RRC Group D Previous Year Paper 66 (Held On: 24 Oct 2018 Shift 2)

Shortcut Trick

By using the rule of Alligation:

Ratio of frequencies = (Mean of Set 2 − Combined Mean) : (Combined Mean − Mean of Set 1)

⇒ Ratio = (15 − 12.5) : (12.5 − 12)

⇒ Ratio = 2.5 : 0.5 = 5 : 1

∴ The correct answer is 5 : 1.

Alternate Method

Given:

Mean of 1^st set of numbers (x₁) = 12

Mean of 2^nd set of numbers (x₂) = 15

Combined mean (x) = 12.5

Formula Used:

Combined Mean (x) = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂)

Where n₁ and n₂ are the frequencies of the 1^st and 2^nd set of numbers respectively.

Combined 12.5

Set 1 Mean

12

Set 2 Mean

15

15 − 12.5

2.5

12.5 − 12

0.5

Ratio = 2.5 : 0.5 = 5 : 1

Calculations:

⇒ 12.5 = (12 × n₁ + 15 × n₂) ÷ (n₁ + n₂)

⇒ 12.5n₁ + 12.5n₂ = 12n₁ + 15n₂

⇒ 12.5n₁ − 12n₁ = 15n₂ − 12.5n₂

⇒ 0.5n₁ = 2.5n₂

⇒ n₁ ÷ n₂ = 2.5 ÷ 0.5

⇒ n₁ : n₂ = 5 : 1

∴ The correct answer is 5 : 1.

Additional Information

Rule of Alligation

It is used to find the ratio in which two ingredients or sets at their respective prices or averages are mixed to produce a mixture at a given combined average. The formula is: Ratio = (Rate of Dearer − Combined Rate) / (Combined Rate − Rate of Cheaper).

Combined Average

When 'n' groups have individual averages A₁, A₂, ... A_n and their respective sizes are N₁, N₂, ... N_n, then their combined average is evaluated as (N₁A₁ + N₂A₂ + ... + N_nA_n) ÷ (N₁ + N₂ + ... + N_n).

The correct answer is Manipur.

• The Indian boxing champion Mary Kom belongs to Manipur.

Key Points

• Mary Kom:
• Mary Kom was born in Kagathei village, Churachandpur district of rural Manipur in India.
• Mary Kom won a silver medal at the 2008 Asian Women's Boxing Championship in India and a fourth successive gold medal at the 2008 AIBA Women's World Boxing Championships in China.
• Mary Kom also won a gold medal at the 2009 Asian Indoor Games in Vietnam.

Additional Information

Mary Kom awards are:

The logic followed here is:-

Hence, "option 4" is the correct answer.

• In an ordinary year, there are 365 days and on dividing 365 by 7, we get remainder = 1, so this extra one day is taken as an odd day.
• Similarly, in a leap year, there are 366 days and on dividing 366 by 7, we get remainder = 2, so these extra days are taken as the odd days.

 

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

• 1946 = 1600 + 300 + 46 years
• In 1600 years the odd days = 0
• In 300 years the odd days = 1
• In 46 years (from 1901 to 1946), = 46/4 = 11 leap years and 35 normal years.
• In 11 leap years, odd days = 22, and 35 normal years = 35 odd days
• So total = 22 + 35 = 57 odd days i.e. 57/7 = 1 odd day

In 1947, the number of days up to 17th August,

31 + 28 + 31 + 30 + 31 + 30 + 31 + 17 = 229 or 5 odd days. 

 

Total in 1947 years up to 17th August = 0 + 1 + 1 + 5 = 7/7 = 0 odd days.

The codes for the weekdays are as follows:

 

• The day of the week on August 17th, 1947 was Sunday.

Hence, "option 4" is the correct answer.

The correct answer is Adish Praveen.

• Adish Praveen has awarded the Best Child Actor Award for the film 'Kunju Devam' at the 64th National Film Awards held in April 2017.
• ​Adish Praveen is an Indian actor, who works in the Malayalam film industry, known for Iblis (2018), Kunju Daivam (2018).

Key Points

• Kunju Daivam is an Indian Malayalam film.
• Written and directed by: Jeo Baby.
• Production company: Ocean pictures.
• Music by: Mathews Pulickan.

Additional Information

• 67th National Film Awards
• Dadasaheb Phalke Award - Rajinikanth

Shortcut Trick

Total time duration = 5 years ago to 5 years later = 10 years.

Total increase: Jaimini = 300 × 10 = ₹3000; Jatin = 100 × 10 = ₹1000.

Let initial salaries be 1x and 3x. Final condition: 1x + 3000 = 3x + 1000.

2x = 2000 ⇒ x = 1000. Jatin's salary 5 yrs ago = 3 × 1000 = ₹3000.

Present salary of Jatin = 3000 + (100 × 5) = ₹3500.

∴ The correct answer is ₹3500.

Alternate Method

Given: Ratio 5 years ago = 1 : 3. Yearly increments = ₹300 and ₹100. Equality after 5 years from today (Total 10 years).

⇒ Let Jaimini's salary 5 years ago = 1x

⇒ Let Jatin's salary 5 years ago = 3x

⇒ Total increment for Jaimini in 10 years = 300 × 10 = ₹3000

⇒ Total increment for Jatin in 10 years = 100 × 10 = ₹1000

⇒ Equation: 1x + 3000 = 3x + 1000

⇒ 2x = 2000 ⇒ x = 1000

⇒ Jatin's salary 5 years ago = 3 × 1000 = ₹3000

⇒ Jatin's present salary = 3000 + (100 × 5) = ₹3500

∴ The correct answer is ₹3500.

Additional Information

Ratio and Proportion

When values are in ratio a : b, they can be represented as ax and bx. Changes are added/subtracted directly to these terms.

Time Gap Calculation

The total duration between 'n' years ago and 'm' years later is calculated as (n + m) years.

Uniform Increment

If an amount increases by 'k' every year, total increase after 't' years is simply k × t.

• The mirror image of the question figure is figure C.

Hence, "option 2" is the correct answer.

The correct answer is 42nd.

• 42nd amendment act was the word 'Secular' added to the Constitution of India.

Key Points

• The term secular was added by the 42nd Constitutional Amendment Act of 1976. 
• The Indian Constitution embodies the positive concept of secularism ie, all religions in our country (irrespective of their strength) have the same status and support from the state.
• The 42nd Amendment changed the description of India from a sovereign democratic republic to a sovereign, socialist secular democratic republic, and also changed the words unity of the nation to unity and integrity of the nation.
• The constitutionality of sections 4 and 55 of the 42nd Amendment was challenged in Minerva Mills v. Union of India when Charan Singh was caretaker Prime Minister.

Additional Information

The correct answer is 12.57%.

Given:

Mass of common salt = 46 g

Mass of water = 320 g

Formula used:

The concentration of solution = Mass of common salt/Mass of solution × 100

Calculation:

According to the question

Mass of solution = Mass of common salt + Mass of water

⇒ (46 + 320) g

⇒ 366 g

Concentration of solution = Mass of common salt/Mass of solution × 100

⇒ (46/366 × 100)

⇒ 12.5638% ~ 12.57%

∴ The required solution is 12.57%

The least possible Venn diagram is as follows:

Conclusion:

1. Some white are porcelain. → Follows (As can be seen from the Venn diagram, some porcelain are white so its converse is also true.)
2. No cup is white. → Does not follow (it is possible but not definite)

Hence, " option 3" is the correct answer.

The correct answer is the number of valence electrons.

• All the elements in the group of the periodic table have the same number of valence electrons.

Key Points

• Periodic Table:
• It is a tabular presentation of the chemical elements, organised on the basis of their properties.
• Mendeleev’s Periodic Table (1869):
• It is based upon Mendeleev’s periodic law, which states, “Properties of the elements are the periodic function of their atomic masses.”
• Mendeleev is known as the father of the periodic table.
• Modern Periodic Law was given by Moseley.
• According to him: “The physical and chemical properties of the elements are the periodic function of their atomic numbers.”
• Modern Periodic Table:
• It is a graphical representation of the Aufbau principle.
• It is based on the electronic configuration of elements and contains 118 elements.
• There are 7 periods and 18 groups.
• Modern periodic table is classified as:
  

i. s-block;

ii. p-block;

iii. d-block;

iv. f-block.

• The elements in each group of the periodic table have the same number of valence electrons.
• Hence, the elements in the same group display similar properties and reactivity.

The correct answer is poisonous (deformed).

Key Points

• Denatured spirit or alcohol is ethanol which is made unfit for drinking by adding poisonous substances like methanol or any other substance that will impart bad taste, foul smell, or colour.
• A blue dye is also added to it so that it is easily recognized.
• The four types of alcohol are:
• Ethyl.
• Denatured.
• Isopropyl.
• Rubbing.
• Distilled spirits are all alcoholic beverages in which the concentration of ethyl alcohol has been increased above that of the original fermented mixture by a method called distillation.
• The principle of alcoholic distillation is based upon the different boiling points of alcohol (78.5 °C, or 173.3 °F) and water (100 °C, or 212 °F).

Additional Information

The correct answer is India.

• India will host the 46th Congress of the International Hockey Federation.

Key Points

• 46th Congress of the International Hockey Federation:
• It was held in New Delhi.
• The biennial four-day event.
• It comprised meetings, social events, networking opportunities and presentations.
• Narinder Batra Former Hockey India chief was elected as the first non-European FIH President in 2016.
• International Hockey Federation (FIH):
• It is the apex governing body of field hockey and indoor field hockey.
• Its headquarters are in Lausanne, Switzerland.
• Dr Narinder Dhruv Batra is the current president.

Additional Information

• Hockey:
• ‘Blackheath Rugby and Hockey Club’ was the first hockey club in the world.
• It was set up in the year 1861 in England.
• Hockey was introduced in the Olympic Games for the first time in 1908 in London.
• Indian Hockey Federation (IHF) was formed in 1925 at Gwalior.
• The first Hockey World Cup was organised in Barcelona (Spain) in 1971.
• It was won by Pakistan.

The correct answer is Hydrochloric acid.

• Hydrochloric acid is secreted in the human digestive system.

Key Points

• The human digestive system includes the mouth, pharynx (throat), oesophagus, stomach, small intestine, large intestine, rectum, and anus.
• It also includes the salivary glands, liver, gallbladder, and pancreas.
• These organs make digestive juices and enzymes which help the body digest food and liquids.
• Hydrochloric acid is secreted by the human digestive system.

The logic followed here is:-

• Flour, pancake, and cream are edible items
• A ladle is a type of spoon.

Hence, " option 1" is the correct answer.

The correct answer is Elements present in group 17 are called alkaline metals.

• Elements present in group 17 are called halogens.​

Key Points

• Halogen:
• Elements in group 17 are called halogens.
• These are fluorine (F), chlorine (Cl), bromine (Br), iodine (I), astatine (At), and tennessine (Ts).
• Uses of halogens:
• Fluorine is used in the preparation of UF6 and SF6 for energy production and as a dielectric constant, respectively.
• Chlorofluorocarbon is known as Freon
• It is used as refrigerant and aerosol.
• Non-stick utensils are made up of Teflon.
• Chlorine is used to manufacture PVC, insecticides herbicides, etc.
• Bromine is used in ethylene bromide synthesis which is mixed with leaded petrol.

Shortcut Trick

Assume Total Wealth as the LCM of denominators (2, 4, 5) = 20 units.

Son 1 = 1/2 of 20 = 10 units | Son 2 = 1/4 of 20 = 5 units | Son 3 = 1/5 of 20 = 4 units.

Total distributed to first three sons = 10 + 5 + 4 = 19 units.

Remaining for the fourth son = 20 − 19 = 1 unit.

Given: 1 unit = ₹1,000 → Total Wealth (20 units) = 20 × 1,000 = ₹20,000.

∴ The correct answer is ₹20,000.

Alternate Method

Given:

Share of Son 1 = 1/2 of Total Wealth

Share of Son 2 = 1/4 of Total Wealth

Share of Son 3 = 1/5 of Total Wealth

Share of Son 4 = ₹1,000

Formula:

Sum of all shares = Total Wealth

Let the Total Wealth be 'x'.

⇒ (x/2) + (x/4) + (x/5) + 1000 = x

⇒ [(10x + 5x + 4x) / 20] + 1000 = x

⇒ (19x / 20) + 1000 = x

⇒ x − (19x / 20) = 1000

⇒ (20x − 19x) / 20 = 1000

⇒ x / 20 = 1000

⇒ x = 1000 × 20

⇒ x = 20,000

∴ The correct answer is ₹20,000.

Additional Information

Sum of Fractions

To add or subtract fractions, find a common denominator (LCM of denominators) to make them like fractions.

Unitary Method

When the value of 1 part is known, the value of the total whole (n parts) is found by multiplying the unit value by n.

Remaining Portion

Remaining portion = 1 − (Sum of all given fractional parts). Here, 1 − 19/20 = 1/20.

Shortcut Trick Find the LCM of 2, 4, and 6, which is 12. The smallest cube number divisible by these must be a multiple of the cube of their LCM or the cube of a common multiple. Calculation: 123 = 12 × 12 × 12 = 1728. Since 1728 > 1000, it is the smallest such cube number. ∴ The correct answer is 1728.

Alternate Method

Given numbers: 2, 4, 6 Condition 1: Number must be a perfect cube. Condition 2: Number must be greater than 1000. Condition 3: Number must be divisible by 2, 4, and 6. ⇒ LCM(2, 4, 6): ⇒ 2 = 21 ⇒ 4 = 22 ⇒ 6 = 2 × 3 ⇒ LCM = 22 × 3 = 4 × 3 = 12 ⇒ Any number divisible by 2, 4, and 6 must be a multiple of 12. ⇒ We need the smallest cube of a multiple of 12 that is > 1000. ⇒ 123 = 1728 ⇒ Since 103 = 1000 and 12 > 10, 1728 is clearly greater than 1000. ∴ The correct answer is 1728.

Additional Information Perfect Cube Definition An integer n is a perfect cube if there exists an integer x such that n = x3. LCM and Divisibility If a number is divisible by several integers, it must be divisible by their Least Common Multiple (LCM). Common Cubes 103 = 1000, 113 = 1331, 123 = 1728, 163 = 4096, 183 = 5832.

The correct answer is contraception.

• Contraception is the method by which Copper-T is placed in the uterus.

Key Points

• Contraception:
• It is also known as birth control.
• It is a method used to prevent pregnancy.
• Methods of contraception:
• combined pill
• condoms
• contraceptive injection
• contraceptive patch
• diaphragms
• intrauterine device (IUD) (Copper-T)
• intrauterine system (IUS)
• Copper-T is placed in the uterus.

Shortcut Trick

An irrational square root occurs if the number is not a perfect square.

Check the last digit and digital sum: all options end in 4 (possible for perfect squares).

Test digital sums: 2704 → 4; 2304 → 9; 3264 → 6; 1764 → 9 (All are possible).

Divide by 4 or check nearest squares: 50² = 2500, 60² = 3600. 3264 is not a square of any integer.

∴ The correct answer is 3264.

Alternate Method

Given: Numbers 2704, 2304, 3264, 1764.

Formula Used: If a number is a perfect square, its square root is rational. Otherwise, it is irrational.

⇒ Case 1: √2704 = 52 (Rational)

⇒ Case 2: √2304 = 48 (Rational)

⇒ Case 3: √3264 ≈ 57.131... (Irrational because 3264 is not a perfect square)

⇒ Case 4: √1764 = 42 (Rational)

∴ The correct answer is 3264.

Additional Information

Perfect Square Properties

A perfect square never ends in 2, 3, 7, or 8. Its digital sum must be 1, 4, 7, or 9.

Irrational Numbers

The square root of any prime number or any non-perfect square integer is always irrational.

Rational vs Irrational

Rational numbers can be written as p/q; irrational numbers have non-terminating, non-recurring decimals.

Shortcut Trick

Sum of Weekly Visitors = (30 + 30 + 40 + 30 + 40 + 55 + 45) = 270

Admission Charge = Rs. 100 per person

Total Income = Total Visitors × Rate

Total Income = 270 × 100 = 27,000

∴ The correct answer is Rs. 27,000.

Alternate Method

Given Data:

Number of visitors on Monday, Tuesday, Thursday = 30 persons each day

Number of visitors on Wednesday, Friday = 40 persons each day

Number of visitors on Saturday = 55 persons

Number of visitors on Sunday = 45 persons

Admission fee per person = Rs. 100

⇒ Total visitors for the week = (3 × 30) + (2 × 40) + 55 + 45

⇒ Total visitors = 90 + 80 + 100

⇒ Total visitors = 270

⇒ Total Weekly Income = Total number of visitors × Charge per admission

⇒ Total Weekly Income = 270 × 100

⇒ Total Weekly Income = 27,000

∴ The correct answer is Rs. 27,000.

Additional Information

Total Revenue Formula

The total income or revenue in such data interpretation problems is always calculated as: Total Quantity × Unit Price.

Average Daily Visitors

To find the daily average, divide the weekly total by 7: Average = Total Sum ÷ Number of Days. Here, 270 ÷ 7 ≈ 38.57 visitors/day.

Weekend vs. Weekday Contribution

Weekend visitors (Sat+Sun) = 100. Weekday visitors (Mon-Fri) = 170. Weekend contribution % = (100 ÷ 270) × 100 ≈ 37.04%.

Shortcut Trick

Apply alligation to the averages: (Higher Avg − Combined Avg) : (Combined Avg − Lower Avg).

Ratio of members = (10 − 9.2) : (9.2 − 8) = 0.8 : 1.2 = 2 : 3.

Since 2 units represent 12 members, then 1 unit = 6 members.

Therefore, n = 3 units = 3 × 6 = 18.

∴ The correct answer is 18.

Alternate Method

Given:

Number of members in Group 1 = 12 | Average of Group 1 = 8

Number of members in Group 2 = n | Average of Group 2 = 10

Combined average of both groups = 9.2

Formula Used:

Combined Average = [(n₁ × x₁) + (n₂ × x₂)] ÷ (n₁ + n₂)

Calculations:

⇒ 9.2 = [(12 × 8) + (n × 10)] ÷ (12 + n)

⇒ 9.2 × (12 + n) = 96 + 10n

⇒ 110.4 + 9.2n = 96 + 10n

⇒ 110.4 − 96 = 10n − 9.2n

⇒ 14.4 = 0.8n

⇒ n = 14.4 ÷ 0.8

⇒ n = 18

∴ The correct answer is 18.

Additional Information

Weighted Average Concept

It is used when groups have different weights or sizes. The formula is Sum of (Value × Weight) ÷ Sum of Weights.

Alligation Rule

Ratio of quantities = (Value of dearer − Mean value) : (Mean value − Value of cheaper). It is the fastest method for mixture and average problems.

Deviation Method

Assumed Average + (Total Deviation ÷ Total Count). Total deviation from the actual average is always zero.

Shortcut Trick

Probability = (Favorable outcomes) ÷ (Total outcomes)

Required Probability = (13/52) × (13/51) × 2 (for two possible orders: Heart-Spade or Spade-Heart)

Required Probability = (1/4) × (13/51) × 2 = 13/102

∴ The correct answer is 13/102.

Alternate Method

Given:

Total cards in a deck = 52

Number of Heart cards = 13

Number of Spade cards = 13

Formula: Probability P(E) = n(E) / n(S)

⇒ Total ways to draw 2 cards from 52 = ⁵²C₂

⇒ n(S) = (52 × 51) / (2 × 1) = 1326

⇒ Favorable ways to draw 1 Heart and 1 Spade = ¹³C₁ × ¹³C₁

⇒ n(E) = 13 × 13 = 169

⇒ Probability = 169 / 1326

⇒ Dividing both numerator and denominator by 13: 13 / 102

∴ The correct answer is 13/102.

Additional Information

Card Deck Composition

A standard deck has 52 cards divided into 4 suits (Hearts, Diamonds, Spades, Clubs), each containing 13 cards.

Combinations Rule

The number of ways to select r items from n is given by ⁿC_r = n! / [r!(n−r)!].

Multiplication Rule in Probability

If events are independent, P(A and B) = P(A) × P(B). For dependent events (without replacement), P(A and B) = P(A) × P(B|A).

The correct answer is Akbar.

• Akbar started Din-i-Ilahi.

Key Points

• Akbar (1556 AD-1605 AD):
• He undertook the title of Jalaluddin Muhammad Akbar Badshah Ghazi at the young age of 14 at Kalanaur, Punjab and his tutor Bairam Khan was appointed as the regent.
• The Second Battle of Panipat,1556 was fought between Hemu, the Hindu General of Muhammad Adil Shah and Bairam Khan, the regent of Akbar.
• Hemu was defeated, captured and slain by Bairam Khan.
• He also ended the interference from Petticoat Government (1560 AD-1562 AD) which was represented by Maham Anaga and Adham Khan Junta.
• He built Buland Darwaza at Fatehpur Sikri.
• He also built Fatehpur Sikri, Agra Fort, Lahore Fort, Allahabad Fort and Humayun’s Tomb in Delhi.
• He proclaimed a new religion, Din‑i‑Ilahi, in 1581 AD.
• Birbal was the only Hindu who followed Din-i-Ilahi.
• Abul Fazal wrote Akbarnama, the appendix of which was called Ain-i-Akbari.

The correct answer is Capt. D.K. Sharma.

• Capt. D.K. Sharma is the present spokesperson of the Indian Navy.

Key Points

• Indian Navy:
• ​It was founded on 26 January 1950.
• Its headquarters is located at Integrated Defence Headquarters, Ministry of Defence, New Delhi.
• Motto: शं नो वरुणः 
• ​May the Lord of Water be auspicious unto us.
• Indian Navy Day:
• ​4 December is celebrated as the Indian Navy day to recognize the achievements and role of the Indian Navy to the country.
• It was chosen as Navy day in the year 1971, after the successful completion of Operation Trident.
• In the operation, the Indian Navy sank four Pakistani Naval ships and vessels.
• The day is also remembered for the ones killed in the Indo-Pakistan War of 1971.
• Capt. D.K. Sharma is the present spokesperson of the Indian Navy.

Shortcut Trick

Let Actual Speed be s. Distance = 36 km, Time saved = 6 min = 1/10 hr, Speed increase = 4 km/hr.

Using the formula: Distance = [s × (s + Δs) / Δs] × Δt

⇒ 36 = [s × (s + 4) / 4] × (1/10) ⇒ s(s + 4) = 36 × 40 = 1440.

By splitting 1440 into factors with a difference of 4: 1440 = 36 × 40.

Comparing s(s + 4) = 36(36 + 4), we get s = 36.

∴ The correct answer is 36 km/hr.

Alternate Method

Given:

Distance = 36 km, Time delay = 6 minutes = 6/60 hour = 0.1 hour.

Let the Actual Speed of the train be x km/hr.

Increased Speed = (x + 4) km/hr.

⇒ Time difference = (36/x) − (36/(x + 4)) = 0.1

⇒ 36 [ (x + 4 − x) / (x(x + 4)) ] = 1/10

⇒ 36 [ 4 / (x² + 4x) ] = 1/10

⇒ 144 × 10 = x² + 4x

⇒ x² + 4x − 1440 = 0

⇒ x² + 40x − 36x − 1440 = 0

⇒ x(x + 40) − 36(x + 40) = 0

⇒ (x − 36)(x + 40) = 0

⇒ x = 36 km/hr (Since speed cannot be negative).

∴ The correct answer is 36 km/hr.

Additional Information

Speed-Distance Relation

When distance is constant, speed is inversely proportional to time (S ∝ 1/T).

Time Delay Formula

Distance = (S₁ × S₂ / |S₁ − S₂|) × Total Time Difference.

Average Speed

For two equal distances with speeds x and y, Average Speed = 2xy / (x + y).

1. A is heavier than C and D.

A > C and D

• Here, there is no information given about the weight of B. Therefore, statement 1 alone is not sufficient.

2. D is the lightest among them

• No information is given about the weight of A, B, and C. Therefore, statement 2 alone is not sufficient.

3. B is heavier than A.

B > A

• No information is given about the weight of C and D. Therefore, statement 3 alone is not sufficient.
• From statements 1, 2, and 3:-

B > A > C > D, B is the heaviest.

• Here, statements 1, 2 and 3 are sufficient.

Hence, "option 4" is the correct answer.

The correct answer is it is helpful in the rotation of the black hole.

• Gravity does not help in the rotation of the black hole.

Key Points

• Gravity:
• The acceleration due to gravity is the rate of increase of velocity of a body falling freely towards the earth.
• It is represented by $g= {GM_e \over R_e^2}$
• where M_e is the mass of the earth and R_e is the radius of the earth.
• The value of g at the surface of the earth is 9.8 m/s².
• Variation in g:
• The value of g decreases with height or depth from the earth’s surface.
• g is maximum at poles. Hence, it will be maximum at the Camp in Antarctica
• g is minimum at the equator.
• g decreases due to the rotation of the earth.
• g decreases if the angular speed of the earth increases and increases if the angular speed of the earth decreases.
• Gravity also helps in preventing planetary atmospheres from separating from them.
• It keeps the stars connected together.
• It helps the moon to stay in its orbit.
• Black holes are formed by gravity pulling matter together and the rotation of the black hole is caused by a conserved quantity called angular momentum.

The correct answer is Thallophyta.

• Algae belong to Thallophyta.

Key Points

• Thallophyta:
• These are found in moist and wet places.
• They lack roots and vascular tissue
• They are autotrophic in nature.
• They have an autotrophic mode of nutrition.
• Their reserve food is generally starch.
• The cell wall is composed of cellulose around the cells.
• Tissues like xylem and phloem are absent.
• Sex organs are simple and are single-celled
• There is no embryo formation after fertilization.
• Example: algae and fungi.

The logic followed here is:-

• Figures A, B, and C have two triangles with one of the corners connected with each other
• In figure D, one corner of a triangle is connected to the base of the other triangle.

So, figure D is different from others.

Hence, "option 3" is the correct answer.

The logic followed here is:-

• All the symbols are moving clockwise one behind the other.
• Triangle (

) rotates 900 anticlockwise directions in each step.

• Both symbols

 rotate one place in the clockwise direction in each step and the symbol $Ω$ flips in alternate step.

• Symbols (

) rotate in the clockwise direction in each step and symbol 

changes to symbol ± in alternate steps.

• The symbol 

 rotates in the clockwise direction in each step.

So, the next image of the given series is figure C.

Hence, "option 2" is the correct answer.

Calculation:

Total revenue of company in 2016 was = $36,82,000

The revenue from Tennis kits = 5%

⇒ (36,82,000 × 5/100) = 184,100

The revenue from Football kits = 25%

⇒ (36,82,000 × 25/100) = 920,500

The revenue from cricket kits = 30%

⇒ (36,82,000 × 30/100) = 1,104,600

The revenue from basketball kits = 20%

⇒ (36,82,000 × 20/100) = 736,400

The revenue from hockey kits = 10%

⇒ (36,82,000 × 10/100) = 368,200

The revenue from other sports kits = 10%

⇒ (36,82,000 × 10/100) = 368,200

∴ The least amount received by tennis games equipment.

Shortcut Trick

Assume Total Distance = 100 units and Total Time = 100 units. Average Speed = 1 unit.

Distance covered in first 20% time = 80% of speed × 20% time = 0.8 × 20 = 16 units.

Remaining Distance = 100 − 16 = 84 units.

Required Speed for remaining 80% time = 84 ÷ 80 = 1.05 units.

New Speed % = 1.05 × 100 = 105%.

∴ The correct answer is 105%.

Alternate Method

Given: Initial speed = 80% of average speed, Time spent = 20% of total time.

Formula Used: Distance = Speed × Time; Average Speed = Total Distance ÷ Total Time.

⇒ Let total distance be D, total time be T, and required average speed be S.

⇒ D = S × T

⇒ Distance₁ = (0.8 × S) × (0.2 × T) = 0.16 × ST = 0.16D

⇒ Remaining Distance = D − 0.16D = 0.84D

⇒ Remaining Time = 0.8T

⇒ Required Speed = 0.84D ÷ 0.8T = 1.05 × (D/T) = 1.05S

⇒ Required Percentage = 1.05 × 100 = 105%

∴ The correct answer is 105%.

Additional Information

Average Speed Concept

Average speed is defined as the total distance traveled divided by the total time taken (S_avg = Total Distance ÷ Total Time).

Weighted Average of Speeds

When time intervals are given, Average Speed = (s₁t₁ + s₂t₂) ÷ (t₁ + t₂).

Shortcut Trick

Ratio of numbers = 6 : 1. Let the numbers be 6k and k.

Product: 6k × k = 96 ⇒ 6k² = 96 ⇒ k² = 16 ⇒ k = 4.

Numbers are 24 (6×4) and 4 (1×4).

Product of sum and difference = (24 + 4) × (24 − 4) = 28 × 20 = 560.

∴ The correct answer is 560.

Alternate Method

Given: Division of numbers = 6, Product of numbers = 96.

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

⇒ Let the numbers be x and y.

⇒ x ÷ y = 6 ⇒ x = 6y

⇒ x × y = 96

⇒ (6y) × y = 96

⇒ 6y² = 96 ⇒ y² = 16 ⇒ y = 4

⇒ x = 6 × 4 = 24

⇒ Sum = x + y = 24 + 4 = 28

⇒ Difference = x − y = 24 − 4 = 20

⇒ Product of sum and difference = 28 × 20 = 560

∴ The correct answer is 560.

Additional Information

Algebraic Identity

The product of the sum and difference of two numbers is equal to the difference of their squares: (x + y)(x − y) = x² − y².

Sum and Difference Formula

The relationship between sum, difference, and product can also be expressed as: (x + y)² − (x − y)² = 4xy.

Ratio and Proportion

If the division of two numbers is 'n', then the numbers are in the ratio n : 1.

The correct answer is At the equator.

• The minimum weight of a body is at the equator.

Key Points

• Due to the effect of gravity, the weight of the body is minimum at the equator.
• As the distance of the equator from the center of the earth is maximum, so the force of attraction is lowest on the body at the equator. Hence the weight of a body is minimum at the equator.
• Gravity:
• The acceleration due to gravity is the rate of increase of velocity of a body falling freely towards the earth.
• It is represented by $g= {GM_e \over R_e^2}$
• where Me is the mass of the earth and Re is the radius of the earth.
• The value of g at the surface of the earth is 9.8 m/s².
• Variation in g:
• The value of g decreases with height or depth from the earth’s surface.
• g is maximum at poles. Hence, it will be maximum at the Camp in Antarctica
• g is minimum at the equator.
• g decreases due to the rotation of the earth.
• g decreases if the angular speed of earth increases and increases if the angular speed of earth decreases

The correct answer is 400 meters.

Given:

Initial position of car (u) = 0

Final position of car (v) = 144 km/h = (144 × 5/18) = 40 m/s

Time (t) = 20 sec

Formula used:

v = u + at

s = ut + 1/2at²

Calculation:

According to the question

v = u + at

⇒ 40 = 0 + (a × 20)

⇒ 40 = 20a

⇒ a = 2 m/s²

Now,

s = ut + 1/2at²

⇒ s = 1/2at²

⇒ s = (1/2 × 2 × 20²) m

⇒ (1/2 × 2 × 400) m

⇒ s = 400 m

∴ The required value is 400 meter

Concept Used:   

Follow the BODMAS rule according to the table given below:

Calculation:

15.5 × 15.5 – 2.5 × 2.5 = ?

⇒ 240.25 – 2.5 × 2.5 = ?

⇒ 240.25 – 6.25 = ?

⇒ 234 = ?

∴ The required value of ? is 234

Shortcut Trick

Rate of decrease = 10% = 1/10.

Ratio of smokers (Original : New) for 1 year = 10 : 9.

For 3 years, ratio = 10³ : 9³ = 1000 : 729.

Given 729 units = 8748 ⇒ 1 unit = 8748 ÷ 729 = 12.

Original smokers = 1000 × 12 = 12000.

∴ The correct answer is 12000.

Alternate Method

Given: Present smokers (A) = 8748, Rate (R) = 10%, Time (n) = 3 years.

Formula Used: A = P(1 − R/100)ⁿ

⇒ 8748 = P(1 − 10/100)³

⇒ 8748 = P(9/10)³

⇒ 8748 = P × (729/1000)

⇒ P = (8748 × 1000) ÷ 729

⇒ P = 12 × 1000 = 12000

∴ The correct answer is 12000.

Additional Information

Depreciation Formula

When a value decreases at a constant rate R, the value after n years is given by V = P(1 − R/100)ⁿ.

Successive Percentage Decrease

If a value decreases by x% and then y% successively, the net decrease is [x + y − (xy/100)]%.

Population Increase

If the population increases at rate R, the population after n years is P(1 + R/100)ⁿ.

The correct answer is Group number.

• The number of electrons in the valence shell is equal to its Group number.

Key Points

• Group number: 
• The number of electrons in the outermost shell of an atom of the element.
• Elements in the same group have the same properties and same valency.

Additional Information

• Periodic Number:
• It is the number of protons in the nucleus of an atom of that element.
• Mass Number (A):
• It is equal to the sum of a number of protons and the number of neutrons.
• It is written as a superscript to the right of the symbol of the atom e.g., C12 here 12 is the mass number of carbon (C).

The correct answer is 1000 N.

Key Points

• Gravity
• The acceleration due to gravity is the rate of increase of velocity of a body falling freely towards the earth.
• It is represented by $g= {GM_e \over R_e^2}$
  

where M_e is the mass of the earth and R_e is the radius of the earth.

• The value of g at the surface of the earth is 9.8 m/s².
• The value of g on the Moon is 1/6th of that on the earth.
• ​$g_m = 1/6g_e$
• Given,
• M_e= 6000 N
• M_m=?
• ${g_e\over g_m}= {6000 \over M_m}$
• Hence, M_m=1000 N

The Venn Diagram is given below:-

• The girls who like blue or pink colours but not the white colour = p + v + q.

Hence, "option 2" is the correct answer.

The correct answer is 29 March 1982.

• The Telugu Desam Party was founded by N.T. Rama Rao 29 march 1982.

Key Points

• Telugu Desam Party:
• It was founded by N. T. Rama Rao on 29 March 1982.
• The party is headed by N. Chandrababu Naidu.
• The party's headquarters is NTR Bhavan in Hyderabad.

The correct answer is Tamil Nadu.

• Tamil Nadu state government formally launched the 'Ammvin Aran' app related to women's safety in 2017.

Key Points

• Ammavin Aran:
• The app was launched by the AIADMK General Secretary TTV Dhinakaran.
• The app is a women safety app.
• The meaning of the word Ammvin Aran is 'mother's fortress.
• The app will provide the user details to the nearest police station and hospital along with map details and phone number.
• The app also has an in-built whistle, which can manipulate the phone speaker to create a loud noise when pressed by anyone in distress.

The logic followed here is:-

Hence, "option 4" is the correct answer.

The correct answer is Tamil Nadu.

• Tamil Nadu has won the 2016-17 Deodhar Trophy.

Key Points

• Deodhar Trophy:
• The tournament is being administrated by BCCI.
• Tamil Nadu won the 2016-17 trophy by defeating India B.
• Dinesh Karthik scored the most number of runs in the tournament.
• Dhaval Kulkarni took the most number of wickets.

Additional Information

• Cricket: 
• The first official cricket test match was played in the year 1877 between Australia and England in Melbourne.
• The First One Day International cricket match was played in the year 1971 between England and Australia in Melbourne.
• The first World Cup of one-day matches was played in 1975 in London.
• The apex institution of world cricket is the International Cricket Council (ICC) and its headquarters are now in Dubai.
• Earlier it was in Lords (England).
• The ICC was founded in 1909.
• The Board of Control for Cricket in India (BCCI) was formed in 1927.
• Terminologies used in cricket are Toss, Run, Wicket, Bails, Crease, Pavilion, Maiden Over, Follow-on, Bowled, Stump Out, Run Out, L.B.W. Hit Wicket, No ball, Wide ball, Dead ball, Overthrow, Bye, Leg bye, Cover drive, Late cut, Hook, Glance, Stroke, Spot, Pull, Sixer, Followthrough, Googly, Cover, Gully, Long on, Silly point, Midwicket, Mid on, Forward short leg.

The correct answer is P. Parameswaran.

• P. Parameswaran was awarded Padma Vibhushan for his contribution in the field of literature and education in the year 2018.

Key Points

• P. Parameswaran:
• He is famously known as Parameswarji.
• He was also the Vice‑President of the Jan Sangh.
• He was president of Vivekananda Kendra.
• He was awarded Padma Vibhushan for his contribution to the field of literature and education in the year 2018.
• He was also awarded Padma Shri in the year 2004.

Additional Information

• Sharda Sinha was awarded Padma Bhushan in the year 2018 for her contribution to art and music.
• Laxman Pai was awarded Padma Bhushan award for his contribution in art and painting.
• Arvind parikh was awarded Padma Bhushan in the year 2018.

Shortcut Trick

Identify the quadrant for 135°, which lies in the Second Quadrant (90° to 180°).

In the second quadrant, secant is negative.

Using sec(90° + θ) = −cosec θ, we get sec(90° + 45°) = −cosec 45°.

∴ The correct answer is −cosec 45°.

Alternate Method

Given: Angle = 135°

Formula Used: sec(180° − θ) = −sec θ or sec(90° + θ) = −cosec θ

⇒ sec 135° = sec(90° + 45°)

⇒ Since sec(90° + θ) = −cosec θ

⇒ sec 135° = −cosec 45°

⇒ Value of −cosec 45° = −√2

∴ The correct answer is −cosec 45°.

Additional Information

ASTC Rule

In trigonometry, the All-Silver-Tea-Cups rule determines signs: Q1 (All +), Q2 (Sin/Cosec +), Q3 (Tan/Cot +), Q4 (Cos/Sec +).

Trigonometric Identities of 3x

cos 3x = 4cos³x − 3cos x and sin 3x = 3sin x − 4sin³x are standard Triple Angle identities.

Complementary Angles

sec θ = cosec(90° − θ). When crossing the 90° or 270° axis, the ratio changes to its co-ratio (sec → cosec).

The correct answer is Both A and B are correct.

Key Points 

• Speed of Sound
• In a medium, the speed of sound depends upon the elasticity and density of the medium.
• When sound enters from one medium to another medium, its speed and wavelength change but frequency remains unchanged.
• In a medium, the speed of sound is independent of frequency.
• Speed of sound is maximum in solids and minimum in gases.
• The speed of sound is more in humid air than in dry air because the density of humid air is less than the density of dry air.
• The unit of loudness is the decibel (dB).
• Effect of pressure on the speed of sound:
• The speed of sound is independent of pressure.
• Effect of temperature on the speed of sound:
• The speed of sound increases with the increase of the temperature of the medium.
• The speed of sound in helium gas is 965m/s. Hence statement A is correct.
• The speed of sound in hydrogen gas is 1284m/s. Hence statement B is correct.

The correct answer is 5.6.

Given,

Power= 100 W

Time, T= 8 hours

Energy consumed by bulb in one day = 8 *100W = 800 WH

We know, 1 KWH=1000 WH = 1 unit

Hence 800 WH = 0.8 unit for 1 day.

For 1 week= 0.8*7

                  = 5.6

Additional Information

• Power:
• The rate of doing work is called power.
• SI unit of power is watt named with a respect to the scientist James Watt or Joule Per second and it is a scalar quantity.
• 1 W = 1 J/s
• 1 kW = 10³ W
• 1 MW = 10³ W
• 1 Watt/s (W–s) = 1 J
• Horse power is a practical unit of power.
• 1 H.P. = 746 watt.
• Kilowatt is the SI unit of electric power.
• ​kilowatt hour = 3.6 × 10⁶ joule.

The correct answer is 55 J.

Given,

charge, Q= 5C

Potential difference, V= 11V

W= Q*V

   =  5*11

   = 55 J

• Potential Difference:
• Work done in bringing a unit positive charge from one point to another point is the potential difference between the two points.
• Its SI unit is volt.
• It is a scalar quantity.

The logic followed here is:-

• Wild buffalo, horses, and yak are herbivores.
• Lion is a carnivore. So, the lion is different from others.

Hence, "option 1" is the correct answer.

The correct answer is 330W.

Key Points

• Given,
• mass of body (m) = 50 kg
  

h = 44×15 = 660 cm = 6.60 m

t=10 s, g = 10 ms^-2

Potential energy = mgh

= 50 × 10 × 6.60

= 3300 W

• $Power = {Work done \over time}$
• $= { 3300\over 10}$
• 330W

Additional Information

• Potential Energy:
• It is the energy possessed by a body by virtue of its position.
• PE of a body in the gravitational field of the earth is mgh.
• where m = mass, g = acceleration due to gravity, h = height of the body from the surface of the earth.
• When a body is falling downwards, then its potential energy goes on changing to kinetic energy.

The correct answer is the Communist Party of India (Marxist).

• Communist Party of India (Marxist) of India strongly supports left-wing politics, such as the right to work on land for all and strongly opposes neo-liberal policies such as globalization, capitalism and privatization.

Key Points

• Communist Party of India (Marxist):
• The party came into existence after its split from the Communist Party of India (CPI) in November 1964.
• The party is leading the state government in Kerala.
• Its General Secretary is Sitaram Yechury.
• It also has its own newspapers by the name People's Democracy, Ganashakti, Deshabhimani and Theekkathir.
• The party strongly supports left-wing politics.

Additional Information

• Bharatiya Janata Party is a right-wing party.
• Shiv Sena is a right-wing Marathi regionalist and ultranationalist party.

Shortcut Trick

Total Savings % = 100% − (50% + 20%) = 30%

30% of Salary = ₹1500

1% of Salary = 1500 ÷ 30 = ₹50

100% (Total Salary) = 50 × 100 = ₹5000

∴ The correct answer is ₹5000.

Alternate Method

Given:

Expenditure on Food = 50%

Expenditure on Rent = 20%

Monthly Savings = ₹1500

Calculations:

⇒ Total Expenditure = 50% + 20% = 70%

⇒ Savings Percentage = 100% − 70% = 30%

⇒ Let Monthly Salary be X

⇒ 30% of X = 1500

⇒ (30/100) × X = 1500

⇒ X = (1500 × 100) ÷ 30

⇒ X = 50 × 100 = 5000

∴ The correct answer is ₹5000.

Additional Information

Percentage Change

Percentage change = (Difference ÷ Original Value) × 100. Useful for calculating salary increments.

Successive Percentage

If spending is from the remaining balance, use X × (100−a)/100 × (100−b)/100 = Savings.

Base Change Rule

If A is x% more than B, then B is [x/(100+x)] × 100% less than A.

Shortcut Trick Profit percentage = 17.5% = 175/1000 = 7/40. Ratio of Cost Price (CP) to Selling Price (SP) = 40 : (40 + 7) = 40 : 47. Given SP = 47 units = Rs. 2,632. 1 unit = 2,632 ÷ 47 = 56. CP = 40 units = 40 × 56 = Rs. 2,240. ∴ The correct answer is Rs. 2,240.

Alternate Method Given: Selling Price (SP) = Rs. 2,632, Profit% = 17.5%. Formula: CP = [SP ÷ (100 + Profit%)] × 100

⇒ CP = [2,632 ÷ (100 + 17.5)] × 100 ⇒ CP = [2,632 ÷ 117.5] × 100 ⇒ CP = 22.4 × 100 ⇒ CP = Rs. 2,240 ∴ The correct answer is Rs. 2,240.

Additional Information Cost Price and Selling Price The price at which an article is purchased is called its Cost Price (CP), and the price at which it is sold is called its Selling Price (SP). Profit Calculation Profit occurs when SP > CP. Profit = SP − CP. To find CP when profit% is given: CP = [100 ÷ (100 + P%)] × SP.

The correct answer is the reverse repo rate.

• The rate at which the Reserve Bank of India takes loans from other banks is called the reverse repo rate.

Key Points

• Reverse Repo Rate:
• It is the rate, at which banks park short-term excess liquidity with the RBI.
• The current reverse repo rate is 3.35%

Additional Information

• Bank Rate:
• It is also called the rediscount rate.
• It is the rate, at which the RBI gives finance to commercial banks.
• Cash Reserve Ratio (CRR):
• The RBI (Amendment) Bill, 2006, empowers RBI to prescribe CRR–Cash that banks deposit with the RBI without any floor rate or ceiling rate.
• The current CRR rate is 4.5%.
• Statutory Liquidity Ratio (SLR):
• It is the ratio of liquid assets, which all commercial banks have to keep in the form of cash, gold, and unencumbered approved securities equal to not more than 40% of their total demand and time deposit liabilities (ranges is 25‑40%).
• The current SLR is 18.00%.
• ​Repo Rate:
• It is the rate, at which RBI lends short-term money to the bank against securities.
• Open Market Operations (OMOs):
• Under OMOs, the RBI sells G-securities in the market.

The correct answer is Potential energy is converted into kinetic energy.

• Potential energy is converted into kinetic energy during rain.​

Key Points

• The raindrops gain potential energy when they come out of the cloud (due to its height).
• They gradually gain kinetic energy while falling on the ground.

Additional Information

• Potential Energy:
• It is the energy possessed by a body by virtue of its position.
• PE of a body in the gravitational field of the earth is mgh.
• where m = mass, g = acceleration due to gravity, h = height of the body from the surface of the earth.
• When a body is falling downwards, then its potential energy goes on changing to kinetic energy.
• Kinetic Energy:
• If a body of mass m is moving with velocity v, then kinetic energy
• $KE =1/2{mv^2}= {P^2 \over 2m}$
  

where p is the linear momentum.

• When momentum is doubled, kinetic energy becomes four times.
• If a body is moving in a horizontal circle then its kinetic energy is the same at all points, but if it is moving in a vertical circle, then the kinetic energy is different at different points.

The correct answer is Cytokines.

• Cytokines promote cell division.

Key Points

• Cytokines:
• Cytokines are small proteins
• They are crucial in controlling the growth and activity of other immune system cells and blood cells.
• Cytokines affect the growth of all blood cells and promote cell division.
• They also affect the other cells that help the body's immune and inflammation responses.

Additional Information

• Auxin is a plant hormone that regulates growth.
• Gibberellins are plant hormones that regulate developmental processes like stem elongation, germination, dormancy, flowering, flower development, and leaf and fruit senescence.

The correct answer is 30.

• The rank of India in the latest World Economic global manufacturing index is 30.

Key Points

• World Economic Forum (WEF) Global Manufacturing Index:
• Japan was awarded the top spot in the ‘Readiness for the future of production report’ due to its structure of production.
• India was ranked 30th.
• It was ahead of fellow BRICS nations, such as Russia who ranked 35th, Brazil’s spot at 41, and South Africa at 45.
• Russia was ranked 35th Brazil was ranked 41st and South Africa was ranked 45th.
• World Economic Forum (WEF):
• It was founded in the year 1971.
• It was founded by Klaus Schwab.
• Its headquarters are located in Cologny, Switzerland.

The correct answer is CO.

• CO is not acidic.

Key Points

• Carbon monoxide (CO):
• It is a colourless, odourless, tasteless gas that is produced by burning fossil fuels, wood, propane and charcoal.
• It is formed by incomplete combustion.
• It is a neutral oxide.

Additional Information

• Oxides of sulfur:
• These are a group of molecules made of sulfur and oxygen atoms, such as sulfur dioxide (SO₂) and sulfur trioxide (SO₃).

The logic followed here is:-

• Figure 1 to figure 2: the four parts of a square in figure 1 are separately shown in figure 2.

Similarly,

• Figure 3 to figure 4: the four parts of a circle in figure 3 should be separately shown in figure 4. This is only possible in figure A.

Hence, "option 1" is the correct answer.

The correct answer is 29th.

• Telangana as a geographical and political entity was created on June 2, 2014, as 29th and the smallest state of the Union of India.

Key Points

• Telangana:
• The state of Telangana was created on June 2, 2014.
• Governor: Tamilisai Soundararajan
• Capital: Hyderabad
• Chief minister: K. Chandrashekar Rao
• Telangana shares its borders with Maharashtra, Andhra Pradesh, Karnataka and Chhattisgarh.

• The number of students studying French and Spanish = 20 + 4 = 24

Hence, "option 4" is the correct answer.

The question is simply whether advertisements for selling products be allowed or banned.

• Argument I says that it should be banned and justifies it by explaining that the products become expensive because of the money invested in advertising them. An increase in the price of products being advertised could be detrimental to its sale. So, argument I is strong.
• Argument II says that if advertisements are banned then the products will not be sold. Advertisements are not the only way of selling products. So, argument II is not strong.

Hence the correct answer is option 1.

The logic followed here is:-

• In options 1, 3, and 4, the inner part is a circle
• In option 2, the inner part is a triangle
• Thus, option 2 is different from others.

Hence, "option 2" is the correct answer.

The correct answer is Vivian Q.

• Vivian Q won the Best Director award at the 48th International Film Festival held in Goa.

Key Points

• 48th International Film Festival of India:
• It was held in Goa.
• The theme of the festival was Celebrating the Future of Cinema.
• Following awards were presented at the festival:
• Best Film Golden Peacock Award was given to BPM (Beats per Minute) by Robin Campillo
• Best Director was given to Vivian Qu for Angels for Wear White
• Best Debut Film of a Director was given to Kiro Russo for Dark Skull
• Best Male Actor was given to Nahuel Pérez Biscayart for BPM (Beats per Minute)
• Best Female Actor was given to Parvathy for Take-Off
• ICFT UNESCO Gandhi Medal was given to Film Kshitij A Horizon by Manoj Kadaamh.
• Special Jury Award was given to Mahesh Narayanan for Take-Off.

Shortcut Trick

Let the present ages of Ram and Sita be R and S.

From the condition: When Ram was S, Sita was (S − (R − S)) = 2S − R.

Given: R = 2 × (2S − R) ⇒ R = 4S − 2R ⇒ 3R = 4S ⇒ R/S = 4/3.

Sum of ratios = 4 + 3 = 7 units. Given sum = 63 years. ∴ 1 unit = 9 years.

Ram's age = 4 × 9 = 36 years; Sita's age = 3 × 9 = 27 years.

∴ The correct answer is 36, 27.

Alternate Method

Let Ram's age be R and Sita's age be S.

⇒ R + S = 63 ---(i)

The difference in their ages remains constant. Let the difference be d. ⇒ R − S = d.

When Ram was Sita's present age (S), the time elapsed was d years ago.

⇒ Sita's age at that time was (S − d).

According to the problem: R = 2 × (S − d)

⇒ R = 2 × (S − (R − S))

⇒ R = 2 × (2S − R) ⇒ R = 4S − 2R

⇒ 3R = 4S ⇒ R = 4S/3

Substitute R in equation (i):

⇒ 4S/3 + S = 63 ⇒ 7S/3 = 63

⇒ S = (63 × 3) / 7 = 27 years.

⇒ R = 63 − 27 = 36 years.

∴ The correct answer is 36, 27.

Additional Information

Age Difference Invariance

The difference between the ages of two people always remains constant, regardless of the number of years passed or preceding.

Ratio Balancing

If the sum and a linear relationship between ages are given, use ratio units to solve faster than using two-variable algebraic equations.

The correct answer is Both A and B are true.

• Rancidity:
• It is a condition produced by the oxidation of unsaturated fat present in foods and other products, which ultimately results in an unpleasant odour or flavour.
• Hence, statement A is true.
• Corrosion:
• It is the process of oxidative deterioration of a metal surface by the action of the environment to form unwanted corrosion.
• Hence, statement B is true.
• Corrosion of iron is called rusting.
• It is prevented by the following methods:
• By electroplating
• By surface coating
• By alloying
• By galvanisation of iron

The correct answer is Arun Jaitley.

• Arun Jaitley presented the Union Budget (2018-19) in the Parliament of India.

Key Points

• The then Finance minister Late Arun Jaitley presented the Union Budget (2018-19) in the Parliament of India.

• He also held the cabinet portfolios of Finance, Defence, Commerce and Industry, Corporate Affairs, and Law and Justice under the Vajpayee government and Narendra Modi government.

• He was awarded the Padma Vibhushan posthumously in 2020 in the field of Public Affairs.

• Nirmala Sitharaman is the current Finance minister.

Additional Information

• Piyush Goyal is the current Minister of Textiles.
• Yashwant Sinha was the Former Minister of State for Finance.

The family tree is given below:-

Vanita is the stepsister of Neena.

Hence, "option 2" is the correct answer.

The logic followed here is:-

It moves in 180⁰ clockwise direction.

Hence, "option 3" is the correct answer.

Shortcut Trick

Count the frequency of each observation in the data set.

Frequency of 4 → 2 | Frequency of 5 → 2 | Frequency of 6 → 2

Frequency of 7 → 4 | Frequency of 8 → 3 | Frequency of 9 → 2 | Frequency of 10 → 1

Since 7 occurs maximum number of times (4 times), it is the mode.

∴ The correct answer is 7.

Alternate Method

Given: Data set = {4, 6, 5, 7, 9, 8, 10, 4, 7, 6, 5, 8, 9, 8, 7, 7}

Formula Used: Mode = Observation with the highest frequency.

⇒ Arranging data in ascending order: 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 10

⇒ Count of 4 = 2

⇒ Count of 5 = 2

⇒ Count of 6 = 2

⇒ Count of 7 = 4

⇒ Count of 8 = 3

⇒ Count of 9 = 2

⇒ Count of 10 = 1

⇒ Maximum Frequency = 4 (for the value 7)

∴ The correct answer is 7.

Additional Information

Empirical Relationship

The relationship between Mean, Median, and Mode is given by: Mode = 3 × Median − 2 × Mean.

Types of Mode

A data set can be Unimodal (one mode), Bimodal (two modes), or Multimodal (more than two modes).

Median of Data

For 16 observations, Median = Average of 8^th and 9^th terms = (7 + 7) ÷ 2 = 7.

The correct answer is fallopian tubes.

• Fertilization in humans occurs in fallopian tubes.

Key Points

• Fallopian tubes are part of the female reproductive organ in humans and animals.
• It carries the egg from the ovary to the uterus.
• It is the fallopian tubes where the fertilization in humans takes place.

 

Additional Information

• The ovary is a ductless reproductive gland in which the female reproductive cells are produced.
• The uterus is the hollow, pear-shaped organ.
• The uterus is where a fetus develops and grows.
• It is also called the womb.
• Vagina connects the outer sex organs to the uterus.

The correct answer is MV.

• Density = M/V.

Key Points

• Density:
• The density of a substance (ρ) is defined as the ratio of its mass (M) to its volume (V).
• $Density= {Mass \over Volume}$
• The density of water is maximum at 4°C.
• The relative density is defined as the ratio of the density of the substance to the density of water at 4°C.
• Ice floats on the water surface as its density (0.92 g/cm³) is lesser than the density of water (1g/cm³).
• If ice floating in water in a vessel melts, the level of water in the vessel does not change.
• The density of seawater is more than that of normal water.
• This explains why it is easier to swim in seawater.

The logic followed here is:-

Similarly,

Hence, "option 3" is the correct answer.

The diagram is given below:-

• Priyanka is facing north-east because the opposite direction of the southwest is the northeast.

Hence, "option 4" is the correct answer.

The logic followed here is:-

• Figure 1 to figure 2 - The two circles intersect at least two sides of the triangle in figure 1. They intersect two vertices in figure 2.

Similarly,

• Figure 3 to figure 4 - The two circles intersect at least two sides of the rectangle in figure 3. They intersect two vertices in figure 4.

Hence, "option 1" is the correct answer.

The least possible Venn diagram is given below:-

Conclusions:

1. Some monkeys are gorillas. → does not follow (it is possible but not definite)
2. Some Langurs are Gorillas. → follows (As shown in the diagram, all the Gorillas are a part of Langur. So, some Langurs are Gorillas)

Hence, "option 3" is the correct answer.

Additional Information

The correct answer is Nagaland.

• Rhododendron is the state flower of Nagaland.

​ 

Key Points 

• Nagaland:
• Capital: Kohima.
• Governor: Jagdish Mukhi
• Chief Minister: Neiphiu Rio
• State animal: Mithun.
• State bird: Blyth's tragopan.
• State flower: Rhododendron.
• State tree: Alder

Additional Information

• Nag Kesar is the state flower of Tripura.
• Tangedu Puvvu is the state flower of Telangana.
• The noble orchid is the state flower of Sikkim.

The correct answer is fallopian tubes.

• Fallopian tubes carry the egg from the ovary to the uterus.

Key Points

• Fallopian tubes are part of the female reproductive organ in humans and animals.
• It carries the egg from the ovary to the uterus.

Additional Information

• The vagina connects to the uterus.

• In an ordinary year, there are 365 days and on dividing 365 by 7, we get remainder = 1, so this extra one day is taken as an odd day.
• Similarly, in a leap year, there are 366 days and on dividing 366 by 7, we get remainder = 2, so these extra days are taken as the odd days.

 

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

• 1949 = 1600 + 300 + 49 years
• In 1600 years the odd days = 0
• In 300 years the odd days = 1
• In 300 years, there will be 15 days, 14 days (2 weeks) + 1 odd day. So, 300 years have 1 odd day. (Number of odd days in 300 years = (5 x 3) = 15 = (14+1) = 1 odd day.
• In 49 years (from 1901 to 1949), = 49/4 = 12 leap years and 37 normal years.
• In 11 leap years, odd days = 24, and 37 normal years = 37 odd days
• So total = 24 + 37 = 61 odd days i.e. 61/7 = 5 odd days

In 1950, the number of days up to 29 January = 29 days = 1 odd day. 

 

Total in 1950 years up to 29 January = 0 + 1 + 5 + 1 = 7/7 = 0 odd days.

The codes for the weekdays are as follows:

 

• The day of the week on 29 January 1950 was Sunday.

 

Hence, "option 4" is the correct answer.

The statement asks if banks should give home loans at affordable rates.

• Argument I agrees with it and suggests that affordable rates will make it easy for people to give monthly EMIs. Thus, it makes a strong point.
• Even at affordable rates, banks won't lose money by giving loans. Because any loan when repaid by the customer is profitable to the bank because it is returned with interest. So, argument II is not strong.

Hence the correct answer is option 1.

Shortcut Trick

Convert speed: 78 × (5/18) = 65/3 m/s.

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

Length of train = Total distance − Platform length = 585 − 455 = 130 m.

∴ The correct answer is 130 m.

Alternate Method

Given:

Speed of train = 78 km/hr

Length of platform = 455 m

Time taken = 27 sec

Formula used:

Distance = Speed × Time

Speed in m/s = Speed in km/hr × (5/18)

Calculations:

⇒ Speed = 78 × (5/18) = 65/3 m/s

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

⇒ Length of Train + 455 = (65/3) × 27

⇒ Length of Train + 455 = 65 × 9

⇒ Length of Train + 455 = 585

⇒ Length of Train = 585 − 455

⇒ Length of Train = 130 m

∴ The correct answer is 130 m.

Additional Information

Unit Conversion

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

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

Given:

11.31 ÷ 0.0029 = ?

Calculation:

According to the question

11.31 ÷ 0.0029 = ?

⇒ (1131/100 ÷ 29/10000) = ? 

⇒ (1131/100 × 10000/29) = ?

⇒ (39 × 100) = ?

⇒ 3900 = ?

∴ The required value of ? is 3900

The correct answer is Lawn tennis.

• Jelena Ostapenko represents the sport of lawn tennis.

Key Points

• Jelena Ostapenko:
• She is a Latvian tennis player.
• She has career-high WTA rankings of No. 5 in singles.
• she also achieved world No. 17 rank in doubles.

Additional Information

• Terminologies used in tennis are Service, Grandslam, Advantage, Deuce, Game Point, Breakpoint; Smash, Shot, Grass Court. Break, Drop shot, Netplay, Baseline, etc.

The logic followed here is:-

Hence, "option 3" is the correct answer.

Shortcut Trick Identify the nearest perfect squares: 502 = 2500 and 602 = 3600. Since 2601 is slightly more than 2500, the square root must be slightly more than 50. The unit digit of 2601 is 1, so the square root must end in 1 or 9. Comparing 51 and 59, 51 is closer to 50, and 512 ends in 1. ∴ The correct answer is 51.

Alternate Method Given: Number = 2601 Method: Prime Factorization or Long Division ⇒ 2601 = 3 × 867 ⇒ 2601 = 3 × 3 × 289 ⇒ 2601 = 3 × 3 × 17 × 17 ⇒ √2601 = √(32 × 172) ⇒ √2601 = 3 × 17 ⇒ √2601 = 51 ∴ The correct answer is 51.

Additional Information Unit Digit Rule for Square Roots If a perfect square ends in 1, its square root ends in 1 or 9. If it ends in 4, the root ends in 2 or 8. Range Estimation For a 4-digit number ABCD, if 2500 < ABCD < 3600, the square root lies between 50 and 60. Square of Numbers ending in 5 (n5)2 = [n × (n+1)] followed by 25. Example: 552 = (5×6)25 = 3025.