RRC Group D Previous Year Paper 68 (Held On: 31 Oct 2018 Shift 1)

Mistake Points

Most two points represent the number who has been involved in all the two parts.

The Venn diagram is given below:-

The total number of students who like at most two sports = (9 + 12 + 12 + 14 + 20 + 13) = 80

Hence, "option 4" is the correct answer.

The correct answer is Na < Mg > AI < Si.

• The correct order of first ionization potential in Na < Mg > AI < Si.

Key Points

• The ionisation potential increases as we go along the period from left to right due to a decrease in atomic size.
• The elements Na(11), Mg(12), Al(13), Si(14) all belong to the 3^rd period.
• Therefore trend in ionization potential value should be Si>Al>Mg>Na.
• But, the Mg has a higher ionization potential than Al because it has electronic configuration 1s²2s²3p⁶3s² which has fulfilled 3s orbital and it's difficult to remove an electron from the fulfilled orbital.
• On the other hand, Al has the electronic configuration 1s²2s²3p⁶3s²3p¹ and it's easier to remove the 3p electron.
• Therefore, Mg has a higher ionisation potential than Al and the correct order of the first ionization potential is Na < Mg > AI < Si.

The correct answer is Shoonyta.

• Shunyata has won the Best Short Film award at the Los Angeles Film Festival, 2018.

Key Points

• Shunyata is a 22-minute short fiction film directed by Chintan Sarda.
• Actor Jackie Shroff has performed in the movie.
• It won the best film award at the 2018 Best of India Short Film Festival.
• The festival was held at Mack Sennett Studios in Los Angeles, the United States.
• The prize includes a cash prize of $1,000.$

The correct answer is mutation.

• The basic source of biological diversity is mutation.

Key Points

• Mutation:
• It is a change in a DNA sequence.
• It can be a result of DNA copying mistakes made during cell division, exposure to chemicals called mutagens, exposure to ionizing radiation, or infection by viruses.
• It is the basic source of biological diversity.

Additional Information

• Cosmic evolution is the study of change that includes the study of the vast number of developmental and generative changes, accumulated during all time and across all space, from the big bang to humankind.
• Fermentative action is a metabolic process that produces chemical changes in organic substrates through the action of enzymes.

The correct answer is lung inflation.

• During inhalation, the lungs fill with air due to lung inflation.

Key Points

• Inhalation:
• It is the process of intake of air.
• During inhalation, muscles of the diaphragm contracts and flattens.
• The lower ribs are raised upward and outwards, the chest cavity enlarges, the air pressure in the lungs is decreased, air rushes into the lungs and the lungs inflate.

Additional Information

• Exhalation
• Expiration is breathing out of air.
• During expiration, relaxation of muscles of the ribs and diaphragm takes place.
• The diaphragm again becomes dome-shaped.
• The Chest cavity is reduced and the air is forced outward through the nose and trachea.

Shortcut Trick

Apply Cross-Multiplication to find the ratio of x : y from the given equation.

5 × (10x + 3y) = 9 × (5x + 2y) ⇒ 50x + 15y = 45x + 18y ⇒ 5x = 3y ⇒ x/y = 3/5.

Substitute x = 3 and y = 5 into the required ratio (2x + y) : (x + 2y).

(2 × 3 + 5) : (3 + 2 × 5) = (6 + 5) : (3 + 10) = 11 : 13.

∴ The correct answer is 11 : 13.

Alternate Method

Given: (10x + 3y) / (5x + 2y) = 9 / 5

Step 1: Solve for x and y

⇒ 5(10x + 3y) = 9(5x + 2y)

⇒ 50x + 15y = 45x + 18y

⇒ 50x − 45x = 18y − 15y

⇒ 5x = 3y

⇒ x / y = 3 / 5

Step 2: Calculate the required ratio

⇒ Required Ratio = (2x + y) / (x + 2y)

⇒ Divide numerator and denominator by y: [2(x/y) + 1] / [(x/y) + 2]

⇒ [2(3/5) + 1] / [(3/5) + 2]

⇒ (6/5 + 1) / (3/5 + 2) = (11/5) / (13/5)

⇒ 11 / 13

∴ The correct answer is 11 : 13.

Additional Information

Ratio and Proportion Basics

If a : b = c : d, then ad = bc. This is known as the Product of Extremes = Product of Means.

Componendo and Dividendo

If a/b = c/d, then (a+b)/(a−b) = (c+d)/(c−d). This rule is helpful in simplifying complex linear ratio equations.

Substitution Method

In homogeneous expressions (where the power of variables in each term is the same), we can directly substitute the ratio values into the expression to find the final result.

Given:

The product of the two numbers is 0.432.

One of them is 1.6

Concept used:

Calculation:

Let the other number be P.

According to the question,

1.6 × P = 0.432

⇒ P = 0.27

∴ The other number is 0.27.

The Venn diagram is given below:-

Conclusion:

I. All cakes are sour. → False (it is possible but not definite)

II. Some cakes are sour. → False (it is possible but not definite.)

• Thus, neither conclusion I nor II follows

Hence, "option 2" is the correct answer.

Additional Information

Shortcut Trick

Let Total Work be LCM of (8, 12, 6) = 24 units.

Efficiency: (A+B) = 3, (B+C) = 2, (A+B+C) = 4.

Efficiency of C = (A+B+C) − (A+B) = 4 − 3 = 1 unit/day.

Efficiency of A = (A+B+C) − (B+C) = 4 − 2 = 2 units/day.

Combined efficiency of (A+C) = 2 + 1 = 3 units/day.

Time for twice the work (48 units) = 48 ÷ 3 = 16 days.

∴ The correct answer is 16 days.

Alternate Method

Given: (A+B) time = 8 days, (B+C) time = 12 days, (A+B+C) time = 6 days.

Formula: Efficiency = Total Work ÷ Time

⇒ Efficiency of A = Efficiency(A+B+C) − Efficiency(B+C) = 4 − 2 = 2

⇒ Efficiency of C = Efficiency(A+B+C) − Efficiency(A+B) = 4 − 3 = 1

⇒ Combined Efficiency of (A + C) = 2 + 1 = 3 units/day

⇒ Twice the work = 2 × 24 = 48 units

⇒ Time taken by (A + C) = 48 ÷ 3 = 16 days

∴ The correct answer is 16 days.

Additional Information

Total Work Assumption

Always assume Total Work as the Least Common Multiple (LCM) of the given time periods to avoid calculations in fractions.

Efficiency Relation

Time and Efficiency are inversely proportional. If time taken is doubled for the same work, efficiency is halved.

Combined Work Formula

If A does work in x days and B in y days, together they do it in (x × y) ÷ (x + y) days.

The correct answer is New Delhi.

• The Indira Gandhi Indoor Stadium is located in New Delhi.

Key Points

• Indira Gandhi Indoor Stadium:
• The stadium was earlier known as Indraprastha Stadium and Indira Gandhi Arena.
• It is the largest indoor sports arena in India and also among the largest in Asia.
• It was used the host the events of the indoor game in the 1982 Asian Games.

Shortcut Trick

Side ratio of smaller triangle to larger triangle = 2 : 5.

Area ratio = (2/5)² = 4/25.

Total area of 3 smaller triangles = 3 × 4 = 12 units.

Area of larger triangle = 25 units.

Remaining area = 25 − 12 = 13 units.

∴ The correct answer is 12 : 13.

Alternate Method

Let the side of the larger triangle be s.

Area of larger triangle (A_L) ∝ s².

Side of smaller triangle (s_s) = (2/5)s.

Area of one smaller triangle (A_s) ∝ ((2/5)s)² = (4/25)s².

⇒ A_s = (4/25) × A_L.

⇒ Total Area of 3 smaller triangles = 3 × (4/25)A_L = (12/25)A_L.

⇒ Remaining area = A_L − (12/25)A_L = (13/25)A_L.

⇒ Required Ratio = (12/25)A_L : (13/25)A_L = 12 : 13.

∴ The correct answer is 12 : 13.

Additional Information

Area of Similar Triangles

If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides: Area₁/Area₂ = (side₁/side₂)².

Equilateral Triangle Area

For an equilateral triangle with side 'a', Area = (√3/4) × a².

Ratio Properties

If the ratio of part to whole is a:b, then the ratio of part to remaining part is a:(b−a).

The correct answer is Vidarbha.

• Vidarbha won the Ranji Trophy in 2017.

Key Points

• Ranji Trophy:
• It is a domestic first-class cricket championship with multiple teams representing regional and state cricket associations.
• It was first held in 1934–35.
• It currently consists of 38 teams, with all 28 states in India and four of the eight union territories having at least one representation.
• It is named after the first Indian cricketer who played international cricket, Ranjitsinhji.
• He was also known as 'Ranji'.
• Bombay is the most successful team in the tournament.
• Vidarbha team won the 2017 tournament by defeating Delhi by 9 wickets.

The correct answer is acceleration.

Key Points

• When two balls made of iron and aluminium falls then the acceleration due to gravity will be the same for both.
• This is because, in a free fall, the acceleration does not depend on the mass of the object.

Additional Information

• Acceleration:
• Acceleration of an object is defined as the rate of change of velocity of the object.
• It is a vector quantity and its SI unit is metre/second² (m/s²).
• If velocity decreases with time then acceleration is negative and is called retardation.
• 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 $g= {GM_e \over R_e^2}$

The logic followed here is:-

Hence, "option 2" is the correct answer.

Shortcut Trick

For a set of n numbers, if the mean of the first (n−1) numbers is M₁ and the mean of the last (n−1) numbers is M₂:

Range = (M₂ − M₁) × (n − 1)

Range = (21 − 19) × 3 = 2 × 3 = 6

∴ The correct answer is 6.

Alternate Method

Let the four numbers in ascending order be a, b, c, and d.

Given:

⇒ Mean of the three smallest numbers (a, b, c) = 19

⇒ Mean of the three largest numbers (b, c, d) = 21

Calculations:

⇒ Sum of smallest three: a + b + c = 19 × 3 = 57 — (Equation 1)

⇒ Sum of largest three: b + c + d = 21 × 3 = 63 — (Equation 2)

⇒ Range = Largest value − Smallest value = d − a

⇒ Subtracting Equation 1 from Equation 2:

⇒ (b + c + d) − (a + b + c) = 63 − 57

⇒ d − a = 6

∴ The correct answer is 6.

Additional Information

Range of Data

The Range is the simplest measure of variability, calculated as the difference between the maximum and minimum values in a dataset.

Arithmetic Mean

The Mean is the sum of all values divided by the number of values. Sum = Mean × Count.

Overlap Principle

In a sequence of n numbers, the difference between the sum of the last k numbers and the first k numbers is directly related to the difference between the extreme values when the middle terms cancel out.

Shortcut Trick Identify two numbers whose sum is 3 and product is 2. The factors of 2 are 1 and 2, and 1 + 2 = 3. Since the condition x < y is given, we must have x = 1 and y = 2. Substitute these values into the expression x3 − y3. 13 − 23 = 1 − 8 = −7. ∴ The correct answer is -7.

Alternate Method Given: x + y = 3, xy = 2, and x < y. Formula Used: (x − y)2 = (x + y)2 − 4xy and x3 − y3 = (x − y)(x2 + xy + y2)

⇒ (x − y)2 = (3)2 − 4(2) ⇒ (x − y)2 = 9 − 8 = 1 ⇒ x − y = ±1. Since x < y, then x − y = −1. ⇒ x2 + y2 = (x + y)2 − 2xy = 32 − 2(2) = 5. ⇒ x3 − y3 = (x − y)(x2 + xy + y2) ⇒ x3 − y3 = (−1) × (5 + 2) = −7. ∴ The correct answer is -7.

Additional Information Algebraic Expansion of x3 − y3 The difference of cubes is given by: x3 − y3 = (x − y)(x2 + xy + y2) or x3 − y3 = (x − y)3 + 3xy(x − y). Sum of Cubes Identity The sum of cubes is given by: x3 + y3 = (x + y)(x2 − xy + y2) or x3 + y3 = (x + y)3 − 3xy(x + y). Relation between (x+y) and (x-y) The identity connecting sum and difference is (x + y)2 − (x − y)2 = 4xy.

The correct answer is Bryophyta.

• Riccia comes under Bryophyta.

Key Points

• Bryophyta
• In Bryophyta, there is a lack of xylem and phloem tissues.
• They lack true roots, stem and leaves.
• This community is also called the amphibian category of the plant kingdom.
• Examples of Bryophyta are Riccia, liverworts and hornworts.

Additional Information

• Thalophyta
• This is the largest group of the plant kingdom.
• There is no conducting tissue.
• Pteridophyta
• In Pteridophytes, the body of the plant is differentiated into root, stem and leaf.

Shortcut Trick

Find LCM of 12, 16, 24, and 36 minutes.

LCM (12, 16, 24, 36) = 144 minutes.

144 minutes = 2 hours 24 minutes.

Time = 6 : 00 + 2 : 24 = 8 : 24 am.

∴ The correct answer is 8 : 24 am.

Alternate Method

Given: Intervals are 12, 16, 24 and 36 minutes. Starting time is 6 : 00 am.

Formula Used: Common time for recurring events = LCM of individual intervals.

⇒ Prime factorization of 12 = 2² × 3

⇒ Prime factorization of 16 = 2⁴

⇒ Prime factorization of 24 = 2³ × 3

⇒ Prime factorization of 36 = 2² × 3²

⇒ LCM = 2⁴ × 3² = 16 × 9 = 144 minutes.

⇒ Total time in hours = 144 ÷ 60 = 2 hours 24 minutes.

⇒ Next ringing time = 6 : 00 am + 2 hours 24 minutes = 8 : 24 am.

∴ The correct answer is 8 : 24 am.

Additional Information

LCM (Least Common Multiple)

The smallest number that is a multiple of two or more numbers. Used for simultaneous events like traffic lights or bells.

HCF (Highest Common Factor)

The largest number that divides two or more numbers. Used for maximum capacity or length problems.

Time Conversion

Always convert minutes to hours by dividing by 60 to calculate the clock time accurately.

The correct answer is It has a measurable amount of thermal energy obtained through the work done by the microwave oven, which in turn takes electrical energy from the electrical grid.

Concept:

Energy

• The capacity of doing work is called energy.
• SI unit of energy is the joule.
• Various forms of energy are heat energy, light energy, nuclear energy, electrical energy, mechanical energy, etc.
• Energy can be converted from one form to another.
• This happens through various processes or using certain appliances.
• For example, when a bulb glows by electricity, electrical energy is converted into light energy.

Explanation:

This question is about the conversion of energy for making a cup of coffee in a microwave oven. The process must follow in a sequence.

• It has a measurable amount of thermal energy gained through the work done by the microwave oven, which in turn takes potential energy from the electrical grid. - Thermal - Work done microwave - Potential energy (false) - Electrical energy.
• It has a measurable amount of thermal energy obtained through the work done by the microwave oven, which in turn takes electrical energy from the electrical grid. Thermal - Work done microwave -  Electrical energy - Electrical grid. - Correct Sequence
• It consists of a measurable amount of kinetic energy acquired through the work done by the microwave oven. - False
• It contains a measurable amount of thermal energy obtained through the work done by the microwave oven, which in turn takes chemical energy from the electrical grid. Thermal energy - Work done - Chemical energy (false) - Electric grid

The correct answer is Vijaynagar.

• Vijaynagar empire was founded by the Sangam princes - Harihara and Bukka.

Key Points

• Vijayanagar Empire (1336 AD-1580 AD)
• Vijayanagar empire and the city were founded by Harihar and Bukka.
• Muhammad-bin-Tughlaq, converted them to Islam and sent them to the South to control rebellion but motivated by a Bhakti saint Vidyaranya, they established the Vijayanagar kingdom in 1336 AD.
• The period of Vijayanagar can be divided into four distinct dynasties, that are Sangam, Saluva, Tuluva and Aravidu.

Important Points

• The Bahamani kingdom of Deccan was founded by Hasan Gangu.

The correct answer is Shahrukh Khan.

• Shahrukh Khan was selected for the Yash Chopra Memorial National Award, 2017.

Key Points

• Yash Chopra Memorial Award:
• It was instituted in 2013 by the T. Subbarami Reddy from TSR Foundation in memory of the late producer-director Yash Chopra,
• Yash Chopra died in 2012.
• The award was first awarded to melody queen Lata Mangeshkar.
• T. Subbarami Reddy is an industrialist, politician, film producer and philanthropist.
• In the year 2017, the award was given to Shahrukh Khan.

Shortcut Trick

Ratio 6 years ago = 6 : 5 | Ratio 4 years hence = 11 : 10

Difference in ratio parts = 11 − 6 = 5 units and 10 − 5 = 5 units.

Total time gap = 6 + 4 = 10 years.

5 units = 10 years ⇒ 1 unit = 2 years.

Sagar age 6 years ago = 5 units × 2 = 10 years.

Sagar present age = 10 + 6 = 16 years.

∴ The correct answer is 16 years.

Alternate Method

Given: Ratio of Saina and Sagar 6 years ago = 6 : 5. Ratio 4 years later = 11 : 10.

Let the ages of Saina and Sagar 6 years ago be 6x and 5x.

⇒ Present age of Sagar = 5x + 6

⇒ Age of Saina after 4 years = 6x + 6 + 4 = 6x + 10

⇒ Age of Sagar after 4 years = 5x + 6 + 4 = 5x + 10

⇒ (6x + 10) / (5x + 10) = 11 / 10

⇒ 10(6x + 10) = 11(5x + 10)

⇒ 60x + 100 = 55x + 110

⇒ 5x = 10 ⇒ x = 2

⇒ Present age of Sagar = 5(2) + 6 = 16 years.

∴ The correct answer is 16 years.

Additional Information

Concept of Age Ratio

The difference between the ages of two people always remains constant regardless of the time elapsed.

Ratio Balancing

If the difference in ratio parts is not equal, multiply ratios by the difference of the opposite ratio to balance the units.

Time Interval Calculation

The total time gap between 'n' years ago and 'm' years hence is calculated as (n + m) years.

The correct answer is Gopal Guru.

• In January 2018, Gopal Guru was appointed as the editor of the Economic and Political Weekly.

Key Points

• Gopal Guru was appointed as the editor of the Economic and Political Weekly.
• Gopal Guru is currently a Professor at the Centre for Political Studies at the Jawaharlal Nehru University in New Delhi.
• He replaced Paranjoy Guha Thakurta.

Additional Information

• Economic and Political Weekly:
• It started in 1949.
• Its Publisher is Sameeksha Trust.

• Shoes, cars, and bicycles all are different things.
• The most appropriate Venn diagram is as follows:

 

Hence, "option 2" is the correct answer.

Important Points

• 2 November is the earliest date among the given options.
• So, we will calculate the day on 2 November and then use that information to calculate the day on the other dates of November if needed.

Concept:

• 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.

• 1999 = 1600 + 300 + 99 years
• In 1600 years the odd days = 0
• In 300 years the odd days = 1
• In 99 years (from 1901 to 1999), = 99/4 = 24 leap years and 75 normal years.
• In 24 leap years, odd days = 48, and 75 normal years = 75 odd days
• So total = 48 + 75 = 123 odd days i.e. 123/7 = 4 odd days

In 2000, the number of days up to 2 November 

= 31 (Jan) + 29 (Feb - leap year) + 31 (Mar) + 30 (Apr) + 31 (May) + 30 (Jun) + 31 (Jul) + 31 (Aug) + 30 (Sep) + 31 (Oct) + 2 (Nov)

= 307 days

= 6 odd days. 

 

Total in 2000 years up to 2 November = 0 + 1 + 4 + 6 = 11/7 = 4 odd days.

The codes for the weekdays are as follows:

 

• Thus, the day of the week on 2 November 2000 was Thursday.
• Now, 2 November + 14 days (0 odd days) = 16 November. So, 16 November is also a Thursday.

 

Hence, "option 4" is the correct answer.

Given series:-

3 R # 2 A $ K 5 % T 7 & N Y ÷ X B / L Q @ 1

Second half: & N Y ÷ X B / L Q @ 1

The second half of the above series is reversed, then the new series is:-

3 R # 2 A $ K 5 % T 7 1 @ Q L / B X ÷ Y N &

From the above series:-

Similarly,

Hence, "option 2" is the correct answer.

The correct answer is Finance.

• The term 'Financial Deficit' is related to the Finance Ministry of the Government of India.

Key Points

• Fiscal Deficit:
• It is the difference between total expenditure (revenue, capital, and loans net a repayment) and the revenue receipts plus those capital receipts which are not in the form of borrowings but which in the end accrue to the government.
• The term is related to the Finance Ministry of the Government of India.

1. M is taller than R and S.

M > R and S

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

2. M is wearing a sky coloured shirt.

• No information is given about the height of M, N, R, and S. Therefore, statement 2 alone is not sufficient.
• From statements 1 and 2:-

M > R and S. No definite relationship was established.

• Here, statements 1 and 2 are insufficient.

Hence, "option 2" is the correct answer.

The logic followed here is:-

• Figures A, B, and C have 5-pointed stars inside them.

​

• Figure D has a 6-pointed star.

​

So, figure D is different from the rest.

Hence, "option 2" is the correct answer.

The correct answer is Knight of the Legion of Honor.

• Knight of the Legion of Honor was given to former French President Nicolas Sarkozy in 2004.

Key Points

• Nicolas Sarkozy:
• He served as the President of France from May 2007 until May 2012.
• The Russo-Georgian War and the Arab Spring took place during his tenure.
• He was awarded the Knight of the Legion of Honour by President Chirac in 2005.

Given:

32 - 2(10 + 16 ÷ 4 × 3 - 5 × 2) + 30

Concept used:

Calculation:

32 - 2(10 + 16 ÷ 4 × 3 - 5 × 2) + 30

⇒ 32 - 2(10 + 4 × 3 - 5 × 2) + 30

⇒ 32 - 2(10 + 12 - 10) + 30

⇒ 32 - 24 + 30

⇒ 38

∴ The required value of 32 - 2(10 + 16 ÷ 4 × 3 - 5 × 2) + 30 is 38.

The logic followed here is:-

Hence, "option 4" is the correct answer.

The correct answer is Balwant Rai Mehta Committee.

• Balwant Rai Mehta Committee recommended that the decision-making power should be decentralized and elected local bodies should be set up.

Key Points

• Balwant Rai Mehta Committee
• The Government of India appointed a committee in 1957.
• This committee was set up to examine the work of the Community Development Programme (1952), and the National Extension Service (1953).
• The committee submitted its report in 1958.
• Recommendations
• This committee recommends three levels of governance viz Zila Parishad, Panchayat Samiti (Block) and Gram Panchayat (village).
• The district collector should be a chairperson of Zila Parishad.
• The members of Zila Parishad and Panchayat Samiti should be elected indirectly while the members of Gram Panchayat should be elected directly.
• These recommendations were accepted by National Development Council (NDC) in Jan 1958.

The correct answer is Slaked lime.

• On adding water to CaO, a Slaked lime compound is obtained.

Key Points

• Quick lime is chemically called calcium oxide (CaO), when it is added to water, calcium hydroxide is formed.
• Calcium hydroxide is also called slaked lime.
• This reaction is highly exothermic in which a large amount of heat is released in the process.
• CaO + H2O → Ca(OH)2

Additional Information

• The chemical formula of washing soda is Na₂CO₃.

The correct answer is 

Key Points

• Given, 
• Current, I= 4A.
• The potential difference, V= 60 V
• According to Ohm's Law, V= IR
• $R = {V \over I}$
• $R = {60 \over 4}$
• = 15 Ω
• New current, I= 127.5 V
• $I = {V\over R}$
• $I = {127.5 \over 15}$
• = 8.5 A

Additional Information

• Ohm’s Law
• The electric current flowing through a conductor is directly proportional to the potential difference across its ends.
• It is given by the formula:
• V=IR

The logic followed here is:-

• Figures A, B, and D have 3 red balloons and 3 blue balloons.
• Figre C has 2 red balloons and 4 blue balloons.

So, figure C is different from the rest.

Hence, "option 4" is different from others.

Shortcut Trick

Total interest to be paid (SI) for 3 years @ 10% = 10% × 3 = 30%

Total interest to be earned (CI) for 2 years (from end of year 1 to 3) @ 10% = 10 + 10 + (10 × 10) ÷ 100 = 21%

Net loss percentage = Interest Paid % − Interest Earned % = 30% − 21% = 9%

Loss amount = 9% of Rs. 40,000 = 40,000 × 0.09 = Rs. 3,600

∴ The correct answer is Rs. 3,600.

Alternate Method

Given:

Principal amount (P) = Rs. 40,000

Rate of interest (R) = 10% p.a.

Time for borrowing (T₁) = 3 years (from Year 0 to Year 3)

Time for lending (T₂) = 2 years (from Year 1 to Year 3)

Formula Used:

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

Compound Interest (CI) = P × [(1 + R ÷ 100)^T − 1]

Calculations:

⇒ Interest to be paid (SI) = (40,000 × 10 × 3) ÷ 100

⇒ SI = 40,000 × 0.30 = Rs. 12,000

⇒ Interest to be earned (CI) = 40,000 × [(1 + 10 ÷ 100)² − 1]

⇒ CI = 40,000 × [(1.1)² − 1] = 40,000 × [1.21 − 1]

⇒ CI = 40,000 × 0.21 = Rs. 8,400

⇒ Net Profit/Loss = Interest Earned − Interest Paid

⇒ Net Result = 8,400 − 12,000 = −Rs. 3,600

⇒ A negative result indicates a Loss.

∴ The correct answer is Rs. 3,600.

Additional Information

Effective Interest Rate

For Compound Interest over 2 years, the effective rate is given by R_eff = x + y + (x × y) ÷ 100, where x and y are rates for the first and second years.

Difference between SI and CI

For the same principal and rate over 2 years, the difference is CI − SI = P(R ÷ 100)². This rule only applies when the time period and principal are identical for both.

Compound Interest for 'n' years

The amount A in CI is P(1 + r/n)^nt. When compounded annually, n = 1, so A = P(1 + r)^t.

Shortcut Trick

Total interest percentage = Rate × Time

Interest % = 5% × 3.5 years = 17.5%

Given: 17.5% of Principal = ₹18,480

100% of Principal = (18,480 ÷ 17.5) × 100 = 1,05,600

∴ The correct answer is ₹1,05,600.

Alternate Method

Given:

Simple Interest (SI) = ₹18,480

Rate (R) = 5% per annum

Time (T) = 3 years 6 months = 3.5 years = 7/2 years

Formula Used:

Simple Interest = (Principal × Rate × Time) ÷ 100

⇒ 18,480 = (P × 5 × 7/2) ÷ 100

⇒ 18,480 = (P × 35) ÷ 200

⇒ P = (18,480 × 200) ÷ 35

⇒ P = (18,480 × 40) ÷ 7

⇒ P = 2,640 × 40

⇒ P = 1,05,600

∴ The correct answer is ₹1,05,600.

Additional Information

Total Amount

Amount (A) is the sum of Principal and Simple Interest: A = P + SI = P[1 + (R × T)/100].

Annual vs. Monthly Rate

Always ensure Time and Rate are in the same unit. If time is in months, divide by 12 to convert to years for annual rates.

Compound Interest Comparison

For the first year, SI and CI are equal if interest is compounded annually. CI formula: A = P(1 + R/100)ⁿ.

Given: 

5.035 + 50.35 + 503.50 - 20.60

Concept used:

Calculation:

5.035 + 50.35 + 503.50 - 20.60

⇒ 5035 × (0.001 + 0.01 + 0.1) - 20.60

⇒ 5035 × 0.111 - 20.60

⇒ 558.885 - 20.60

⇒ 538.285

∴ The value of (5.035 + 50.35 + 503.50 - 20.60) is 538.285.

The correct answer is Alkaline earth metals.

• The second group of elements are called alkaline earth metals.

Key Points

• Alkaline Earth Metals:
• ​It consists of Group 2 (IIa) elements of the periodic table.
• These are beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra).
• Properties of alkaline earth metals:
• they are shiny in appearance.
• They have a silvery-white colour.
• They are reactive metals at standard temperature and pressure.
• They readily lose their two outermost electrons and form cations with a 2⁺ charge.
• They have low densities.
• They have low melting points.
• They have low boiling points.

Additional Information

• Halogens are kept in the Group 17 of the periodic table.
• Alkaline metals are kept in Group 1 of the periodic table.
• Inert gases are kept in the Group 18 of the Periodic Table.

The correct answer is ESL Narasimham.

• ESL Narasimham is the present Governor of Andhra Pradesh and Telangana. (in 2018)

Key Points

• ESL Narasimham:
• He is an IPS officer and served as the Director of the Intelligence Bureau.
• He served as the governor of Andhra Pradesh and Telangana.
• He was the first Governor of Telangana.
• He also served as the Governor of Chhattisgarh.

 

Additional Information

• Biswabhusan Harichandan is the current governor of Andhra Pradesh. (in Jan 2022)
• Tamilisai Soundararajan is the current governor of Telangana. (in Jan 2022)

The correct answer is 5 June.

• World Environment Day is celebrated on the 5^th of June.

Key Points 

• World Environment Day:
• It is celebrated every year on the 5^th of June. It was established in 1972 by the United Nations at the Stockholm Conference on the Human Environment
• It was first celebrated in the year 1974.
• The theme of first-World Environment Day was Only One Earth.
• The theme for world environment day 2022 is Only One Earth.

 

Additional Information

• United Nations:
• The UNO was formed on 24 October 1945.
• At present, 193 countries are members of the UN.
• South Sudan is the latest and the 193^rd member to join the UN in 2011
• The UN Charter came into force on October 24, 1945, when the Governments of China, France, the UK, the Soviet Union, the USA and a majority of other counties had ratified it.
• The headquarters of the UN is situated in New York (USA).

The correct answer is oil and water.

• oil and water can be separated by different funnels.

Key Points

• Separating funnel:
• It is a funnel used to separate immiscible liquids.
• Liquids that do not mix with each other are called immiscible.
• Such two immiscible liquids are oil and water and they can be separated by using a separating funnel.
• The oil and water form two separate layers, with the oil being the less dense liquid being on top.

Additional Information

• The density of oil is 0.930 kg/m³.
• The density of water is 1.003 kg/m³.

Shortcut Trick

Apply the Empirical Formula: Mode = 3 × Median − 2 × Mean.

Substitute the given values: 15 = 3 × Median − 2 × 6.

15 = 3 × Median − 12 ⇒ 3 × Median = 27.

Median = 27 ÷ 3 = 9.

∴ The correct answer is 9.

Alternate Method

Given:

Mode of the data = 15

Mean of the data = 6

Formula Used:

The relationship between Mean, Median, and Mode is given by the empirical formula: Mode = 3(Median) − 2(Mean)

Calculations:

⇒ 15 = 3 × Median − 2 × 6

⇒ 15 = 3 × Median − 12

⇒ 3 × Median = 15 + 12

⇒ 3 × Median = 27

⇒ Median = 27 ÷ 3

⇒ Median = 9

∴ The correct answer is 9.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship is Mode = 3 × Median − 2 × Mean. This is also known as Karl Pearson's formula.

Symmetrical Distribution

The statement highlights the water shortage problem faced by the construction industries in North Karnataka.

• Action I suggests that the government take some steps to address this situation. Since there is a problem, it is reasonable to look for ways to resolve it. Thus, action 1 follows.
• Action II stands illogical with respect to the statement since it says that the construction industries be closed to save water, while the problem of water shortage is faced by those industries themselves. Construction industries are also important for the economy and the citizens. Thus, action II does not follow.

Hence the correct answer is option 4.

The logic followed here is:-

Similarly,

Hence, "option 1" is the correct answer.

The correct answer is Democritus.

• The word atom was discovered by Democritus.

Key Points

• Democritus was a Greek philosopher.
• He was the one who first proposed the Greek word atomos.
• Atomos means uncuttable.
• He further explained that all matter was eventually reducible to discrete, small particles or atomos.

Additional Information

• Laws of Multiple Proportion and the Atomic Theory was proposed by John Dalton.
• Antoine Laurent Lavoisier is known as the father of modern chemistry.

Shortcut Trick

In a set of 11 distinct observations, the median is the 6^th term when arranged in ascending order.

The last five observations are the 7^th, 8^th, 9^th, 10^th, and 11^th terms.

Adding 11 to these terms only increases values that are already greater than the median.

Since the 6^th term remains unchanged, the median of the new set remains the same.

∴ The correct answer is 12.5.

Alternate Method

Given:

Total observations (n) = 11

Median = 12.5

Calculations:

⇒ For n = 11, Median position = (11 + 1) ÷ 2 = 6^th term.

⇒ Let the observations be x₁

Shortcut Trick

Initial petrol = 125/8 l and Leftover petrol = 25/8 l.

Consumed petrol = 125/8 − 25/8 = 100/8 l.

Required fraction = Consumed ÷ Initial = (100/8) ÷ (125/8) = 100/125 = 4/5.

∴ The correct answer is 4/5.

Alternate Method

Given:

Initial quantity of petrol = 15(5/8) l = 125/8 l

Final quantity of petrol = 3(1/8) l = 25/8 l

Calculations:

⇒ Consumed petrol = Initial Quantity − Remaining Quantity

⇒ Consumed petrol = 125/8 − 25/8 = 100/8 l

⇒ Part of initial quantity consumed = Consumed quantity ÷ Initial quantity

⇒ Fraction = (100/8) ÷ (125/8)

⇒ Fraction = 100/125

⇒ Fraction = 4/5

∴ The correct answer is 4/5.

Additional Information

Mixed Fraction Conversion

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

Fractional Consumption

The part or fraction of a whole consumed is calculated as (Value Consumed) ÷ (Total Initial Value).

The logic followed here is:-

Hence, "option 3" is the correct answer.

The correct answer is Pushkar.

• Pushkar is a religious city located in the Rajasthan state of India.

Key Points

• Pushkar:
• Pushkar is a city in the Ajmer district of Rajasthan.
• It is famous for Pushkar Camel Fair.
• It is a trading gathering of cattle, horses and camels.

 

Additional Information

• Rajkot is a city in Gujarat.
• Puri is a city located in Odisha.
• Rishikesh is a city located in Uttarakhand.

The correct answer is Concave Mirror.

• A spherical mirror whose reflecting surface is bent inward is called Concave Mirror.

Key Points

• Concave Mirror:
• A concave mirror is a part of a spherical mirror where the inner surface is the reflecting surface.
• The image formed by a concave mirror is real and virtual.
• Uses of Concave Mirror
• As a shaving glass.
• As a reflector for the headlights of a vehicle, searchlight.
• In ophthalmoscope to examine the eye, ear, nose by doctors.
• In solar cookers.

Additional Information

• Convex Mirror:
• Convex Mirror is a part of a spherical mirror where the reflective surface bulges out towards the light source.
• The images formed by a convex mirror are always virtual and erect.
• Uses of Convex Mirror
• In the rearview mirror in vehicles because it provides the maximum rear field of view and image formed is always erect.
• In sodium reflector lamp.

The correct answer is ICICI Bank.

• ICICI Bank was roped in by the Government of India to introduce cashless payments in e-NAM (Electronic National Agriculture Market), in December 2017.

Key Points

• The government roped in ICICI Bank to enable online payments.
• It will enable online payments at 470 mandis integrated with the national portal of electronic National Agriculture Market (e-NAM).
• The bank will enable BHIM (Bharat Interface for Money) and Unified Payments Interface (UPI) on the e-NAM portal.
• ICICI Bank:
• Its full form is Industrial Credit and Investment Corporation of India (ICICI).
• It was founded in the year 1995.
• Its headquarter is located in Vadodara, Gujarat.
• Sir Arcot Ramasamy Mudaliar was the first Chairman of ICICI bank.
• Girish Chandra Chaturvedi is the current chairperson of ICICI bank.
• Sandeep Bakshi is the current CEO of ICICI bank. (As of Jan 2022).

Shortcut Trick

Convert days to fractions: 35, 175/4 (43.75), 105/2 (52.5).

Take LCM of numerators (35, 175, 105) = 525 units as Total Work.

Efficiency of 2(A+B+C) = 15 + 12 + 10 = 37 units → Efficiency of A+B+C = 18.5 units.

Efficiency of C = (A+B+C) − (A+B) = 18.5 − 15 = 3.5 units.

Days for C = 525 ÷ 3.5 = 150 days.

∴ The correct answer is 150 days.

Alternate Method

Given:

Time taken by (A + B) = 35 days

Time taken by (B + C) = 43.75 days = 175/4 days

Time taken by (C + A) = 52.5 days = 105/2 days

Formula Used:

Total Work = Efficiency × Time

Calculations:

⇒ Adding efficiencies: 2(A + B + C) = 15 + 12 + 10 = 37

⇒ Efficiency of (A + B + C) = 37 ÷ 2 = 18.5

⇒ Efficiency of C = Efficiency of (A + B + C) − Efficiency of (A + B)

⇒ Efficiency of C = 18.5 − 15 = 3.5

⇒ Time taken by C alone = Total Work ÷ Efficiency of C

⇒ Time = 525 ÷ 3.5 = 150 days

∴ The correct answer is 150 days.

Additional Information

Combined Work Efficiency

When work is done in pairs (A+B, B+C, C+A), the sum of efficiencies equals 2 × (A+B+C).

Time and Work Relation

Efficiency is inversely proportional to time taken. If time increases, efficiency decreases proportionally.

LCM Method for Fractions

LCM of fractions = LCM of Numerators ÷ HCF of Denominators. Useful for finding Total Work.

The logic followed here is:-

• Ate is the past tense of "eat".

Similarly,

• Bought is the past tense of "buy".

Hence, "option 4" is the correct answer.

The correct answer is Kaasav.​

Key Points

• Kaasav won the "Best Feature Film" award in 64^th National Film Awards.
• It was released in the year 2016 in the Marathi language.
• Its directors were Sumitra Bhave and Sunil Suthankar
• It was produced by Mohan Agashe
• 64^th National Film Awards:
• Organized by Directorate of Film Festivals to present awards to films of 2016
• Presented by - Pranab Mukherjee
• Jury members - Madhur Bhandakar, Kaushik Ganguly, Radhakrishna Jagalamudi, Mohan Kanda
• Best film-friendly state - Uttar Pradesh
• Best non-feature film - Fireflies in the Abyss
• Best book - Lata: Sur Gatha
• Best film critic - G Dhananjayan
• Dada Saheb Phalke Award - Kasinadhuni Viswanath

Additional Information

• Dada Saheb Phalke Award:
• Dadasaheb Phalke Award is India's highest award in cinema.
• It is presented annually at the National Film Awards ceremony by the Directorate of Film Festivals (an organisation set up by the Ministry of Information and Broadcasting).
• The award prize consists of a golden lotus, a cash prize of ₹10 lakh and a shawl.
• The award is given to people for their outstanding contribution to the growth and development of Indian cinema.
• It was first presented in 1969.
• The first recipient of the award was actress Devika Rani, “the first lady of Indian cinema.

The correct option which will complete the format of the given image is shown below:-

Hence, "option 1" is the correct answer.

The statement highlights the need to popularize alternative medicines for cancer treatment.

• It is reasonable to expect that the government should take responsibility to spread awareness about available alternative cancer treatments. Ensuring the outreach of adequate and appropriate healthcare facilities to the citizens is one of the primary responsibilities of a government. Thus, argument I is strong.
• If the affected people aren't aware of the availability of alternative medicines, they won't be able to approach such centers. Thus, argument II does not hold strong.

Hence the correct answer is option 2.

Given:

5 + (2 × (52 + 3)) - 84

Concept used:

Calculation:

5 + (2 × (52 + 3)) - 84

⇒ 5 + (2 × (25 + 3)) - 84

⇒ 5 + (2 × 28) - 84

⇒ 5 + 56 - 84

⇒ (-23)

∴ The required value of 5 + (2 × (52 + 3)) - 84 is (-23).

The correct answer is 20 Hz to 20000 Hz.

• The audible range of sound for humans is approximately 20 Hz to 20000 Hz.

Key Points 

• Sound Wave
• It is a longitudinal mechanical wave.
• The longitudinal mechanical waves which lie in the range of 20 Hz to 20,000 Hz are called audible or sound waves.
• It cannot travel in a vacuum.
• The longitudinal mechanical waves having frequencies less than 20 Hz are called infrasonic. These are produced by earthquakes, volcanic, eruptions, Ocean waves, elephants, and whales.
• The longitudinal mechanical waves having frequencies greater than 20000 Hz are called ultrasonic waves.

Given:

6 hours

Concept used:

A day = 24 hours

Calculation:

So, 6 hours = (6/24) × 100% = 25% of a day.

∴ 6 hours is 25% of a day.

• The mirror image of the question figure is as follows:

Hence, "option 3" is the correct answer.

The logic followed here is:-

• Soft, tender and hard are used to describe the state or condition of objects.
• Minute is used to describe the size of objects

So, gentle is different from others.

Hence, "option 3" is the correct answer.

The pie chart shows the expenditure of binding is 20% of total expenditure.

A pie chart defines 360° as 100%.

So, The angle subtended at the center of the field related to the expenditure of binding = 360° ÷ (100/20) = 72° 

∴ The angle subtended at the center of the field related to the expenditure of binding is 72°.

The logic followed here is:-

• Figure A - T and its positional value 20
• Figure B - I and its positional value 9
• Figure C - V and 15. Positional value of V is 22.
• Figure D - D and its positional value 4

So, figure C is different from others.

Hence, "option 2" is the correct answer.

The logic followed here is:-

• Work requires efforts

Similarly,

• Sleep provides rest.

Hence, "option 3" is the correct answer.

The correct answer is it is bitter in taste.

Key Points

• Acid:
• An acid is a substance which
• Is sour to taste.
• Turns blue litmus paper into red.
• Contains replaceable hydrogen.
• Gives hydrogen ion (H+) in an aqueous solution.
• Can donate a proton.
• Can accept an electron

Additional Information

• Bases
• A Base is a substance which:
• Is bitter in taste.
• Turns red litmus paper into the blue.
• Gives hydroxyl ions (OH–) in an aqueous solution.
• Can accept a proton.
• Can donate electrons.

The correct answer is Only D.

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: $g= {GM_e \over R_e^2}$

Additional Information

• Gravitational Force:
• Mathematically, it is represented as:
• $F= {GMm\over r^2}$
• Where,
• F is the gravitational force
• G is gravitational constant
• M is the mass of the first particle
• m is the mass of the second particle
• r is the distance between them.
• Substituting G = 6.67 × 10⁻¹¹, m₁ = 2 kg, m₂ = 2 kg, and r = 1 m, the force comes out to 26.68 × 10⁻¹¹ N.
• This is called Newton’s universal law of gravitation.
• The value of G is 6.67 × 10^-11 N m²/kg².
• The value of g on the Moon is 1/6^th of that on the earth.

Mistake Points

• "g" is the Gravitational acceleration but "G" is the Gravitational constant.
• ​g can vary from place to place; on Moon, it is 1.62 m/s², but on earth, it is 9.807 m/s²
• ​But G remains constant.

2Given: 

(334 + 335)

Concept used:

Index

Calculation:

(334 + 335)

⇒ 3³⁴ (1 + 3)

⇒ 3³⁴ × 4

So, 

√(334 + 335)

⇒ √(334 × 4)

⇒ 3¹⁷ × 2

∴ The required value of (334 + 335) is  2 × 317.

The correct answer is Lucknow.

• The headquarter of Small Industries and Development Bank (SIDBI) is located in Lucknow.

Key Points

• Small Industries Development Bank of India (SIDBI):
• It was formed in the year 1990.
• It is the apex regulatory body for the licensing and regulation of micro, small and medium enterprise finance companies in India.
• It comes under the jurisdiction of the Ministry of Finance.
• Its headquarters is located at Lucknow, Uttar Pradesh.
• SIDBI is regulated and supervised by the Reserve Bank of India.

Additional Information

• Reserve Bank of India (RBI):
• RBI was set up on the basis of the Hilton Young Commission recommendation in April 1935, with the enactment of the RBI Act, 1934.
• Its first Governor was C.D. Deshmukh.
• The headquarters of RBI is in Mumbai.
• Current Governor is Shaktikanta Das

The embedded answer figure is shown below:-

Hence, the correct answer is "Option 2".

The correct answer is Rajiv Gandhi Sports Campaign.​

Key Points

• Rajiv Gandhi Sports Campaign is a centrally sponsored scheme in place of Panchayat Yuva Krida and Khel Abhiyan (PYKKA).
• It was launched in 2014.
• The scheme was launched to encourage sports players and find out the talent residing in small villages and districts.
• The scheme was merged with Khelo India in the year 2016.

Additional Information

• Khelo India program was launched in 2017-18.
• Major Dhyan Chand Khel Ratna Award (Rajiv Gandhi Khel Ratna):
• The Rajiv Gandhi Khel Ratna Award is India’s highest honour given for achievement in sports.
• The award was instituted in the year 1991- 92 and was awarded by the Government of India.
• Vishwanathan Anand was the first person to win the Rajiv Gandhi Khel Ratna award.
• The award was rechristened as Major Dhyan Chand Khel Ratna Award in the year 2021.

The correct answer is 331 ms^-1.​

Key Points

• Sound Wave
• It is a longitudinal mechanical wave.
• The speed of sound in air is 331 m/s.
• The longitudinal mechanical waves which lie in the range of 20 Hz to 20,000 Hz are called audible or sound waves.
• It cannot travel in a vacuum.
• The longitudinal mechanical waves having frequencies less than 20 Hz are called infrasonic. These are produced by earthquakes, volcanic, eruptions, Ocean waves, elephants, and whales.
• The longitudinal mechanical waves having frequencies greater than 2000 Hz are called ultrasonic waves.

The correct answer is Oxygen.

• When sulfuric dioxide reacts with zinc, oxygen gas is formed.

Key Points

• The following reaction can be given by
• SO2 + Zn→ ZnS + O2
• Hence, when sulfuric oxide reacts with zinc, oxygen gas is formed.

Additional Information

• Sulphuric acid is also known as the oil of vitriol.
• It is composed of sulfur, hydrogen, and oxygen element.
• The acid has a very strong acidic nature.
• It has several uses such as fertilizer manufacture, mineral processing, oil refining, and wastewater processing.
• It is also known by the name hydrogen sulfate.

The least possible Venn diagram is as follows:

Conclusions:

1. Some monkeys can be humans. → Follows  (The possibility that some monkeys can be humans exists. This is shown in the below possibility diagram.)

The possibility diagram is as follows:

2. Some Langur can be monkeys. → Follows (The possibility that some langur can be monkey exists. This is shown in the below possibility diagram.)

The possibility diagram is as follows:

Hence, "option 1" is the correct answer.

Additional Information

Shortcut Trick

Total boxes = 25. Small boxes = 10 (from Statement 2).

Remaining (Big + Medium) = 25 − 10 = 15.

Ratio of Big to Medium = 1 : 2 (from Statement 1).

Big boxes = 15 × (1 ÷ 3) = 5. Both statements are required to find the exact count.

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

Alternate Method

Given: Total boxes (B + M + S) = 25.

Statement 1: B = M ÷ 2 ⇒ M = 2B.

Statement 2: S = 10.

Calculations:

⇒ Total = Big + Medium + Small

⇒ 25 = B + M + S

⇒ Using Statement 2: 25 = B + M + 10 ⇒ B + M = 15

⇒ Using Statement 1: B + 2B = 15

⇒ 3B = 15

⇒ B = 5

Both statements are needed to solve for the unique value of B.

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

Additional Information

Data Sufficiency

A question is solvable only if the number of independent equations matches the number of unknown variables (here B, M, and S).

Linear Equations in Three Variables

The general form is ax + by + cz = d. To find unique values for x, y, and z, we generally require three distinct statements or constraints.

Ratio and Proportion

If a total T is divided in ratio x : y, the parts are [x / (x+y)] × T and [y / (x+y)] × T.

The correct answer is it is a superficial phenomenon.​

Key Points

• Evaporation
• The process of vapourisation takes place only from the exposed surface of the liquid and that at all temperatures is called evaporation.
• It is a superficial phenomenon.
• Evaporation causes cooling.

Additional Information

• Vaporisation:
• The process by which a substance is changed from a liquid state to a vapour state is called vaporisation.

The logic followed here is:-

Similarly,

Hence, "option 2" is the correct answer.

The correct answer is 67.5 m/s.

Concept:

Kinematic equations of motion:

• These equations define the relationship between initial velocity u, final velocity v, time t, and displacement s of an object with respect to its motion in uniform acceleration a.
• Following are the three kinematic equations for uniformly accelerated motion:

⇒ v = u + at

⇒ s = ut + 0.5at2

⇒ v2 - u2 = 2as

Calculation:

Given

Time t = 13.5 s for going up and coming down

So for going up = t = 13.5/2 = 6.75

For going up initial velocity u = ?

At highest point velocity = v = 0

We know that,

v = u - gt

⇒ 0 = u - (10 × 6.75)

⇒ u = 67.5 m/s

The correct answer is a change in the sequence of nitrogenous bases.

• Gene mutation is caused by the change in the sequence of nitrogenous bases.

Key Points

• Gene Mutation:
• It is a change in one or more genes.
• It is caused by the change in one or more nucleotides of DNA.
• Deoxyribonucleic Acid (DNA):
• It is a long polymer made from repeating units called nucleotides.
• Each nucleotide consists of a nucleoside and a phosphate group, joined together by ester bonds.
• It has four bases, i.e. adenine, guanine, cytosine and thymine.
• DNA double-helix model was discovered by James D Watson and Francis Crick.
• He was awarded the Nobel Prize for this discovery.

The statement implies that the said book is the most informative book on environmental pollution that has ever been available.

• This means among all the available books on environmental pollution, this is the most informative. Hence, there are other books available on the topic. So, Assumption I is implicit.
• Nothing can be said about the number of books that are available or that can be written on environmental pollution from the given statement. Hence, assumption II is not implicit.

Hence the correct answer is option 3.

Additional Information

• In the case of comparative sentences with the word 'never', try to convert it to an affirmative sentence. It helps in understanding the statement easily and clarifies the logic.

The correct answer is Kinetic energy.

• When a compressive spring is released it converts its potential energy into Kinetic energy.

Key Points

• Kinetic Energy:
• If a body of mass m is moving with velocity v, then kinetic energy
• $KE = \frac{1}{2}{mv^2}= {P^2 \over 2m}$, 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.
• 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 diagram is given below:-

1) Mr. X runs a marathon starting from point A. He runs 5 km in the north direction.

2. Reaches point B, then turns right and walks 6 km to reach point C.

3. Then turns right and runs 8 km to reach point D.

4. Then turns right and runs 10 km and reaches point E.

5) Then turns right and runs 6 km and reaches point F.

6. Then turns right and runs 1 km and reaches point G.

7. Then turns right and runs 3 km and reaches point H.

Final, Diagram is represent below:

 

If Mr X turns to the right from point E, then he is facing north direction now.

Hence, "option 4" is the correct answer.

Shortcut Trick

Relative Speed crossing person = 36 + 18 = 54 km/hr = 15 m/s.

Length of Train = Speed × Time = 15 × 24 = 360 m.

Total distance (Train + Platform) at 36 km/hr (10 m/s) for 80 s = 10 × 80 = 800 m.

Length of Platform = 800 − 360 = 440 m.

∴ The correct answer is 440 m.

Alternate Method

Given: Speed of Train A (S_A) = 36 km/hr, Speed of Person (S_P) = 18 km/hr, Time to cross person (T₁) = 24 s, Time to cross platform (T₂) = 80 s.

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

⇒ Speed of Train A in m/s = 36 × (5/18) = 10 m/s

⇒ Speed of Person in m/s = 18 × (5/18) = 5 m/s

⇒ Relative speed (Opposite) = 10 + 5 = 15 m/s

⇒ Length of Train = Relative Speed × Time = 15 × 24 = 360 m

⇒ Let Length of Platform be L_P

⇒ Total Distance = Train Length + Platform Length = 360 + L_P

⇒ 360 + L_P = Speed of Train × Time to cross platform

⇒ 360 + L_P = 10 × 80

⇒ 360 + L_P = 800

⇒ L_P = 800 − 360 = 440 m

∴ The correct answer is 440 m.

Additional Information

Relative Speed Concept

When two objects move in the opposite direction, their relative speed is the sum of their individual speeds (S₁ + S₂). If they move in the same direction, it is the difference (|S₁ − S₂|).

Crossing Stationary vs Moving Objects

To cross a platform, a train covers distance equal to (Length of Train + Length of Platform). To cross a person/pole, distance covered is just the Length of the Train.

Unit Conversion

Always ensure units are consistent. Multiply km/hr by 5/18 to get m/s, and multiply m/s by 18/5 to get km/hr.

Shortcut Trick

Higher value (Ranjit) = (Sum + Difference) ÷ 2 = (210 + 56) ÷ 2 = 133

Lower value (Rohan) = (Sum − Difference) ÷ 2 = (210 − 56) ÷ 2 = 77

Required Ratio = 133 : 77 = 19 : 11 (Dividing both by 7)

∴ The correct answer is 19 : 11.

Alternate Method

Given: Total balls = 210, Difference = 56

Formula Used: Ratio = Ranjit's balls : Rohan's balls

⇒ Let Rohan get x balls, then Ranjit gets (x + 56) balls.

⇒ x + (x + 56) = 210

⇒ 2x + 56 = 210

⇒ 2x = 210 − 56 = 154

⇒ x = 77 (Rohan's share)

⇒ Ranjit's share = 77 + 56 = 133

⇒ Ratio = 133 : 77 = (133 ÷ 7) : (77 ÷ 7) = 19 : 11

∴ The correct answer is 19 : 11.

Additional Information

Sum and Difference Formula

If sum of two numbers is S and difference is D, then Greater Number = (S+D)/2 and Smaller Number = (S−D)/2.

Ratio Simplification

To simplify a ratio a : b, divide both terms by their Highest Common Factor (HCF).

• 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.
• 2007 = 2000 + 7 years
• In 2000 years the odd days = 0
• In 7 years (from 2001 to 2007), = 7/4 = 1 leap year and 6 normal years.
• In 1 leap year, odd days = 2, and 6 normal years = 6 odd days
• So total = 2 + 6 = 8 odd days i.e. 8/7 = 1 odd day
• In 2008, the number of days up to 18 April = 31 (Jan) + 29 (Feb - leap year) + 31(Mar) + 18(Apr) = 109/7 = 4 odd days.
• Total in 2008 years up to 18 April = 0 + 1 + 4 = 5 odd days.

The codes for the weekdays are as follows:

 

• The day of the week on 18 April 2008 was Friday.

Hence, "option 1" is the correct answer.

The correct answer is S = D/T.

• The correct relation of speed, distance and time is S = D/T.

Key Points

• Speed:
• Distance travelled by the moving object in unit time interval is called speed.
• It is a scalar quantity and its SI unit is metre/second (m/s).
• It is given by the formula: $Speed = { Distance \over Time}$

The correct answer is 6.673 × 10-11 Nm2kg^-2.

• The value of G is 6.673 × 10-11 Nm2kg^-2.

Key Points

• Gravitational Force:
• Mathematically, it is represented as:
• $F= {GMm\over r^2}$
• Where,
• F is the gravitational force
• G is gravitational constant
• M is the mass of the first particle
• m is the mass of the second particle
• r is the distance between them.
• This is called Newton’s universal law of gravitation.
• The value of G is 6.67 × 10^-11 N m²kg^-2.

Additional Information

• 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