RRC Group D Previous Year Paper 38 (Held On: 10 Oct 2018 Shift 2)

• Mumbai team was the winner of Vijay Hazare trophy 2018-19.
• It was the 3^rd title of the Mumbai team, in which the Mumbai team beat the Delhi team.
• Vijay Hazare Trophy is also known as Ranji one day trophy which was started in 2002-03 as a limited over cricket domestic cricket competition, in which the state team is involving from the Ranji trophy plates.
• The name of this trophy is after the name of the famous International Indian cricketer Vijay Hazare.
• In 2019, Karnataka won the Vijay Hazare trophy by defeating Tamil Nadu.

According to given conditions,

Pavani is facing north direction now.

Hence, ‘north’ is the correct answer.

The correct answer is 3 Coulomb.

• Work is done when a force is applied on a body and makes a body move i.e. when the body displaces from its position by the act of force.
• For example- Pushing a car horizontally from a rest, Walking upstairs, Shooting a Bullet, etc. Its S.I. Unit is Joule (J).
• Potential Difference is the amount of work done by the positive test charge from one point to another point.
• For example- the movement of free electrons in a metallic conductor. Its S.I. Unit is Volt (V).
• Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.
• They are of two types: positive and negative. Its S.I. unit is Coulomb (C).

​

Concept

 Work done= Potential Difference × Charge.

**Calculation:**​

• Work- 30 J,
• Potential difference- 10 V
• Charge- ?

​By Formula,

• Work = potential difference × charge
• Charge = work / potential difference
• Charge = 30 J / 10 V
• Charge = 3 Coulomb .

The pattern followed is,

Hence, UF21 is the correct answer.

The correct answer is A Horse Walks Into a Bar.

• A Horse Walks Into a Bar is a book written by David Grossman, won the Man Booker prize in 2017.
• David Grossman has become the first Israeli author to win the Man Booker prize.
• This book shines a spotlight on the effects of grief, without any hint of sentimentality.
• This is not just a book about Israel, it's about people and societies horribly functioning.

Additional Information

Important Points

• PH Newby was the first winner of the Booker prize in 1969 with "something to answer for ".
• From 1969 to 2001 this prize called a Booker prize.
• From 2002, the Man group sponsored this prize known as Man Booker prize.
• Yann Martel the first winner of the Man Booker prize with "Life of Pie" in 2002.
• Indian winner of Man Booker prize is Arundhati Roy for "The God of Small Things" in 1997, Salman Rushdie for " Midnight's Children" in 1981, Sir V.S.Naipaul for "In a Free State" in 1971.

Shortcut Trick

Multiply the entire equation by the LCM of denominators 3 and 4, which is 12, to eliminate fractions.

⇒ 4 × (x − 5) − 3 × (x − 2) = 12 × (7 ÷ 2)

⇒ 4x − 20 − 3x + 6 = 42

⇒ x − 14 = 42

⇒ x = 56

∴ The correct answer is 56.

Alternate Method

Given:

(x − 5) ÷ 3 − (x − 2) ÷ 4 = 7 ÷ 2

Method: Fractions subtraction and Linear Equation simplification.

⇒ [4(x − 5) − 3(x − 2)] ÷ 12 = 7 ÷ 2

⇒ (4x − 20 − 3x + 6) ÷ 12 = 7 ÷ 2

⇒ (x − 14) ÷ 12 = 3.5

⇒ x − 14 = 3.5 × 12

⇒ x − 14 = 42

⇒ x = 42 + 14

⇒ x = 56

∴ The correct answer is 56.

Additional Information

Linear Equation in One Variable

A linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. The general form is ax + b = 0.

Least Common Multiple (LCM)

When solving equations involving fractions, multiplying every term by the LCM of the denominators is an efficient way to clear fractions instantly.

Sign Convention in Brackets

When a negative sign is outside a bracket, the signs of all terms inside the bracket change when expanded: − (a − b) = −a + b.

Shortcut Trick

Let Total Capacity of the tank be LCM(4, 6, 8) = 24 units.

Efficiency of Inlet A = 6, Inlet B = 4, and Outlet C = −3.

Work done by A and B in 1 hour = 6 + 4 = 10 units.

Remaining work = 24 − 10 = 14 units.

Combined efficiency of all three pipes = 6 + 4 − 3 = 7 units/hr.

Time taken for remaining part = 14 ÷ 7 = 2 hours.

∴ The correct answer is 2 hr.

Alternate Method

Given: Inlet 1 = 4 hr, Inlet 2 = 6 hr, Outlet = 8 hr.

Formula Used: Work = Time × Efficiency.

⇒ Total capacity of tank = 24 units

⇒ Work done by A and B in 1st hour = (6 + 4) × 1 = 10 units

⇒ Remaining tank to be filled = 24 − 10 = 14 units

⇒ Combined efficiency of (A + B + C) = 6 + 4 − 3 = 7 units/hr

⇒ Time to fill remaining part = Remaining Capacity ÷ Combined Efficiency

⇒ Time = 14 ÷ 7 = 2 hours

∴ The correct answer is 2 hr.

Additional Information

Inlet and Outlet Pipes

Inlet pipes add water (positive work) while outlet pipes remove water (negative work). Net work is the algebraic sum of their efficiencies.

Pipes and Cisterns Logic

If an inlet fills a tank in x hours and an outlet empties it in y hours (y > x), the net part filled in 1 hour is (1/x − 1/y).

Shortcut Trick

In Δ formed by angle of depression 30°, Width = Height × cot 30°.

Width of river = 15 × √3 ≈ 15 × 1.732 = 25.98 m ≈ 26 m.

In Δ formed by angle of elevation 60°, Height of chimney = Width × tan 60°.

Height = 25.98 × √3 = 25.98 × 1.732 ≈ 45 m.

∴ The correct answer is 26 m and 45 m.

Alternate Method

Given: Height of house (AB) = 15 m, Angle of depression (θ₁) = 30°, Angle of elevation (θ₂) = 60°.

Formula Used: tan θ = Perpendicular / Base

⇒ In ΔABC (where BC is river width), tan 30° = AB / BC

⇒ 1 / √3 = 15 / BC

⇒ BC = 15√3 = 15 × 1.732 = 25.98 m ≈ 26 m

⇒ Let Height of Chimney be CD. In ΔBCD, tan 60° = CD / BC

⇒ √3 = CD / (15√3)

⇒ CD = 15√3 × √3 = 15 × 3 = 45 m

∴ The correct answer is 26 m and 45 m.

Additional Information

Angle of Elevation and Depression

The angle of elevation is the angle between the horizontal line and the line of sight when looking up, while the angle of depression is looking down. Both are numerically equal when measured between parallel horizontal lines.

Trigonometric Ratios for Heights

Standard values used: tan 30° = 1/√3, tan 45° = 1, and tan 60° = √3. These are essential for solving distance and height problems.

The Correct Answer is Jammu and Kashmir.

Key Points

• The Saffron in Jammu and Kashmir is mainly cultivated and harvested in the Karewa highlands in Kashmir Himalayas.
• Iran is the largest producer of saffron in the world and India is very near to it.
• Kashmir saffron is a very precious and costly product recently it has been given the Geographical Indication (GI) tag by the Geographical Indications Registry.

Additional Information

The correct answer is AR Rahman.

• AR Rahaman is the brand ambassador of Sikkim.

Key Points

• Sikkim is a state in northeast India. It is the second smallest among the Indian states.
• Gangtok is the capital and largest city of Sikkim.
• The world's third-highest mountain, Kanchenjunga, is regarded as the guardian deity of Sikkim.
• Prem Singh Tamang, better known as P. S. Golay, is an Indian politician and the current Chief Minister of Sikkim.(Sept 2020)

Additional Information

• Shah Rukh Khan is the brand ambassador of West Bengal.
• West Bengal is situated in eastern India between the Himalayas and the Bay of Bengal.
• Kolkata is the capital of West Bengal.
• Smt. Mamata Banerjee is the current Chief Minister of the state.
• John Abraham is the brand ambassador of Arunachal Pradesh.
• Arunachal Pradesh is a state in North East India.
• Itanagar is the capital of Arunachal Pradesh.
• Pema Khandu is the Current Chief Minister of the state.
• Amitabh Bacchan is the brand ambassador of Gujarat.
• Gujarat is a state on the western coast of India.
• Gandhinagar is the capital of Gujarat.
• Bhupendra Patel was elected the new Chief Minister of Gujarat.

In the question figure, a hexagon is placed exactly in the middle of the rectangle.

Only option D’s hexagon is placed exactly in the middle of the rectangle.

Hence, ‘option 1’ is the correct answer.

The figure that will fit in the blank to complete the series is shown below:

The figure is moving in clockwise direction inside the figure.

Hence, ‘option 4’ is the correct answer.

Shortcut Trick

Difference in expenditure = 350 − 95 = Rs. 255

Since their initial amounts were equal, the difference in their remaining amounts must also be Rs. 255.

Ratio of Rekha's left money to Seema's left money = 4 : 7

Difference in ratio parts = 7 − 4 = 3 units

3 units = Rs. 255 ⇒ 1 unit = Rs. 85

Seema's money left (7 units) = 7 × 85 = Rs. 595

∴ The correct answer is Rs. 595.

Alternate Method

Given:

Initial money with Seema and Rekha = x

Seema's spending = Rs. 95 | Rekha's spending = Rs. 350

Money left with Seema = x − 95

Money left with Rekha = x − 350

According to the question:

⇒ (x − 350) = 4/7 × (x − 95)

⇒ 7 × (x − 350) = 4 × (x − 95)

⇒ 7x − 2450 = 4x − 380

⇒ 7x − 4x = 2450 − 380

⇒ 3x = 2070

⇒ x = 690

Money left with Seema = 690 − 95 = 595

∴ The correct answer is Rs. 595.

Additional Information

Ratio and Difference Property

If two quantities change by different amounts from an equal base, the difference in their final values is exactly equal to the difference in the amounts spent or added.

Fraction to Ratio Conversion

A statement like 'A is 4/7 of B' can be directly written as the ratio A : B = 4 : 7, where B represents the denominator total.

Unitary Method in Ratios

Value of 1 unit = (Actual Difference) ÷ (Difference in ratio parts). This value can then be multiplied by any ratio part to find the absolute value.

The correct answer is the Shiwalik Range.

Key Points

• A Mountain is any natural elevation of the earth's surface. the mountains may have a small summit and a broad base.
• ​The mountains are considerably higher than the surrounding area. some mountains are even higher than the clouds.
• In the Mountains, the climate becomes colder as we go on high altitude.
• Mountains are of three types: 1. Fold mountains  2. Block mountains  3. Volcanic mountains.
• Mountains arranged in a line are known as Range.

Important Points

• The Himalayan mountains are young fold mountains with Rugged relief and high conical peaks.
• Himalaya means "the adobe of snow", in the north they are capped with lofty snow.
• The Himalayas divided into three parallel ranges: 1. The great Himalayas or Himadri - Northernmost range   2. Middle Himalayas or Himanchal - South of Himadri  3. The Shiwaliks - Southernmost range.
• The Shiwalik is the sub-Himalayan range of the northern Indian Sub-continent. It extends from  West to North westwards for more than 1,600Km ( 1,000 miles) from Teesta river in Sikkim state, northeastern India through Nepal, across northwestern India, and into Northern Pakistan.
• Kailash range forms the part of Trans-Himalayan and It is one of the highest and most rugged parts of the Himalayas, located in the southwestern part of the Tibet Autonomous Region, southwestern China. It is known as GANG-TISE to the Tibetans and is the highest peak in the range, with 6,714 meters.
• Kangchenjunga also called Kanchenjunga, the World's Third highest mountain with an elevation of 8,586 meters. It is situated in the eastern Himalayas on the border between Sikkim state, north eastern India, and eastern Nepal. The Mountain is the part of the great Himalayan range.

The correct answer is Himachal Pradesh.

• Jai Ram Thakur is an Indian politician and the current Chief Minister of Himachal Pradesh.
• He defeated Prem Kumar Dhumal in the assembly elections 2017.
• He was the Minister of Rural Development and Panchayati Raj.

Important Points

CALCULATION:

Considering the given equation,

\(22 - \left( {\frac{1}{4}} \right)\left{ { - 5 - \left( { - 48} \right) \div \left( { - 16} \right)} \right} = ?\)

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,

\(22 - \left( {\frac{1}{4}} \right)\left{ { - 5 - \left( { - 48} \right) \div \left( { - 16} \right)} \right}\)

\(\Rightarrow ;22 - \left( {\frac{1}{4}} \right)\left{ { - 5 - 3} \right}\)

$\Rightarrow ;22 - \left( {\frac{{ - 8}}{4}} \right)$

⇒ 22 + 2 = 24

∴ Required value is 24

The correct answer is Tushar Mehta.

• The 2G spectrum scandal involved officials in the government of India illegally undercharging mobile telephony companies for frequency allocation license, which they would use to create a 2G subscription for cell phones.
• The issuing of the 2G licenses occurred in 2008, but the scam came to public notice when the Indian Income Tax Department investigated political lobbyist Niira Radia and the Supreme Court of India took Subramaniam Swamy's complaints on record.

Key Points

• Tushar Mehta is a senior counsel in India and is currently serving as the Solicitor General of India.
• Mehta began his career as an advocate in 1987 and was designated as a senior advocate in 2007 by Gujarat High Court.
• He was appointed as the advocate general in 2008.
• The Centre has appointed Additional Solicitor General Tushar Mehta the special public prosecutor in the 2G spectrum scam.

The use of the word ‘definitely’ indicates the employer’s need for a good computer programmer.

Therefore, conclusion 2 follows.

The author of the statement certainly needs a good computer programmer.

But we cannot conclude that this is the case in general for any employer.

Nor do we know if there are as many jobs as the number of good computer programmer.

Therefore, conclusion 1 does not follow.

Hence, only conclusion 2 follows.

Interchanging the symbols and using BODMAS rule,

Option 1 → + and ÷

Given equation: 5 + 6 ÷ 3 - 2 x 5 = 13

After changing sign

5 ÷ 6 + 3 - 2 x 5

0.83 + 3 – 2 × 5

0.83 + 3 – 10

3.83 – 10 ≠ 13

Option 2 → ÷ and –

Given equation: 5 + 6 ÷ 3 - 2 x 5 = 13

After changing sign

5 + 6 - 3 ÷ 2 x 5

5 + 6 – 1.5 × 5

5 + 6 – 7.5

11 – 7.5 ≠ 13

Option 3 → + and x

Given equation: 5 + 6 ÷ 3 - 2 x 5 = 13

After changing sign

5 x 6 ÷ 3 - 2 + 5

5 x 2 – 2 + 5

10 – 2 + 5

15 – 2 = 13

13 = 13

Option 4 → ÷ and x

Given equation: 5 + 6 ÷ 3 - 2 x 5 = 13

After changing sign

5 + 6 x 3 - 2 ÷ 5

5 + 6 x 3 – 0.4

5 + 18 – 0.4

23 – 0.4 ≠ 13

Hence, option 3 is the correct answer.

The correct answer is Charles Robert Darwin.

• Charles Robert Darwin was a British naturalist and biologist known for his theory of evolution and his understanding of the process of natural selection.
• In 1859, he published his landmark book, On the Origin of Species. Darwin’s theory of evolution and the process of natural selection later became known simply as “Darwinism.”

Important Points

• R.H Whittakar was an American plant ecologist.
• He was the first to propose the five kingdoms taxonomic classification of the world's biota.
• The five kingdoms are Kingdom Monera, Kingdom Protista, Kingdom Fungi, Kingdom Plantae, and Kingdom Animalia.
• He also proposed the Whittaker Biome Classification, which categorized biome-types upon two abiotic factors: temperature and precipitation.
• Carl Linnaeus was a Swedish botanist, zoologist, and physician who formalized binomial nomenclature, the modern system of naming organisms.
• He is known as the "father of modern taxonomy".
• He was the first to frame principles for defining natural genera and species of organisms and to create a uniform system for naming them, known as binomial nomenclature.
• Mendeleyev was a Russian chemist and inventor.
• He is best remembered for formulating the Periodic Law and creating a farsighted version of the periodic table of elements.
• Mendeleev devised the periodic classification of the chemical elements, in which the elements were arranged in order of increasing atomic weight.

The correct answer is G.

• According to Newton's Law of Universal Gravitation, The gravitational constant is the proportionality constant which is denoted by G.
• The value of G is 6.673×10-11 N m² kg^-2.

Important Points

• Newton's law of universal gravitation: The attractive force between two objects (F) is equal to G times the product of their masses (m1, m2) divided by the square of the distance between them (r).
  

F = G(m1m2/r²)

Key Points

• The acceleration of objects due to the gravity on Earth is around 9.8 ms^-2, which is denoted by g.
• To leave Earth’s gravitational pull behind, an object must travel 7 miles/second.
• At the center of the Earth, every object is weightless.

Shortcut Trick

Area of Semicircle = 50 π ⇒ (1/2) × π × r² = 50 π ⇒ r² = 100 ⇒ r = 10.

In an inscribed semicircle where the diameter is the length (L), the breadth (B) equals the radius (r).

Area of Rectangle = L × B = (2r) × r = 2r².

Area of Rectangle = 2 × 100 = 200.

∴ The correct answer is 200.

Alternate Method

Given: Area of semicircle = 50 π. The diameter coincides with the length of the rectangle.

Formula Used: Area of Semicircle = (1/2) × πr²; Area of Rectangle = Length × Breadth.

Calculations:

⇒ Area of Semicircle = (1/2) πr² = 50 π

⇒ r² = 50 × 2 = 100

⇒ r = 10

⇒ For a semicircle inscribed in a rectangle with its diameter as the length:

⇒ Length (L) = Diameter = 2r = 2 × 10 = 20

⇒ Breadth (B) = Radius = r = 10 (since the semicircle touches the opposite side)

⇒ Area of Rectangle = L × B = 20 × 10

⇒ Area of Rectangle = 200

∴ The correct answer is 200.

Additional Information

Properties of Inscribed Semicircle

When a semicircle is inscribed in a rectangle with its diameter on the length, the aspect ratio of the rectangle is always 2:1.

Circle Mensuration

Area of Full Circle = πr²; Perimeter of Semicircle = πr + 2r.

Area Comparison

The ratio of the area of the semicircle to the area of the circumscribing rectangle is π : 4 ≈ 0.785.

The correct answer is Kamal kumbhar​

• Kamal Kumbhar is an Indian social entrepreneur from Osmanabad, Maharashtra.
• She is the founder of Kamal Poultry and Ekta Sakhi Producer Company.
• She started Kamal Poultry and Ekta Sakhi Producer Company with a capital of only "2000" and encouraged around 3,000 women in the drought-prone region of Osmanabad to successfully run poultry farms and to be financially independent.
• Kamal Kumbhar was awarded the CII Foundation Woman Exemplar Award in 2017 by the President of India for her extraordinary contribution to the field of micro-enterprise.

Additional Information

• CII foundation women exemplar award is a part of the CII Foundation Woman Exemplar Program (WEP) which was launched in 2005 by the CII Foundation (CIIF).
• The CII Woman Exemplar Award is given to the exemplary women change-makers from grassroots, who overcame grave personal challenges to create transformative work impacting communities and providing new paradigms for social development.
• The Award promotes women’s empowerment at the community level by discovering and recognizing those who have contributed significantly in the fields of Education & Literacy, Health, and Micro-Enterprise.
• It carries a cash reward of Rs 3,00,000.
• Ms. Bhimavva Chalwadi of Goa, Ms. Vanlalruati of Mizoram, and Ms. Nilima Tigga of Jharkhand have conferred with the awards for education, health, and micro-enterprise respectively at the CII Annual Session 2019 held in New Delhi.

The correct answer is Size - 18-25 µm. 

Key Points

Cells are the basic, fundamental, structural, and functional unit of life responsible for all life's processes, hence they are called Building blocks of life.

On the basis of the count, cells are of three types:- 1. RBCs 2. WBCs 3. Platelets. 

• RBCs are called red blood cells and help in oxygen transport from the lungs to all body organs and tissues.
• WBCs are called white blood cells and help to fight infection and eat up all germs.
• **Platelets help in blood clotting.**​

Important Points

• WBCs are also called leukocytes or white corpuscles.
• The life span of WBCs is 13 to 20 days.
• Total WBCs count ranges from 4,500 to 10,000.
• WBCs are a cellular component of the blood that lacks hemoglobin, has a nucleus, is capable of mobility, and producing antibodies.
• They act as a " Soldier or Guard " of our body.
• The size of WBCs is 12 to 17 µm in diameter and about three times of RBCs.
• WBCs do not have any fixed shape, they may be circular, rhomboid or any other shape.

Shortcut Trick

Total Work = 15 × 20 = 300 units.

Work done in first 10 days = 15 × 10 = 150 units.

Work done in next 5 days = 10 × 5 = 50 units.

Remaining work = 300 − (150 + 50) = 100 units.

Remaining persons = 10 − 5 = 5. Days needed = 100 ÷ 5 = 20 days.

Total Days = 10 + 5 + 20 = 35 days.

∴ The correct answer is 35 days.

Alternate Method

Given: Initial 15 persons can finish the job in 20 days.

Formula Used: Total Work = Number of Persons × Number of Days

⇒ Total Work = 15 × 20 = 300 units

⇒ Work (Phase 1) = 15 × 10 = 150 units

⇒ Work (Phase 2) = (15 − 5) × 5 = 10 × 5 = 50 units

⇒ Total Work done so far = 150 + 50 = 200 units

⇒ Remaining Work = 300 − 200 = 100 units

⇒ Remaining Persons = 10 − 5 = 5 persons

⇒ Time for remaining work = 100 ÷ 5 = 20 days

⇒ Total duration = 10 + 5 + 20 = 35 days

∴ The correct answer is 35 days.

Additional Information

Work-Person Equation

Total work is proportional to the product of efficiency, number of persons, and time (M₁D₁H₁/W₁ = M₂D₂H₂/W₂).

Variable Manpower

When manpower changes periodically, the sum of work done in each interval equals the total work required.

Inverse Proportion

For a constant piece of work, the number of persons is inversely proportional to the number of days taken.

Shortcut Trick

Total percentage gap = 15% (loss) + 10% (gain) = 25%

According to the question, this 25% gap = Rs. 150

Value of 1% = 150 ÷ 25 = 6

Cost Price (100%) = 6 × 100 = 600

∴ The correct answer is Rs. 600.

Alternate Method

Given:

Initial loss = 15%

Expected gain = 10%

Increase in Selling Price = Rs. 150

Formula Used:

Selling Price (SP) = Cost Price (CP) × (100 ± Profit or Loss%) ÷ 100

⇒ Let the Cost Price (CP) of the textbook be Rs. x.

⇒ Initial Selling Price (SP₁) = x − 15% of x = 0.85x

⇒ New Selling Price (SP₂) = x + 10% of x = 1.10x

⇒ Difference = SP₂ − SP₁ = 150

⇒ 1.10x − 0.85x = 150

⇒ 0.25x = 150

⇒ x = 150 ÷ 0.25

⇒ x = 600

∴ The correct answer is Rs. 600.

Additional Information

Relationship between CP and SP

Profit is earned when SP > CP, and Loss occurs when CP > SP. CP is the base for percentage calculation.

Net Percentage Gap

When switching from a loss of L% to a profit of P%, the total change in percentage is (L + P)% of the Cost Price.

Marked Price and Discount

Selling Price is also calculated as Marked Price (MP) − Discount. Discount is always calculated on MP.

The correct answer is the eight-fold path

• The Panchshila of Buddha is comprised of the basic teachings of conduct which are the eight-fold path.
• The Panchshila or Five Precepts and refrain from them are Violence, stealing, sexual misconduct, lying, or gossip, taking intoxicating substances like drugs or alcohol.

​

The logic is:

1. Kapil Dev – is a cricketer by profession.

2. Ravi Shastri – is a cricketer by profession.

3. Sachin Tendulkar – is a cricketer by profession.

4. Pullela Gopichand - is a badminton player by profession.

Hence, ‘Pullela Gopichand’ is the odd one out.

The correct answer is  —C=C—.

Important Points

• In organic chemistry, Hydrocarbons are classified into three:- 1. Alkanes 2. Alkenes 3. Alkynes.
• Hydrocarbons are the derivates of the carbon and hydrogen compounds.
• Alkanes are represented by Single Bond between two carbons and having the chemical formula **C_nH_2n+2, **the first member of the alkane group  - Methane (CH₄₎, Symbolic representation of alkanes is  **—C—C—.**​​
• Methane is colorless, odorless, flammable gas. it is used primarily as fuel to make heat and light. it is used in the manufacturing of organic chemicals.
• Alkenes are represented by Double Bond between two carbons and having chemical formula **C_nH_2n, **the first member of the alkene group  - Ethene (C₂H₄), Symbolic Representation of alkenes is —C=C—.
• Ethene is used in the production of ethylene glycol ( 1,2-ethanediol ) an automotive anti-freezing agent, used in the production of polymers such as polythene, polyvinyl chloride, polystyrene.
• Alkynes are represented by a Triple Bond between two carbons and having chemical formula **C_nH_2n-2, **the first member of the alkyne group - Ethyne (C₂H₂₎, symbolic representation of alkynes is —C=C—.
• Ethyne is also called Acetylene which is used in portable lighting, welding, and cutting, production of Chemicals.
• Water is represented by Two hydrogens attached to one oxygen by a single bond and having chemical formula H₂O, also called as Dihydrogen Oxide, the symbolic representation of water is H —O—H.
• Carbon dioxide is represented by Two oxygens attached to one carbon by a Double bond and having the chemical formula **CO_2, **the symbolic representation of carbon dioxide is O=C=O.

I. The tenant is agitated due to mosquito nuisance. → True (As, “It is hindering my night’s sleep” implies that the tenant is agitated due to mosquito nuisance.)

II. Generally, there are no mosquitoes in highrise buildings. → True (As, “Now-a-days, even in highrise bulidings, there are lot of mosquitoes” the word ‘even’ here clarifies that generally there are no mosquito in buildings.)

Hence, both the conclusions follow.

The correct answer is Berzelius.

• He was the scientist who suggested that the symbols should be made of one or more letters.
• He discovers the chemical elements cerium and selenium and technic of isolate silicon and thorium.

Important Points

The correct mirror image for the question figure is shown below:

Hence, ‘option 4’ is the correct answer.

The correct answer is Ribonucleic acid.

• It is a polymer of nucleotides that is made up of a ribose sugar, a phosphate, and bases such as adenine (A), guanine (G), cytosine (C), and uracil (U).
• It has various biological roles in coding, decoding, regulation, and expression of genes.
• RNA is a nucleic acid messenger between DNA and ribosomes.
• Thymine (T) in DNA is replaced by uracil (U) in RNA.

Important Points

• There are three main types of RNA – rRNA (ribosomal), tRNA (transfer), mRNA (messenger).
• mRNA: It transcribes the genetic code from DNA into a form that can be read and used to make proteins.
  

mRNA carries genetic information from the nucleus to the cytoplasm of a cell.

• rRNA: It directs the translation of mRNA into proteins.
• tRNA: It brings or transfers amino acids to the ribosome that correspond to each three-nucleotide codon of rRNA. The amino acids then can be joined together and processed to make polypeptides and proteins.

Note: The official question of Group D has a discrepancy. Therefore, we have rephrased the first conclusion.

• Early morning exercise has some benefits. → Follows (The word "good" used in the question statement implies that it is beneficial to exercise in the morning in "some" sense. Thus, conclusion I follows.)
• It is wise to choose free time available for workouts. → Does not follow. (The availability of time is not discussed anywhere in the statement. Thus, conclusion II does not follow.)

Hence, only conclusion I follows.

The correct answer is Fe.

• This is one of the limitations of Newlands' Law of Octaves.
• To fit elements into his table, Newlands adjusted two elements in the same slot, but also put some unlike elements under the same note.
• For example, cobalt and nickel were in the same slot and these were placed in the same column as fluorine, chlorine, and bromine which have very different properties than these elements.
• Iron, which resembles cobalt and nickel in properties, had been placed far away from these elements.

Important Points

• Other limitation of Newlands' Octaves law:
• The Law of Octaves was applicable only up to calcium, as after calcium every eighth element did not possess properties similar to that of the first.
• Newly discovered elements' properties did not fit into the Law of Octaves. Newlands assumed that only 56 elements existed in nature and no new elements will be discovered in the future.

Key Points

The logic is:

Hence, ‘33O’ is the correct answer.

The least possible venn diagram is:

1. All the slates are stars. → False (As, All the slates are suns. Some stars are suns. → So, All the slates are stars is possible, but it is not definite)
2. Some stars are slates. → False (As, As, All the slates are suns. Some stars are suns. → So, Some stars are slates is possible, but it is not definite)

Hence, neither (1) nor (2) follows.

The number of circles in the figure is shown below:

Hence, ‘6’ is the correct answer.

In each option except image C, there are four lines outside the circle, while in image C there is only three lines.

Hence, ‘option 2’ is the odd one out.

Shortcut Trick

मान लीजिए तीसरी संख्या 100 है।

पहली संख्या = 100 + 30% = 130

दूसरी संख्या = 100 + 60% = 160

अभीष्ट अनुपात = 130 : 160 = 13 : 16

∴ The correct answer is 13 : 16.

Alternate Method

दिया गया है:

पहली संख्या (A) तीसरी संख्या (C) से 30% अधिक है।

दूसरी संख्या (B) तीसरी संख्या (C) से 60% अधिक है।

गणना:

⇒ मान लीजिए तीसरी संख्या C = x

⇒ पहली संख्या A = x + (30/100) × x = 1.3x

⇒ दूसरी संख्या B = x + (60/100) × x = 1.6x

⇒ अभीष्ट अनुपात = A : B = 1.3x : 1.6x

⇒ A : B = 13 : 16

∴ The correct answer is 13 : 16.

Additional Information

प्रतिशत वृद्धि (Percentage Increase)

यदि किसी संख्या में a% की वृद्धि होती है, तो नई संख्या = मूल संख्या × (100 + a)/100

अनुपात और तुलना (Ratio and Comparison)

जब दो मानों की तुलना किसी तीसरे मान से की जाती है, तो तीसरे मान को 100 या 1 मानना गणना को सरल बनाता है।

प्रतिशत कमी (Percentage Decrease)

यदि किसी संख्या में a% की कमी होती है, तो नई संख्या = मूल संख्या × (100 − a)/100

The logic is:

V = 22

T = 20

L = 12

S = 19

The place value of V, T and L are even numbers, while the place value of S is an odd number.

Hence, ‘option 1’ is the odd one out.

Shortcut Trick

For a set of n numbers where the average of the first (n−1) and last (n−1) numbers are given, the range is calculated as:

Range = (Average of largest group − Average of smallest group) × Number of elements in group

Range = (28 − 22) × 3

Range = 6 × 3 = 18

∴ The correct answer is 18.

Alternate Method

Given:

Four numbers in ascending order: w < x < y < z

Average of smallest three (w, x, y) = 22

Average of largest three (x, y, z) = 28

Formula Used:

Sum of observations = Average × Number of observations

Range = Maximum value − Minimum value

Calculations:

⇒ Sum of smallest three numbers (w + x + y) = 3 × 22 = 66 ... (i)

⇒ Sum of largest three numbers (x + y + z) = 3 × 28 = 84 ... (ii)

⇒ Subtracting equation (i) from equation (ii):

⇒ (x + y + z) − (w + x + y) = 84 − 66

⇒ z − w = 18

The range of the data (z − w) is 18.

∴ The correct answer is 18.

Additional Information

Range of Data

The range is the simplest measure of variability, calculated as the difference between the maximum and minimum values: Range = X_max − X_min.

Properties of Averages

If the average of n observations is A, then the total sum is A × n. When comparing overlapping groups, the difference in sums equals the difference between the non-overlapping elements.

Ascending Order

Arranging data in ascending order ensures that the first element is the minimum and the last element is the maximum, making the range calculation straightforward.

All options except ‘carriage’ are vehicles that run on road, while ‘carriage’ runs on railway track.

Hence, ‘carriage’ is the odd one out.

Shortcut Trick

Subtract 3x and 7 from both sides to group like terms: 9 − 7 ≥ 5x − 3x.

This simplifies to 2 ≥ 2x.

Divide both sides by 2 to isolate the variable: 1 ≥ x.

The condition x ≤ 1 implies that the maximum possible value for x is 1.

∴ The correct answer is 1.

Alternate Method

Given:

3x + 9 ≥ 5x + 7

Method Used:

Solving Linear Inequalities by isolating the variable x.

Calculations:

⇒ 3x + 9 ≥ 5x + 7

⇒ 9 − 7 ≥ 5x − 3x

⇒ 2 ≥ 2x

⇒ 2/2 ≥ x

⇒ 1 ≥ x

⇒ x ≤ 1

Since x can take any value less than or equal to 1, the largest value it can attain is 1.

∴ The correct answer is 1.

Additional Information

Properties of Inequalities

When adding or subtracting the same number on both sides, the inequality sign remains unchanged.

Multiplication by Negative Numbers

If you multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

Maximum and Minimum Values

For an expression x ≤ k, the maximum value is k. For x ≥ k, the minimum value is k.

The family tree diagram is shown below:

Hence, the boy plying cricket is brother of Gaurav.

The correct answer is the Microwave.

Key Points

• A microwave oven uses microwaves to heat food.
• In the case of microwave ovens, the commonly used radio wave frequency is roughly 2,500 megahertz (2.5 gigahertz).
• Radio waves in this frequency range absorbed by water, fats, and sugars. When they are absorbed they are converted directly into atomic motion or vibration.
• Therefore heavy motion or vibration is converted into heat.

Important Points

• Microwaves are not absorbed by most plastics, glass, or ceramics.
• The frequency of the Microwave equals the resonance frequency of water. Therefore foods could be heated up by the oscillation of water molecules.

Additional Information

• An Electric heater, Electric blub (with filament), Electric iron is the electrical device that converts an electric current into heat.
• They working on the principle of the Joule heating effect.
• An electric current passing through a resistor will convert that electrical energy into heat energy.

The correct answer is Fe.

• Rusting is an oxidation reaction. When acidic substances (including water) come in contact with metals, such as iron and/or steel, it forms rust.
• Rust is the result of corroding steel after the iron (Fe) particles have been exposed to oxygen and moisture (e.g., humidity, vapor, immersion).
• When steel is exposed to water, the iron particles are lost to the water’s acidic electrolytes. The iron particles then become oxidized, which results in the formation of Fe⁺⁺.
• Two electrons are released and flow through the steel to another area of the steel known as the cathodic area.
• Balanced equation: 4Fe + 3O₂ + 6H₂O → 4Fe(OH)₃
• Corrosion prevention processes include the use of paint or metallic coatings are the following:
• Hot-dip galvanizing.
• Zinc thermal spraying.
• Aluminum thermal spraying.

Shortcut Trick

Convert Profit% to a fraction: 37.5% = 3/8.

Ratio of Cost Price (CP) to Selling Price (SP) = 8 : (8 + 3) = 8 : 11.

Given 8 units = Rs. 3,880 ⇒ 1 unit = 3,880 ÷ 8 = Rs. 485.

SP = 11 units = 11 × 485 = Rs. 5,335.

∴ The correct answer is Rs. 5,335.

Alternate Method

Given: CP = Rs. 3,880, Profit% = 37.5%

Formulas: SP = CP × (100 + Profit%) ÷ 100

⇒ Selling Price = 3,880 × (100 + 37.5) ÷ 100

⇒ Selling Price = 3,880 × 137.5 ÷ 100

⇒ Selling Price = 3,880 × 1.375

⇒ Selling Price = Rs. 5,335.

∴ The correct answer is Rs. 5,335.

Additional Information

Percentage to Fraction Conversion

Common fractions like 12.5% = 1/8, 25% = 1/4, and 37.5% = 3/8 help in solving Profit and Loss problems quickly using the ratio method.

Profit and Loss Relation

When there is a profit, SP is always greater than CP (SP = CP + Profit). When there is a loss, CP is greater than SP (SP = CP − Loss).

The correct answer is Addition reaction.

• Hydrogenation is a process that uses hydrogen gas to change a liquid vegetable oil into a hard spread/margarine.
• This process stabilizes the oil and prevents spoilage from oxidation.
• Nickel is the preferred catalyst for the hydrogenation of fats and oils to speed up the reaction.
• The hydrogenation process increases the melting point of the fat, which changes liquid oil into solid shortening.

Important Points

Mistake Points

• In addition reaction, hydrogen is added in the presence of any catalyst to make a hydrocarbon saturated
• In a combination reaction two elements combine together to form a single compound.
• so the hydrogenation is an addition reaction. It is done  by using the pd as catalyst

CONCEPT:

Add the digits before and after decimal separately, then add the two.

SOLUTION:

Considering the given statement

30.9 + 3.09 + 0.309 + 0.039 + 309 = ?

Before decimal = 30 + 3 + 0 + 0 + 309 = 342

After decimal = 0.9 + 0.09 + 0.309 + 0.039 = 1.338

Add the two = 342 + 1.338 = 343.338

∴ Value of given statement is 343.338

CONCEPT:

Here we need to look at the graph and find the value in y-axis corresponding to the year asked represented on the x-axis.

SOLUTION:

From the given bar graph we can say that,

Year on x-axis corresponds with value 20 on y-axis.

∴ No. of units sold in 2009 is 20 lakhs.

The correct answer is 1931.

• The Gandhi-Irwin Pact was signed on 5th March 1931 by Mahatma Gandhi and Viceroy Lord Irwin.
• In this pact, Gandhi agreed to end the civil disobedience movement in India against British rule and to join the second Round Table Conference.

Additional Information

• The Poona Pact was signed on 24 September 1932 at Yerwada Central Jail in Poona, India.
• It refers to an agreement between B. R. Ambedkar and Mahatma Gandhi.
• It was signed by B.R Ambedkar for the depressed classes and Madan Mohan Malviya for the upper Caste Hindus resulting in the end of the fast that Gandhi was undertaking in jail as wrath against the MacDonald communal award.

The correct answer is Coelenterata.

• The body wall consisting of two layers of cells, an outer epithelium (ectoderm) and an inner gastrodermis (entoderm).
• In between the two layers, there is a gelatinous non-cellular layer called mesoglea is present.
• Coelenterata or Phylum Cnidaria belongs to the Animalia kingdom.
• Examples: Hydra, Obelia, Physalia physalis, Tubularia.
• Classification of Coelenterates: Hydrozoa, Scyphozoa, Cubozoa, Anthozoa.

Important Points

• Platyhelminthes are triploblastic, bilaterally symmetrical, dorsoventrally flattened, acoelomate flatworms.
• Their organ construction without a definite anus, circulatory, skeletal or respiratory system.
• They have a Protonephridial excretory system and mesenchyme filling the space between the various organ of the body.
• Annelids (ringed worms or segmented worms) are a large phylum belonging to the kingdom Animalia.
• Annelida split into three major groups: Polychaeta, Oligochaeta (earthworms), and Hirudinea (leeches).
• They respire through their body surface.
• Nephridia are the excretory organs.
• They move with the help of Setae.
• Nematoda is also known as “roundworms” belongs to the phylum.
• Nematodes present in the soil feed on the bacteria, fungi, and other nematodes.
• Nematoda plays an important role in nutrient recycling.

CONCEPT:

Here we need to look for the day that has reached the limit i.e. 25 members.

SOLUTION:

From the given bar graph we can say that,

Maximum limit of members that can be accommodated is 25.

On x-axis the day Sunday has the bar raised till 25 corresponding to y-axis.

∴ On Sunday more members cannot be accommodated.

CONCEPT:

Use the concept of BODMAS, so first multiply then subtract and lastly divide.

SOLUTION:

Considering the given statement

$\frac{{\left( {0.54; \times ;0.540 - 0.460; \times ;0.460} \right)}}{{\left( {1 - 0.920} \right)}} = ?$

$\Rightarrow \frac{{\left( {0.2916 - 0.2116} \right)}}{{0.08}}$

$\Rightarrow \frac{{0.08}}{{0.08}} = 1$

Alternate method:

Considering the given statement

$\frac{{\left( {0.54; \times ;0.540 - 0.460; \times ;0.460} \right)}}{{\left( {1 - 0.920} \right)}} = ?$

$\Rightarrow \frac{{{{0.54}^2} - {{0.46}^2}}}{{0.08}}$

$\Rightarrow \frac{{\left( {0.54; + ;0.46} \right); \times ;\left( {0.54 - 0.46} \right)}}{{0.08}}$

$\Rightarrow \frac{{1; \times ;0.08}}{{0.08}} = 1$

The correct answer is Thailand.

• Baht (B) is the official currency of Thailand.
• Thailand is a Southeast Asian country.
• Capital: Bangkok
• King: Maha Vajiralongkorn
• Thailand is called the country of white elephants.

Important Points

Shortcut Trick

Average speed of the whole journey = 300 ÷ 5 = 60 km/hr.

Using Alligation on speeds: (Higher speed 75) − (Average 60) = 15; (Average 60) − (Lower speed 55) = 5.

Ratio of Time (Higher : Lower) = 5 : 15 = 1 : 3.

Total time ratio parts = 1 + 3 = 4 units → 5 hours.

Time at higher speed = (1 ÷ 4) × 5 = 1.25 hours = 1 hr 15 min.

∴ The correct answer is 1 hr 15 min.

Alternate Method

Given: Total Distance = 300 km, Total Time = 5 hours, Speed₁ = 75 km/hr, Speed₂ = 55 km/hr.

Formula Used: Distance = Speed × Time

⇒ Let time spent at 75 km/hr be T hours.

⇒ Then time spent at 55 km/hr is (5 − T) hours.

⇒ 75 × T + 55 × (5 − T) = 300

⇒ 75T + 275 − 55T = 300

⇒ 20T = 25

⇒ T = 25 ÷ 20 = 1.25 hours

⇒ 1 hour + (0.25 × 60) minutes = 1 hr 15 min.

∴ The correct answer is 1 hr 15 min.

Additional Information

Average Speed

Defined as Total Distance divided by Total Time taken for the entire journey.

Alligation Rule for Speed

When alligation is applied to speeds, the resulting ratio is always the ratio of the time taken at those respective speeds.

Unit Conversion

To convert hours to minutes, multiply by 60. Example: 0.25 hr = 0.25 × 60 = 15 minutes.

• The Oxides of non-metals are usually acidic in nature.
• Non-metal react with oxygen in the presence of air and produce non-metal oxides.
• Non-metal oxides are usually gases at room temperature.
• Non-metal oxides are easily dissolved in the water and form an acidic solution.

Shortcut Trick

When the distance for two journeys is equal (X km onward and X km return), use the harmonic mean formula.

Average Speed = (2 × a × b) ÷ (a + b)

Average Speed = (2 × 60 × 90) ÷ (60 + 90) = 10800 ÷ 150 = 72 km/hr.

∴ The correct answer is 72 km/hr.

Alternate Method

Given: Onward speed = 60 km/hr, Return speed = 90 km/hr, Distance = X km.

Formula Used: Average Speed = Total Distance ÷ Total Time

⇒ Time taken for onward journey (t₁) = X ÷ 60

⇒ Time taken for return journey (t₂) = X ÷ 90

⇒ Total Distance = X + X = 2X

⇒ Total Time = (X ÷ 60) + (X ÷ 90) = (3X + 2X) ÷ 180 = 5X ÷ 180 = X ÷ 36

⇒ Average Speed = 2X ÷ (X ÷ 36) = 2X × (36 ÷ X) = 72 km/hr.

∴ The correct answer is 72 km/hr.

Additional Information

Average Speed for Different Distances

If distances are different, use the basic formula: Total Distance (d₁ + d₂ + ...) ÷ Total Time (t₁ + t₂ + ...).

Three Equal Distances

If a train covers three equal distances at speeds u, v, and w, the Average Speed = (3uvw) ÷ (uv + vw + wu).

Relative Speed

In the same direction, relative speed is (u − v). In opposite directions, it is (u + v).

The correct answer is C-12.

• The International Union of Chemists selected the most stable carbon isotope (C-12) or ¹²C as the standard for comparison of the atomic masses of various elements.
• The mass of C-12 is taken as a 12 atomic mass unit (standard).
• A Carbon-12 contains six protons, six neutrons, and six electrons.

Additional Information

• The amount of carbon-14 found in fossils allows paleontologists to determine their age.
• A carbon-14 contains six protons, eight neutrons, and six electrons.
• C-16 is a new Isotope of Carbon.
• Oxygen-16 (¹⁶O) is a stable isotope of oxygen contains 8 neutrons and 8 protons.
• Oxygen is composed of three stable isotopes, ¹⁶O, ¹⁷O, and ¹⁸O.
• N-14 is a stable isotope of nitrogen, contain 7 protons and 7 neutrons.

The correct answer is Solid.

• Sound propagates maximum in a solid because the particles in a solid are closer and tight to each other so the transfer of sound wave moves faster than other media (gas, vacuum, liquid).
• This closeness of particles due to density means that they can collide very quickly.
• The speed of sound in solid is 6000 ms-1 while the speed of sound in steel is equal to 5100 ms^-1.
• The sound travels 35 times faster in diamonds than in the air.

Important Points

• The speed of sound in a vacuum is zero because there are no particles present in the vacuum. So, there is no propagation of sound waves.
• In a space, Sound cannot travel.
• The density of a liquid is greater than the density of a gas, therefore, the distance between molecules in a liquid is more than in solids but are less than in gases. So the speed of sound in liquids is between the speed of sound in solids and gases.
• The speed of sound in water is more than that of the air.
• The speed of sound in water is 1480 ms^-1.
• The speed of sound: Solid > Liquid > Gas.

Key Points

The logic is:

L + 1 = M; M + 1 = N; N + 1 = O

So, answer figure ‘B’ will be the next figure for the given series.

Hence, ‘option 1’ is the correct answer.

The minimum number of lines required to create the following figure is shown below:

Hence, ‘15’ is the correct answer.

Shortcut Trick

Net percentage change in area = x + y + (x × y) / 100

Since it is a square, both dimensions (length and breadth) increase by 10%.

Change = 10 + 10 + (10 × 10) / 100

Change = 20 + 1 = 21%

∴ The correct answer is 21%.

Alternate Method

Given: Increase in side = 10%

Formula Used: Area of Square = Side²

⇒ Let original side be 10 units.

⇒ Original Area = 10 × 10 = 100 sq. units.

⇒ New side = 10 + 10% of 10 = 11 units.

⇒ New Area = 11 × 11 = 121 sq. units.

⇒ Percentage Increase = (121 − 100) / 100 × 100 = 21%.

∴ The correct answer is 21%.

Additional Information

Successive Percentage Formula

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

Square Perimeter Change

If the side of a square increases by x%, the perimeter also increases by exactly x%.

Volume Change for Cube

If the side of a cube increases by 10%, the volume increases by (1.1)³ − 1 = 33.1%.

The correct answer is Public Leadership.

• Maharashtra CM Devendra Fadnavis has been selected for the SIES-Sri Chandrasekarendra Saraswati National Eminence Award in the category of Public Leadership.
• Hari Katha exponent Kamala Murthy has been selected for Social Thinkers, Philosophers, and Pravachana Karthas category.
• John Marr has been felicitated for his work in the International category.
• The ISRO chairman A S Kiran Kumar has been presented the award for Science & Technology category.

Additional Information

• The SIES-Sri Chandrasekarendra Saraswati National Eminence Award is given in memory of the late Seer of Kanchi Sri Chandrasekarendra Saraswati who passed away at the age of 100 in 1994.
• The awards were instituted by the South Indian Education Society (SIES)
• It carries a cash prize of Rs 2.5 lakh, a citation, a shawl, and an ornamental lamp.

The mirror image of the given figure with respect to the line AB is shown below:

Hence, ‘option 3’ is the correct answer.

The correct answer is $ 16 billion.

• US retail giant Walmart Inc will pick up a 77% stake in India’s largest online retailer Flipkart for $16 billion in 2018.

Key Points

• Walmart Inc:
• Owner: Walton family
  

CEO: Doug McMillon

Founder: Sam Walton

• Flipkart :
• CEO: Kalyan Krishnamurthy
• Founders: Sachin Bansal, Binny Bansal
• HQ: Bangalore, Karnataka, India.

From the given pie chart we can say that

Total number of tyres produced by all the companies during the year = 180000

Percentage of tyres produced by company B = 30%

∴ Number of tyres produced by company B in 2017 = 0.3 × 180000 = 54000

The correct answer is Rajasthan.

• Rajasthan has become the second-largest crude oil producer in the country after the offshore field Bombay High.
• The state was producing nearly 90 lakh tonnes of oil annually, which is 24 per cent of the total domestic crude oil production.

The correct answer is Ethane.

• Ethane (C₂H₆) is a simple hydrocarbon seen to be chains of carbon atoms where the spare valencies were occupied by hydrogen atoms.
• At standard temperature and pressure, ethane is a colorless, odorless gas.
• Ethane is mainly used to produce ethylene, which is used by the petrochemical industry.
• The common name of ethane is bimethyl.

Additional Information

• Butane (C₄H₁₀) is considered a hydrocarbon. At standard temperature and pressure, butane is a highly flammable, colorless, easily liquefied gas that quickly vaporizes.
• It is used as a fuel, an aerosol propellant, in cigarette lighters, and to make other chemicals.
• Methane (CH₄) is gas at room temperature with a single carbon atom with four arms of hydrogen atoms.
• Methane is one of the Greenhouse gases absorb energy reflected by Earth’s surface, stopping it from escaping into space.
• Alessandro Volta discovers Methane.
• Methane is used as a fuel for ovens, homes, water heaters, kilns, automobiles, turbines, and other things.
• Activated carbon is used to store methane.
• Propane (C₃H₈) is a three-carbon alkane, is an odorless gas, for this reason, odorant has been added to detect leaks.
• The complete combustion of propane produces clean water vapor and carbon dioxide.

• The pH level is a measure of the number of Hydrogen ions in a solution.
• The lower the solution or compound on the pH scale, the higher will be the concentration of hydrogen ions.
• Therefore the solution having a pH of 2.4 will have the highest concentration of hydrogen ions.
• The pH scale ranges from 0 to 14.
• A pH value of 7 is considered neutral, example - water and pH value > 7 is Basic > pH value < 7 is Acidic

The correct answer is Force.

• For the first time, Newton’s law enabled accurate predictions of motion to be made.
• Force is defined as a push or pulls exerted on one object by another.
• Force measured in Newtons (denoted N, where 1 N is the force required to give a 1 kg mass an acceleration of 1 m/s²).

Important Points

• Newton's 2nd law states that the rate of change of a body’s momentum-the product of its mass and velocity-is proportional to the force applied, and takes place in the direction of the applied force.

Key Points

The correct answer is 20 kg.

• Given, Weight (w) = 196 N , g = 9.8 ms^-2
  

So, mass (m) = (w / g) = 20 kg.

Important Points

• Mass is a measure of the amount of matter in an object.
• Mass is always constant.
• Weight is the force of gravity on an object.
• Weight depends on the gravitational force of attraction.
• Weight (w) = Mass (m) * Gravitational acceleration (g)
• The weight of a body is greater in the pole of the earth than in the equator, because of acceleration of gravity at the poles is 980.665 cm/sec² while at the equator it is 3.39 cm/sec² less due to the centrifugal force.

The correct answer is NH₄OH.

• A base that can dissolve in water is also called an alkali.
• A base is dissolved in water and make a conjugate acid and conjugate base, both are ion.
• The conjugate base is stronger than the conjugate acid.

Key Points

• Ba(OH)₂ (Barium hydroxide, strong base) is soluble in water and gives an alkaline solution.
• Ba(OH)₂ → Ba²⁺ + 2 OH⁻
• NaOH is also a strong base, fully soluble in water, and gives sodium ions (Na⁺) and hydroxyl ions (OH^-).
• NaOH + H2O = Na⁺ + OH^-
• Ca(OH)₂ (Calcium hydroxide or slaked lime) is slightly soluble in water and forming a basic solution called lime water.
• Ca(OH)₂ → Ca²⁺ + 2 OH^-

Shortcut Trick

For a sum to triple itself (n = 3) in 8 years, the interest earned must be 200% of the principal.

Rate (R) = [(n − 1) × 100] ÷ Time

Rate (R) = [(3 − 1) × 100] ÷ 8

Rate (R) = 200 ÷ 8 = 25%

∴ The correct answer is 25%.

Alternate Method

Given:

Let the Principal (P) = ₹100

The sum triples itself, so Amount (A) = ₹300

Time (T) = 8 years

Formula Used:

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

Amount (A) = P + SI

Calculations:

⇒ SI = A − P

⇒ SI = 300 − 100 = ₹200

⇒ 200 = (100 × R × 8) ÷ 100

⇒ 200 = 8 × R

⇒ R = 200 ÷ 8

⇒ R = 25%

∴ The correct answer is 25%.

Additional Information

Sum Doubling Property

To double a sum (n=2) in T years, the rate R = 100 ÷ T. Conversely, time T = 100 ÷ R.

Simple Interest vs Compound Interest

In SI, the Principal remains constant throughout the period, whereas in CI, interest is added to the principal at the end of each period.

Rule of 72 (Approximation for CI)

For Compound Interest, the time to double a sum is approximately 72 ÷ Rate.

Shortcut Trick

Recognize the values as part of a Pythagorean Triplet (a, b, c) where a² + b² = c².

The standard triplet (3, 4, 5) scaled by 4 gives (12, 16, 20).

Since 20 is the hypotenuse and 16 is one side, the remaining side is 12.

∴ The correct answer is 12.

Alternate Method

Given: √(20² − 16²)

Formula Used: Difference of squares identity: a² − b² = (a − b)(a + b)

⇒ √((20 − 16) × (20 + 16))

⇒ √(4 × 36)

⇒ √144

⇒ 12

∴ The correct answer is 12.

Additional Information

Difference of Squares

The expression a² − b² can always be factored into (a + b)(a − b), which simplifies mental square root calculations.

Pythagorean Triplets

Common triplets used in exams include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25). Multiples of these (like 12, 16, 20) also satisfy the Pythagoras theorem.

Perfect Squares

A perfect square is an integer that is the square of an integer. For example, 144 is a perfect square because 12 × 12 = 144.

The correct answer is 137.5 J.

• Given, mass (m) = 11 kg, velocity (v) = 5 ms^-1.
  

Kinetic energy = ${1\over 2} mv^2$

So, the kinetic energy of the object is \({1 \over 2}115^2 = 137.5\) J.

Key Points

• It is the energy of object mass in motion.
• When an objects' mass doubles, its kinetic energy also doubles.
• When an objects' speed doubles, its kinetic energy quadruples.
• When a pendulum goes uphill (top point), it loses kinetic energy.

The logic is:

Hence, ‘89’ is the correct answer.

The correct answer is 1800 ms^-1.

• Given, frequency (f) = 600 Hz, wavelength (λ) = 3 m
  

The velocity of a sound wave is given by v = fλ

so, velocity (v) = 600×3 = 1800 ms^-1

Important Points

• Sound waves create from vibrations, which move through mediums such as air, water, or any solid before reaching our ears.
• Sound waves can't travel through a vacuum.
• The speed of sound is around 767 miles/hour.
• When sound waves traveling through water, the speed around four times faster than when it travels through the air.
• Sound waves in air or fluid are longitudinal waves.
• Particles of the medium through which the sound is transported vibrate parallel to the direction that the sound wave moves.

Shortcut Trick

Difference in Profit percentages = 10% − 5% = 5%.

According to the question, this 5% difference is equivalent to Rs. 30.

Since Cost Price (CP) is always 100%.

5% of CP = 30 ⇒ 1% of CP = 30 ÷ 5 = 6.

100% of CP = 6 × 100 = 600.

∴ The correct answer is Rs. 600.

Alternate Method

Given: Difference between Selling Prices (SP) = Rs. 30, Profit₁ = 5%, Profit₂ = 10%.

Formulas: SP = CP × (100 + Profit%) ÷ 100 | Difference = SP₂ − SP₁.

Let the Cost Price be x.

⇒ SP₁ = x × 105 ÷ 100 = 1.05x

⇒ SP₂ = x × 110 ÷ 100 = 1.10x

⇒ Difference = SP₂ − SP₁ = 1.10x − 1.05x = 0.05x

⇒ 0.05x = 30

⇒ x = 30 ÷ 0.05 = 3000 ÷ 5 = 600.

∴ The correct answer is Rs. 600.

Additional Information

Profit and Loss Basics

Profit occurs when Selling Price (SP) is greater than Cost Price (CP). Profit = SP − CP.

Percentage Difference

When two selling prices are based on the same CP, the difference in SP is equal to the difference in profit/loss percentages multiplied by the CP.

(Implicit - suggested though not directly expressed)

I. Karan is capable of adapting to different writing skills. → True (As, Karan is versatile writer. His comedy and fiction novels are very popular among youngsters, which implies he is capable of adapting to different writing skills.)

II. All writers are versatile. → False (As, the statement gives information related to Karan only and not all writers.)

Hence, only assumption I is implicit.

The correct answer is 2009.

• The Right of Children to Free and Compulsory Education Act commonly known as The Right to Education Act (RTE) was passed by the Parliament in August 2009.

Important Points

• The Act came into force in 2010 resulting in India becoming one among 135 countries where education is a fundamental right of every child.
• It enforces Education as a Fundamental Right under Article 21-A and aims to provide free and compulsory education to all children aged 6 to 14 years in such a manner as the state may determine.
• The above provision was added by the 86th constitutional amendment act of 2002 which aims to 'Education for All'.

The logic is:

Refrigerator: Cool → Refrigerator is an appliance which is used for artificial cooling. (Device – Use)

Similarly,

1. Listen : Radio → Radio is a device which is used for transmission of voice related services. (Use - Device)

2. Sit : Chair → Chair is a furniture used for the general purpose of sitting. (Use - Device)

3. Watch : Television → Television is a device used to display virtual images with sound. (Use - Device)

4. Phone : Talk → Phone is a device which is used for talking. (Device – Use)

Note: The relation in all the above given pairs is similar to that of ‘Refrigerator: Cool’, but the order in which they are written is different. Only ‘Phone : Talk’ follows the same order as followed by the given pair in the question.

Hence, ‘Phone : Talk’ is the correct answer.

The correct answer is Pema Khandu.

• Pema Khandu is the 9^th Chief Minister of Arunachal Pradesh, since July 2016.
• He is currently the youngest CM in India.

Key Points

• Governor of Arunachal Pradesh: B. D. Mishra.

The logic is:

H + 4 = L,

L + 4 = P,

P + 4 = T,

T + 4 = X,

X + 4 = B

Hence, ‘B’ is the correct answer.

(Implicit - suggested though not directly expressed)

I. Student should learn life skills at an early stage as it prepares them for a better future. → True (As, Life skills should be taught right from primary education suggests to learn life skills at an early stage as it prepares them for a better future).

II. Students are taking up paid courses to learn life skills for their jobs. → False (As, it is not mentioned about paid courses in the given statement).

Hence, only assumption I is implicit.

Shortcut Trick

Total Work (LCM of 36, 90, 60) = 180 units.

Efficiency of Sarthak = 180 ÷ 36 = 5 units/day.

Efficiency of Vivan = 180 ÷ 90 = 2 units/day.

Efficiency of Ali (Outlet) = −(180 ÷ 60) = −3 units/day.

Combined Efficiency = 5 + 2 − 3 = 4 units/day.

Time taken = 180 ÷ 4 = 45 days.

∴ The correct answer is 45 days.

Alternate Method

Given:

Time taken by Sarthak (Positive work) = 36 days

Time taken by Vivan (Positive work) = 90 days

Time taken by Ali (Negative work/Emptying) = 60 days