RRC Group D Previous Year Paper 65 (Held On: 24 Oct 2018 Shift 1)

The logic followed here is:-

• In Figures A, B, and C the colour of the aeroplane is red
• In option D there are two colours, red and blue, in the aeroplane. Thus, figure D is the odd one.

Hence, "option 3" is the correct answer.

Shortcut Trick

Net increase in Sum = (Correct values) − (Incorrect values) = (30 + 40 + 50) − (10 + 20 + 30) = 120 − 60 = 60.

Net increase in Mean = Total increase ÷ Number of terms = 60 ÷ 10 = 6.

Correct Mean = Old Mean + Net increase = 49 + 6 = 55.

∴ The correct answer is 55.

Alternate Method

Given: Total terms (n) = 10, Incorrect Mean = 49, Incorrect terms = 10, 20, 30, Correct terms = 30, 40, 50.

Formula: Mean = Sum of observations ÷ Number of observations

⇒ Incorrect Sum = 10 × 49 = 490.

⇒ Sum of incorrectly read terms = 10 + 20 + 30 = 60.

⇒ Sum of correct terms = 30 + 40 + 50 = 120.

⇒ Correct Sum = 490 − 60 + 120 = 550.

⇒ Correct Mean = 550 ÷ 10 = 55.

∴ The correct answer is 55.

Additional Information

Arithmetic Mean Property

The mean is sensitive to every value in the data set. If any value is changed, the mean will change proportionally by (Change ÷ n).

Correction Formula

Correct Mean = [ (Incorrect Mean × n) − (Sum of wrong items) + (Sum of correct items) ] ÷ n.

Linear Transformation

If a constant k is added to or subtracted from all observations, the new mean will be (Original Mean ± k).

The Venn diagram is given below:-

• No. of students who play only basketball = 20
• No. of students who play basketball and football = 13
• No. of students who play basketball and hockey = 14.
• No. of students who play basketball, football, and hockey = 12
• Thus, total students who play basketball in the class = 20 + 13 + 14 + 15 = 62

Hence, "option 2" is the correct answer.

The correct answer is Calcium phosphate.

• Dentin (tooth enamel) is made of Calcium and Phosphate.

Key Points

• Dentin is a composite substance of organic and inorganic material found in the tooth’s interior.
• Dentin is pale yellow and becomes darker with age.
• It constitutes the bulk of the tooth, providing its structure and protecting the more sensitive pulp inside of it.
• It is one of the major components of human teeth. When dentin is damaged or exposed, a variety of problems can occur, such as tooth sensitivity.

Additional Information

• Dentin is one of four major components of a tooth.
• The other layers of a tooth include: 
• Enamel: Calcified tissue that acts as a protective barrier for the crown of the tooth. It is the hardest substance in the human body, composed of hydroxyapatite crystals (calcium and phosphate ions).
• Dental pulp: This soft tissue forms the tooth’s inner core, containing the blood vessels and nerves.
• Cementum: Forms a tough, protective covering of the root of the tooth, anchoring it in the jaw bone.

Shortcut Trick

Area of circular floor = Total Cost ÷ Rate = 1540 ÷ 10 = 154 m².

For a circle, if Area = 154, then Radius (r) = 7 and Circumference (2πr) = 44.

Fencing Cost = Circumference × Rate = 44 × 6 = ₹264.

∴ The correct answer is ₹264.

Alternate Method

Given: Total installation cost = ₹1540, Rate = ₹10/m², Fencing rate = ₹6/m.

Formula Used: Area = πr²; Circumference = 2πr; Total Cost = Area/Length × Rate.

⇒ Area of floor = 1540 ÷ 10 = 154 m²

⇒ (22/7) × r² = 154

⇒ r² = (154 × 7) ÷ 22 = 7 × 7 = 49

⇒ Radius (r) = 7 m

⇒ Circumference = 2 × (22/7) × 7 = 44 m

⇒ Cost of fencing = 44 × 6 = ₹264

∴ The correct answer is ₹264.

Additional Information

Standard Circle Dimensions

If radius r = 7, then Circumference = 44 and Area = 154. This ratio helps solve circular problems faster.

Area and Circumference Formulas

Area of circle = πr²; Perimeter (Circumference) of circle = 2πr or πd, where d is the diameter.

Cost Calculation

Cost of flooring/plastering depends on Area, whereas cost of fencing/bordering depends on Perimeter.

The correct answer is Gravitational force.

• The motion of the moon around the earth is due to gravitational force.

Key Points

• The gravitational attraction provides the centripetal force needed to keep planets in orbit around the Sun and all types of satellites in orbit around the Earth.
• The Earth's gravity keeps the Moon orbiting us. It keeps changing the direction of the Moon's velocity.
• The moon has two movements, the first is that it will revolve around itself in its own axis and the second, it will move around the Earth.
• The moon takes 30 days to move around the Earth and it can be observed in the sky for 15 days and another 15 days it will be another side of the Earth that we cannot see.

Additional Information

• Centrifugal force:
• ​Centrifugal force is a pseudo force in a circular motion which acts along the radius and is directed away from the center of the circle. The force does not exist when measurements are made in an inertial frame of reference.
• Centripetal force:
• ​A centripetal force is a force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous centre of curvature of the path.
• Nuclear force:
• ​The nuclear force is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nuclear force almost identically.

The correct answer is Each and Every.

• Gravitational force exists between each and every object, but it cannot be felt unless the mass of the objects is very high, such as in planets.

Key Points

• Gravity, also called gravitation, in mechanics, is the universal force of attraction acting between all matter.
• On Earth, all bodies have a weight, or downward force of gravity, proportional to their mass, which Earth's mass exerts on them.
• Gravity is measured by the acceleration that it gives to freely falling objects.

Additional Information

• Universal Gravitation Equation.
• This equation describes the force between any two objects in the universe:
• F is the force of gravity (measured in Newtons, N).
• G is the gravitational constant of the universe and is always the same number.
• M is the mass of one object (measured in kilograms, kg).
• m is the mass of the other object (measured in kilograms, kg).
• r is the distance those objects are apart (measured in meters, m).

Formula:

Newton's law of Universal Gravitation

$F=G \frac{m_1 m_2}{r^2}$

where, F = force, G = Gravitational constant, m₁ = mass of object 1, m₂ = mass of object 2, r = distance between centers of masses

The correct answer is Maharashtra.

• Sanjay Gandhi National Park is in Maharashtra.

Key Points

• Sanjay Gandhi National Park is a protected area in Mumbai, Maharashtra State in India. It was established in 1969 with headquarters at Borivali.
• Previously the park was named Krishnagiri National Park in the pre-independence era. At that time the area of the park was only 20.26 sq. km.
• In 1969, the park was expanded to its present size by acquiring various reserve forest properties adjoining the park.
• After this, an independent unit of the Forest Department called Borivali National Park Sub-division administered the area.
• Krishnagiri National Park was created in 1974 and later renamed Borivali National Park.
• In 1981, it was re-dedicated as Sanjay Gandhi National Park in memory of Sanjay Gandhi, the son of ex-Prime Minister of India Indira Gandhi.

Additional Information

The logical Venn diagram is given below:-

Conclusion:

I. Some girls are sisters. → True (this can be seen in the Venn diagram; girls that are doctors are sisters)

 II. All sisters are girls. → False (it is possible but not definite.)

Hence, "option 3" is the correct answer.

The correct answer is Quaternary Atom.

• Quaternary Atom is the atomicity of phosphorus.

Key Points

• Atomicity is the number of atoms of an element present in one molecule of that element.
• The number of atoms present in a molecule of phosphorus is 4. So the atomicity of phosphorus is 4.

Additional Information

• Atomicity is defined as the total number of atoms present in a molecule.
• Atomicity, molecules can be classified as below:
• Monatomic: Composed of one atom e.g. He, Ne, Ar, Kr (all noble gases are monatomic).
• Diatomic: Composed of two atoms e.g. H2, N2, O2, F2, Cl2 (all halogens are usually diatomic).
• Triatomic: Composed of three atoms e.g. O3.
• Polyatomic: Composed of three or more atoms e.g. P4, S8.

Shortcut Trick

For two intersecting chords in a circle, the product of their segments is equal.

Logic: Product of segments of chord AB = Product of segments of chord CD

4 × 15 = 60

Required segment DE = 60 ÷ 2.5

DE = 24 cm

∴ The correct answer is 24 cm.

Alternate Method

Given: AE = 4 cm, BE = 15 cm, CE = 2.5 cm.

Formula Used: AE × BE = CE × DE (Intersecting Chords Theorem)

E A B C D O 4 cm 15 cm 2.5 cm DE = ?

The correct answer is Ni; Cr.

• When iron is mixed with Ni and Cr, we get stainless steel.
• Stainless steel is steel containing at least 10.5% chromium, less than 1.2% carbon, and other alloying elements.

Key Points

• Stainless steel is an alloy of Iron, Nickel, and chromium. This alloy makes the metal strong, durable, and corrosion-resistant.
• Stainless steel is an alloy of iron, chromium, and nickel.
• Because of the interactions between the atmosphere and its alloying components, stainless steel is known to remain stainless and avoid rusting.
• Chromium plays an important role in the production of stainless steel. It gives hardness to the stainless steel and makes it tough. It improves corrosion resistance, particularly at high temperatures.

Additional Information

Given:

$\left(\frac{2}{3} \times \frac{4}{6}\right) + \left(\frac{5}{3} \times \frac{7}{10}\right) - \left(\frac{11}{2} \times \frac{4}{33}\right)$

Concept used:

Calculation:

$\left(\frac{2}{3} \times \frac{4}{6}\right) + \left(\frac{5}{3} \times \frac{7}{10}\right) - \left(\frac{11}{2} \times \frac{4}{33}\right)$

⇒ 4/9 + 7/6 - 2/3

⇒ 17/18

∴ The required value of $\left(\frac{2}{3} \times \frac{4}{6}\right) + \left(\frac{5}{3} \times \frac{7}{10}\right) - \left(\frac{11}{2} \times \frac{4}{33}\right)$ is 17/18.

The logic followed here is:-

Hence, "option 4" is the correct answer.

The correct answer is Eight.

• Eight positions of India in the Most Valuable Nation Brands list as per the Brand Finance 'Nation Brands 2017' list.

Key Points

• The NBI looks at each nation's reputation along six dimensions of national competence:
• The Anholt Ipsos Nation Brands Index is a global nation brand survey. The NBI examines the images of around 50 nations each year, by conducting online interviews with 20,000 adults aged 18 and over, in 20 core panel countries.
• The NBI looks at each nation’s reputation along six dimensions of national competence: Exports, Governance, Culture, People, Tourism, Immigration, and Investment. Together these provide an overall indication of a nation’s reputation.
• The Scottish Government subscribed to the NBI in 2008 (collecting baseline data reported in the NPF) and 2009 and has subscribed on a biannual basis since 2010.

Additional Information

• Most valuable nation brands worldwide in 2021:

Given:

There is a number whose 12% is 9

Concept used:

Application of percentage

Calculation:

Let the number P.

According to the question,

P × 12% = 9

⇒ P = 75

∴ 12% of 75 is 9.

The diagram is given below:-

 

• Mr Z facing west at point B.

Hence, "option 3" is the correct answer.

The logic followed here is:-

Similarly,

Hence, "option 1" is the correct answer.

The logic followed here is:-

• Code of a letter = digit in the units place of its positional value - 1

 

Similarly,

 

Hence, "option 1" is the correct answer.

The figure is given below:-

 

• The minimum number of lines to make the question figure is 11.

Hence, "option 3" is the correct answer.

The correct answer is I am That Woman.

• The Union Ministry of Women and Child Development has launched an online campaign with an aim to end gender bias against women is I am that women.

Key Points

• The Union Ministry of Women and Child Development (WCD) has launched an online campaign #IamThatWoman to end gender bias in women against women.
• Through the campaign, the Ministry seeks to highlight the various aspects of women standing by and for women.
• The purpose of the campaign is to shed light on the enormous contributions made by women for women.

Additional Information

• Twitter and Facebook users have been encouraged to tag and share stories of women helping women with a photograph and post online with the hashtag #IamThatWoman.

Shortcut Trick

Net profit % = (Part₁ × Profit₁%) − (Part₂ × Loss₂%)

Net profit % = (2/3 × 6%) − (1/3 × 3%) = 4% − 1% = 3%

According to the question, 3% of Total Cost = Rs 540

1% = 540 ÷ 3 = Rs 180

100% (Total Cost) = 180 × 100 = Rs 18,000

∴ The correct answer is Rs 18,000.

Alternate Method

Given: 2/3 part sold at 6% profit, 1/3 part sold at 3% loss, Total profit = Rs 540.

Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100 | Total Profit = Profit₁ − Loss₂

⇒ Let the Total Cost Price be 300x.

⇒ CP of 2/3 part = 2/3 × 300x = 200x. Profit on this = 6% of 200x = 12x.

⇒ CP of remaining 1/3 part = 100x. Loss on this = 3% of 100x = 3x.

⇒ Net Profit = 12x − 3x = 9x.

⇒ Given 9x = 540 ⇒ x = 60.

⇒ Total Cost = 300 × 60 = Rs 18,000.

∴ The correct answer is Rs 18,000.

Additional Information

Weighted Average Profit

When different parts of an inventory are sold at different profit/loss rates, the overall profit/loss% is the weighted average of the individual rates.

Cost Price Calculation

Total Cost Price = (Total Profit Amount × 100) ÷ (Overall Profit Percentage).

The correct answer is 2014.

• In 2014 the initiative “Swachh Bharat Abhiyan” was introduced by the Government of India.

Key Points

• Swachh Bharat Abhiyan is a national level campaign by the Government of India covering 4041 statutory towns to clean the streets, roads and infrastructure of the country.
• The campaign is India's biggest ever cleanliness drive and 3 million government employees and schools and colleges students of India participated in this event.
• On 2nd October 2014, Swachh Bharat Mission was launched throughout length and breadth of the country as a national movement.
• The campaign aims to achieve the vision of a Clean India by 2nd October 2019.
• The mission aims to cover 1.04 crore households, provide 2.5 lakh community toilets, 2.6 lakh public toilets, and a solid waste management facility in each town.

Additional Information

• Objectives of Swachh Bharat Abhiyan:
• Villages to be kept clean with Solid and Liquid Waste Management.
• Construction of individual, cluster and community toilets.
• To eliminate or reduce open defecation. Open defecation is one of the main causes of deaths of thousands of children each year.
• Solid and liquid waste management through gram panchayats.
• To provide toilets, separately for Boys and Girls in all schools by 15.8.2015.

Shortcut Trick

For 2 years, use the effective rate of interest formula: Effective Rate = x + y + (x × y)/100.

Effective Rate = 3 + 3 + (3 × 3)/100 = 6 + 0.09 = 6.09%.

Compound Interest (CI) = Principal × Effective Rate / 100.

CI = 2000 × 6.09 / 100 = 20 × 6.09 = ₹121.80.

∴ The correct answer is ₹121.80.

Alternate Method

Given:

Principal (P) = ₹2,000

Rate (R) = 3% p.a.

Time (n) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Compound Interest (CI) = Amount (A) − Principal (P)

Calculations:

⇒ Amount (A) = 2000 × (1 + 3/100)²

⇒ A = 2000 × (103/100) × (103/100)

⇒ A = 2000 × 1.03 × 1.03

⇒ A = 2000 × 1.0609

⇒ A = ₹2,121.80

⇒ CI = A − P

⇒ CI = 2121.80 − 2000

⇒ CI = ₹121.80

∴ The correct answer is ₹121.80.

Additional Information

CI − SI Difference for 2 Years

The difference between compound interest and simple interest for 2 years is given by P(R/100)².

Effective Interest Rate

For successive growth over n years, the total percentage change is the compound interest rate equivalent.

Quarterly and Half-Yearly Compounding

For half-yearly, R becomes R/2 and n becomes 2n. For quarterly, R becomes R/4 and n becomes 4n.

Shortcut Trick

Net efficiency = Efficiency of A + Efficiency of B − Efficiency of C.

Using LCM of 5, 15, and 5 = 15 units as Total Work.

Efficiencies: A = 3, B = 1, C = 3.

Combined efficiency = 3 + 1 − 3 = 1 unit/hr.

Time required = 15 ÷ 1 = 15 hours.

∴ The correct answer is 15 hr.

Alternate Method

Given: Filling time Tap A = 5 hr, Tap B = 15 hr; Emptying time Tap C = 5 hr.

⇒ Total Work (LCM of 5, 15, 5) = 15 units.

⇒ Total Efficiency = Efficiency(A) + Efficiency(B) + Efficiency(C)

⇒ Total Efficiency = 3 + 1 + (−3) = 1 unit/hr.

⇒ Time taken = Total Work ÷ Total Efficiency

⇒ Time taken = 15 ÷ 1 = 15 hr.

∴ The correct answer is 15 hr.

Additional Information

Pipes and Cisterns Efficiency

Filling pipes have positive efficiency, while leakage/outlet pipes have negative efficiency.

Net Work Formula

If two pipes fill in x and y hours and one empties in z hours, the part filled in 1 hour is (1/x + 1/y − 1/z).

Time and Work Relation

Time is inversely proportional to Efficiency; Total Work = Efficiency × Time.

The correct answer is Pandya.

• Pandya ruled the region around Madurai and attained supremacy in the thirteenth century.

Key Points 

• The Pandyas established their dynastic rule in southern Tamil Nadu by the end of the sixth century CE after Kalabhras.
• The foundation for the Pandya supremacy in south India was laid by Maravarman Sundara I.
• Pandya ruled initially from Korkai, a seaport on the southernmost tip of the Indian peninsula, and in later times moved to Madurai.
• Jatavarman Sundara Pandyan expanded their empire into the Telugu country and invaded Sri Lanka to conquer the northern half of the island.
• The Pandyan Kingdom finally became extinct after the establishment of the Madurai Sultanate in the 14th century CE.

Additional Information

The logic followed here is:-

• Figure 1 to Figure 2: lines inside the internal square are interchanged with the lines inside the external square

Similarly, 

• Figure 3 to Figure 4: lines inside the internal circle should be interchanged with the lines inside the external square
• Therefore, figure B will be the next figure.

Hence, "option 3" is the correct answer.

Shortcut Trick

Initial clerks = 1/4 of total; Non-clerks = 3/4 of total.

Remaining clerks = 3/4 of initial clerks = 3/4 × 1/4 = 3/16 of original total.

Remaining total = 3/4 (non-clerks) + 3/16 (clerks) = 15/16 of original total.

Required % = (3/16 ÷ 15/16) × 100 = (3/15) × 100 = 20%.

∴ The correct answer is 20%.

Alternate Method

Given:

Total employees = 6400

Initial Clerk employees = 1/4 × 6400 = 1600

Non-clerk employees = 6400 − 1600 = 4800

Calculations:

⇒ Reduction in clerks = 1/4 × 1600 = 400

⇒ Remaining clerks = 1600 − 400 = 1200

⇒ Total remaining employees = 1200 (clerks) + 4800 (non-clerks) = 6000

⇒ Required Percentage = (Remaining clerks ÷ Total remaining employees) × 100

⇒ Required Percentage = (1200 ÷ 6000) × 100

⇒ Required Percentage = 1/5 × 100 = 20%

∴ The correct answer is 20%.

Additional Information

Percentage Change

Percentage change = (Change / Original Value) × 100. It is used to express the relative change in a quantity.

Successive Percentage

When a value is changed by a% and then by b%, the net change is [a + b + (ab/100)]%.

Fraction to Percentage Conversion

1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.66%.

The total expenditure is Rs. 50,000.

The expenditure on transportation = (50000 × 10%) = Rs. 5000

∴ The expenditure on transportation is Rs. 5000.

The logic followed here is:-

• In figure A, the inner square is shaded and the outer square is not.
• In figure B, the inner pentagon is shaded and the outer square is not.
• In figure A, the inner pentagon is shaded and the outer square is not.
• In figure D, the outer square is shaded and the inner triangle is not.

So figure D is different from others.

Hence, "option 4" is the correct answer.

Total pie chart that 360° circle represents 100% of the data.

So, the share of the segment corresponding to the sales of 'Others' = 360/100 × 40 = 144° 

∴ The share of the segment corresponding to the sales of 'Others' is 144°.

The correct answer is Sikkim.

• Oscar-winning composer A.R. Rahman has become the official brand ambassador of Sikkim state.

Key Points

• AR Rahman was born on 6 January 1967, is an Indian film composer, record producer, singer, and songwriter who works predominantly in Tamil and Hindi films.
• In 2010, the Indian government awarded him the Padma Bhushan.
• In 1992, he was approached by director Mani Ratnam to compose the score and soundtrack for his Tamil film, Roja.
• Rahman's film career began in 1992 when he started Panchathan Record Inn, a recording and mixing studio in his backyard.

Additional Information

The correct answer is Kinetic Energy.

Key Points

• Kinetic energy is a form of energy that an object or a particle has by reason of its motion.
• If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy.
• There are many forms of kinetic energy, vibrational (the energy due to vibrational motion), rotational (the energy due to rotational motion), and translational (the energy due to motion from one location to another).
• Kinetic energy is a scalar quantity, it does not have a direction. Unlike velocity, acceleration, force, and momentum, the kinetic energy of an object is completely described by magnitude alone.

Additional Information

• Kinetic Energy Concept:

The correct answer is Collenchyma.

• The permanent tissue that provides elasticity is called Collenchyma.

Key Points

• Collenchyma cells are long elongated cells with an irregular thick wall. They have thick walls which provide support and elasticity to the plant's part.
• They provide structural support and flexibility to the growing stems. It acts as a supporting tissue in the stems of young plants. It provides mechanical support, elasticity, and tensile strength to the plant body.
• Elasticity is provided by collenchyma because of the presence of hydrated pectin in their cell walls.
• Collenchyma consists of narrow cells.

Additional Information

• Collenchyma mainly provides mechanical strength to the growing plant parts.
• Collenchyma generally occurs in the hypodermis of the dicot stem. It is absent in the roots and also occurs in petioles and pedicels.

Given:

2.06 and 3.1

Calculation:

So, (3.10 - 2.06) = 1.04 should be added.

∴ 1.04 should be added to 2.06 to get 3.1.

Shortcut Trick

Total cake = LCM of denominators (12 and 3) = 12 units.

Nalini ate = 1/12 × 12 = 1 unit.

Tanvi ate = 1/3 × 12 = 4 units.

Rashi ate = 12 − (1 + 4) = 7 units.

Share of Rashi = 7/12th.

∴ The correct answer is 7/12 th.

Alternate Method

Given:

Share of Nalini = 1/12

Share of Tanvi = 1/3

Formula Used:

Remaining share = 1 − (Sum of individual shares)

Calculations:

⇒ Total share consumed by Nalini and Tanvi = 1/12 + 1/3

⇒ Total share = (1 + 4)/12 = 5/12

⇒ Share of Rashi = 1 − 5/12

⇒ Share of Rashi = (12 − 5)/12

⇒ Share of Rashi = 7/12

∴ The correct answer is 7/12 th.

Additional Information

Addition of Fractions

To add fractions with different denominators, find the Least Common Multiple (LCM) to make denominators common.

Total Representation

In fraction-based problems, the whole entity is always represented as 1 or 100%.

Ratio Conversion

If required, the ratio of shares of Nalini, Tanvi, and Rashi is 1 : 4 : 7.

The correct answer is Kinetic Energy.

• Kinetic energy increases with speed.

Key Points

• Kinetic energy is seen when the object is in motion. Energy is exerted on the object in order to make it move.
• The kinetic energy of the object is dependent on the mass of the object and the speed at which it moves.

Kinetic Energy Concept:

 

Additional Information

• Chemical energy:
• ​Chemical energy is energy stored in the bonds of chemical compounds, like atoms and molecules. This energy is released when a chemical reaction takes place.
• Potential energy:
• ​Potential energy, stored energy that depends upon the relative position of various parts of a system. Spring has more potential energy when it is compressed or stretched.
• Electrical energy: 
• ​Electrical energy is energy derived as a result of the movement of electrically charged particles. This energy is supplied by the combination of electric current and electric potential that is delivered by an electrical circuit.

The correct answer is 10 cm.

Concept:

• Concave mirror: The mirror in which the rays converge after falling on it is known as the concave mirror.
• Concave mirrors are also known as  converging mirror.
• The focal length of a concave mirror is negative according to the sign convention.
• Mirror Formula: The following formula is known as the mirror formula:

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

where,

f = focal length 

v = the distance of the image from the mirror,

u = the distance of the object from the mirror.

Calculation:

Here the rays of the sun are focussed at 5 cm away from the mirror, so the focus of the mirror is 5 cm. 

f = -5 cm

u = -10 cm

v = ?

We know that, 

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

⇒$\frac{1}{-5}=\frac{1}{-10}+\frac{1}{v}$

⇒ v = -10 cm i.e in front of the mirror

Alternate Method When the object is at double the focus point i.e at C, then the image is also formed at C in concave mirror.

Hence the image is at 10 cm

Additional Information

The logic followed here is:-

• Figure A to figure B: Hexagon changes to pentagon (one side decreased); no. of circles increases by 1 and only the middle circle is shaded

Similarly,

• Figure C to figure D: Square should change to triangle (one side decreases); no. of circles should increase by 1 and only the middle circle will be shaded. This condition is satisfied by figure 1.

Hence, "option 4" is the correct answer.

The correct answer is HF.

Key Points

• Silica is soluble in HF.
• Silica is the name given to a group of minerals composed of silicon and oxygen, the two most abundant elements in the earth's crust.
• Silica is found commonly in the crystalline state and rarely in an amorphous state.
• It is composed of one atom of silicon and two atoms of oxygen resulting in the chemical formula SiO₂.
• Silica exists in nine different crystalline forms or polymorphs with the three main forms being quartz, which is by far the most common, tridymite and cristobalite.

Additional Information

• Hydrofluoric acid has the ability to dissolve (most) oxides, glass, and silicates.
• SiO₂+6HF→H₂SiF₆+2H₂O.
• The dissolution process of silica and silicates from rocks into water is mainly due to the hydrolysis of silica-oxygen-silica bonds, resulting in the liberation of silicic acid (Si(OH)4) and silicates into the aqueous phase.

Important Points

The correct answer is Manjuli Island.

• In December 2017, the central government launched a new scheme to protect Manjuli Island from floods and erosion in Assam.

Key Points

• The scheme was sanctioned by Government in March 2017 and funding for it will be from the Ministry of Development of the North Eastern Region (DoNER).
• The major components of the scheme include are:
• Bank revetment with geo bags filled with earth/sand for a reach length of 27 km in 14 locations.
• RCC porcupine works in 41 locations.
• Construction of a sluice.
• Construction of a Pilot channel of the length of 3.50 km.

Additional Information

• Manjuli Island:
• Majuli Island is the largest river island in the world and the first island district in the country.
• It is formed by the Brahmaputra River in the south and Kherkutia Xuti, another branch of Brahmaputra, joined by Subansiri River in the north.
• Geomorphologically, the entire Majuli island is part of the alluvial flood plains of the Brahmaputra river.
• The problem of erosion was exacerbated after the 1950 disastrous earthquake and has become a severe environmental issue as it remains mostly uncontained.

The correct answer is 405C.

Key Points

• A filament of an electric bulb carries a current of 0.75 A in 9 minutes. Find the amount of electric charge flowing through the current;
• ​Current (I): 0.75 A.
• Time (t): 9 minutes.
• Time in minutes can be converted into seconds as follows.
• Time (t) = 9 × 60
• t = 540 sec
• Q = I X t
• Q = 0.75 X 540
• Q = 405C

The correct answer is Gujarat.

• Essar Steel Limited, Hazira is located in Gujarat.

Key Points

• Essar Steel was a steel manufacturing company of the Essar Group of Companies.
• Its main subsidiary was Essar Steel India Limited, a fully integrated flat carbon steel manufacturer based in Mumbai, which owned and operated a steel mill in Hazira, Surat district of Gujarat state.
• In addition, it had also a beneficiation plant at Bailadilla, Chhattisgarh, and pellet plants at Visakhapatnam, Andhra Pradesh, and Paradeep, Odisha.
• Essar Steel India Limited was acquired by ArcelorMittal Nippon Steel India Limited. Aditya Mittal is the Chairman of ArcelorMittal Nippon Steel and Dilip Oommen is the CEO.

Additional Information

• Hazira:
• Hazira is a suburb and a transshipment port in Surat City in the Gujarat state of India. It is the westmost end of Surat.
• Hazira is one of the major ports of India and the most important element of the Surat Metropolitan Region.

Important Points

• Argument I agrees with the statement and justifies it by explaining that dental treatment is costly so it will be good for the employees if covered by insurance. So, Argument I is strong.
• Argument II disagrees with the statement. It would be unreasonable if necessary cosmetic changes that are expensive are not considered. Minor cosmetic changes are inevitable sometimes in treatments like burns and injuries too. So, argument II is not strong.

Hence the correct answer is option 3.

The correct answer is M.N. Roy.

• M.N.Roy first gave the idea of ​​Constituent Assembly for India.

Key Points

• An official demand for a Constituent Assembly to frame the Constitution of India was made for the first time by Indian National Congress in 1935.
• Finally, in 1940, this demand was accepted by the British Government in the August Offer.

Additional Information

• The idea of a Constituent Assembly for India for the first time was put forward by M.N. Roy was a pioneer of the communist movement in India in 1934.
• On behalf of the Indian National Congress, Jawaharlal Nehru declared that the Constitution of free India must be framed by a Constituent Assembly elected on the basis of the adult franchise without outside interference.
• At the point when this interest was acknowledged by the August Offer Sir Stafford Cripps, an individual from the bureau, came to India in 1942 with a draft proposal of the British Government on the outlining of an autonomous Constitution to be received after World War II.
• As the Muslim League wanted India to be divided into two autonomous states with two separate Constituent Assemblies, thus they rejected the Cripps Proposals.
• Under this scheme formulated by the Cabinet Mission Plan, in November 1946, the Constituent Assembly was constituted. The Constituent Assembly was to be a partly nominated and partly elected body.

Important Points

• The elections to the Constituent Assembly were held in July-August 1946.
• 208 seats were won by the Indian National Congress, 73 seats by the Muslim League, and 15 by the small groups and independents.
• However, the princely states were allotted 93 seats but these were not filled as they decided to stay away from the Constituent Assembly.

The logic followed here is:-

  - arrow moves 90^° clockwise direction in each step.

 moves 90° anticlockwise direction in each step

Hence, "option 4" is the correct answer.

Given:

$\left(-\sqrt{\frac{144}{576}}\right) \times - (\frac{16}{\sqrt{64}})$

Calculation:

$\left(-\sqrt{\frac{144}{576}}\right) \times - (\frac{16}{\sqrt{64}})$

⇒ (-12/24) × (-16/8)

⇒ 1

∴ The required value of $\left(-\sqrt{\frac{144}{576}}\right) × - \frac{16}{\sqrt{64}}$is 1.

The correct answer is Nitesh Tiwari.

• Nitesh Tiwari was awarded the Best Director Award for the film Dangal for the 64th National Awards 2017.
• 16-year-old Zaira Wasim, who played Aamir Khan's on-screen daughter in Dangal, won her first National Award. Zaira won the award for her portrayal of young Geeta Phogat.

Key Points

• Nitesh Tiwari is a writer and director, known for Dangal (2016), Chhichhore (2019) and Bareilly Ki Barfi (2017).
• He made his directorial debut by co-directing Chillar Party (2011) which won the National Film Award for Best Children's Film for that year.
• In 2016, Tiwari scripted and directed Dangal which was screened at the Beijing International Film Festival in April 2017 and second BRICS festival in June 2017.
• Nitesh Tiwari Awards are:
• National Film Award for Best Feature Film in Hindi (2021).
• Filmfare Award for Best Director (2017).
• National Film Award for Best Screenplay (2012).
• Screen Award for Best Dialogue (2017).

Shortcut Trick

Net Speed = Original Speed − Decrease in Speed = P − Q km/h.

Using Speed = Distance ÷ Time.

P − Q = 1 ÷ R.

∴ The correct answer is 1/R = P − Q.

Alternate Method

Given:

Original Speed = P km/h

Reduction in Speed = Q km/h

Distance = 1 km

Time = R hours

Formula Used:

Speed = Distance / Time

Calculations:

⇒ Effective Speed = P − Q

⇒ (P − Q) = 1 / R

⇒ 1/R = P − Q

∴ The correct answer is 1/R = P − Q.

Additional Information

Speed-Distance-Time Relation

Distance = Speed × Time. If distance is constant, speed is inversely proportional to time (S ∝ 1/T).

Relative Speed

When two objects move in the same direction, relative speed is the difference of their speeds. Here, the reduction acts as a negative factor on the movement.

Average Speed

Average Speed = Total Distance ÷ Total Time. For different speeds over equal distances, Avg Speed = 2v₁v₂ ÷ (v₁ + v₂).

The correct answer is Khel Ratna Award.

• The National Sports Award for continuous outstanding performance for four years is Khel Ratna Award.

Key Points

• Khel Ratna Award:
• Khel Ratna Award is the highest sporting honor of India. It is awarded annually by the Ministry of Youth Affairs and Sports.
• As of 2020, the award comprises a medallion, a certificate, and a cash prize of Rs 25 lakh.
• Khel Ratna Award was established in 1991–1992.
• The award since August 6, 2021, is named after Major Dhyan Chand, an Indian field hockey player, widely regarded as one of the greatest field hockey players of all time.
• The Khel Ratna Award was first received by Viswanathan Anand in the chess game 1992.

Additional Information

• Arjuna Award:
• The Arjuna Award for Outstanding Performance in Sports and Games is the second-highest sporting honor of India**.**
• It was established in 1961.
• Dronacharya Award:
• ​The Dronacharya Award for Outstanding Coaches in Sports and Games in the sports coaching honor of the Republic of India.
• It was established in 1985.

The correct answer is Phenotype.

• The word denotes physical characteristics Phenotype.

Key Points

• The term phenotype refers to the observable physical properties of an organism, these include the organism's appearance, development, and behavior.
• An organism's phenotype is determined by its genotype, which is the set of genes the organism carries, as well as by environmental influences upon these genes.
• Due to the influence of environmental factors, organisms with identical genotypes, such as identical twins, ultimately express nonidentical phenotypes because each organism encounters unique environmental influences as it develops.
• Examples of phenotypes include height, wing length, and hair color.

Additional Information 

• Genotype:
• ​A genotype is an individual's collection of genes.
• The genotype is expressed when the information encoded in the genes' DNA is used to make protein and RNA molecules.
• Monotype:
• A monotypic species is one that does not include subspecies or smaller, infraspecific taxa.
• a monotypic genus is a genus in the special case where a genus and a single species are simultaneously described.

Shortcut Trick

Total Annual Sales = Monthly Sales × 12 = 60,000 × 12 = 7,20,000.

Espresso Sales = 55% of Total Annual Sales.

Espresso Sales = 0.55 × 7,20,000.

Espresso Sales = 3,96,000.

∴ The correct answer is Rs. 3,96,000.

Alternate Method

Given: Average monthly sales = Rs. 60,000, Espresso sales percentage = 55%.

Formulas: Annual Sales = Monthly Sales × 12 | Required Value = (Percentage ÷ 100) × Total Value.

⇒ Monthly sales from Espresso = 55% of 60,000

⇒ Monthly Espresso sales = (55 ÷ 100) × 60,000 = 55 × 600 = Rs. 33,000

⇒ Annual sales from Espresso = Monthly Espresso sales × 12 months

⇒ Annual Espresso sales = 33,000 × 12 = Rs. 3,96,000

∴ The correct answer is Rs. 3,96,000.

Additional Information

Percentage Calculation

To find x% of a value y, use the formula: (x × y) ÷ 100.

Annual Conversion

Always ensure the time period matches the question requirement (1 year = 12 months).

Shortcut Trick

Total ratio parts = 4 (Males) + 7 (Women) = 11 units.

Given, 11 units = 77 People.

1 unit = 77 ÷ 11 = 7.

Total Women = 7 units × 7 = 49.

∴ The correct answer is 49 women.

Alternate Method

Given:

Total number of People = 77

Ratio of Males to Women = 4 : 7

Formula Used:

Value of a specific part = (Ratio of part ÷ Sum of ratios) × Total value

Calculations:

⇒ Sum of ratio parts = 4 + 7 = 11

⇒ Number of Women = (7 / 11) × 77

⇒ Number of Women = 7 × 7

⇒ Number of Women = 49

∴ The correct answer is 49 women.

Additional Information

Ratio and Proportion

A ratio indicates how many times one number contains another. If a quantity is divided in the ratio a:b, the parts are a/(a+b) and b/(a+b) of the total.

Compound Ratio

The compound ratio of two ratios a:b and c:d is (a×c):(b×d).

The correct answer is TDP.

• As of August 2018, TDP political party is currently ruling the state of Andhra Pradesh.
• As of January 2022 YSR congress party, a political party is currently ruling the state of Andhra Pradesh.

Key Points

• The Telugu Desam Party is a regional Indian political party active in the southern states of Andhra Pradesh and Telangana.
• The party was founded by N. T. Rama Rao on 29 March 1982.
• Since 1995 the party has been headed by N. Chandrababu Naidu, former Chief Minister of Andhra Pradesh.
• The party's headquarters is located at NTR Bhavan in Hyderabad.
• TDP was the first regional party to become the main opposition party at the 8th Lok Sabha from 1984 to 1989.
• On 16 March 2018, the TDP walked out of the National Democratic Alliance (NDA).

Additional Information

The correct answer is Mahesh Bhupathi.

• Mahesh Bhupathi is the founder of the International Premier Tennis League.

Key Points

• International Premier Tennis League:
• The International Premier Tennis League was an annual team tennis league that took place in various cities in Asia.
• It was founded in 2013, the elite level exhibition tennis tournament took place for the first time in November 2014.

Additional Information

The correct answer is Unequal.

• An example of the unequal speed of a bus on a congested road.

Key Points

• In a crowded road, moving through different traffic conditions, a bus travels at different speeds at different points of time. So, this is an example of unequal motion.
• Unequal motion:
• This type of motion is defined as the motion of an object in which the object travels with varied speed and it does not cover some distance in equal time intervals, irrespective of the time interval duration.

Additional Information

• Uniform motion:
• This type of motion is defined as the motion of an object in which the object travels in a straight line and its velocity remains constant along that line as it covers equal distances in equal intervals of time, irrespective of the duration of the time.
• Circular Motion:
• ​In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path.
• Linear motion:
• ​Linear motion, also called rectilinear motion, is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension.

The correct answer is no work done occurs.

• No work done occurs when the direction of force is applied and the direction of motion of the object is perpendicular to each other.

Key Points

• Force: It is defined as the push/pull which is required to change the state of the object.
• Work: It is the amount of force required to move an object.
• Work = Force x Displacement.
• If the direction of applied force and direction, in which an object moves, are perpendicular to each other, then the work is done = 0 i.e no work is done.
• Work is done only when a certain force is applied to an object and the object moves a certain distance in the direction of the applied force. Hence work done is zero when the direction is perpendicular.

Given:

$\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{...}}}}}$

Concept used:

Middle term factor

Calculation:

Let $\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{...}}}}}$ be P.

So,

P = $\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{...}}}}}$

⇒ P² = 30 + $\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{...}}}}}$

⇒ P² = 30 + P

⇒ P² - P - 30 = 0

⇒ (P - 6) (P + 5) = 0 

So, P = 6 (∵ Sum of positive numbers can't be negative)

∴ The value of $\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{...}}}}}$ is 6.

Shortcut Trick

Ratio of Normal Speed to Reduced Speed = 1 : (1 − 1/5) = 5 : 4.

Since Distance is constant, Time Ratio is the inverse of Speed Ratio = 4 : 5.

Difference in time units = 5 − 4 = 1 unit → 16 min.

Normal Time = 4 units = 4 × 16 = 64 min = 64/60 hours.

Distance = 90 km/hr × 64/60 hr = 96 km.

∴ The correct answer is 96 km.

Alternate Method

Given:

Normal average speed (S₁) = 90 km/hr

Speed reduction = 1/5 of normal

Time increase = 16 min = 16/60 hr = 4/15 hr

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Reduced speed (S₂) = 90 − (1/5 × 90) = 90 − 18 = 72 km/hr

⇒ Let the length of the stretch be D km.

⇒ Time taken at normal speed = D/90 hours

⇒ Time taken at reduced speed = D/72 hours

⇒ According to the question: D/72 − D/90 = 16/60

⇒ (5D − 4D) / 360 = 4/15

⇒ D / 360 = 4 / 15

⇒ D = (4 × 360) / 15

⇒ D = 4 × 24 = 96 km

∴ The correct answer is 96 km.

Additional Information

Speed-Time Relationship

When distance is constant, speed is inversely proportional to time (S ∝ 1/T). If speed becomes x/y of original, time becomes y/x of original.

Average Speed Formula

For two equal distances traveled at speeds x and y, the Average Speed is given by (2 × x × y) / (x + y).

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert minutes to hours, divide the value by 60.

The logical Venn diagram is given below:-

Conclusion:

1. Some monkeys are human. → False (it is possible but not definite)
2. No monkey is human..→ False (it is possible but not definite)

• Statements 1 and 2 form a complementary pair.
• Therefore, "either statement 1 or 2 follows.."

Hence, "option 4" is the correct answer.

The least possible Venn diagram is as follows:

Conclusion:

I. Some apples are not violets. → False (as can be seen in the Venn diagram, this is not possible because all apples are violets)

II. All horses being train is a possibility. → True (the possibility exists as shown in the below Venn diagram).

• Possibility diagram for conclusion II:

Hence, "Conclusion II follows" is the correct answer.

Note: In the original paper, the second conclusion was "Some violets being train is a possibility." and it was stated as true. This is incorrect. So, we have changed it.

The family tree is given below:-

The son of N is the cousin of Y.

Hence, "option 3" is the correct answer.

Shortcut Trick

Apply the Tangent-Secant Theorem: (Tangent)² = (Outer Part of Secant) × (Whole Secant).

Let BD = x cm. Then AD = (x + 7) cm.

⇒ DE² = BD × AD

⇒ 12² = x × (x + 7)

⇒ 144 = 9 × (9 + 7) = 9 × 16 (By observation or solving quadratic)

⇒ x = 9 cm

∴ The correct answer is 9 cm.

Alternate Method

Given:

Length of chord AB = 7 cm

Length of tangent DE = 12 cm

Formula Used:

According to the Tangent-Secant Theorem, if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

DE² = BD × AD

D B A E O 7 cm

The logic followed here is:-

• We have

 in figure A, B, and, C

• In figure D, there is an additional line segment.  

Thus, Figure D is different from others.

Hence, "option 4" is the correct answer.

The correct answer is Philippines.

• The Philippines is the headquarter of the Asian Development Bank.

Key Points

• Asian Development Bank is an international development finance institution whose mission is to help its developing member countries reduce poverty and improve the quality of life of their people.
• Asian development bank established in 1966, ADB is owned and financed by its 67 members, of which 48 are from the region and 19 are from other parts of the globe.
• Under Strategy 2020, a long-term strategic framework adopted in 2008, ADB will follow three complementary strategic agendas: inclusive growth, environmentally sustainable growth, and regional integration.
• As of now January 2022 the president of the Asian development bank is Masatsugu Asakawa.

Key Points

The correct answer is Bahadur Shah Zafar.

• Bahadur Shah Zafar was prosecuted for leading the rebels of the Revolt of 1857 and exiled to Rangoon, where he died in 1862.

Key Points

• The Indian Rebellion of 1857 was a major uprising in India in 1857–58 against the rule of the British East India Company, which functioned as a sovereign power on behalf of the British Crown.
• The main centers of revolt, commonly known as the sepoy mutiny in these regions namely Kanpur, Lucknow, Bareilly, Jhansi, Gwalior, and Arrah in Bihar.
• The impact that the revolt of 1857 created was to develop unity & patriotism among the nation.

Additional Information

• Leaders of Revolt of 1857:

Important Points

• Bahadur Shah Zafar:
• He was born in 1775 in old Delhi.
• Bahadur Shah Zafar ascended the Mughal throne in 1837 at the age of 62.
• Zafar had been on the throne for twenty years when the First War of Independence took place in 1857.
• On 4th December 1858, Zafar along with his family was transported from Diamond Harbor to Rangoon on the Ship Magoera.

The correct answer is Chemical properties.

• Elements in the same group have the same chemical properties.

Key Points

• The elements in the periodic table are arranged according to the Modern periodic law.
• It states that the physical and chemical properties of the elements are periodic functions of their atomic numbers.
• The physical and chemical properties depend on the number of valence electrons in an atom.

Additional Information

• A vertical column in the periodic table of elements is called a group.
• There are a total of 18 groups present in the periodic table. In the basic theme of organization of elements in the periodic table, elements having a similar outer electronic configuration in their atoms are arranged in the same group.
• So, we should know that an element’s group number also denotes the number of electrons present in its outermost shell or valence shell.
• These valence electrons are responsible for the vast majority of physical properties, chemical properties, and reactivities of the elements.
• If the valence shell electronic configuration remains the same within a group, physical and chemical properties tend to remain somewhat consistent.

Given: 14Q16P4R7S10

 

• After replacing the symbols with their meanings, we get: 14 × 16 ÷ 4 + 7 - 10

14 × 16 ÷ 4 + 7 - 10

= 14 × 4 + 7 - 10

= 56 + 7 - 10

= 63 - 10

= 53

Hence, "53" is the correct answer.

The correct answer is Mustard.

• Mustard is known as a bisexual flower.

Key Points

• Bisexual Flower:
• The flowers which contain both male and female reproductive organs are known as full or bisexual flowers.
• The bisexual flower will self-pollinate themselves.
• Examples: Tulip, Sunflower, and Lily.
• **Unisexual flowers:**​
• The flowers which contain only the male or female reproductive organs are called unisexual flowers. They are called incomplete flowers. To reproduce they undergo cross-pollination.
• They do not have both stamen and carpels.
• Examples: Papaya, White mulberry, and Watermelon.

Additional Information 

Important Points

• Mustard is a bisexual flower. Here the male reproductive system is stamens and the female reproductive system is the pistil.

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

If the first half of the above series is reversed then:-

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

• 18th term from the right end = K
• 7 T % 5 K S A 2 # R 3 & N Y + X B / L Q @ 1
• 15th term to the right of K = Q
• 7 T % 5 K S A 2 # R 3 & N Y + X B / L Q @ 1

Hence, "Q" is the correct answer.

The correct answer is Hind Swaraj.

• Hind Swaraj's book was written by Mahatma Gandhi.

Key Points

• Gandhi was an Indian lawyer, anti-colonial nationalist, and political ethicist who employed nonviolent resistance to lead the successful campaign for India's independence from British rule.
• His birthday (2nd October) is commemorated worldwide as International Day of Nonviolence.
• Mohandas Karamchand Gandhi was assassinated in the garden of the former Birla House.
• Gandhi Ji set up a small colony, Tolstoy Farm at an 1100 acre site, 21 miles from Johannesburg, South Africa for his colleagues in the Satyagraha struggle.
• Books are written by Mahatma Gandhi:
• The Story of My Experiments with Truth (1927).
• Hind Swaraj (1909).
• India of my dreams (1947).
• Satyagraha in South Africa (1928).

Additional Information

Shortcut Trick

Total time for Amit = 7 × 2 = 14 days.

Total time for Alam = 9 × 2 = 18 days.

Combined time = (Product) ÷ (Sum) = (14 × 18) ÷ (14 + 18).

Combined time = 252 ÷ 32 = 63/8 days.

∴ The correct answer is 63/8 Days.

Alternate Method

Given: Amit completes 1/2 work in 7 days. Alam completes 1/2 work in 9 days.

Formula Used: Total Days = Total Work ÷ Combined Efficiency

⇒ Amit full work days = 7 ÷ (1/2) = 14 days.

⇒ Alam full work days = 9 ÷ (1/2) = 18 days.

⇒ LCM of 14 and 18 = 126 (Total Work).

⇒ Total Efficiency = 9 + 7 = 16.

⇒ Required Days = 126 ÷ 16 = 63/8 days.

∴ The correct answer is 63/8 Days.

Additional Information

Combined Work Formula

If A does a work in x days and B in y days, together they take (xy)/(x+y) days.

Efficiency and Time

Efficiency is inversely proportional to time. If time ratio is a:b, efficiency ratio is b:a.

Fractional Work

If 1/n part of work is done in T days, full work is completed in n × T days.

The correct answer is Red Brown.

Key Points

• Rust, commonly referred to as oxidation, occurs when iron or metal alloys that contain iron, such as steel, are exposed to oxygen and water for a long period of time.
• Rust forms when iron undergoes the process of oxidation but not all oxidation forms rust. As stated previously, only iron or alloys that contain iron can rust, but other metals can corrode in a similar way.

Additional Information

• Corrosion:
• Corrosion occurs when an element that easily loses its electrons (like some metals) combines with an element that absorbs extra electrons (oxygen) and then comes into contact with an electrolyte solution (water).
• The job of the water in the corrosion process is to accelerate the flow of electrons from the metal to oxygen.
• This process is called a redox reaction and is actually two chemical processes that happen at the same time: reduction and oxidation.​

Important Points

• Reduction:
• A reduction Reaction refers to a reaction in which either the addition of Hydrogen takes place or the removal of oxygen takes place.

Oxidation:

• Oxidation Reaction refers to a reaction in which either the addition of Oxygen takes place or the removal of Hydrogen takes place.

The correct answer is a rear mirror.

• In the rear mirror, a concave mirror is not used.
• A rear-view mirror is a flat mirror in automobiles and other vehicles, designed to allow the driver to see rearward through the vehicle's rear window.

Key Points

• Magnification: In a concave mirror, the magnification is the ratio of the height of the image to the height of the object.
• When the image is real, the magnification will be negative because the real image is inverted.
• When the image is virtual, the magnification will be positive because the virtual image is erect.
• The concave mirror can form a magnified image when the object is kept at a certain distance.

Additional Information

The logic followed here is:-

The knife is used by a butcher.

Similarly,

Scissors are used by a hair dresser.

Hence, "option 1" is the correct answer.

The correct answer is Plantae.

• In Plantae, all organisms, are multicellular eccentric with a cell wall.

Key Points

• Plantae is a taxonomic group that includes land plants and green algae.
• In the older classification of organisms, there are basically five kingdoms according to Robert Whittaker: Animalia, Plantae, Fungi, Protista, and Moner.
• Kingdom Plantae includes multicellular, (mostly) autotrophic eukaryotes that (usually) conduct photosynthesis.

Additional Information

• Protista:
• ​A protist is any eukaryotic organism that is not an animal, plant, or fungus. While it is likely that protists share a common ancestor, the exclusion of other eukaryotes means that protists do not form a natural group or clade.
• Monera:
• ​Monera is a biological kingdom that is made up of prokaryotes. As such, it is composed of single-celled organisms that lack a true nucleus. The taxon Monera was first proposed as a phylum by Ernst Haeckel in 1866.
• Animalia:
• ​Animals are multicellular, eukaryotic organisms in the biological kingdom Animalia.
• With few exceptions animals consume organic material breathe oxygen, are able to move can reproduce sexually and go through an ontogenetic stage in which their body consists of a hollow sphere of cells the blastula during embryonic development.

Given that:-

X, Y, T, U, and V, when arranged in ascending order of their weights.

1. X weighs less than T. U weighs twice as much as T.

• X < T, U = 2T ⇒ X < T < U
• Here, there is no information about Y and V. Therefore, statement 1 alone is not sufficient.

2. The weight of Y and V is less than that of X.

• Y and V < X
• No information is given about T and U. Therefore, statement 2 alone is not sufficient.

From statements 1 and 2 we get the following cases:

• Case 1: Y < V < X < T < U
• Case 2: V < Y < X < T < U
• So, either V or Y would be second from the beginning.

Thus, statements 1 and 2  both are not sufficient to answer the question.

Hence, "option 4" is the correct answer.