RRC Group D Previous Year Paper 32 (Held On: 1 Oct 2018 Shift 3)

According to the given information,

Conclusion 1: This follows, because pedestrian crossing is safe.

Conclusion 2: This does not follow, because it is not mentioned that children know what is

pedestrian crossing.

Hence, “only conclusion 1” follows.

Shortcut Trick

For two numbers a and b, the third proportional is given by b² ÷ a.

Here, a = 9 and b = 12.

Third Proportional = (12 × 12) ÷ 9 = 144 ÷ 9 = 16.

∴ The correct answer is 16.

Alternate Method

Given: First number (a) = 9, Second number (b) = 12.

Formula Used: If x is the third proportional to a and b, then a : b :: b : x.

⇒ 9 / 12 = 12 / x

⇒ 9 × x = 12 × 12

⇒ 9x = 144

⇒ x = 144 ÷ 9

⇒ x = 16

∴ The correct answer is 16.

Additional Information

Mean Proportional

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

Fourth Proportional

If four quantities a, b, c, d are in proportion (a:b = c:d), then d is the fourth proportional, calculated as (b × c) ÷ a.

Continued Proportion

Three numbers a, b, c are in continued proportion if a/b = b/c, which implies b² = ac.

Shortcut Trick

To find the total number of students, we need both the number of boys and girls.

Statement I gives only the number of boys (10).

Statement II gives the girls relative to boys (Boys + 2).

Neither statement alone provides both values, but combining them gives Boys = 10 and Girls = 12.

∴ The correct answer is Both statements I and II are sufficient.

Alternate Method

Given:

Statement I: Number of boys (B) = 10

Statement II: Number of girls (G) = B + 2

Formula Used:

Total Students (T) = Boys (B) + Girls (G)

Calculations:

⇒ From Statement I: B = 10

⇒ From Statement II: G = B + 2

⇒ Substitute B from I into II: G = 10 + 2 = 12

⇒ Total Students = 10 + 12 = 22

⇒ Since we used information from both statements to find the unique total, both are necessary.

∴ The correct answer is Both statements I and II are sufficient.

Additional Information

Data Sufficiency Rules

In Data Sufficiency, a question is solvable if the given statements provide a unique value. You do not need to calculate the actual answer, only determine if it can be calculated.

Independent vs. Dependent Statements

If one statement depends on a variable defined in another (like Girls depending on Boys), both statements must be analyzed together to find the solution.

Variable Elimination

For n unknown variables, you generally require n independent equations or pieces of information to find a specific solution.

The pattern followed is,

Similarly,

Hence, “KHLO” is the correct answer.

Oersted  is the intensity of a magnetic field in vacuum.

Similarly,

Watt is the unit of power.

‘Watt’  is related to the third words on the same basis as the second word is related to the first word.

Hence, “watt” is the correct answer.

Let kalyan’s  age be  2x, kalyan’s sister age be x.

Kalyan’s father’ s age is 10x

After two years their combined age will be 58

X + 2 + 2x + 2 + 10x + 2 = 58

13x + 6 = 58

13x = 52

x= 4

x is Kalyan’s sister’s age, which is 4.

Hence, “4” is the correct answer.

Drawing diagram according to the given information,

There is a moment of 45⁰ anti clock – wist .

If east becomes, north – east, the north becomes ‘north – west’.

Hence, “north – west” is the correct answer.

The correct answer is option 4 i.e Unnat Jyoti by Affordable LEDs for All​ (UJALA).

• The Government of India announced Unnat Jyoti by Affordable LEDs for All (UJALA) scheme to help replace incandescent bulbs with LED bulbs and promote lightening, enhance awareness on using efficient equipment with less electricity bill and help preserve the environment.
• The scheme was launched by Prime Minister of India Narendra Modi on 1 May 2015.
• The scheme comes under the Ministry of Power.
• In May 2017, the Government of India expanded the LED distribution project to the United Kingdom.

Reversing the second half of the series,

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

The pattern followed is,

For +%2 : /$3,

There is a gap of 9 between ‘+’ and ‘%’ and there a gap of 4 between ‘%’ and ‘2’

And,

There is a gap of 9 between ‘/’ and ‘$' and there a gap of 4 between '$’ and ‘3’

Similarly,

For @y$: _

There is a gap of 6 between ‘@’ and ‘y’ and there a gap of 13 between ‘y’ and ‘$’

And,

Similarly,

There is a gap of 6 between ‘T’ and ‘B’ and there a gap of 13 between ‘B’ and ‘#’

Hence, “TB#” is the correct answer.

Shortcut Trick

Marks = 58% of 450

Calculate 50% + 8% of 450

50% of 450 = 225

8% of 450 = 36

Total = 225 + 36 = 261

∴ The correct answer is 261 marks.

Alternate Method

Given:

Maximum Marks = 450

Percentage Obtained = 58%

Formula Used:

Marks Obtained = (Percentage ÷ 100) × Total Marks

⇒ Marks = (58 ÷ 100) × 450

⇒ Marks = 0.58 × 450

⇒ Marks = 58 × 4.5

⇒ Marks = 261

∴ The correct answer is 261 marks.

Additional Information

Percentage Change

Percentage change = (Difference ÷ Original Value) × 100. It measures how much a value has increased or decreased relative to its base.

Fraction to Percentage Conversion

To convert a fraction to a percentage, multiply the fraction by 100. For example, 3/5 = (3/5) × 100 = 60%.

Base Change Property

x% of y is always equal to y% of x. This is useful for easier mental calculations (e.g., 16% of 50 = 50% of 16 = 8).

Given:

Number of children vaccinated = 120000

Calculation:

Percentage of kids from city B who were vaccinated = 30%

∴ Number of kids from city B who were vaccinated = 1,20,000 × 30/100 = 36,000

Utensils, furniture and clothes are represented separately.

The correct Venn diagram is,

Hence, option 1 is the correct answer.

Shortcut Trick

Convert mixed fractions to improper fractions: Distance = 62/3 km and Time = 31/4 hours.

Speed = Distance ÷ Time ⇒ (62/3) ÷ (31/4).

Speed = (62/3) × (4/31) = 2 × (4/3) = 8/3 kmph.

8/3 kmph = 2(2/3) kmph.

∴ The correct answer is 2(2)/(3)km.

Alternate Method

Given:

Distance covered by Sindhu = 20(2/3) km

Time taken = 7(3/4) hours

Formula Used:

Speed = Distance ÷ Time

Calculations:

⇒ Distance = 20(2/3) = (20×3 + 2)/3 = 62/3 km

⇒ Time = 7(3/4) = (7×4 + 3)/4 = 31/4 hours

⇒ Speed = (62/3) / (31/4)

⇒ Speed = (62/3) × (4/31)

⇒ Speed = (2 × 4) / 3

⇒ Speed = 8/3 = 2(2/3) kmph

∴ The correct answer is 2(2)/(3)km.

Additional Information

Unit Conversion

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

Average Speed

Average Speed = Total Distance ÷ Total Time. If distances are equal, Average Speed = 2xy/(x+y).

According to the given information,

Conclusion 1: This is strong, because pain killers should be avoided for small aches.

Conclusion 2: This is not strong, because taking too many pain killers will affect the liver.

Hence, “only argument 1” is strong.

Shortcut Trick

Effective Simple Interest rate = 1.5 × 8% = 12%

If 12% → ₹360, then 100% (Principal) = (360 ÷ 12) × 100 = ₹3000

For Compound Interest, Time = 1.5 × 2 = 3 years

Effective CI rate for 3 years at 8% = 25.9712%

CI = 3000 × 25.9712% = ₹779.136

∴ The correct answer is ₹779.13.

Alternate Method

Given: Simple Interest (SI) = ₹360, Rate (R) = 8% p.a., Time (T₁) = 1.5 years

Formula Used: SI = (P × R × T) ÷ 100 | CI = P[(1 + R/100)ⁿ − 1]

⇒ SI = (P × 8 × 1.5) ÷ 100

⇒ 360 = (P × 12) ÷ 100

⇒ Principal (P) = (360 × 100) ÷ 12 = ₹3000

⇒ New Time (n) = 1.5 × 2 = 3 years

⇒ Compound Interest (CI) = 3000 × [(1 + 8/100)³ − 1]

⇒ CI = 3000 × [(1.08)³ − 1]

⇒ CI = 3000 × [1.259712 − 1]

⇒ CI = 3000 × 0.259712 = ₹779.136

∴ The correct answer is ₹779.13.

Additional Information

Effective Rate of Compound Interest

For 3 years at rate R%, effective CI rate = 3R.3R²R³ (using decimal positions for calculations).

Difference between CI and SI

Difference for 2 years = P(R/100)². Difference for 3 years = P(R/100)² × (3 + R/100).

Compound Interest Formula

Amount (A) = P(1 + R/100)ⁿ, where P is Principal, R is Rate, and n is Time in years.

The correct answer is option 3 i.e Ranchi.

• Ranchi is the capital of Indian state Jharkhand.
• The Jharkhand state was formed on 15 November 2000.
• The current chief minister of Jharkhand is Hemant Soren.
• The current Governor of  jharkhand  is Ramesh Bais.

Shortcut Trick

Total time taken = 15 days. Rathin left 5 days before, so Bratin worked alone for the last 5 days.

Rathin & Bratin together worked for 15 − 5 = 10 days.

Work left by both in 2 days (12 − 10) = Work done by Bratin in 5 days.

Efficiency Ratio (R+B) : B = 5 : 2 → Efficiency of B = 2 units, Total Work = 5 × 12 = 60 units.

Time for Bratin = 60 ÷ 2 = 30 days.

∴ The correct answer is 30 days.

Alternate Method

Given: (Rathin + Bratin) can do work in 12 days. Total time taken = 15 days. Rathin left 5 days before completion.

Let efficiency of Rathin be R and Bratin be B.

⇒ Total Work = 12 × (R + B)

⇒ According to question: 10 × (R + B) + 5 × B = 12 × (R + B)

⇒ 5B = 2 × (R + B)

⇒ 5B = 2R + 2B

⇒ 3B = 2R → R/B = 3/2

⇒ Let B = 2 and R = 3. Total Work = 12 × (3 + 2) = 60 units.

⇒ Time for Bratin = 60 ÷ 2 = 30 days.

∴ The correct answer is 30 days.

Additional Information

Work Left Before Completion

If a person leaves 'n' days before completion, add their 'n' days of work to the total work and divide by combined efficiency.

Efficiency and Time

Efficiency is inversely proportional to the time taken to complete the work (E ∝ 1/T).

Man-Days Formula

M₁D₁H₁/W₁ = M₂D₂H₂/W₂, used for comparing work done by different groups.

The correct answer is Olfactory indicators​.

• The substances whose odour changes in an acidic or basic medium are called olfactory indicators.
• In an olfactory indicator, smell varies depending on whether it is mixed with an acidic or basic solution.
• These are mainly used in laboratories to check whether a given solution is a basic or an acidic solution by a process called olfactory titration.
• Examples: Onion, clove oil, and vanilla extract.

The correct answer is option 3 i.e Both A and B are true.

• Both statements are true.
• The speed of sound in oxygen gas at 25°C is 316 m/s.
• The speed of sound in water (distilled) at 25°C is 1498 m/s.
• The speed of sound decreases when it passes from solid to gaseous state of a given medium.
• Sound travels fastest through solids.
• The speed of sound depends on the medium through which it is travelling and the temperature and pressure of that medium.

Additional Information 

https://ncert.nic.in/ncerts/l/iesc112.pdf

Shortcut Trick

Prime factorize 4050: 4050 = 81 × 50 = 81 × 25 × 2.

4050 = 9² × 5² × 2¹.

To make it a perfect square, multiply by the missing factor 2.

New number = 4050 × 2 = 8100.

Square root = √8100 = 90.

∴ The correct answer is 90.

Alternate Method

Given: Number = 4050.

Step 1: Find the prime factors of 4050.

⇒ 4050 = 2 × 2025

⇒ 4050 = 2 × 3 × 675

⇒ 4050 = 2 × 3 × 3 × 225

⇒ 4050 = 2 × 3 × 3 × 3 × 75

⇒ 4050 = 2 × 3 × 3 × 3 × 3 × 25

⇒ 4050 = 2¹ × 3⁴ × 5²

Step 2: Identify the factor with an odd exponent.

⇒ The factor 2 has an exponent of 1.

⇒ To make it a perfect square, we multiply by 2.

Step 3: Calculate the square root of the resulting number.

⇒ Square root = √(2² × 3⁴ × 5²)

⇒ Square root = 2 × 3² × 5

⇒ Square root = 2 × 9 × 5 = 90

∴ The correct answer is 90.

Additional Information

Perfect Square Condition

A number is a perfect square if all the exponents in its prime factorization are even numbers.

Square Root of a Product

The property √(a × b) = √a × √b is used to simplify the calculation of roots after factorization.

Least Positive Integer

To find the least multiplier for a perfect square, multiply the number by the product of all prime factors that have odd powers.

The correct answer is option 3 i.e Stomata.

• Transpiration takes place through the stomata.
• Stomata is a tiny opening or pore, found in the epidermis of leaves, stems, and other organs, that facilitates gas exchange.
• Stomata are typically found in plant leaves but can also be found in some stems.
• The pore is surrounded by a pair of specialized parenchyma called guard cells that are responsible for regulating the size of the stomatal opening.

By decoding given information,

7N12L48P4M6

7 × 12 + 48 ÷ 4 – 6

Using BODMAS rule,

7 × 12 + 12 – 6

84 + 12 – 6

96 – 6

90

Hence, “90” is the correct answer.

The correct answer is option 4 i.e 11.5 A.

Given,

Potential difference(V)= 60 V.

Current (I)= 4 A.

Using ohm's law:

$V= I\ \times \ R$

Resistance (R)= $V \over I$

∴ R=  ${60 \over 4} = 15\ \Omega$

If the potential difference is increased to 172.5 V

V= 172.5 V

R= 15 Ω

Current (I)=${V \over R}= {172.5 \over 15}= 11.5 \ A$.

∴The heater will draw 11.5 A current if the potential difference is increased to 172.5 V.

The correct answer is option 1 i.e Saina Nehwal

• Saina Nehwal was the shuttler who represented the Olympic committee in the Badminton World Federation.
• Saina is the only female player from India and overall the second Indian player who attains the world no. 1 ranking after Prakash Padukone.
• She has represented India three times in the Olympics.
• Autobiography: Playing to Win: My Life On and Off Court.
• Saina joined the Bharatiya Janata Party on 29 January 2020.

The given figure is embedded in,

Hence, option 4 is the correct answer.

Gold and platinum are metals.

The correct Venn diagram is,

Hence, option 1 is the correct answer.

Shortcut Trick

Net Simple Interest rate for 3 years = 9% × 3 = 27%.

Net Compound Interest rate for 3 years at 10% = 33.1%.

Difference in interest percentage = 33.1% − 27% = 6.1%.

Total gain = 6.1% of ₹32,000 = 0.061 × 32,000 = ₹1,952.

∴ The correct answer is ₹1,952.

Alternate Method

Given: Principal (P) = ₹32,000, SI rate (R₁) = 9%, CI rate (R₂) = 10%, Time (T) = 3 years.

Formula Used: SI = (P × R × T) / 100 | CI = P × [(1 + R/100)^T − 1]

Calculations:

⇒ Simple Interest (SI) = (32,000 × 9 × 3) / 100

⇒ SI = 320 × 27 = ₹8,640

⇒ Compound Interest (CI) = 32,000 × [(1 + 10/100)³ − 1]

⇒ CI = 32,000 × [(1.1)³ − 1] = 32,000 × [1.331 − 1]

⇒ CI = 32,000 × 0.331 = ₹10,592

⇒ Total Gain = CI − SI = 10,592 − 8,640

⇒ Gain = ₹1,952

∴ The correct answer is ₹1,952.

Additional Information

Effective Rate for 10% Compound Interest

For 2 years, effective CI rate = 10 + 10 + (10 × 10)/100 = 21%. For 3 years, it is 21 + 10 + (21 × 10)/100 = 33.1%.

Difference between CI and SI

When rates are equal (R), the difference for 2 years is P(R/100)² and for 3 years is P(R/100)² × (3 + R/100).

Simple Interest Nature

Simple Interest remains constant every year because it is always calculated on the original Principal amount.

The correct answer is option 2 i.e Modern periodic law.

• Modern periodic law states that "Properties of elements are a periodic function of their atomic number".
• Modern periodic law was proposed by Henry Moseley in 1913.
• Mendeleev's periodic law is slightly different from Moseley's, it states that "Properties of the elements are periodic functions of their atomic mass".
• Mendeleev's periodic law was proposed by Dmitri Ivanovich Mendeleev.

The correct answer is option 4 i.e Ohm.

• The relation between the potential difference (V) and current (I) was discovered by Georg Ohm.
• The law was named after the scientist who discovered it and hence it is known as ohm's law.
• Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
• $V= I\ \times \ R$

The pattern followed is,

In figure A, there is a triangle inside a triangle, in figure B there is a circle inside a circle and in figure

C there is a square inside a square.

But,

In figure D, there is a rhombus inside a hexagon, both the figures are not same.

Hence, figure D is different from the rest.

The correct answer is option 4 i.e Negative.

• The work done by the wind on the car while it is blowing, from the opposite direction of the car will be negative.
• Work is the product of force and displacement.
• The SI unit of work is the joule (J).
• The work done by a force can be either positive or negative or zero.

The correct answer is option 4 i.e Watt.

Key Points

• The SI unit of power is Watt.
• The Watt is named after James Watt.
• Power is the amount of energy transferred per unit time.
• 1 watt (W) = 1.00 joules per second (J/sec).
• Power is a scalar quantity.

Additional Information

Shortcut Trick

Total Work = LCM(81, 97.2, 162) = 486 units.

Efficiency of (A+B+C) = 486 ÷ 81 = 6 units/day.

Efficiency of (A+B) = 486 ÷ 97.2 = 5 units/day.

Efficiency of (B+C) = 486 ÷ 162 = 3 units/day.

Efficiency of B = (A+B) + (B+C) − (A+B+C) = 5 + 3 − 6 = 2 units/day.

Time taken by B = 486 ÷ 2 = 243 days.

∴ The correct answer is 243 days.

Alternate Method

Given: (A+B+C) = 81 days, (A+B) = 97.2 days, (B+C) = 162 days.

Formula Used: Efficiency = Total Work ÷ Time; Time = Total Work ÷ Efficiency.

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

⇒ Efficiency of C = 6 − 5 = 1 unit/day.

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

⇒ Efficiency of B = 3 − 1 = 2 units/day.

⇒ Time taken by B = 486 ÷ 2 = 243 days.

∴ The correct answer is 243 days.

Additional Information

Total Work Assumption

Total work is always assumed to be the Least Common Multiple (LCM) of the number of days taken by the individuals to simplify efficiency calculations.

Inverse Relation of Time and Efficiency

Efficiency is inversely proportional to the time taken to complete a work. If time increases, efficiency decreases and vice versa.

Additive Nature of Efficiency

When people work together, their individual efficiencies are added to get the combined rate of work per day.

The correct answer is option 1 i.e 27

• Mass number is 27.
• The mass number is the total number of protons and neutrons in an atomic nucleus.
• The number of protons = 10.
• Number of neutrons = 17.
• Mass number = Number of protons + Number of neutrons = 10 + 17 =  27.

Sound is heard with the help of ears.

Similarly,

Scent is smelled with the help of nose.

‘Nose’ is related to the third word on the same basis as the second word is related to the first word.

Hence, “nose” is the correct answer.

Calculation:

Let n = 0.41

n = 0.41         ---- (i)

n = 0.4141

Two digits are repeated after the decimal point,

So we multiply both sides by 100.

100n = 41.41          ---- (ii)

From (ii) - (i) 

⇒ 100n - n = 41.41 - 0.41

⇒ 99n = 41

⇒ n = 41/99

∴ The value of n {999……9(ntimes)} is 2.

According to the given information,

Bratin’ s age is 18 years

His cousin’ s age is 7 years

Verifying the given options,

Option 1→ 15 years

Bratin’ s age after 15 years is 33

His cousin’s age after 15 years is 22

22 × 1.5 = 33

Option 2 → 16 years

Bratin’ s age after 16 years is 34

His cousin’s age after 16 years is 23

23 × 1.5 is not equal to 34

Option 3 → 13 years

Bratin’ s age after 13 years is 31

His cousin’s age after 13 years is 20

20 × 1.5 is not equal to 31

Option 4 → 14 years

Bratin’ s age after 14 years is 32

His cousin’s age after 14 years is 21

21 × 1.5 is not equal to 32

Hence, “15 years” is the correct answer.

The pattern followed is,

In figures A, C and D the arrow mark is present on the sides of the triangle.

Whereas,

In figure B, the arrow is at the base of the triangle.

Hence, figure B is the odd one.

The correct answer is option 1 i.e 1835.

• The British made English the medium of instruction in India in 1835.
• Macaulay's minute of 1835 leads to the inclusion of the English language as the medium of instruction in government schools and colleges in India.
• Lord William Bentinck was the governor-general of India during Macaulay's minute of 1835.
• Macaulay has a major role in the introduction of Western concepts to education in India.
• The famous Infiltration theory was introduced by Macaulay.
• As a part of developments in the education sector, the Elphinstone College (Bombay) and the Calcutta Medical College were established. in 1835.

Drawing the family tree,

Srilekha’s brother’s only sister’s father’s sister is the paternal aunt to her.

Hence, “paternal aunt” is the correct answer.

Given:

A fraction when added to $\frac{{17}}{3}$ gives 4.

Concept:

Whenever there is a need of taking a fraction, take it as ‘x/1’ as this will reduce calculation.

Example: Find the fraction which is equal to the reciprocal of 2.

Suppose, fraction = x/1

x/1 = ½ ⇒ x = ½ or Fraction = ½

Calculation:

Let the fraction be x

According to the question

x + 17/3 = 4

⇒ x = 4 - 17/3

⇒ x = (12 - 17)/3

⇒ x = -5/3

⇒ x $-1\frac{{2}}{3}$

∴ The fraction $-1\frac{{2}}{3}$

The correct answer is option 1 i.e Both A and B are true.

• Both statements are true.
• An acid or base's strength refers to its degree of ionization.
• Strong acids completely dissociate into their ions in water.
• The strong acids are hydrochloric acid (HCl), sulfuric acid(H₂SO₄, hydrobromic acid, and nitric acid(HNO₃).
• Weak acids only partially dissociate into their ions in water.
• Most organic acids are weak acids.
• The examples of these acids are Acetic acid(CH₃COOH), Carbonic acid (H₂CO₃₎, Sulfoxylic acid (H₂SO₂).

The correct answer is option 1 i.e Krishna Kumari.

• Krishna Kumari, Odisha nurse has bagged the prestigious Florence Nightingale award 2017.
• She received the award from former President Pranab Mukherjee at a function at the Rashtrapati Bhawan in New Delhi on the occasion of International Nurses Day.
• Florence Nightingale was an English reformer and the founder of modern nursing.
• The Florence Nightingale Awards are given for nursing professionals, as a mark of recognition for the meritorious services of nurses.
• Award was instituted by the Health ministry in 1973.
• The National Florence Nightingale Award 2019 was presented by President Ram Nath Kovind to Lini Puthussery, the nurse from Kerala who died due to the Nipah virus.

​The correct answer is option 3 i.e Pascal.

• Pascal (Pa) is the SI unit of pressure.
• The unit of pressure is named after scientist Blaise Pascal.
• The pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
• The Barometer is a scientific instrument that is used to measure air pressure.

Shortcut Trick

The difference of roots for any quadratic equation Ax² + Bx + C = 0 is given by √D/|A|.

Since α, β, γ, δ are in Arithmetic Progression (A.P.), the difference between consecutive roots is the same.

⇒ |β − α| = |δ − γ| = d (common difference).

⇒ √D₁/|a| = √D₂/|p|

⇒ D₁/a² = D₂/p² ⇒ D₁ : D₂ = a² : p².

∴ The correct answer is a²/p².

Alternate Method

Given: ax² + bx + c = 0 has roots α, β and px² + qx + r = 0 has roots γ, δ.

Formula Used: (α − β)² = (α + β)² − 4αβ = D/a².

⇒ For ax² + bx + c = 0, sum (α + β) = −b/a and product αβ = c/a.

⇒ (α − β)² = (−b/a)² − 4(c/a) = (b² − 4ac)/a² = D₁/a².

⇒ Similarly for px² + qx + r = 0, (γ − δ)² = (q² − 4pr)/p² = D₂/p².

⇒ Since α, β, γ, δ form an Arithmetic Progression, let the common difference be d.

⇒ β − α = d and δ − γ = d.

⇒ d² = D₁/a² and d² = D₂/p².

⇒ Equating both: D₁/a² = D₂/p².

⇒ D₁/D₂ = a²/p².

∴ The correct answer is a²/p².

Additional Information

Discriminant and Nature of Roots

The discriminant (D = b² − 4ac) defines the roots: If D > 0, roots are real and unequal; if D = 0, roots are real and equal; if D < 0, roots are complex conjugates.

Difference of Roots

The absolute difference between roots is |α − β| = √D / |a|, which is useful when roots are related by a constant gap.

Arithmetic Progression (A.P.) Properties

In an A.P., any four terms x₁, x₂, x₃, x₄ satisfy the condition that x₂ − x₁ = x₄ − x₃ = d, where d is the common difference.

Shortcut Trick

The angle between the altitude and the angle bisector of the vertical angle is half the positive difference of the base angles.

∠DAO = 1/2 × |∠ABC − ∠ACB|

∠DAO = 1/2 × (65° − 23.5°) = 1/2 × 41.5° = 20.75°

20.75° = 20° + 3/4° = 20^3°/₄

∴ The correct answer is 20^3°/₄.

Alternate Method

Given: ∠B = 65°, ∠C = 23.5°, AD ⊥ BC, AO is bisector of ∠A.

Formula Used: Angle sum property of triangle = 180°.

⇒ In ΔABC, ∠BAC = 180° − (65° + 23.5°) = 180° − 88.5° = 91.5°

⇒ Since AO is the angle bisector, ∠BAO = 91.5° ÷ 2 = 45.75°

⇒ In right-angled ΔABD, ∠BAD = 90° − ∠B = 90° − 65° = 25°

⇒ ∠DAO = ∠BAO − ∠BAD = 45.75° − 25° = 20.75°

⇒ 20.75° = 20 + 75/100 = 20 + 3/4 = 20^3°/₄

∴ The correct answer is 20^3°/₄.

Additional Information

Internal Angle Bisector Theorem

In a triangle, the internal bisector of an angle divides the opposite side in the ratio of the sides containing the angle: AB/AC = BD/CD.

Altitude of a Triangle

The altitude is a line segment through a vertex and perpendicular to the opposite side. The three altitudes intersect at the orthocenter.

Angle Sum Property

The sum of the interior angles of any triangle is always 180°. For a right-angled triangle, the sum of the two acute angles is 90°.

The mirror image of the given figure if the mirror is placed at line MN is,

Hence, option 4 is the correct answer.

​The correct answer is Bahlul Lodi.

Key Points

• The Lodi dynasty was founded by Bahlul Khan Lodi.
• The Lodi dynasty was an Afghan dynasty.
• The Lodi dynasty was the last dynasty in Delhi Sultanate, ruled from 1451 to 1526.
• Sikandar Lodi was the son of Bahlul founded Agra in 1504.
• Ibrahim Lodi was the son of Sikandar Lodi and he was the last Lodi Sultan of Delhi.
• The Mughal emperor Babur defeated and killed Ibrahim Lodi in the Battle of Panipat, in 1526.
• The death of Ibrahim Lodi ended the 320 years long Delhi Sultanate, and the Mughal Empire replaced it.

The correct answer is option 3 i.e China.

• Indian Women's hockey team won the Asia Cup 2017 by defeating China.
• Host country: Japan.
• This is India's second title.
• The tournament organized by the Asian Hockey Federation.
• Headquarters of the Asian Hockey Federation: Kuala Lumpur, Malaysia.
• President of the Asian Hockey Federation: Al-Sultan Abdullah Sultan Ahmad Shah.
• South Korea has won the most titles(3).
• 2017 Men's Hockey Asia Cup: India won the third title after defeating Malaysia.

Shortcut Trick

Ratio of Boys to Girls using the Alligation method:

(Girls Mean − Total Mean) : (Total Mean − Boys Mean)

⇒ (14 − 13.1) : (13.1 − 12) = 0.9 : 1.1 = 9 : 11

Given: 9 units = 18 boys ⇒ 1 unit = 2

Total students = (9 + 11) units = 20 units × 2 = 40 students

∴ The correct answer is 40 students.

Alternate Method

Given:

Number of Boys (n_b) = 18

Mean score of Boys (x_b) = 12

Mean score of Girls (x_g) = 14

Overall Average (x_total) = 13.1

Formula Used:

Overall Average = [(n_b × x_b) + (n_g × x_g)] ÷ (n_b + n_g)

Let the number of Girls be G.

⇒ 13.1 = [(18 × 12) + (G × 14)] ÷ (18 + G)

⇒ 13.1 × (18 + G) = 216 + 14G

⇒ 235.8 + 13.1G = 216 + 14G

⇒ 14G − 13.1G = 235.8 − 216

⇒ 0.9G = 19.8

⇒ G = 19.8 ÷ 0.9 = 22

⇒ Total Students = 18 + 22 = 40

∴ The correct answer is 40 students.

Additional Information

Weighted Average

It calculates the average of a combined set where each group has a different number of observations: Avg = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Alligation Rule

The ratio of the quantities is inversely proportional to the differences of their individual averages from the target mean: n₁/n₂ = (A₂ − A_m) / (A_m − A₁).

Mean Properties

The sum of deviations of all observations from the mean is always zero. The overall mean always lies between the lowest and highest group means.

Drawing diagram according to the given information,

Manya is south – east with respect to Anya.

Hence, “south – east" is the correct answer.

Formula:

Distance remaining to be covered = Total distance - Distance covered

Calculation:

Let total distance be x km.

Distance covered by the person by walking = x × 2/5 = 2x/5

⇒ Remaining distance = x - 2x/5 = 3x/5

1/3^rd part of remaining distance covered by bus then

Distance covered by the bus = 3x/5 × 1/3 = x/5

Now final remaining distance

⇒ Remaining distance = x - 2x/5 - x/5 = 2x/5

∴ Required fraction = 2x/5 × 1/x = 2/5

The correct answer is option 4 i.e Surabhi Lakshmi.

• Surabhi Lakshmi won the Best Actress Award at the 64th National Film Awards in 2017.
• Surabhi won this award for her role in the Malayalam film Minnaminungu.
• Award was presented by former Indian President Pranab Mukherjee.
• Best Feature Film: Kaasav (Marathi).
• Best Actor: Akshay Kumar (Hindi film Rustom).

The correct answer is option 4 i.e Ahmedabad.

• Ahmedabad is India's first World Heritage City recognised by UNESCO.
• As per the official records, Ahmedabad is the first Indian city honoured with World Heritage City Status by UNESCO (Third city in Asia, after Bhaktapur(Nepal) and Galle(Srilanka)).
• UNESCO stands for United Nations Educational Scientific and Cultural Organization.
• Headquarters of UNESCO: Paris, France.
• Director-General of UNESCO: Audrey Azoulay.
• Ahmedabad city was founded by Sultan Ahmed Shah.
• Recently, the Jaipur was declared as India's second city in UNESCO World Heritage Site on July 6, 2019.

The correct answer is option 2 i.e Force and Pressure.

Key Points

• Force and pressure do not have the same SI unit.
• SI unit of force is the newton(N).
• SI unit of pressure is the pascal(Pa).
• The SI unit of distance and displacement is the meter (m).
• The SI unit of energy and work is the joule (J).
• The SI unit of speed and velocity is meter per second (m/s).

According to the given information,

Argument 1:  This is strong, because young entrepreneurs help in the development of the country.

Argument 2: This is not strong, because nothing is mentioned about losses in the statement and

young entrepreneurs reduces burden on the employment market.

Hence, “only argument 1” is strong.

The correct answer is option 4 i.e. 3.

The number of moles present in 81 grams of aluminium is 3 moles.

${{Number \ of\ moles}={Mass\ of \ substance \over Mass\ of\ one\ mole}}$

Mass of substance= 81 grams

Mass of one mole(molar mass) aluminum= 27.

The number of moles=${81 \over 27}= 3$ moles.

The correct answer is option 1 i.e m/s.

• The SI unit of speed is meter per second(m/s).
• The speed of an object is the magnitude of the change of its position.
• Speed is a scalar quantity.
• The most common unit of speed in everyday usage is kilometre per hour (km/h).
• For air and marine travel the knot is commonly used as the unit of speed.

According to the given statements,

Statement 1: Rajesh is the only son of Vijay’s mother-in-law.

Rajesh is the brother – in – law of Vijay.

Statement 2: Verma is Rajesh’s only sister.

From, statement 1, we can say that Rajesh is the brother – in – law of Vijay.

Hence, “data in 1 alone” is sufficient.

Total hours when clock on the 4th day at 8 pm = 24 + 24 + 24 + 17 =  89 hours

Clock losses in 24 hours = 16 minutes

Clock losses in 1 hour = ${\ {16} \over 24}$ minutes

In 89 hours clock losses = ${\ {16} \over 24} × 89$ = ${\ {2} \over 3} × 89$ = ${\ {178} \over 3}$ = 59. 33 minutes ≈ 1 hr

So Actual time  when girl sees the clock on the 4th day at 8 pm = 8 + 1 = 9 pm

Hence, "9.00 pm" is the correct answer.

The picture that replaces the (?) symbol is,

Hence, option 3 is the correct answer.

The correct answer is option 3 i.e 15 Kg.

Given,

Velocity (v) = 4ms^-1.

Kinetic energy = 120 J.

Using the equation of kinetic energy,

Kinetic energy= ${1 \over 2}{mv^2}$

∴ Mass(m) = $2 \times Kinetic \ Energy \over v^2$(= {2 \times 120 \over16 }\)= 15 Kg.

Hence the mass of the object is 15 Kg.

The correct answer is option 4 i.e Chlorine.

Key Points

• Among the options, all except Chlorine, are noble gasses
• Chlorine belongs to the halogen family.
• The naturally occurring noble gases are helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and, radon (Rn).
• Noble gases belong to group 18 in the periodic table.
• Oganesson is a synthetic chemical element with the symbol Og and atomic number 118.

The correct answer is option 1 i.e Rajesh Mapuskar.

• The Famous Indian director Rajesh Mapuskar was conferred with the Best Director Award in the 64th National Film Awards.
• Rajesh Mapuskar was awarded for directing a Marathi film named Ventilator.
• Best Film Friendly State (2017): Uttar Pradesh.
• Best Film Friendly State (2019): Uttarakhand.
• The Best Director in 66th National Film Awards (2019): Aditya Dhar.
• Aditya Dhar was awarded for directing a Hindi film named Uri: The Surgical Strike.

Drawing the diagram,

The man is the cousin to Pankaj.

Hence, “cousin” is the correct answer

Shortcut Trick

Use the identity sec²x = 1 + tan²x.

10(1 + tan²x) − 9 tan²x = 13

10 + 10 tan²x − 9 tan²x = 13

tan²x = 3 ⇒ tan x = √3

∴ The correct answer is 60°.

Alternate Method

Given: 10 sec²x − 9 tan²x = 13

Formula Used: sec²x − tan²x = 1

⇒ 10 sec²x − 9 tan²x = 13

⇒ (9 sec²x − 9 tan²x) + sec²x = 13

⇒ 9(sec²x − tan²x) + sec²x = 13

⇒ 9(1) + sec²x = 13

⇒ sec²x = 13 − 9

⇒ sec²x = 4

⇒ sec x = 2

⇒ x = cos⁻¹(1/2) = 60°

∴ The correct answer is 60°.

Additional Information

Trigonometric Identities

Fundamental Pythagorean identities include sin²x + cos²x = 1, 1 + tan²x = sec²x, and 1 + cot²x = cosec²x.

Specific Angles

Common values for tan x: tan 30° = 1/√3, tan 45° = 1, tan 60° = √3.

Reciprocal Relations

sec x = 1/cos x, cosec x = 1/sin x, and cot x = 1/tan x.

Concept:

Deduce each fraction into its simplest form and then check for its value.

Example: a/b

If ‘a’ is divided by ‘c’ and it gives 5 as quotient then ‘b’ on division by ‘c’ should give 9 as quotient to make a/b = 5/9.

Calculation:

Option 1: 105/198

Write the fraction in the simplest form so, divide the numerator and denominator of the fraction by 3.

⇒ 35/66

Option 2: 80/144

Write the fraction in the simplest form so, divide the numerator and denominator of the fraction by 16.

⇒ 5/9

Option 3: 40/72

Write the fraction in the simplest form so, divide the numerator and denominator of the fraction by 8.

⇒ 5/9

Option 4: 25/45

Write the fraction in the simplest form so, divide the numerator and denominator of the fraction by 5.

⇒ 5/9

∴ 105/198 cannot ne written in the form of 5/9.

Shortcut Trick

Efficiency ratio of Men to Women: 20M × 10 = 12W × 10 ⇒ 5M = 3W ⇒ M/W = 3/5.

Total Work = 20 × 3 × 10 = 600 units.

Efficiency of (15M + 6W) = (15 × 3) + (6 × 5) = 45 + 30 = 75 units/day.

Time taken = 600 ÷ 75 = 8 days.

∴ The correct answer is 8 days.

Alternate Method

Given: 20 men can do work in 10 days; 12 women can do work in 10 days.

Formula Used: Total Work = Number of persons × Efficiency × Days

⇒ Efficiency of 20 men = 120 ÷ 10 = 12 units/day

⇒ Efficiency of 1 man = 12 ÷ 20 = 0.6 units/day

⇒ Efficiency of 12 women = 120 ÷ 10 = 12 units/day

⇒ Efficiency of 1 woman = 12 ÷ 12 = 1 unit/day

⇒ Total Efficiency of (15 men + 6 women) = (15 × 0.6) + (6 × 1)

⇒ Total Efficiency = 9 + 6 = 15 units/day

⇒ Days required = Total Work ÷ Total Efficiency = 120 ÷ 15

⇒ Days required = 8 days

∴ The correct answer is 8 days.

Additional Information

Work Equivalence Formula

M₁D₁H₁/W₁ = M₂D₂H₂/W₂ where M is number of workers, D is days, H is hours and W is work done.

Efficiency and Time

Efficiency is inversely proportional to the time taken to complete a task when the work remains constant.

Pipes & Cisterns

Similar to time and work, the rate of filling a tank is its efficiency, and total capacity is the total work.

The correct answer is option 1 i.e Increases.

• When light travels from a denser medium to a rare medium speed of light will increase.
• The refraction of light is the phenomenon of bend or change the direction of light rays when it passes from one medium to another.
• When light travels from denser to rarer medium, it bends away from the normal.
• According to Snell's Law: ${\sin \theta_2 \over \sin \theta_1}= {\nu_2 \over \nu_1}={n_1 \over n_2}$
• Denser medium has a greater refractive index(n₁) when compared to an optically rarer medium (n₂).
• According to Snell's law, speed will Increase while travelling from a denser medium to rarer, i.e.(v₁>v₂).

The correct answer is option 4 i.e Palash.

• Palash is the state flower of Jharkhand and Uttar Pradesh.
• State animal of Jharkhand: Indian elephant.
• State bird of Jharkhand: Asian Koel.
• Jharkhand state was formed on 15 November 2000.
• Chief Minister of Jharkhand: Hemant Soren.
• Rohira is the state flower of Rajasthan.
• Orchid is the state flower of Arunachal Pradesh.
• Lotus is the National Flower of India and the state flower of Karnataka.

The pattern followed is,

Hence, “Q” is the correct answer.

The mirror image of the given image is,

Hence, option 1 is the correct answer.

The correct answer is Tissue culture.

Key Points

• Tissue culture is the phenomenon that many plants are grown from one parent in disease-free conditions.
• The production of plants by the method of tissue culture is also known as micropropagation
• This technique is being used increasingly for the production of ornamental plants like orchids, dahlia, carnation, chrysanthemum, etc.
• The new plants produced by tissue culture are disease-free is an advantage of this technique.

Drawing the Venn diagram,

Conclusion 1: Some cots are not sheets → False (This is definitely false)

Conclusion 2:Some sheets are cots → True (This is definitely true)

Hence, “only conclusion 2” follows.

Tortoise and Crocodile are generally classified into reptiles but they don't have any relation with Amphibians.

The correct Venn diagram is,

Hence, "Option 4" is the correct answer.

Important Points

1. Crocodile can live both on land as well as water but it is not an amphibian. Crocodiles are very similar to amphibians but they are not termed under amphibians. In fact, they are a part of the reptile family. 2. Tortoises are exclusively land animals. Most other turtles live in the water much of the time, but not tortoises.
2. Reptiles are born with lungs, typically lay their eggs on dry land, and have scaly skin. Most amphibians are born with gills but later develop lungs, typically lay their eggs in water, and have thin, moist skin (without scales).

Crocodiles lay their eggs on the land unlike the amphibians.

The correct answer is option 1 i.e People First' mobile application.

• N. Chandrababu Naidu, the Andhra Pradesh former Chief Minister, has launched ‘People First’ mobile application at the Collectors’ conference in Vijayawada.
• As the name mentions(People First' mobile application), the application will "empower citizens with real-time governance".
• Andhra Pradesh has the second-longest coastline after Gujarat (Longest in south India).
• Andhra Pradesh is the first state formed on linguistic basis in India.
• Governor of Andhra Pradesh: Biswabhusan Harichandan.
• Chief Minister of Andhra Pradesh: Y. S. Jaganmohan Reddy.

The correct answer is option 2 i.e Vascular

• The vascular system transports fluids from one place to another.
• The plant vascular system helps to deliver various resources to the different plant organs and provides mechanical support.
• Xylem tissue helps for the transportation of water and minerals to the leaves.
• Phloem tissue helps for the transportation of food from the leaves to different parts of the plant.

The correct answer is option 4 i.e Xylem.

• Xylem tissues are composed of mainly dead cells.
• Xylem is one of the transport tissues in vascular plants.
• Transportation of water from roots to stems and leaves is the major function of xylem.
• The term xylem was first used by Carl Nägeli in 1858.
• Xylem vessels are a long straight chain made of long-dead cells known as vessel elements.

The pattern followed is,

Hence, “43” is the correct answer.

The correct answer is option 3 i.e Trivendra Singh Rawat.

• Trivendra Singh Rawat is the Chief Minister of Uttarakhand who was elected in 2017.
• He was elected from the assembly constituency of Doiwala, In 2017
• Governor of Uttarakhand: Baby Rani Maurya.
• Statehood of Uttarakhand: 9 November 2000.
• Uttarakhand is often referred to as the "Devabhumi" (Land of the Gods).
• On June 8, 2020, Uttarakhand declared Gairsain as the new summer capital (Winter capital: Dehradun).

The correct answer is option 1 i.e Electrolysis.

• Aluminium metal can be extracted only by Electrolysis.
• Aluminium is more reactive than carbon so it must be extracted from its compounds using electrolysis
• The atomic number of aluminium is 13.
• Third most abundant element and also the most abundant metal on earth crust.
• Bauxite is the ore of aluminium.

The correct answer is option 3 i.e 2 gases, one liquid, and 2 solids.

• Halogens contain 2 gases, one liquid, and 2 solids.
• Halogens are elements of group 17 in the periodic table consisting of five elements: fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At).
• Fluorine and chlorine are gases.
• Bromine is liquid.
• Iodine and astatine are solids.
• Because of their great reactivity, the free halogen elements are not found in nature.

According to the given information,

Argument 1: This is not strong, because nothing about earnings is given in the statement.

Argument 2: This is strong, because people must learn to share their wealth for the betterment of

other people.

Hence, “only argument 2” is strong.

The correct answer is option 1 i.e 9.09%.

Mass of common salt (solute)=32 g

Mass of water =320 g.

Mass of solution= Mass of common salt (solute) + Mass of water = 32+320 = 352.

Using the equation:

Concentration of solution= ${Mass\ of\ common\ salt (solute) \over mass\ of\ solution}{\times 100}$