RRC Group D Previous Year Paper 29 (Held On: 27 Sept 2018 Shift 2)

Shortcut Trick

Let Raman’s age 6 years from now be 2x, then Mother’s age will be 3x.

Present ages: Raman = 2x − 6, Mother = 3x − 6.

12 years ago: (2x − 18) = (3x − 18)/2 + 6 ⇒ 4x − 36 = 3x − 18 + 12 ⇒ x = 30.

Present age of Raman = 2(30) − 6 = 54 years.

∴ The correct answer is 54 years.

Alternate Method

Let Raman’s present age be R and Mother’s present age be M.

According to the first condition (12 years ago):

⇒ R − 12 = (M − 12)/2 + 6

⇒ 2R − 24 = M − 12 + 12 ⇒ M = 2R − 24 ... (i)

According to the second condition (6 years hence):

⇒ M + 6 = 1.5 × (R + 6)

⇒ M + 6 = 1.5R + 9 ⇒ M = 1.5R + 3 ... (ii)

Equating (i) and (ii):

⇒ 2R − 24 = 1.5R + 3

⇒ 0.5R = 27

⇒ R = 27 / 0.5 = 54

∴ The correct answer is 54 years.

Additional Information

Ratio Method in Ages

If the age ratio changes over time, ensure the age difference between two people remains constant by multiplying ratios with suitable factors.

Linear Equations

For age problems involving multiple conditions, substitution or elimination methods are effective for solving variables R and M.

The correct option is 1 i.e., Vaporization

Vaporization:

• Vaporization is the change for an object from the liquid state to the gaseous state.
• There are two types of vaporization:

1. Evaporation
2. Boiling

Acidification:

• Acidification is the process of decreasing the pH level.
• Ocean acidification is mainly caused by carbon dioxide gas dissolving into the ocean.

Liquification:

• Liquification is the process of converting a solid or a gas into a liquid.

Solidification:

• Solidification is the process of transformation of a liquid to a solid.

Shortcut Trick

For a quadratic equation to have no real solution, the Discriminant (D) must be less than zero.

Given x² + kx + 3k = 0 → D = k² − 4(1)(3k) < 0.

k² − 12k < 0 ⇒ k(k − 12) < 0.

The product is negative when k lies between the roots 0 and 12.

∴ The correct answer is 0 < k < 12.

Alternate Method

Given: Quadratic equation x² + kx + 3k = 0.

Formula Used: For ax² + bx + c = 0, no solution exists if D = b² − 4ac < 0.

⇒ Here, a = 1, b = k, c = 3k.

⇒ D = k² − 4 × 1 × 3k < 0

⇒ k² − 12k < 0

⇒ k(k − 12) < 0

⇒ Let f(k) = k(k − 12). The roots of f(k) are k = 0 and k = 12.

⇒ By the sign convention for quadratic inequalities, the expression is negative between the roots.

⇒ Thus, 0 < k < 12.

∴ The correct answer is 0 < k < 12.

Additional Information

Nature of Roots (D = b² − 4ac)

1. If D > 0, the roots are real and distinct. 2. If D = 0, the roots are real and equal. 3. If D < 0, there are no real roots (imaginary).

Relationship between Roots and Coefficients

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

Quadratic Inequality Rule

For (x − a)(x − b) < 0 where a < b, the solution set is a < x < b. For (x − a)(x − b) > 0, the solution set is x < a or x > b.

Considering the given statement

75 – (96 – 18 ÷ 6 – 58) ÷ 5 + 4 × 17 = ?

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

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

⇒ 75 – (96 – 3 – 58) ÷ 5 + 4 × 17 = ?

⇒ 75 – 35 ÷ 5 + 4 × 17 = ?

⇒ 75 – 7 + 4 × 17 = ?

⇒ 75 – 7 + 68 = ?

⇒ 143 – 7 = ?

⇒ 136 = ?

∴ Required value is 136

Shortcut Trick

Height of tower above platform level = Distance × tan(Angle).

⇒ h = 50√3 × tan(30°) = 50√3 × (1/√3) = 50 m.

Total height of tower = Platform height + h = 17 + 50 = 67 m.

∴ The correct answer is 67 m.

Alternate Method

Given: Height of platform = 17 m, Horizontal distance = 50√3 m, Angle of elevation (θ) = 30°.

Formula Used: tan θ = Perpendicular / Base

⇒ Let the height of the tower above the platform be h.

⇒ tan 30° = h / 50√3

⇒ 1/√3 = h / 50√3

⇒ h = (1/√3) × 50√3 = 50 m

⇒ Total height of tower = Platform height + h

⇒ Total height = 17 + 50 = 67 m

∴ The correct answer is 67 m.

Additional Information

Angle of Elevation

The angle formed by the line of sight with the horizontal when an object is viewed above the horizontal level.

Trigonometric Ratios for Standard Angles

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

Relationship between Height and Distance

Total Height = Observation Point Height + (Distance × tan θ).

Here, 

Hence, U42 is the next term in the given series.

The correct answer is West Bengal.

• India's largest wetland area is Sunderbans Wetland.

Ramsar Convention on Wetlands

• It is an international treaty for “the conservation and sustainable use of wetlands”.
• It is also known as the Convention on Wetlands.
• It is named after the city of Ramsar in Iran.

The correct option is 4  i.e., Sachin Tendulkar

• ‘Playing It My Way’ is the autobiography of Sachin Tendulkar

Some important autobiographies of the famous cricket players:

The correct option is 4 i.e., respiration

• During the respiration process, heat energy is formed.
• The process of releasing energy from glucose is called respiration. The energy in glucose can be released in a single reaction. When this happens heat energy is released as glucose burns

There are two main types of respiration

• Aerobic
• Anaerobic

Difference between Aerobic and Anaerobic:

The logic followed here is:

In each figure the minimum number of lines is same i.e. 5. In the answer figures, figure B has 5 lines.

Hence, B is the correct answer.

Considering the given statement,

$1\frac{7}{9} + \frac{5}{{12}} + \frac{7}{{18}}$

Now,

$\Rightarrow \frac{{16}}{9} + \frac{5}{{12}} + \frac{7}{{18}}$

⇒ (64 + 15 + 14)/36

⇒ 93/36

∴ Required value = 31/12

Hence, a minimum of 9 lines are required to create the given figure.

The correct option is 4 i.e., Parenchyma and collenchyma

• Cells of parenchyma and collenchyma tissues are living cells.

Permanent tissues can be classified into two types:

• Simple permanent tissue
• Complex Permanent tissue

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Average Speed = 150 m ÷ 60 s

Average Speed = 2.5 ms⁻¹

∴ The correct answer is 2.5 ms⁻¹.

Alternate Method

Given:

Length of the pool = 75 m

Total distance covered by Ram = 150 m (75 m one way + 75 m back)

Total time taken = 1 minute = 60 seconds

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance = 150 m

⇒ Total Time = 1 × 60 s = 60 s

⇒ Average Speed = 150 ÷ 60

⇒ Average Speed = 15 ÷ 6

⇒ Average Speed = 2.5 ms⁻¹

∴ The correct answer is 2.5 ms⁻¹.

Additional Information

Average Velocity

It is the ratio of Total Displacement to Total Time. Since the swimmer returns to the starting point, displacement is 0, making average velocity 0 ms⁻¹.

Scalar vs Vector

Speed is a scalar quantity (has magnitude only), whereas Velocity is a vector quantity (has both magnitude and direction).

Unit Conversion

To convert m/s to km/h, multiply the value by 18/5. To convert km/h to m/s, multiply by 5/18.

The correct option is 2 i.e., 11.66 N 

Given,

⇒ mass = 7kg

⇒ t = 3s

⇒ Initial velocity u = 3m/s

⇒ Final velocity v = 8m/s

So,

The acceleration will be,

⇒ $a= {v - u\ \over t}$​

⇒ $a= {8-3 \ \over 3}$

⇒ accelaraion = 1.66m/s²

⇒ Now force = Mass × acceleration

so,

⇒ Force = 7 × 1.66

= 11.66 N 

So the magnitude of the applied force is 11.66 N

The correct option is 1 i.e., Alloy

• Bronze is an alloy.
• Bronze is an alloy of copper and tin

Some important alloys:

Shortcut Trick

Assume Total Work = 54 units (LCM of 9, 13.5, 4.5, 18).

Efficiency of A = 6, B = 4, A+B+C = 12.

Efficiency of C = 12 − (6 + 4) = 2 units/day.

Efficiency of C+D = 54 ÷ 18 = 3, so D = 3 − 2 = 1 unit/day.

Time taken by D = 54 ÷ 1 = 54 days.

∴ The correct answer is 54 days.

Alternate Method

Given: A = 9 days, B = 13.5 days, A+B+C = 4.5 days, C+D = 18 days.

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

⇒ Efficiency of C = 12 − (6 + 4) = 2 units/day

⇒ Efficiency of D = Efficiency of (C+D) − Efficiency of C

⇒ Efficiency of D = 3 − 2 = 1 unit/day

⇒ Time taken by D = Total Work ÷ Efficiency of D

⇒ Time taken by D = 54 ÷ 1 = 54 days

∴ The correct answer is 54 days.

Additional Information

Efficiency Concept

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

Combined Work Formula

If individuals work together, their efficiencies are additive: E_total = E₁ + E₂ + ... + E_n.

Work and Wages

Wages are generally distributed in the ratio of the work done or the ratio of efficiencies when time is constant.

The correct option 2 is  i.e., Mercury

• Mercury has the least electron affinity.
• Hg is the symbol for Mercury.
• Mercury's atomic number is 80.
• Mercury belongs to the 12^th group.
• Mercury (Hg), also called quicksilver.
• Chlorine has the highest electron affinity.
• Chlorine belongs to the 3^rd period and the 17^th group.
• Chlorine has atomic number 17.

The statement proves that the interview process has loopholes by claiming that even incompetent candidates are often selected.

Therefore, conclusion 1 follows.

The statement suggests that the interview panel often fails to make good selection.

Therefore, it can be concluded that the interview panel is not sufficient to provide good candidates.

Hence, both conclusions 1 and 2 follow.

The logic followed here is that each alphabet is coded by its positional value.

SOAP → S(19), O(15), A(1), P(16)

Similarly,

OPTION → O(15), P(16), T(20), I(9), O(15), N(14)

Hence, the code for ‘OPTION’ is 15162091514.

The correct option is 1 i.e., Magnesium.

• Magnesium is an example of an alkaline earth metal.
• They are called alkaline earth metals because they form alkaline solutions, hydroxides when they react with water
• The alkaline earth metals are six chemical elements in group 2 of the periodic table.

They are:

Shortcut Trick

Total marks for Pragya = 24 × 15 = 360 marks.

Current marks for Zareen = 23 × 12 = 276 marks.

Marks Zareen needs in 3 tests = 360 − 276 = 84 marks.

To find the minimum score in one test, maximize the other two (30 marks each).

Minimum required score = 84 − (30 × 2) = 24 marks.

∴ The correct answer is 24.

Alternate Method

Given:

Pragya's Average = 24 marks in 15 tests.

Zareen's Average = 23 marks in 12 tests.

Maximum marks per test = 30 marks.

Formula Used:

Total Marks = Average × Number of Tests

Calculations:

⇒ Total marks obtained by Pragya = 24 × 15 = 360 marks

⇒ Total marks obtained by Zareen so far = 23 × 12 = 276 marks

⇒ Total marks Zareen needs in remaining 3 tests to match Pragya = 360 − 276 = 84 marks

⇒ Let the scores in the remaining 3 tests be T₁, T₂, and T₃.

⇒ T₁ + T₂ + T₃ = 84

⇒ To find the minimum possible score in any one test (say T₁), we must assume the highest possible scores in the other two tests.

⇒ Maximum score in any test = 30

⇒ T₁ + 30 + 30 = 84

⇒ T₁ + 60 = 84

⇒ T₁ = 84 − 60 = 24 marks

∴ The correct answer is 24.

Additional Information

Average and Sum Relation

The fundamental property of averages is Sum = Average × Number of entities. To find a missing value in a set, subtract the known sum from the total sum.

Maximizing/Minimizing in a Set

To minimize one value in a fixed total sum, all other values must be maximized (kept at their upper limit). To maximize one value, all other values must be minimized.

Weighted Average

When combining two groups, the combined average is (n₁ × avg₁ + n₂ × avg₂) ÷ (n₁ + n₂).

Number of odd days from 5 Feb 2009 till 31 Dec 2009:

1 Jan till 5 feb = 31 + 5 = 36 days

Number of odd days = 365 – 36 = 329 days = 0

Number of odd days from 1 Jan 2010 till 31 Dec 2017 = No. of odd days in 6 ordinary years + No. of days in 2 leap years = 3

Number of odd days in 2018:

1 Jan till 5 feb = 31 + 5 = 36 days

Number of odd days = 1

Number of odd days from 5 Feb 2009 till 5 Feb 2018 = 3 + 1 = 4

Hence, if it was Monday on 5^th February 2018, the day of the week on 5^th February 2009 was Thursday.

Alternate Method5 Feb 2009 to 5 Feb 2018 = 9 Year

→ 9 Years = 2 leap years and 7 Ordinary year

Odd days in 2 leap years(Leap year = 366 days) = 2 × 2 = 4 days.

Odd days in 7 Ordinary Year = 7 × 1 = 7 days.

Total odd days = 4 + 7 = 11 → 1 weak and 4 odd days.

Now, 5 Feb 2009 = Monday - 4 = Thursday.

Hence, the correct answer is "Thursday".

The logic followed here is:

(2 × 3) + 2 → 8;

(8 × 3) + 2 → 26;

Similarly,

(26 × 3) + 2 → 80;

S + 3 = V;

V + 3 = Y;

Similarly,

Y + 3 = B;

Hence, the next term will be 80B.

The correct option is 1 i.e., Raghuram Rajan

• Raghuram Rajan is the author of the book ‘I Do What I do’, published in 2017

Some other important books:

Heat and Light can be obtained from sun.

Hence, the figure given above correctly represents the relationship.

The correct option is 2 i.e., ​B

• Boron (B) is the first metalloid in the modern periodic table.
• Metalloids have properties of both metals and non-metals.

Metalloids table:

Hence, she is 3 km from her starting point.

The correct option is 3 i.e., West Bengal

• The Sunderbans Tiger Reserve is in West Bengal.
• Project Tiger is a tiger conservation program launched in April 1973 by the Government of India.
• Nagpur is also known as the ‘Tiger Capital’ of India

Some important Tiger Reserve:

The logic followed here is:

Each figure has four parts. In each part there is a symbol Ω, ±, triangle with a dash and # or *(alternatively). All these are changing position by one place in clockwise direction. Also, triangle itself turns by 90 degrees in anticlockwise direction.

Hence, the answer figure C follows next in the given series.

Shortcut Trick

Ratio of Distance (Samar : Swapnali) = 3 : 5

Ratio of Time (Samar : Swapnali) = 5 : 7

Ratio of Speeds (S = D/T) → Samar : Swapnali = (3/5) : (5/7) = 21 : 25

For the same distance, Time is inversely proportional to Speed → Time ratio = 25 : 21

Swapnali takes 21 units = 42 minutes ⇒ 1 unit = 2 minutes

Samar takes 25 units = 25 × 2 = 50 minutes

∴ The correct answer is 50 minutes.

Alternate Method

Given: Distance covered by Samar (D₁) = 3/5 × Distance of Swapnali (D₂)

Given: Time taken by Samar (T₁) = 5/7 × Time taken by Swapnali (T₂)

Formula: Speed (S) = Distance / Time

⇒ Speed of Samar (S₁) = (3/5)D₂ / (5/7)T₂

⇒ S₁ = (3/5 × 7/5) × (D₂/T₂) = (21/25) × S₂

⇒ To cover the same distance (D₂), Time taken by Samar = D₂ / S₁

⇒ Time = D₂ / (21/25 × S₂) = 25/21 × (D₂/S₂)

⇒ Time = 25/21 × 42 minutes

⇒ Time = 25 × 2 = 50 minutes

∴ The correct answer is 50 minutes.

Additional Information

Inverse Proportion Rule

When the distance is constant, speed and time are inversely proportional (S₁/S₂ = T₂/T₁).

Direct Proportion Rule

When time is constant, distance and speed are directly proportional (D₁/D₂ = S₁/S₂).

Average Speed

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

The first argument claims that people consume more power than what is produced.

Thus, reducing any unnecessary consumption can be considered equivalent to producing a good amount of power. Thus, argument I strengthens the statement.

Argument II simply rejects the idea of keeping a check on consumption and fails to explain the irrelevance of the suggestion in the statement.

Hence, only argument I is strong.

The correct option is 4 i.e., Amitabh Bachchan.

• Amitabh Bachchan was honored with the Indian Film Personality of the 2017 Award at the 48^th International Film Festival Of India (IFFI).
• "Celebrating the Future of Cinema" was set as the festival's theme.
• The International Film Festival of India was founded in 1952.
• The 50^th International Film Festival of India was held from 20 to 28 November 2019 in Goa.
• Isabelle Hupert won the Lifetime Achievement Award in 2019.
• Icon of Golden Jubilee of IFFI, a special award was given to Rajinikanth.

If the population is increased\decrease by a% then increase/decrease is given by 100 ± a%

Here,

Time = 2 years, rate = 4%         

Present population = 12 lakh

As the population is increasing so,

Population of the city after 2 years = 12,00,000 × 104/100 × 104/100 = 12,97,920

∴ Population after 2 years = 1297920

The correct option is 2  i.e., Argentina

• The famous football player Maradona belongs Argentina

Other famous football players:

Given:

30 - \left[ {29 - \left{ {;28 - \left( {25 - ;\overline {21 - 22} } \right)} \right}} \right] = ;?

Concept:

Follow the BODMAS rule according to the table given below:

Now,

Calculation:

30 - \left[ {29 - \left{ {;28 - \left( {25 - ;\overline {21 - 22} } \right)} \right}} \right] = ;?

⇒ 30 – [29 – {28 – (25 + 1)}] = ?

⇒ 30 – [29 – {28 – 26}] = ?

⇒ 30 – [29 – 2] = ?

⇒ 30 – 27 = ?

⇒ 3 = ?

∴ The required value is 3.

The correct option is 1, i.e., ​Linnaeus.

Key Points

• The system of scientific naming or nomenclature was introduced by Linnaeus.

Additional Information

Some important inventions and discoveries:

The correct option is 2 i.e., Bhubaneswar.

• The 14^th Hockey World Cup was held in Bhubaneswar of India in 2018.
• Belgium won its first World Cup after defeating the Netherlands in 2018
• The 14^th Hockey World Cup final was held at the Kalinga Stadium in Bhubaneswar.
• The 2019 IIHF World Championship was hosted by Slovakia
• India will host the Men's Hockey World Cup for the second consecutive time in 2023.
• The 2023 Men's Hockey World Cup will be held in Bhubaneswar and Rourkela.

The correct option is 4  i.e., high

• An insulator offers high resistance.
• Resistance is a measure of the opposition to current flow in an electrical circuit.
• S.I unit of resistance is ohms.

Resistance depends on the following factors:

• Length: It is directly proportional to the resistance of the conductor.
• Area: It is inversely proportional to the resistance to the cross-sectional area of the conductor.
• Temperature: It is directly proportional to resistance.
• Resistivity: It is directly proportional to the resistance of the conductor.

Formula:

⇒  R = (p*l)/A

where,

• R = resistance.
• p = Resistivity.
• l = length.
• A = area.

Shortcut Trick

Effective Simple Interest Rate = 6% × 5.75 years = 34.5%.

Total Amount percentage = 100% (Principal) + 34.5% (Interest) = 134.5%.

Given 134.5% = ₹3,228 ⇒ Principal (100%) = (3228 ÷ 134.5) × 100 = 24 × 100 = ₹2,400.

∴ The correct answer is ₹2,400.

Alternate Method

Given: Amount (A) = ₹3,228, Rate (R) = 6% per annum, Time (T) = 5³/₄ years = 5.75 years.

Formula Used: Amount (A) = P × [1 + (R × T) ÷ 100], where P is the Principal.

Calculations:

⇒ 3228 = P × [1 + (6 × 5.75) ÷ 100] ⇒ 3228 = P × [1 + 34.5 ÷ 100] ⇒ 3228 = P × [1 + 0.345] ⇒ 3228 = P × 1.345 ⇒ P = 3228 ÷ 1.345 ⇒ P = 3228000 ÷ 1345 ⇒ P = 2400

∴ The correct answer is ₹2,400.

Additional Information

Simple Interest Formula

SI = (P × R × T) ÷ 100, where P is Principal, R is Rate per annum, and T is Time in years.

Amount Calculation

Total Amount (A) = Principal (P) + Simple Interest (SI). It represents the total money returned at the end of the term.

Relationship between SI and CI

For the first year (when interest is compounded annually), Simple Interest and Compound Interest are always equal.

Effective Rate Method

Effective Rate = Rate × Time. This is the simplest way to find the total interest percentage on the principal.

The correct option is 4 i.e., 640 J

Given that, the mass of 20 kg is moving with a uniform velocity of 8m/s

We know that the kinetic energy (K.E) possessed by a body of mass (m), moving with a uniform velocity (v) is:

$K.E= {1m{v^2} \over 2}$

Here,

mass = 20 kg

velocity = 8m/s

So the kinetic energy possessed by the body is 640 Joules.

The logic followed here is:

Hence, 8978 and 91078 will complete the series.

Considering the given statement

$\frac{{\sqrt[3]{{0.000027}}}}{{\sqrt {0.0004} }}$

Now.

$\Rightarrow \frac{{\sqrt[3]{{0.03 \times 0.03 \times 0.03}}}}{{\sqrt {0.02 \times 0.02} }}$

⇒ 0.03/0.02

⇒ 1.5

∴ Required value is 1.5

The correct option is 2 i.e., Atomicity

• The number of atoms constituting a molecule is called Atomicity
• Molarity indicates the number of moles of solute per liter of solution.
• Normality is a measure of concentration equal to the gram equivalent weight per liter of solution.
• Valency is the combining capacity of an atom.

Some important valencies:

Shortcut Trick

Identify the Cost Price (CP) as ₹ 132 and Profit% as 15%.

Use the multiplier method: Selling Price (SP) = CP × (100 + P%) ÷ 100.

SP = 132 × 115 ÷ 100.

SP = 132 × 1.15 = 151.80.

∴ The correct answer is ₹ 151.80.

Alternate Method

Given: Cost Price (CP) = ₹ 132, Profit Percentage = 15%. Formulas: Profit = (Profit% ÷ 100) × CP | SP = CP + Profit.

⇒ Profit = (15 ÷ 100) × 132 ⇒ Profit = 0.15 × 132 = ₹ 19.80 ⇒ Selling Price (SP) = 132 + 19.80 = ₹ 151.80

∴ The correct answer is ₹ 151.80.

Additional Information

Cost Price & Selling Price

The Cost Price is the original value paid, while Selling Price includes the profit or loss margin.

Profit Percentage

Profit% is always calculated on the Cost Price unless specified otherwise. Formula: (Profit ÷ CP) × 100.

The correct option is 4 i.e., H⁺ and OH^- ions are equal.

• In pure water, the concentration(s) of H⁺ and OH^- ions are equal.
• The pH of a solution is a measure of the concentration of hydrogen ions in the solution.
• The pH of pure water is 7.
• Blood is normally slightly basic, with a normal pH range of about 7.35 to 7.45.
• The normal pH range for saliva is 6.2 to 7.6.
• Lemon juice has a pH falling between 2 and 3.
• Milk has a pH of around 6.5 to 6.7.

The correct option is 3 i.e., Dominated

• Dominated character predominates and is clearly seen in FI Generation.
• Mendel stated three laws known as Mendel’s laws of inheritance:

These laws are:

Mendel’s law of segregation:

• It states that during the formation of gamete, each gene separates from each other so that each gamete carries only one allele for each gene.

Mendel's law of dominance:

• It states that when parents with pure contrasting traits are crossed together, only one form of trait appears in the next generation.
• The hybrid offsprings will exhibit only the dominant trait in the phenotype.

Mendel's law of independent assortment:

• It states that during a dihybrid cross an assortment of each pair of traits is independent of the other

Considering the given statement

1.004 - 0.4

⇒ 0.604

∴ Required value is 0.604

The correct option is VAT.

Key Points

• VAT is a consumption tax placed on a product whenever value is added at each stage of the supply chain, from production to the point of sale.
• VAT was introduced on April 1, 2005, in the country.
• VAT is an Indirect tax.
• Indirect taxes are those taxes that can be transferred on others by the taxpayers
• Goods and Service Tax (GST) is an indirect tax levied on the supply of goods and services.
• GST has replaced many indirect tax laws that previously existed in India.

Tax subsumed under the GST:

It can be assumed that Laliltha likes ice cream and wants to have one as she is the one offering it to her friend.

The conversation is between Lalitha and her ‘friend’.

Thus, it can be assumed that Lalitha is offering ice cream because her friend likes it.

Therefore, assumption II is implicit.

However, the conversation does not suggest that Lalitha has already eaten ice cream earlier.

Hence, only assumption II is implicit.

The lateral mirror image is as follows:

Hence, the lateral mirror image of TOUCH will be option figure B.

The correct option is 4 i.e., Uranium

• The fuel used in the nuclear reactor is Uranium.
• Heavy water and graphite are used as a moderator in a nuclear reactor.
• D₂O is the formula for Heavy water.
• Graphite is extremely soft, cleaves with very light pressure, and has a very low specific gravity.
• Under high pressures and temperatures, graphite converts to diamond.
• Graphite is a good conductor of heat and electricity.
• Graphite is used in pencils and lubricants.

Shortcut Trick

Subtract the Start Time from the End Time using the borrowing method for time.

End Time: 11 : 35 : 35 | Start Time: 01 : 44 : 41

Subtracting seconds: 35 − 41 (Borrow 1 min) → 95 − 41 = 54 sec

Subtracting minutes: 34 − 44 (Borrow 1 hr) → 94 − 44 = 50 min

Subtracting hours: 10 − 1 = 9 hr

∴ The correct answer is 9 hr 50 min 54 sec.

Alternate Method

Given:

Switch-on Time = 01 hr 44 min 41 sec

Switch-off Time = 11 hr 35 min 35 sec

Calculations:

⇒ Duration = 11 hr 35 min 35 sec − 01 hr 44 min 41 sec

⇒ As 35 < 41, borrow 1 minute (60 sec): (35 + 60) − 41 = 54 sec

⇒ Minutes remaining = 35 − 1 = 34. As 34 < 44, borrow 1 hour (60 min): (34 + 60) − 44 = 50 min

⇒ Hours remaining = 11 − 1 = 10. 10 − 1 = 9 hr

⇒ Total Duration = 9 hr 50 min 54 sec

∴ The correct answer is 9 hr 50 min 54 sec.

Additional Information

Time Conversion Units

1 hour = 60 minutes and 1 minute = 60 seconds. To borrow during subtraction, add 60 to the smaller unit and subtract 1 from the larger unit.

24-Hour Format

If the end time is on the next day, add 24 hours to the end time before performing the subtraction to find the total elapsed duration.

Total Seconds Method

Convert both times into total seconds: (H × 3600) + (M × 60) + S. Subtract the totals, then convert back to H:M:S format.

The correct option is 2 i.e., National Institution for Transforming India

NITI Aayog:

• The full form of NITI is National Institution for Transforming India
• The NITI Aayog was formed on January 1, 2015.
• One of the objectives of NITI Aayog is to promote cooperative federalism.

NITI Aayog Composition:

• Prime Minister of India is the Chairperson
• Governing Council consists of the Chief Ministers of all the States and Lt. Governors of Union Territories in India.
• Regional Councils will be created to address particular issues and possibilities affecting more than one state.
• Special invitees: Eminent experts, specialists with relevant domain knowledge, which will be nominated by the Prime Minister.

The given series consists of two series:

Series 1: 3, 5,7,……

3 + 2 = 5;

5 + 2 = 7;

7 + 2 = 9

So, the next term in series 1 is 9.

2 + 2 = 4;

4 + 2 = 6;

Since, the next term will be of series 1, the next term is 9.

Hence, 9 is the correct answer.

Flour is used to make Bread.

Similarly,

Clay is used to make Pot.

Hence, Pot is the correct answer.

The least possible Venn diagram is as follows:

Conclusions:

1. All chips are mobiles - False (it is possible but not definite)
2. All mobiles are chips - True (as shown in the figure above)

Hence, ‘only conclusion 2 follows’ is the correct answer.

Shortcut Trick

Total Capacity = Number of Barrels × Capacity per Barrel

Total capacity remains constant → 13 × 51 = n × 17

Divide both sides by 17 → n = 13 × (51 ÷ 17) = 13 × 3

n = 39 barrels

∴ The correct answer is 39 barrels.

Alternate Method

Given: Initial barrels = 13, Initial capacity = 51 litres, New capacity = 17 litres

Formula Used: Volume = n₁ × c₁ = n₂ × c₂

⇒ Total volume of tank = 13 × 51 litres

⇒ Total volume = 663 litres

⇒ Let the number of required barrels be x

⇒ x × 17 = 663

⇒ x = 663 ÷ 17

⇒ x = 39

∴ The correct answer is 39 barrels.

Additional Information

Inverse Proportion

When the total volume is constant, the number of containers is inversely proportional to the capacity of each container (n₁c₁ = n₂c₂).

Unitary Method Application

If capacity decreases by a factor (51/17 = 3), the number of barrels needed increases by the same factor (13 × 3 = 39).

The logic followed here is that each alphabet is coded as first digit of its positional value.

BELL is coded as:

B → 2; E → 5; L → 1 from 12; L → 1 from 12;

Similarly,

Y → 2; E → 5; A → 1; R → 1 and N → 1;

Hence, YEARN is coded as 25111.

The correct answer is option 3 i.e Prakash Javadekar.

• As of August 2018, Prakash Javadekar was the union HRD minister of India.
• The current minister is Ramesh Pokhriyal as of June 2020.

The correct answer is option 2 i.e., Rajnath Singh.

• Rajnath Singh was the Union Home Minister of India in March 2018.
• But as of May 2020, Rajnath Singh is Union Defence Minister.

Other important Portfolio as of May 2020:

Shortcut Trick

Total Sum (N+S+A) = (147 + 173 + 150) ÷ 2 = 470 ÷ 2 = ₹ 235.

Navin's share = Total Sum − (Santanu + Advani).

Navin = 235 − 173 = ₹ 62.

∴ The correct answer is ₹ 62.

Alternate Method

Given:

N + S = ₹ 147 --- (i)

S + A = ₹ 173 --- (ii)

A + N = ₹ 150 --- (iii)

Calculations:

⇒ Adding (i), (ii), and (iii):

⇒ 2(N + S + A) = 147 + 173 + 150

⇒ 2(N + S + A) = 470

⇒ N + S + A = 235 --- (iv)

⇒ To find Navin's money, subtract equation (ii) from (iv):

⇒ N = (N + S + A) − (S + A)

⇒ N = 235 − 173

⇒ N = 62

∴ The correct answer is ₹ 62.

Additional Information

Linear Equations in Three Variables

When the sum of variables is given in pairs (A+B, B+C, C+A), adding them gives twice the total sum 2(A+B+C).

Individual Values Calculation

To find any individual value, subtract the pair not containing that variable from the total sum (e.g., A = Total − (B+C)).

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total Distance = 176 m

Total Time = 1 minute = 60 seconds

Average Speed = 176 ÷ 60 = 2.9333... ms⁻¹

∴ The correct answer is 2.93 ms⁻¹.

Alternate Method

Given:

Length of the pool = 88 m

Total distance covered (Round trip) = 176 m

Total time taken = 1 minute = 60 seconds

Formula Used:

Average Speed = Total Distance Covered / Total Time Taken

Calculations:

⇒ Total distance = 176 m

⇒ Total time = 60 s

⇒ Average speed = 176 / 60

⇒ Average speed = 2.933... ms⁻¹

∴ The correct answer is 2.93 ms⁻¹.

Additional Information

Average Velocity

Average velocity is defined as the Total Displacement divided by Total Time. In this case, since Ram returns to the starting point, displacement is 0, so average velocity is 0 ms⁻¹.

Unit Conversion

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

Uniform Speed

An object moving with uniform speed covers equal distances in equal intervals of time, regardless of the direction of motion.

The logic followed here is

Each figure has four parts. In each part there is a symbol Ω, * , / , a triangle. Also, symbol ∑ is in upper right part of each figure. All the four symbols are changing position by one place in clockwise direction in each figure. Also, in each figure triangle is turning by 90 degrees in clockwise direction.

Hence, the answer figure C will be the next figure in the series.

Considering the given statement

129 \div \left[ {46 - \left{ {93 \div \left( {35 - 132 \div \overline {11 \times 3} } \right)} \right}} \right]

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

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now,

⇒ 129 ÷ [46 – {93 ÷ (35 – 132 ÷ 33)}]

⇒ 129 ÷ [46 – (93 ÷ (35 – 4)}]

⇒ 129 ÷ [46 – (93 ÷ 31)]

⇒ 129 ÷ [46 – 3]

⇒129 ÷ 43

⇒ 3

∴ Required value is 3

The logic followed here is that each alphabet is coded as second digit of its positional value.

The MEND will be coded as:

M(13) → 3;

E(05) → 5;

N(14) → 4;

D (04) → 4;

Similarly,

C (03) → 3

U (21) → 1

R (18) → 8

V (22) → 2

E(05) → 5

Hence, CURVE is coded as 31825.

In the question figure, a smiley lies inside the hexagon in one of its corners.

Therefore, A, B, and D get eliminated.

In C, the smiley is the water image of that of the question figure.

This is the closest resemblance of the original figure.

Hence, C is the correct answer.

Shortcut Trick

Ratio of My age (M) to Cousin age (C) is (M × 7/9) = (C × 5/6).

M/C = (5/6) × (9/7) = 15/14. Let ages be 15x and 14x.

39 years ago: (15x − 39) = 2 × (14x − 39).

15x − 39 = 28x − 78 ⇒ 13x = 39 ⇒ x = 3.

My current age = 15 × 3 = 45 years.

∴ The correct answer is 45 years.

Alternate Method

Given: (7/9) × My Age = (5/6) × Cousin Age

Formula: Ratio and linear equation based on time shifts.

⇒ Let My current age be M and Cousin age be C.

⇒ 7M/9 = 5C/6 ⇒ M/C = (5 × 9)/(6 × 7) = 45/42 = 15/14.

⇒ Let M = 15x and C = 14x.

⇒ Thirty-nine years ago: (15x − 39) = 2 × (14x − 39).

⇒ 15x − 39 = 28x − 78.

⇒ 78 − 39 = 28x − 15x ⇒ 39 = 13x ⇒ x = 3.

⇒ My current age = 15 × 3 = 45 years.

∴ The correct answer is 45 years.

Additional Information

Ratio of Ages

If the ratio of ages is a:b, the ages can be assumed as ax and bx to simplify algebraic equations.

Time Shift

To represent an age 'n' years ago, subtract n from the current age (Age − n); for 'n' years hence, add n (Age + n).

Linear Equations in One Variable

Problems involving two people's ages are best solved by expressing both ages in terms of a single variable x using the given ratio.

The correct option is 3 i.e., India’s first venture in interplanetary space

• Mangalyaan on the reverse of the Indian ₹ 2,000 banknotes depicts India’s first venture in interplanetary space
• The front side of this note has a picture of Mahatma Gandhi
• This is the highest currency note printed by RBI that is in active circulation
• The ₹2000 banknote has its amount written in 17+1 languages as Braille language added on new currency notes for visually impaired.
• Mangalyaan was launched on 5 November 2013 by the Indian Space Research Organisation
• Indian Space Research Organisation headquarters in the city of Bengaluru.
• ISRO was founded by Vikram Sarabhai.
• It was founded on 15 August 1969.

The correct answer is Option 3 i.e 22 + (XX).

Key Points

• The chromosomal condition in human females is 22 + (XX).
• Humans have a pair of sex chromosomes (XX or XY) plus 22 pairs of autosomes, totalling 23 pairs altogether or 46 chromosomes.
• Men have an X and a Y chromosome and Women have 2X or  XX chromosomes.
• Sperm can contain either an X or a Y chromosome.

Upon fertilization,

• An X sperm and an X egg = baby girl (XX)
• A Y sperm and an X egg = baby boy (XY)

Shortcut Trick

Given Product = 55 and One number = 2.50.

Direct calculation: Second number = 55 ÷ 2.5.

Convert 2.5 to fraction: 2.5 = 5/2.

Result = 55 × (2/5) = 11 × 2 = 22.

∴ The correct answer is 22.

Alternate Method

Given:

Product of two numbers = 55

First number (n₁) = 2.50

Formula Used:

Product = n₁ × n₂

Calculations:

⇒ 2.50 × n₂ = 55

⇒ n₂ = 55 / 2.50

⇒ n₂ = (55 × 100) / 250

⇒ n₂ = 5500 / 250

⇒ n₂ = 550 / 25

⇒ n₂ = 22

∴ The correct answer is 22.

Additional Information

Decimal Division

To divide by a decimal, multiply both the dividend and divisor by a power of 10 to make the divisor a whole number.

LCM and HCF Relationship

For any two numbers, Product of two numbers = HCF × LCM.

Reciprocal Multiplication

Dividing by a number is equivalent to multiplying by its reciprocal (e.g., ÷ 2.5 is same as × 0.4).

The first argument says that awareness will help people understand the need to use fuel judiciously as fuel production adds pressure on natural resources. Thus, it will help the cause of responsible usage of fuel.

Therefore, argument I is strong.

Argument II says that educating the masses is ‘difficult’ because they are accustomed to a comfortable life. But this need not mean that the task is impossible.

Therefore, argument II fails to give a strong reason to reject the idea of generating awareness through campaigns.

Hence, only argument II is strong.

The correct option is 3 i.e., Indus River

• The name ‘India’ comes from the Indus River.
• The Indus River is one of the longest rivers in Asia
• The Indus River originates in the Tibetan plateau in the vicinity of Lake Manasarovar.

Tributaries of Indus:

1) Monday there is heavy traffic on Route-2 and Route-3 (Means he will take Route 1)

2) Tuesdays and Wednesdays there would be multiple diversions on Route-1 and Route-3 (Means he will take route - 2 for these two days)

3) Thursday and Friday he prefers to go by Route-3

So, For 4 consecutive weeks he will take route -2 = 4 × 2 = 8 days

Route-2 is 7 km (He goes to the office and comes back from the same Route)

 Total number of kilometres he traveled on Route-2 = 2 × 7 × 8 = 112 Km

Hence, option 3) is the correct answer.

The correct option is 2 i.e., $ 2.597 trillion

• According to the World Bank, India’s GDP at the end of 2017 was $ 2.597 trillion.
• The GDP in India was worth 2800 billion US dollars in 2019

GDP:

• GDP stands for "Gross Domestic Product"
• GDP represents the total monetary value of all final goods and services produced within a country during a period of time typically 1 year

World bank:

• The World Bank is an international financial institution.
• World Bank headquarters at Washington, D.C.

 It comprises two institutions:

• International Bank for Reconstruction and Development
• International Development Association

Shortcut Trick For a quadratic equation to have equal roots, the Discriminant must be zero. Direct formula for equal roots in cx2 + bx + c = 0 is b2 = 4 × c × c. ⇒ b2 = 4c2 ⇒ (b/c)2 = 4 ⇒ b/c = 2/1 ∴ The correct answer is 2 : 1. Alternate Method Given Equation: cx2 + bx + c = 0 Condition: The equation has equal roots. Formula Used: For a general quadratic equation Ax2 + Bx + C = 0, the roots are equal if the Discriminant (D) = B2 − 4AC = 0. Comparing the given equation with the standard form: ⇒ A = c, B = b, C = c ⇒ D = b2 − 4 × c × c = 0 ⇒ b2 − 4c2 = 0 ⇒ b2 = 4c2 ⇒ b/c = √4 ⇒ b/c = 2/1 ⇒ b : c = 2 : 1 ∴ The correct answer is 2 : 1. Additional Information Nature of Roots The value D = b2 − 4ac determines the nature: D > 0 (Real and Distinct), D = 0 (Real and Equal), D < 0 (Imaginary/Complex). Sum and Product of Roots For Ax2 + Bx + C = 0, the sum of roots is −B/A and the product of roots is C/A. Perfect Square Condition A quadratic expression is a perfect square if and only if the discriminant of its corresponding equation is zero.

1. The statement only talks about the event manager's decision to perform a comedy show and a skit.
2. It does not suggest anything about the likes or dislikes of the manager.
3. Hence, neither conclusion I nor II follows.

The correct option is 2 i.e., Kajol.

• Kajol has been chosen as an Advocacy Ambassador of Hindustan Unilever Limited (HUL)’s ‘Swachh Aadat, Swachh Bharat’ programme in line with the Government of India’s Swachh Bharat Abhiyan

List of Brand Ambassadors:

Scale, Ruler and Inch tape are used to measure length whereas rope is not used to measure length.

Hence, rope does not belong to this group.

The correct option is 4 i.e., Vijayapura.

• The Gol Gumbaz, having the second-largest dome in the world, is located in Vijayapura.
• Gol Gumbaz at Bijapur is the mausoleum of king Muhammad Adil Shah.

Golconda:

• The Qutb Shahi dynasty ruled the Golconda Sultanate in south India
• Golconda Fort is a fort of Southern India and the capital of the medieval sultanate of the Qutb Shahi dynasty in the west of Hyderabad.

Berar:

• Berar was a province in British India, ruled by the Nizam of Hyderabad.

Gulbarga:

• Gulbarga is a city in the Indian state of Karnataka.

According to the question

Total number of user who use swimming pool = 300

Charge for Swimming Pool = Rs. 600

Total money received by swimming pool in a month = 600 × 300 = 1,80,000.

∴ Required money they received from swimming pool usage is Rs. 180000

The correct option is 2 i.e., Medium.

• The matter or subject through which sound is transmitted is called as Medium.
• Sound is produced by the vibrations of the particles of the medium.
• Sound cannot travel in vacuum.

A sound wave can be described by five characteristics:

• Wavelength
• Amplitude
• Time-Period
• Frequency
• Velocity or Speed.

The square root of 8836 is

⇒ √8836

⇒ √(2 × 2 × 47 × 47)

⇒ 2 × 47

⇒ 94

∴ Square root of 8836 is 94

The correct option is 2 i.e., Amitabh Bachchan

• Amitabh Bachchan has been selected as the Horticulture Ambassador of Maharashtra.
• EC appoints Madhuri Dixit as a goodwill ambassador for Maharashtra Assembly polls which was scheduled on 21 October 2019.
• Sambhaji Raje Bhosale is the brand ambassador for Maharashtra Tourism.
• Salman Khan is the brand ambassador of BharatPe.
• Aamir Khan is the brand ambassador of Phonepe.

Concept:

Power:

It is the rate of doing work.

Mathematically,

$Power = {energy\over time}$

Calculation:

Given:

Work = Energy ⇒ 100 J and t = 20 sec.

$Power = {energy\over time}$

$Power = {100\over 20}$

∴ P = 5 W

Statement 1: There are 25 students in a class.

No information is given about Nitya. So, statement 1 is not sufficient.

Statement 2: There are 15 students who have scored less than Nitya

No information is given about the total number of students. So, statement 2 is not sufficient.

Combining statements 1 and 2:

There are 25 students in a class. There are 15 students who have scored less than Nitya.

Here, Nitya scored 10^th rank.

Hence, statement 1 and 2 together are sufficient.

Steam, Boil and Bake are process for cooking whereas make is a general term representing manufacture or creation of something.

Hence, make is the correct answer.

The correct option is 3 i.e., ​potential energy to kinetic energy

• When an arrow is released from its bow, its energy is transformed from potential energy to kinetic energy.

Kinetic energy:

• The kinetic energy of an object is the energy that it possesses due to its motion.

 $K.E= {1m{v^2} \over 2}$

where, 

• m = mass
• v = velocity

Potential energy:

• Potential energy is the energy held by an object because of its position or configuration.

$P.E. = mgh$

where,

• m = mass
• g = the acceleration due to gravity
• h = height

Statement 1: B is heavier than A.

B > A

No information given about C. So, statement 1 is not sufficient.

Statement 2: A is lighter than C.

A < C

No information is given about B. So, statement 2 is not sufficient.

Combining statement 1 and 2: B is heavier than A. A is lighter than C

B > A; C > A

No information is given about the relation between C and B.

Hence, statement 1 and 2 together are not sufficient.