2024 is less than 24 hours)

Number of Days in normal year = 365 days

Number of days in leap year = 366 days (and the extra day falls on February)

Calculation:

Number of Days = 11 May 2023 to 12 May 2024 = 367 days (As 2024 is a leap year)

Time = 12^th May 2024 (2:38 pm) to 13^th May 2024 (2:29 pm)

The difference in Time = 23 hours 51 minutes

∴ Required Answer = 367 days 23 hours 51 minutes

While calculating the number of Days, we use 365 days instead of 366 days (as they considered the year is not completed).

While calculating the time duration, Many of the candidates subtracted bigger value to smaller i.e, 38 minutes - 29 minutes (which is incorrect). We have to find the time difference from 38 minutes to 60 minutes first (i.e, 22 minutes) and then added these 22 minutes in 29 minutes of the next hour. (22 + 29 = 51 minutes).

Conclusion 1: This follows, the proverb given in the statement, means the same as given in conclusion. Humans always do not consider their possibilities and they are not satisfied in their life.

Conclusion 2: This does not follow as anything related to the conclusion is not given in the statement.

Hence, “only conclusion 1” follows.

• Fakhar Zaman is the first Pakistani cricket player to score a double century in ODIs.
• He made 210 runs off 156 balls against Zimbabwe in the fourth ODI at Bulawayo in 2018. He became the sixth international batsman to make double-hundreds in ODIs.
• Batsmen who have scored double centuries in ODI- Rohit Sharma, Martin Guptill, Virendra Sehwag, Chris Gayle, Sachin Tendulkar, Fakhar Zaman.
• Rohit Sharma is the only player to score three double-centuries in ODI.

• Yogi Adityanath had earlier served as Priest of a temple.
• He is the current Chief Minister of Uttar Pradesh.
• He is the head priest of the Gorakhnath Math which is a Hindu temple in Gorakhpur.
• He became a disciple of Mahant Avaidyanath at the age of 21 after renouncing his family in 1993. After the death of Avaidyanath, Adityanath became the head priest.
• Vijay Rupani is the chief minister of Gujarat.
• Mayawati is the former Chief Minister of Uttar Pradesh.
• Late Manohar Parrikar served as Chief Minister of Goa. He was also the Minister of Defense.

Pemba Island is famous for the cultivation of cloves. 

• This island is part of the Zanzibar Archipelago of Tanzania (coast of East Africa). It is in the Indian Ocean.
• Clove is the dried unopened flower buds of Syzygium aromaticum. Indonesia, Zanzibar, and Madagascar are the major producers of cloves.
• Clove is a tropical plant and it requires a warm humid climate. However, Cloves are best suited in deep black loam soil with high humus content found in the forest region.
• When a coffee plant is planted, it starts to produce flowers in three to four years. The cherries appear from these flowers. When the cherries ripe, it changes color from green to red and they are harvested. They are best grown in deep sandy loam. They are primarily produced in Brazil, Vietnam, Colombia, Indonesia, etc.
• Rice is one of the most cultivated crops in India as well as in Asian countries. It is a staple diet of a major part of India. It is grown successfully in humid to sub-humid regions under a subtropical and temperate climate.
• Wheat is one of the world's most commonly consumed cereal grains. Loam soil is the best for wheat cultivation.

• The enzyme Trypsin is present in the pancreatic juice, converts proteins to amino acids.
• It helps in the digestion of proteins. Trypsin breaks down proteins in the small intestine and hence continuing the process of digestion. Please note that it is produced by the pancreas in an inactive form called trypsinogen.
• Pepsin is also an enzyme in gastric juice that digests proteins. Glands in the mucous-membrane which line the stomach make and store an inactive protein known as pepsinogen. When pepsinogen is released into the stomach and mixed with gastric juice, it is converted into pepsin.
• Pepsin partially degrades proteins into smaller units called peptides.
• Lipase is also an enzyme that helps in absorbing fats. This enzyme is also released by Pancreas.
• Amylase is also an enzyme that catalyzes the hydrolysis of starch into sugars such as glucose and maltose. It made by your pancreas and by glands in and around our mouth and throat. It helps to digest carbohydrates.

• Gandhiji launched the Champaran Satyagraha in a small village called Champaran. It is in Bihar.
• The Champaran Satyagraha of 1917 was the first Satyagraha movement led by Gandhi.
• The satyagraha made as the farmers were forced to grow indigo without any payment for it.
• Gandhiji reached Champaran at the request of Rajkumar Shukla, where he started an effort to free the farmers suffering from the Tinkathia system.
• Gandhiji received the support of two persons Rajendra Prasad and Anugraha Narayan Sinha during this movement.

• This is a structure of Benzene (C₆H₆).
• It is an organic chemical compound. It is found in crude oil and is a major part of gasoline.
• It is a widely used industrial chemical. Benzene is used in making plastics,synthetic fibers, rubber lubricants, dyes, drugs, pesticides, etc.
• Cyclohexane (C6H₁₂) is an alicyclic hydrocarbon comprising a ring of six carbon atoms. It is widely used as a raw material in the manufacture of nylon.
• Cycloheptane (C₇H14) is also a cycloalkane and a colorless liquid. It is used to make other chemicals.
• Naphthalene (C10 H 8) is a polycyclic aromatic hydrocarbon. It is obtained from either coal tar or petroleum distillation. It has been used in mothballs and moth flakes.

Distance between hour hand and minute is = 5 min

As we know,

60 min = 360°

⇒ 1 min = 6°

⇒ 5 min = 5 × 6° = 30°

∴ Required angle = 30° + 25/2 = 30° + 12.5° = 42.5°

Shortcut Trick

In a proportion a : b :: c : d, the product of extremes equals the product of means.

Fourth term (d) = (Second term × Third term) ÷ First term

⇒ d = (5 × 21) ÷ 3 = 5 × 7 = 35

∴ The correct answer is 35.

Alternate Method

Given: First three terms are 3, 5, and 21.

Formula Used: If a, b, c, d are in proportion, then a/b = c/d.

Calculations:

Let the fourth term be x.

⇒ 3 : 5 :: 21 : x

⇒ 3/5 = 21/x

⇒ 3 × x = 21 × 5

⇒ x = (21 × 5) / 3

⇒ x = 7 × 5

⇒ x = 35

∴ The correct answer is 35.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b).

Third Proportional

If a, b, c are in continued proportion (a:b = b:c), then the third proportional c = b²/a.

Properties of Proportion

Invertendo (b/a = d/c), Alternando (a/c = b/d), and Componendo & Dividendo ((a+b)/(a−b) = (c+d)/(c−d)).

Linen is a type of cloth woven from flax.

Similarly,

Gold is type of metal

Hence, “Metal” is the correct answer.

Shortcut Trick

In a 30°−60°−90° triangle, the ratio of sides opposite to these angles is 1 : √3 : 2.

The side opposite to 60° (height of tower) is 32√3 m.

⇒ √3 units = 32√3 m

⇒ 1 unit (distance from building) = 32 m.

∴ The correct answer is 32 m.

Alternate Method

Given:

Height of the tower (AB) = 32√3 m

Angle of depression = 60° ⇒ Angle of elevation from foot of building (C) to top of tower (A) = 60°.

Formula Used:

tan θ = Perpendicular ÷ Base

Calculations:

Let the distance between the tower and the building be x.

In ΔABC:

⇒ tan 60° = AB ÷ BC

⇒ √3 = 32√3 ÷ x

⇒ x = (32√3) ÷ √3

⇒ x = 32 m

∴ The correct answer is 32 m.

Additional Information

Angle of Depression

The angle formed by the line of sight with the horizontal when the object is below the horizontal level. It is numerically equal to the angle of elevation.

Trigonometric Ratios

For 30°, tan 30° = 1/√3. For 45°, tan 45° = 1. For 60°, tan 60° = √3.

Shortcut Trick

Since DE is parallel to BC, triangle ADE is similar to triangle ABC.

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides:

Corresponding sides ratio = AD ÷ AB = AD ÷ (AD + BD) = 2 ÷ (2 + 3) = 2/5

Ratio of areas = (AD ÷ AB)² = (2/5)² = 4/25

∴ The correct answer is 4/25.

Alternate Method

Given:

In ΔABC, D and E are points on AB and AC respectively such that DE || BC.

AD = 2 cm

BD = 3 cm

Formula Used:

If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides:

ar(ΔADE) ÷ ar(ΔABC) = (AD ÷ AB)²

Calculations:

⇒ AB = AD + BD

⇒ AB = 2 + 3 = 5 cm

⇒ In ΔADE and ΔABC:

⇒ ∠ADE = ∠ABC (Corresponding angles as DE || BC)

⇒ ∠AED = ∠ACB (Corresponding angles as DE || BC)

⇒ ∴ ΔADE ˜ ΔABC (By AA similarity criterion)

⇒ By the property of similar triangles:

⇒ ar(ΔADE) ÷ ar(ΔABC) = (AD ÷ AB)²

⇒ ar(ΔADE) ÷ ar(ΔABC) = (2 ÷ 5)²

⇒ ar(ΔADE) ÷ ar(ΔABC) = 4/25

Explanation of Options:

• Option (1) 4/9 is incorrect because it represents the ratio (AD ÷ BD)² = (2 ÷ 3)² = 4/9, which incorrectly uses the segment BD instead of the full side AB.

• Option (2) 16/81 is incorrect because it represents an incorrect higher power of the ratio.

• Option (3) 4/25 is the correct ratio of the areas of the two similar triangles.

• Option (4) 2/5 is incorrect because it is the ratio of the corresponding sides (AD ÷ AB), not the ratio of their areas (which must be squared).

∴ The correct answer is 4/25.

Additional Information

Basic Proportionality Theorem (Thales Theorem)

If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio. Thus, AD ÷ BD = AE ÷ EC.

Area of Similar Triangles Theorem

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides, altitudes, medians, or perimeters.

AA Similarity Criterion

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

Shortcut Trick

The unit digit of base 3 repeats every 4 powers (3, 9, 7, 1).

Divide the exponent 31 by the cyclicity of 4.

31 ÷ 4 ⇒ Remainder = 3.

The unit digit of 3³¹ = Unit digit of 3³ = 27.

∴ The correct answer is 7.

Alternate Method

Given: Base = 3, Exponent = 31

The unit digit of powers of 3 follows a cyclic pattern:

Step-by-step calculation:

⇒ Identify Cyclicity: 3¹=3, 3²=9, 3³=27, 3⁴=81. The unit digits are 3, 9, 7, 1.

⇒ Length of Cycle = 4.

⇒ Divide Exponent by 4: 31 ÷ 4 = 7 with Remainder 3.

⇒ Determine Unit Digit: Since remainder is 3, the unit digit is the 3^rd value in the cycle.

⇒ Unit digit = 3³ = 27 → 7.

∴ The correct answer is 7.

Additional Information

Cyclicity of Digits

Digits 2, 3, 7, and 8 have a cyclicity of 4. To find their unit digit, divide the power by 4 and check the remainder.

Digits with Cyclicity 1

The unit digits of numbers ending in 0, 1, 5, or 6 never change, regardless of the power (e.g., 5ⁿ always ends in 5).

Power of 4 and 9

These have a cyclicity of 2. For 4: 4^odd ends in 4, 4^even ends in 6. For 9: 9^odd ends in 9, 9^even ends in 1.

Zero Remainder Rule

If the remainder is 0 when dividing the power by cyclicity, use the cyclicity value itself as the power (e.g., if power ÷ 4 has remainder 0, calculate Base⁴).

Shortcut Trick Identify the nearest square greater than 4042. We know 602 = 3600 and 702 = 4900. Try 632 = 3969 and 642 = 4096. Number to be added = 4096 − 4042 = 54. ∴ The correct answer is 54. Alternate Method Given: Number = 4042 Formula Used: (Next Integer)2 − Given Number

⇒ Using the long division method for square root of 4042: ⇒ 6 × 6 = 36. Remainder is 4. Bring down 42. New dividend is 442. ⇒ Double 6 is 12. 123 × 3 = 369. (442 − 369 = 73 remainder). ⇒ Since 632 < 4042, the next perfect square is 642. ⇒ 642 = 64 × 64 = 4096. ⇒ Least number to be added = 4096 − 4042 = 54. ∴ The correct answer is 54. Additional Information Perfect Square Properties A perfect square never ends in 2, 3, 7, or 8. Digit sum of a perfect square is always 1, 4, 7, or 9. Finding Number to Subtract To find the least number to subtract to make a perfect square, simply calculate the remainder using the long division method.

Drawing the Venn diagram,

Conclusion 1: All brooms are handles → True (This is definitely true)

Conclusion 2: No plastic is a broom → False (This is definitely false)

Hence, “only conclusion 1” follows.

• The parenchyma consists of relatively unspecialised cell with thin cell well.
• Parenchyma tissues are a type of permanent tissue and are loosely packed. It provides support to plants and helps in the storage of food. As cells are loosely packed, large air cavities are present which gives buoyancy to the plants to help them float.
• Phloem is conducting tissues. It transports food from leaves to other parts of the plant. The four elements of phloem are - sieve tubes, companion cells, phloem fibres and the phloem parenchyma. Phloem cells are living cells except for phloem fibres.
• Sclerenchyma is also permanent tissue. It makes the plant hard and stiff. This tissue is present in stems, in the veins of leaves, and in the hard covering of seeds and nuts. Please note that the cells are dead.
• Collenchyma are also permanent tissue. It allows the bending of plants without breakage. These tissues are found in leaf stalks below the epidermis. Please note that cells are living.

Assumption 1: This is not implicit, because headmistress did not mention anything about interest in English.

Assumption 2: This is implicit, because speaking in the assembly will reduce stage fear.

Hence, “only assumption 2” is implicit.

• As per the RBI Annual Report 2016-17, the estimated value of demonetized banknotes received was Rs. 15.28 lakh crore as of June 2017.
• This amount is 99 percent of the Rs 15.44-lakh-crore scrapped currency notes.
• On November 8, 2016, the Government of India decided that the denominations of Rs. 500 and Rs. 1000 would cease to be legal tender with effect from November 9, 2016. The 86 percent of the circulation money stood not eligible for legal tender on that day.
• This move of demonetization was to stem the circulation of black money, fake currency and to choke terror funding and corruption.
• The value of banknotes in circulation declined by 20.2 percent at end-March 2017. The volume of banknotes increased by 11.1 percent, primarily due to a higher infusion of banknotes of a lower denomination in circulation.

• Shanta Rangaswamy won the BCCI Lifetime achievement award for Women at the BCCI Annual Awards held in Bengaluru in March 2017.
• She had also been a captain of the Women Cricket Team of India.
• Shubhangi Kulkarni also used to play cricket. She was the secretary of the Women's Cricket Association of India before merger with BCCI.
• Diana Edulji used to play Test Cricket. She is a recipient of Padma Shri.
• Purnima Rau was also a cricket player in the Indian Women's team.
• BCCI Lifetime achievement award for Women 2018-Anjum Chopra.
• The award consists of Citation, trophy and cheque for Rs. 25 lakhs.

Lily, Lotus and Jasmine are flowers.

Whereas,

Cantaloupe is a fruit.

Hence, “cantaloupe” does not belong to the group.

• Candidiasis is not a sexually transmitted disease.
• It is a fungal infection that affects the mouth and throat. It is generally an allergic reaction to a yeast called Candida albicans.
• Syphilis- It is a bacterial infection that starts as a painless sore on the genitals, rectum or mouth. It can be sexually transmitted to another person on sexual contact.
• Gonorrhea- It is a bacterial infection that can cause infertility. It can be transmitted through sexual contact.
• Warts are caused by various strains of human papillomavirus. Different strains may cause warts in different parts of the body. It can be transmitted through sexual contact.

CONCEPT:

• Friction: The property of a surface that opposes the relative motion between two surfaces is called friction.

Friction (f) = μ N

Where μ is the coefficient of friction and N is the normal force

EXPLANATION:

1. Tension: It is the force which is transmitted through a rope or wire when pulled by forces acting from opposite sides. In other words, it is simply the force exerted by a string when it is subjected to pull.
2. Momentum: It is the strength contained in the object due to its motion. It is the product of the mass of an object and the velocity with which it is moving.
3. Impulse: It is the product of force and time. One can also say that it is the change in momentum.
4. If no force is applied to a moving object, then it will stop due to Friction. So option 4 is correct. 

• As per the first law of motion-" an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force".
• So, if no force is applied to a moving object, it should remain in motion as per the first law of motion. But, it is stopped due to friction.

Total NPAs under all the banks are = Rs. 300 lakh crores,

∴ NPA’s of B = 300 × 25/100 = 75 lakh crores.

Shortcut Trick

Smallest four-digit number = 1000.

Divide 1000 by 47 → 1000 ÷ 47 = 21 with remainder 13.

To find the next multiple: 1000 + (47 − 13) = 1034.

∴ The correct answer is 1034.

Alternate Method

Given: Divisor = 47, Target = Smallest 4-digit number.

Formula Used: Required Number = Dividend + (Divisor − Remainder)

⇒ Smallest 4-digit number = 1000

⇒ Perform division: 1000 ÷ 47

⇒ 47 × 21 = 987

⇒ 47 × 22 = 1034

⇒ Remainder when 1000 is divided by 47 is 13.

⇒ Required number = 1000 + (47 − 13)

⇒ Required number = 1000 + 34 = 1034

∴ The correct answer is 1034.

Additional Information

Divisibility Rule for 47

To check divisibility by 47, multiply the last digit by 14 and add it to the remaining number. Repeat until a multiple of 47 is found.

Smallest/Largest n-digit Numbers

Smallest n-digit number is 10ⁿ⁻¹ and largest n-digit number is (10ⁿ − 1).

Division Algorithm

Dividend = (Divisor × Quotient) + Remainder. For perfect divisibility, Remainder must be 0.

• When washing soda reacts with hydrochloric acid, Carbon dioxide gas is evolved.
• Washing soda- It is sodium carbonate. The chemical formula is Na₂CO₃. It is a natural cleaner and cleaning booster.
• Sodium carbonate, when added to water, helps to remove magnesium and calcium ions, and increases detergent efficiency.
• The following chemical reaction takes place as per the statement:-
• Na₂CO₃+ 2HCl → 2NaCl + CO₂ + H₂O

The pattern followed is,

Hence, “28K” is the correct answer.

Shortcut Trick

Side of square = √31684 = 178 m

Perimeter = 4 × 178 = 712 m

Total wire needed for 4 rounds = 4 × (1.05 × 712)

Total wire = 4 × 747.6 = 2990.4 m

∴ The correct answer is 2990.4 m.

Alternate Method

Given:

Area of square field = 31684 m²

Number of wire rounds = 4 (at heights 1m, 2m, 3m, 4m)

Extra length per round = 5% of perimeter

Calculations:

⇒ Side (a) = √Area = √31684

⇒ Side (a) = 178 m

⇒ Perimeter = 4 × a = 4 × 178 = 712 m

⇒ Length of one wire round = 105% of 712 = 1.05 × 712 = 747.6 m

⇒ Total length for 4 rounds = 4 × 747.6 = 2990.4 m

∴ The correct answer is 2990.4 m.

Additional Information

Square Properties

For a square with side 'a', Area = a² and Perimeter = 4a. The diagonal is given by a√2.

Fencing Concept

Fencing length is always based on the perimeter of the field. Total wire = Number of rounds × (Perimeter + Extra allowance).

Percentage Increase

To increase a value by x%, multiply the original value by (1 + x/100).

CONCEPT:

• Kinetic energy (KE): The energy possessed by a body by virtue of its motion is called kinetic energy.

$KE = \frac{1}{2}m{v^2}$

Where m = mass of the body and v = velocity of the body

​EXPLANATION:

• $KE = \frac{1}{2}m{v'^2} = \frac{1}{2}m{(2v)^2} = 2mv^2$
• As the kinetic energy is directly proportional to the square of the velocity. So if the velocity becomes twice, the kinetic energy would be four times (square of twice gives four).
• Since we have a cycle that will not change, so there is no change in mass.

The mirror image for the following figure when the mirror is kept at the MN line is,

Hence, option 2 is the correct answer.

• Avogadro number is represented by NA.
• It is an absolute number. It represents the number of units in one mole of any substance.
• It is equal to 6.02214076 × 10²³.
• Now, the units can be anything-electrons, atoms, ions, or molecules.
• Avogadro’s law states that equal volumes of different gases contain an equal number of molecules under the same conditions of temperature and pressure. It can be derived from the ideal gas equation.
• If V is the volume of the gas and n denotes the amount of gaseous substance (moles), V/n would be constant. It means that the ideal gas constant is the same value for all gases.

The correct answer is Option 1, i.e Terbium.

• Actinide series of periodic tables contains 15 elements with atomic numbers from 89 to 103.
• The general symbol of these elements is An.
• Terbium is not an actinoid. Its atomic number is 65 and its atomic symbol is Tb.
• Actinoid elements are radioactive and very poisonous. Every actinoid isotope also undergoes radioactive decay.
• These are the elements in the series - Actinium (Ac), Thorium (Th), Protactinium (Pa), Uranium (U), Neptunium (Np), Plutonium (Pu), Americium (Am), Curium (Cm), Berkelium (Bk), Californium (Cf), Einsteinium (Es), Fermium (Fm), Mendelevium (Md), Nobelium (No), and Lawrencium (Lr).

• ‘Kalamkari’, a Painting form belongs to Andhra Pradesh.
• It is a 3000-year-old art form practiced in Andhra Pradesh and Telangana.
• It refers to the ancient style of hand painting, done with a tamarind pen using natural dyes. It is primarily done on cotton or silk fabric.
• The art primarily uses earthy colors like indigo, mustard, rust, black, and green.
• There are 23 steps to complete this painting which include dyeing, bleaching, hand painting, block-printing, starching, cleaning, and more.
• There are a variety of motifs drawn in this painting-flowers, peacock, paisleys to divine characters of Hindu epics like Mahabharata and Ramayana.
• However, nowadays, this art can be seen as Kalamkari sarees also.

Shortcut Trick

Convert the radical value into a quadratic equation: 2x − 1 = √3 ⇒ 4x² − 4x − 2 = 0 ⇒ 2x² − 2x − 1 = 0.

Express the target polynomial in terms of this quadratic factor: 4x³ + 2x² − 8x + 7 = (2x + 3)(2x² − 2x − 1) + 10.

Substitute the value of the quadratic factor (0) into the expression: (2x + 3) × 0 + 10 = 10.

∴ The correct answer is 10.

Alternate Method

Given: x = (√3 + 1) / 2

Method: Reducing high-degree polynomial using characteristic equation.

⇒ 2x = √3 + 1

⇒ 2x − 1 = √3

Squaring both sides:

⇒ (2x − 1)² = (√3)²

⇒ 4x² − 4x + 1 = 3

⇒ 4x² − 4x − 2 = 0

⇒ 2x² − 2x − 1 = 0

Now, rewrite the given expression 4x³ + 2x² − 8x + 7:

⇒ 2x(2x² − 2x − 1) + 4x² + 2x + 2x² − 8x + 7

⇒ 2x(0) + 6x² − 6x + 7

⇒ 3(2x² − 2x − 1) + 3 + 7

⇒ 3(0) + 10

⇒ 10

∴ The correct answer is 10.

Additional Information

Conjugate Roots Theorem

If a quadratic equation with rational coefficients has one root as a + √b, then the other root must be its conjugate a − √b.

Polynomial Division

For any polynomial P(x) and divisor D(x), P(x) = D(x) × Q(x) + R(x). If D(x) = 0 for a given value of x, then P(x) equals the remainder R(x).

Algebraic Identity

Standard identity: (a − b)² = a² − 2ab + b² is used to remove square roots from linear radical expressions.

• An element has an atomic number of 20. Beryllium would show similar chemical properties as the element.
• Calcium has atomic number 20. Beryllium has atomic number 4.
• Two different elements are likely to have similar chemical properties when they have the same number of valence electrons.
• Beryllium has 2 valence electrons and calcium also has 2 valence electrons.
• The vertical columns on the periodic table which are called groups have similar chemical behavior.
• Beryllium and calcium are in the second group of the periodic table.

• NTPC had adopted the maintenance of Charminar in Hyderabad as part of the Swachh Bharat Mission in 2018.
• NTPC Ltd and the Greater Hyderabad Municipal Corporation had signed a memorandum of understanding for implementation of development and beautification works under the Charminar Pedestrianization Project in Hyderabad.
• As per the MoU, the work included providing battery-operated vehicles for visitors, bollards to prevent traffic, Swachh Auto Tippers for carting garbage, mechanical sweeping vehicles and litter picking machines, decorative and halogen lighting of four arches, construction of public utilities, toilets and drinking water ATM kiosks.
• Charminar was constructed by Muhammad Quli Qutb Shahi in 1591 AD. It lies near the bank of the river Musi.
• It is believed that he made it construct to celebrate the end of a deadly plague.

• Hydrogen is the only non-metal present in Group 1 of the Modern Periodic Table.
• The vertical columns in periodic table is called a group and horizontal row is called period.
• There are 18 groups and 7 periods in modern periodic table.
• The elements in one group share similar chemical properties because they have same number of valence electrons.
• Group 1 contains alkali metals with the exception of hydrogen. The alkali metals are lithium, sodium, potassium, rubidium, cesium, and francium.
• Since hydrogen shares the same electronic configuration as with other elements of group 1, it is placed there.
• Cobalt atomic number-27 and symbol Co. It is in group 9.
• Rubidium atomic number-37 and symbol Rb. It is in group 1.
• Potassium atomic number-19 and symbol K. It is in group 1.

CONCEPT:

• Force: The interaction which after applying on a body changes or try to change the state of rest or state of motion of the body is called force.

Force (F) = Mass (m) × acceleration (a) 

• Retardation: The force acting in the opposite direction to the motion of a body is called the retarding force. This force produces negative acceleration for the body which is called retardation or deacceleration.

Retardation (a) = Force/Mass

The equation of motion is given below:

V = u + a t

Where V is final velocity,C is initial velocity, a is acceleration and t is time

CALCULATION:

Given that: 

Mass (m) = 30 kg, Initial velocity (u) = 20 m/s

Force (F) = - 60 N

Acceleration (a) = F/m = - 60/30 = - 2 m/s2

Final velocity (V) = 0 m/s​

• We know that body is stopped, it means the final velocity is 0.

V = u + a t

0 = 20 + (-2)t

2t = 20

Time taken (t) = 10 seconds. So option 2 is correct.

The pattern followed is,

Hence, “33” is the correct answer

The pattern followed is,

The given figure consists of four symbols.

The first three symbols are moving by one place towards their right and the fourth symbol is constant.

The figure which will come next in the pattern is,

Hence, option 3 is the correct answer.

CONCEPT:

• Echo: If we shout or clap near a suitable reflecting object such as a tall building or a mountain, we will hear the same sound again a little later. This sound which we hear is called an echo.
• Echoes are heard due to the phenomenon of Reflection of sound waves.
• To hear the echo clearly, the reflecting object must be more than 17.2 m from the sound source for the echo to be heard by a person standing at the source.

EXPLANATION:

• Echoes are heard due to the phenomenon of reflection of sound. So option 1 is correct.

• In the case of resonance, interference, and refraction of sound there is no echo. So options 2, 3, and 4 are wrong.

• SONAR (sound navigation ranging) uses the principle of reflection of soundwaves and submarine can detect objects nearby or distant.

• Echolocation is widely used by bats and whales.

• Bats cannot see but they send out waves from the mouth or nose and perceives the echo to know to the approximate distance of the object.

• Most mammals like whales produce high-frequency sound or sonar clicks. Whales can recognize the size of the object and the distance almost instantly when they receive echo.

• The velocity of sound in dry air is approximately 343 m/s at a temperature of 25 °C.

• A Papaya is a unisexual flower.
• A unisexual flower would either have stamens or carpels. But it can never possess both together.
• Stamen is the male fertilizing organ of a flower and carpel is the female fertilizing organ of a flower.
• Simply, we can say that it can either be male flower or female flower.
• Coconut flowers, Watermelon, Cucumber, Maize, etc are some examples of unisexual flower.
• Gulmohar is widely grown as a street tree or an ornamental tree because it is very colorful. It is also known as royal poinciana.
• Hibiscus are large colorful flowers. The flowers and leaves can be made into teas and liquid extracts that can help treat a variety of conditions.
• Mustard plant is yellow in color and can produce seed in as few as 60 days. The seeds of mustard plants are widely used in spices.

Jupiter and earth are planets.

Vegetation is found mainly on earth.

The correct Venn diagram representation is,Hence, option 1 is the correct answer.

Hence, option 1 is the correct answer.

• Anil K.Tripathi had been awarded “Bharat Gaurav Award” 2017 in Science and Technology category.
• He is a Director at Institute of Science & Professor, School of Biotechnology, Banaras Hindu University.
• He won the award in 2017 as recognition for his meritorious achievements, outstanding performance and individual excellence throughout his life.
• In 2012, Sanskriti Yuva Sanstha started “Bharat Gaurav Award”  as a felicitation program for people from all our World who achieve a landmark in their working area and made India proud.
• First ‘Bharat Gaurav Award' Ceremony was held in 2012 at Hotel Hilton ,New Jersey,USA.

Drawing the Venn diagram,

Conclusion 1: All metals are pins → False (This is definitely false)

Conclusion 2: Some metals are sharp → True (This is definitely true)

Hence, “only conclusion 2” follows.

The correct answer a double covalent bond.

Key Points

• A molecule of Oxygen has a double covalent bond.
• A covalent bond is a chemical bond in which atoms share electron pairs. There is a balance of attractive and repulsive forces between atoms.
• In a double covalent bond, two pairs of electrons are shared between the atoms.
• As in the case of Oxygen (Atomic number 8), it has six valence electrons. Each O atom of the oxygen molecule shares 2 electrons to form two covalent bonds. This way, both oxygen atoms complete their octet and achieve stable structures.
• Three pairs of electrons are shared between the two combining atoms in a triple covalent bond.
• In an electrovalent bond, one atom loses an electron to form a positive ion and the other atom gains the electron to form a negative ion. And since these ions are oppositely charged, these are held by electrostatic attraction forming an electrovalent bond.

Shortcut Trick

Net percentage change in area of a square = x + x + (x × x)/100

Given increase in side (x) = 30%

⇒ Net increase = 30 + 30 + (30 × 30)/100

⇒ 60 + 9 = 69%

∴ The correct answer is 69%.

Alternate Method

Given: Increase in side = 30%

Formula Used: Area of square = side²

⇒ Let original side = 10 units

⇒ Original Area = 10² = 100 sq. units

⇒ New side = 10 + 30% of 10 = 13 units

⇒ New Area = 13² = 169 sq. units

⇒ Increase in area = 169 − 100 = 69 units

⇒ % Increase = (69/100) × 100 = 69%

∴ The correct answer is 69%.

Additional Information

Successive Percentage Change

For two successive changes a% and b%, the effective change is (a + b + ab/100)%.

Area of 2D Figures

If dimensions of a rectangle are changed by x% and y%, area changes by (x + y + xy/100)%.

Square Properties

Area = (side)² or (diagonal)²/2. All sides are equal and all angles are 90°.

• When phenolphthalein is added to vinegar, the solution becomes colourless.
• Phenolphthalein- C₂₀H₁₄O₄.
• It is used as an indicator in acid-base titrations.
• When ph is put in a basic solution, it turns pink and when it is put in acidic solution, it turns colorless.
• Hence, it remains colourless below pH 8.5 and attains a pink to deep red hue above pH 9.0.
• Vinegar is nothing but an aqueous solution of acetic acid (CH₃COOH).
• That is why the solution would remain colorless as ph shows no change in acidic solutions.

Shortcut Trick

Time = Distance ÷ Velocity

Time = 480 ÷ 60 = 8 seconds.

∴ The correct answer is 8 s.

Alternate Method

Given:

Velocity (v) = 60 m/s

Distance (d) = 480 m

Formula Used:

Time (t) = Distance (d) / Velocity (v)

Calculations:

⇒ t = 480 ÷ 60

⇒ t = 8 seconds

∴ The correct answer is 8 s.

Additional Information

Constant Velocity

When an object moves with constant velocity, the acceleration is zero, and the distance covered is directly proportional to time.

Unit Conversion

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

Average Speed

Average speed is calculated as Total Distance ÷ Total Time taken for the entire journey.

Shortcut Trick

Notice that Team B scored exactly 1 goal more than Team A in every single match.

Shortcut: Average B = Average A + 1.

Calculate Average A: (2 + 1 + 1 + 4) ÷ 4 = 8 ÷ 4 = 2.

Therefore, Average B = 2 + 1 = 3.

∴ The correct answer is Team A : 2, Team B : 3.

Alternate Method

Given:

Goals of Team A: 2, 1, 1, 4

Goals of Team B: 3, 2, 2, 5

Total Games: 4

Formula Used:

Average Score = Sum of Goals ÷ Total Number of Games

Calculations:

⇒ Total Goals for Team A = 2 + 1 + 1 + 4 = 8

⇒ Average Score of Team A = 8 ÷ 4 = 2

⇒ Total Goals for Team B = 3 + 2 + 2 + 5 = 12

⇒ Average Score of Team B = 12 ÷ 4 = 3

∴ The correct answer is Team A : 2, Team B : 3.

Additional Information

Arithmetic Mean

The most common type of average, calculated by adding all numbers in a data set and then dividing by the count of those numbers.

Effect of Constant Addition

If every value in a data set is increased by a constant k, the new average will be the old average plus k.

Range of Data

The difference between the maximum and minimum values in a set. For Team A, Range = 4 − 1 = 3; for Team B, Range = 5 − 2 = 3.

• Jairam Ramesh is the author of the book ‘Indira Gandhi – A Life in Nature'.
• It was published in 2017 and Simon & Schuster India was the publisher.
• This book includes the personal, political, and environmental history of Indira Gandhi. Jairam has talked about how her views on the environment remained steadfast even as her political and economic stances changed and she took significant decisions particularly regarding forests and wildlife.
• Jairam Ramesh is a Member of Parliament representing Karnataka state in the Rajya Sabha.
• Other books by him - Old History, New Geography: Bifurcating Andhra Pradesh (2016), To the Brink and Back: India's 1991 Story (2015), Legislating for Justice: The 2013 Land Acquisition Law (2015), Green Signals: Ecology, Growth and Democracy in India (2015), etc.
• Books by Natwar Singh - One Life is enough, Treasured Epistles, Profiles and Letters, etc.
• Books by Sonia Gandhi - Rajiv, Rajiv's World, etc.
• Book by Priyanka Vadra - Ranthambhore: The Tiger's Realm

Statement 1: Number of students is not given in this statement.

Statement 2: This is sufficient, because it is mentioned that there are 6 girls and 8 boys in the class.

Hence, “only 2” is sufficient.

Shortcut Trick

Total distance (Train + Platform) = Speed × Time

Convert speed to m/s: 57 × (5/18) = 15.833 m/s

Total distance = 15.833 × 39 = 617.5 m

Platform length = 617.5 − 156.5 = 461 m

∴ The correct answer is 461 m.

Alternate Method

Given: Length of train (L_T) = 156.5 m, Speed (S) = 57 km/hr, Time (t) = 39 seconds.

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

⇒ Speed in m/s = 57 × (5/18) = 285/18 = 15.8333... m/s

⇒ Total Distance = (Length of Train + Length of Platform)

⇒ (156.5 + L_P) = (285/18) × 39

⇒ 156.5 + L_P = (285 × 13) / 6

⇒ 156.5 + L_P = 3705 / 6

⇒ 156.5 + L_P = 617.5

⇒ L_P = 617.5 − 156.5

⇒ L_P = 461 m

∴ The correct answer is 461 m.

Additional Information

Unit Conversion

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

Relative Speed

When two objects move in the same direction, relative speed is S₁ − S₂. In the opposite direction, it is S₁ + S₂.

Crossing Objects

When a train crosses a pole or man, distance = train length. When it crosses a bridge or platform, distance = train length + object length.

In all the figures, except in figure B the outer figure has four sides.

Whereas,

In figure B the outer figure has 6 sides.

Hence, figure “B” is the odd one.

The given figure has two circles on the outer layer and a sphere immersed inside them.

Similarly,

Figure C also has two circles and a sphere immersed in it.

Figure C resembles the given figure.

Hence, option 1 is the correct answer.

Drawing diagram according to the given information,

He is facing ‘east’ now.

Hence, “east” is the correct answer.

• S. S. Rajamouli is the director of the blockbuster movie ‘Bahubali’.
• Baahubali: The Beginning was made in 2015 and it was shot in both Telugu and Tamil.
• The film was made on a budget of Rs. 180 crore and it was the most expensive movie at that time.
• It is the highest-grossing South Indian film and it is the third highest-grossing Indian film worldwide.
• It also won the National Film Award for Best Special Effects and Best Feature Film.
• In 2017, the director came with the sequel named "Baahubali 2: The Conclusion". This movie became the second highest-grossing Indian film worldwide.
• The first position is held by Aamir Khan's Dangal.

CONCEPT:

• Momentum: The product of the mass and velocity of an object is called momentum. It is denoted by P.

Momentum (P) = Mass (m) × Velocity (v)

• Newton’s Second law of motion: The rate of change of momentum of any object is directly proportional to the applied force on the body.

${\rm{Force;}}\left( {\rm{F}} \right) = \frac{{{\rm{Δ }}P}}{{{\rm{Δ }}t}}$

Where Δ P = Change in momentum and Δ t = change in time taken

EXPLANATION:

• According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the Applied force. So option 2 is correct.

• Bakelite is a kind of synthetic plastic whereas other are metals and alloys. Hence, Bakelite does not belong to the group.
• Bakelite is obtained by the polymerization of phenol and formaldehyde.
• Chemical Formula of Bakelite-(C₆H₆O-CH₂OH)_n.
• Leo Baekeland created Bakelite. He has also invented Velox photographic paper.
• Bakelite is a thermosetting resin and it can be molded very easily. It shows high resistance to electricity and heat, hence it was used for all non-conducting parts of radios and other electrical devices.
• Atomic number of Aluminium- 13. Symbol-Al.
• Atomic number of Iron- 26. Symbol-Fe.
• Brass is an alloy of copper and zinc.

The pattern followed is,

In the first figure there are two triangles and in the second figure there is a triangle inside the triangle.

Similarly,

There are two circles in the third figure and in the fourth figure there must be a circle inside a circle.

The pattern followed is,

Hence, option 2 is the correct answer.

• The element of the Lanthanide series having the atomic number 58 is Cerium .
• This series has 14 elements from atomic number 57 to 71. They are also called "rare earth elements".
• Lanthanides and Actinides are the only elements that fill the f-orbitals.
• The elements of Lanthanide series are very difficult to extract. The isolation of an individual element may involve hundreds of fractional crystallizations.
• These elements are used as alloys to impart strength and hardness to metals.
• The elements are- lanthanum, cerium , praseodymium , neodymium , promethium , samarium , europium , gadolinium , terbium , dysprosium , holmium , erbium , thulium , ytterbium , and lutetium .
• Thorium is a weak radioactive element. Symbol -Th and Atomic number -90.

CONCEPT: 

• Resistance: The property of any conductor that opposes the flow of electric current through it is called resistance.
• It is denoted by R and the SI unit is the ohm (Ω).
• Superconductors are said to have zero resistance.
• One can control Voltage and Current by altering the resistance of the circuit.

The resistance (R) is given by:

R = ρL/A

where ρ is resistivity, L is the length and A is the area of the cross-section. 

EXPLANATION:

1. The resistance of a conductor does not depend on Pressure. So option 1 is correct.
2. Conductors show less resistance and Insulators show very high resistance. So it depends on the material.
3. It is inversely proportional to the cross-sectional area of the wire.
4. The r esistance is directly proportional to the length of the wire and resistivity of the material used in making the wire.

Drawing the Venn diagram,

Conclusion 1: All flowers are soft → True (This is definitely true)

Conclusion 2: Some soft are petal → True (This is definitely true)

Hence, “both conclusions” follow.

Shortcut Trick

Total hours = Number of days × Daily reading hours

Daily reading hours = 1 3/4 = 7/4 hours.

Total hours = 6 × 7/4 = 42/4 = 10 1/2 hours.

∴ The correct answer is 10 1/2 hr.

Alternate Method

Given:

Total days taken to read the novel = 6 days

Time spent reading per day = 1 3/4 hours

Formula Used:

Total Time = Number of Days × Time per Day

Calculations:

⇒ Convert mixed fraction to improper fraction: 1 3/4 = (1 × 4 + 3) / 4 = 7/4 hours

⇒ Total hours = 6 × 7/4

⇒ Total hours = (6 × 7) / 4 = 42 / 4

⇒ Simplify the fraction: 42 / 4 = 21 / 2

⇒ Convert back to mixed fraction: 21 / 2 = 10 1/2 hours

∴ The correct answer is 10 1/2 hr.

Additional Information

Mixed Fraction Conversion

To convert a mixed fraction a b/c to an improper fraction, use the formula: (a × c + b) / c.

Total Work Calculation

Total quantity = Unit rate × Number of units. In time-based problems, Total Time = Daily Rate × Number of Days.

• Kisan Urja Suraksha evam Utthaan Mahaabhiyan (KUSUM) has been launched by the union government for promoting solar farming.
• It was approved by the Cabinet Committee on Economic Affairs, chaired by Hon'ble Prime Minister Shri Narendra Modi in 2019.
• The objective of the scheme is to provide financial and water security to farmers.
• There are three components of the scheme :-
• 10,000 MW of Decentralized Ground Mounted Grid Connected Renewable Power Plants.
• Installation of 17.50 lakh standalone Solar Powered Agriculture Pumps.
• Solarisation of 10 Lakh Grid-connected Solar Powered Agriculture Pumps.
• The scheme aims to add a solar capacity of 25,750 MW by 2022.

The number of triangles in the given figure is,

Hence, “40” is the correct answer.

Let Ritika's present age be "x".

Priyamvada's present age is five years more than twice the age of his cousin Ritika.

∴ Priyamvada's present age = 2x + 5

After 16 years, 

Ritika's age will be "x + 16"

and Priyamvada's age will be "2x + 5 + 16" i.e. 2x + 21.

Priyamvada's age will be 150% of that of Ritika's age.

From the above condition,

2x + 21 = 150% of (x + 16)

(2x + 21) × 100 = 150 × (x + 16)

∴ 200x + 2100 = 150x + 2400

∴ 200x - 150x = 2400 - 2100

∴ 50x = 300

∴ x = 6

Hence, Ritika's present age is 6 years.

Whereas, Priyamvada's present age will be,

(2 × 6) + 5 = 17

Hence, 17 is the correct answer.

Shortcut Trick

Find the effective interest rate: 1.6% × 15 = 24%.

Calculate 24% of the Principal (₹1250).

Interest = 0.24 × 1250 = ₹300.

∴ The correct answer is ₹300.

Alternate Method

Given:

Principal (P) = ₹1250

Time (T) = 15 years

Rate (R) = 1.6% per annum

Formula Used:

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

Calculations:

⇒ SI = (1250 × 1.6 × 15) ÷ 100

⇒ SI = (1250 × 24) ÷ 100

⇒ SI = 12.5 × 24

⇒ SI = ₹300

∴ The correct answer is ₹300.

Additional Information

Simple Interest Concept

Simple interest is calculated only on the principal amount of a loan or deposit. It does not account for interest earned in previous periods.

Total Amount Formula

The total amount (A) after T years is the sum of the principal and the interest: A = P + SI or A = P(1 + RT/100).

Rate and Time Conversion

Ensure the rate (R) and time (T) are in consistent units. If time is in months, convert to years by dividing by 12.

The pattern followed is,

Hence, “KK” is the correct answer.

The correct answer is National Payments Corporation of India.

Important Points

• NPCI-National Payments Corporation of India.
• It is an umbrella organization for operating retail payments and settlement systems in India.
• It is an initiative of the RBI and Indian Banks’ Association under the provisions of the Payment and Settlement Systems Act, 2007. It is registered under section 8 of the Companies Act 2013.
• It intends to provide infrastructure to the entire Banking system in India for physical as well as electronic payment and settlement systems.
• The ten core promoter banks are State Bank of India, Punjab National Bank, Canara Bank, Bank of Baroda, Union Bank of India, Bank of India, ICICI Bank, HDFC Bank, Citibank N. A. and HSBC.
• MD and CEO-Dilip Asbe.

Shortcut Trick

Speed Ratio (S₁ : S₂) = 10 : 15 = 2 : 3.

Since distance is constant, Time Ratio (T₁ : T₂) = 3 : 2.

Difference in time units = 3 − 2 = 1 unit → 12 minutes.

Total time for first horse = 3 × 12 = 36 minutes = 36/60 hours = 0.6 hours.

Distance = Speed × Time = 10 × 0.6 = 6 km.

∴ The correct answer is 6 km.

Alternate Method

Given:

Speed of first horse (S₁) = 10 km/hr

Speed of second horse (S₂) = 15 km/hr

Time difference (Δt) = 12 minutes = 12/60 hours = 1/5 hours

Formula Used:

Distance (D) = [ (S₁ × S₂) / (S₂ − S₁) ] × Δt

Calculations:

⇒ D = [ (10 × 15) / (15 − 10) ] × (12/60)

⇒ D = [ 150 / 5 ] × (1/5)

⇒ D = 30 × (1/5)

⇒ D = 6 km

∴ The correct answer is 6 km.

Additional Information

Inverse Proportion of Time and Speed

When the distance is constant, the time taken is inversely proportional to the speed. If speeds are in ratio a:b, time taken will be in ratio b:a.

Average Speed for Same Distance

If an object covers the same distance at two different speeds S₁ and S₂, the Average Speed is given by (2 × S₁ × S₂) / (S₁ + S₂).

Relative Speed

When two objects move in the same direction, relative speed is S₁ − S₂. In opposite directions, it is S₁ + S₂.

Important Points 

• Do not get tensed by the complexity of the figures.
• Carefully understand the structure of the given question figure.
• The embedded figure may not be of exact size. It may be small or big.
• Sometimes the rotation or reflection of the figures may be confusing.
• So think wisely before selecting the answer.

When the sheet is folded at the dotted line it resembles,

Hence, option 1 is the correct answer.

Key Points

• In animal cells, Cuboidal epithelium forms the inner lining of the kidney to provide mechanical support.
• Cuboidal epithelium is a single layer thick and made of cube-shaped cells. This tissue is found lining parts of the body such as the kidney tubules and walls of the respiratory bronchioles.
• Glandular epithelium-It is a type of epithelial tissue that covers the exocrine and endocrine glands.
• Columnar epithelium- These tissues are made of a single layer of long epithelial cells in regions where absorption and secretion are important. They also form the lining of the stomach and intestines.
• Squamous epithelium- It is a single layer of flat cells. These are in contact with the basal lamina of the epithelium. The tissues are permeable and occur where small molecules need to pass through membranes via diffusion.

• Kandaleru Dam is located in Andhra Pradesh.
• It is built on the Kandaleru River in Rapur Mandal, Nellore district.
• It is primarily built for irrigation purposes. This dam was a part of the Telugu Ganga project which basically supplies drinking water to Chennai city from the Srisailam reservoir on Krishna River.
• Other dams in Andhra Pradesh - Nagarjuna Sagar Dam, Srisailam Dam, etc.
• Dams in Kerala - Idukki Dam, Mullaperiyar Dam, Kakkayam Dam, etc.
• Dams in Tamil Nadu - Mettur Dam, Sholayar Dam, etc.
• Dams in Karnataka - Tungabhadra Dam, Almatti Dam, etc.

The pattern followed is,

For LET,

The place value for L is 12

The place value for E is 5

The place value for T is 20

So,

Let is coded as 12520

Similarly,

For WIN,

The place value for W is 23

The place value for I is 9

The place value for N is 14

WIN is coded as 23914

Hence, “23914” is the correct answer.

Shortcut Trick

Profit ratio is same as investment stake ratio.

Ratio of Tejal : Ashank = 40% : 60% = 2 : 3.

If 2 units = ₹10,00,000 (Tejal's profit), then 1 unit = ₹5,00,000.

Ashank's profit = 3 units = 3 × ₹5,00,000 = ₹15,00,000.

∴ The correct answer is ₹15 lakh.

Alternate Method

Given: Tejal's stake = 40%, Ashank's stake = 60%, Tejal's profit = ₹10,00,000.

Formula Used: Profit Share = (Individual Stake / Total Stake) × Total Profit

⇒ Let the total profit of the firm be P.

⇒ 40% of P = ₹10,00,000

⇒ (40/100) × P = 10,00,000

⇒ P = (10,00,000 × 100) ÷ 40

⇒ P = ₹25,00,000

⇒ Ashank's profit = 60% of P

⇒ Ashank's profit = (60/100) × 25,00,000

⇒ Ashank's profit = 0.6 × 25,00,000 = ₹15,00,000

∴ The correct answer is ₹15 lakh.

Additional Information

Partnership Profit Distribution

In a partnership, profit is shared in the ratio of Investment × Time Period. If the time is constant, the ratio is simply based on the capital stake.

Active vs Sleeping Partner

An active partner manages the business and may receive an additional salary or commission before the remaining profit is shared according to the investment ratio.

Shortcut Trick

Initial Ratio (Sugar : Flour) = 4 : 7 (Total parts = 11)

New Ratio = 2 : 5 → Multiply by 2 to keep Sugar constant → 4 : 10

Initial dough = 22 kg ⇒ 11 parts = 22 kg ⇒ 1 part = 2 kg

Increase in Flour = 10 − 7 = 3 parts

Flour added = 3 × 2 kg = 6 kg

∴ The correct answer is 6 kg.

Alternate Method

Given: Initial dough = 22 kg, Initial Ratio = 4 : 7, Final Ratio = 2 : 5

Calculations:

⇒ Sugar in initial dough = (4/11) × 22 = 8 kg

⇒ Flour in initial dough = (7/11) × 22 = 14 kg

⇒ Let additional flour added be x kg.

⇒ New ratio of Sugar to Flour = 8 / (14 + x) = 2 / 5

⇒ 8 × 5 = 2 × (14 + x)

⇒ 40 = 28 + 2x

⇒ 2x = 12

⇒ x = 6 kg

∴ The correct answer is 6 kg.

Additional Information

Constant Quantity Concept

When one component is added to a mixture, the quantity of the other component remains unchanged. Equating this constant component in both ratios simplifies the calculation.

Ratio Balancing

To balance ratios, multiply the terms of one or both ratios by a common factor so that the parts representing the unchanged quantity become equal.

Mixture Replacement

If a part of the mixture is replaced by a pure component, the total quantity remains the same, but the internal ratio changes significantly.

Platinum is a metal.

And,

Oxygen is a colourless, odourless gas.

The correct Venn diagram representation is,

Hence, option 4 is the correct answer.

Shortcut Trick

To find how much less one value is than another, perform direct subtraction.

Difference = 42.3 km − 28.8 km

Difference = 13.5 km

∴ The correct answer is 13.5 km.

Alternate Method

Given:

First distance = 42.3 km

Second distance = 28.8 km

Formula Used:

Difference = Larger Value − Smaller Value

Calculations:

⇒ Required value = 42.3 km − 28.8 km

⇒ Aligning decimals: 42.3 − 28.8

⇒ 13.5 km

∴ The correct answer is 13.5 km.

Additional Information

Decimal Subtraction

Always align the decimal points vertically before performing subtraction or addition of decimal numbers.

Unit Consistency

Ensure both quantities are in the same unit (e.g., both in km or both in m) before comparing or subtracting them.

Shortcut Trick

An irrational number is a number that cannot be expressed as a simple fraction p/q.

√16 = 4 (Rational)

⁶√1 = 1 (Rational)

³√8 = 2 (Rational)

⁴√4 = √(√4) = √2 ≈ 1.414... (Irrational)

∴ The correct answer is √2.

Alternate Method

Given: Four numerical expressions to identify the irrational one.

Concept: A number is rational if it is a perfect n^th root of an integer; otherwise, it is irrational if it results in a non-terminating, non-recurring decimal.

⇒ Option 1: √16 = √(4²) = 4

⇒ Option 2: ⁶√1 = ⁶√(1⁶) = 1

⇒ Option 3: ⁴√4 = ⁴√(2²) = 2^2/4 = 2^1/2 = √2

⇒ Since √2 is a well-known irrational number, ⁴√4 is irrational.

⇒ Option 4: ³√8 = ³√(2³) = 2

∴ The correct answer is ⁴√4.

Additional Information

Definition of Irrational Numbers

Numbers that cannot be written in the form p/q, where p and q are integers and q ≠ 0. Their decimal expansions are non-terminating and non-recurring.

Properties of Surds

A radical ⁿ√x is irrational if x is not a perfect n^th power of a rational number.

Common Irrational Constants

Examples include π (pi), e (Euler's number), and square roots of non-perfect squares like √2, √3, and √5.

CONCEPT:

• Sound: The sound is a longitudinal wave in which the particles of the medium through which the sound is transported vibrate parallel to the direction that the sound wave moves.
• Loudness: The phenomenon of sound waves that depend on the amplitude and energy of the sound wave is called Loudness.
• When the amplitude of the sound is large, then the sound wave is considered to be loud.

1. Frequency: The number of wave cycles happening per second is called frequency.
2. Amplitude: The maximum amount of displacement of the medium particles from its mean position is called the amplitude of the wave.
3. Wavelength: The distance between two adjacent maxima or two adjacent minima of a wave is called wavelength of that wave. It is denoted by λ.
4. Pitch: The response of the ear to the frequency of sound is called the pitch of the sound.

EXPLANATION:

• Sound is a wave and a high amplitude wave carries a large amount of energy. It means a low amplitude wave carries a small amount of energy.
• The loudness of a sound wave is directly proportional to the square of the amplitude of that wave.
• The loudness of the sound produced by a radio increases by increasing the amplitude. So option 2 is correct.

Assumption 1: This is implicit, because safety, quality and nutritional value of the food we eat is of fundamental importance to our health and well-being.

Assumption 2: This is not implicit because, nothing is mentioned about monitoring in the given statement.

Hence, “only conclusion 1” is implicit.

92 – [71 + {4 – (5 – (4 – 2))}]

⇒ 92 – [71 + {4 – (5 – 2)}]

⇒ 92 – [71 + {4 – 3}]

⇒ 92 – [71 + 1]

⇒ 92 – 72

⇒ 20

• Sh. Amitabh Kant is the former CEO of NITI Aayog.
• NITI-National Institution for Transforming India
• He has also written a book-"Branding India – An Incredible Story".
• NITI Aayog is a policy think tank of the Government of India which replaced Planning Commission of India. It was established with the aim at achieving sustainable development goals with cooperative federalism by fostering the involvement of State Governments in the economy policies.
• One of the objectives of NITI Aayog is to develop mechanisms to formulate credible plans at the village level and aggregate these progressively at higher levels of government.

Important Points

• Chairman - PM Narendra Modi
• Suman Bery is the current vice-chairperson of the NITI Aayog.
• Currently, Parameswaran Iyer is the CEO of NITI Aayog appointed in June 2022.

CONCEPT:

• Potential energy: The energy of any object due to its position with respect to a reference point is called potential energy. It is denoted by PE.

Potential energy is given by:

PE = m g h.

Here, PE is the Potential Energy, m is the mass, g is the acceleration due to gravity, and h is the height at which the object is placed

CALCULATION:

Given that: 

Mass (m) = 50 Kg

Height (h) = 6 m

PE = 50 x 10 x 6

PE = 3000 J

 PE = 3 kJ

• Kinetic energy: The energy due to the motion of the object is called kinetic energy.

Kinetic energy (KE) = 1/2 (mv2)

Where m is mass and v is velocity. 

• Since the object is stationary (at rest) so the velocity is zero. Hence the kinetic energy of the object will be zero.
• Only the potential energy of the object will be there at the height.

• India signed a pact with Myanmar for the socio-economic development of Rakhine State in Dec 2017.
• At that time, hundreds of thousands of mainly Muslim Rohingyas had fled from Rakhine(a predominantly Buddhist region) to Bangladesh.
• The memorandum of understanding was signed between S. Jaishankar and U. Soe Aung.
• It was intended to help Myanmar achieve its objective of restoration of normalcy in Rakhine State and enable the return of displaced persons.
• The GoI proposed to take up a project to build prefabricated housing in Rakhine State.
• Myanmar Capital - Naypyitaw
• Currency - Burmese kyat

Let the present age of Srinivas's daughter is "x",

Hence, Srinivas's present age is "4x",

5 years ago,

Srinivas's daughter's age was "x - 5",

and Srinivas's age was "4x - 5".

According to the given condition,

Srinivas was nine times as old as his daughter was at that time.

∴ 9 (x - 5) = 4x - 5

∴ 9x - 45 = 4x - 5

∴ 9x - 4x = 40

∴ 5x = 40

∴ x = 8

Hence, Srinivas's daughter's present age is '8' years.

The correct answer is Option 2, i.e Isotopes.

• Isotopes have similar chemical properties but different atomic masses.
• Isotope of an element has a different number of neutrons but have the same number of protons.
• For instance, isotopes of Hydrogen are Protium, Deuterium and Tritium.
• Isomers - They share the same formula but a different arrangement of atoms in the molecule which make them, possess different properties. The atomic number and atomic mass are equal but the energy states are different.
• Actinides - It is the third group in the periodic table. These are the elements from atomic numbers 89 to 103.These have properties of both the d-block and the f-block elements, but they are also radioactive.
• Isobars -They have the same mass number but a different atomic numbers (number of protons).

• The regulation was passed on 1829 to ban the practice of Sati.
• The Sati was practiced primarily by Hindu communities where a widow was supposed to be burn with her dead husband either voluntarily or non voluntarily.
• Raja Rammohan Roy raised his voice against this cruel practice and spread awareness among people to discontinue it. He is also known as the pioneer of women’s rights in India.
• Lord William Bentinck passed the Bengal Sati Regulation in all jurisdictions of British India.
• However, it is believed that many mughal emperors such as Humayun, Akbar, Aurangzeb, etc tried to abolish Sati.

• India won the 2017 Women’s Hockey Asia Cup title. It was the ninth edition of the cup.
• The winner of this tournament was to qualified for the 2018 World Cup in England and India qualified for it.
• The team was led by Skipper Rani Rampal.
• The final was played at Kakamigahara in Japan. India defeated China by 5-4 goals in penalty shootout.
• That win made India two times champion of Women’s Asia Cup title. The first time was in 2004.

Assumption 1: This is implicit, because participation in the debate improves convincing skills.

Assumption 2: This is implicit, because participation in the debate improves communication skills.

Hence, “both 1 and 2” are implicit.

• Shah Rukh Khan has been awarded Crystal award on 22nd January 2018 at WEF, World Economic forum Annual Summit held at Davos.
• He was awarded for his leadership in championing children’s and women’s rights in India
• The theme of the event was-"Creating a Shared Future in a Fractured World".
• Cate Blanchett was also awarded for her leadership in raising awareness of the refugee crisis.
• Elton John was also awarded for his leadership in the fight against HIV/AIDS.
• Theaster Gates, Jin Xing, Deepika Padukone, and Lynette Wallworth are named as 2020 Crystal Award.
• Deepika Padukone is named for her leadership in raising mental health awareness.