RRB Group D Previous Year Paper (Held on: 26 Aug 2022 Shift 3)

The correct answer is 'Both the statements are true'.

Key Points

• The neutralization process between an acid and a base produces the compound known as salt.
• Strong acid and strong base react to generate salts, which are naturally neutral since the bonds within the salt solution are stable. They often hydrate without hydrolyzing and have a pH value of 7.
• Strong base and weak acid react to generate salts that are basic in nature and have a pH higher than 7.
• Strong acid and weak base react to generate salts that are acidic in nature and have a pH lower than 7.
• Depending on the types of acids and bases involved, salts created by neutralizing weak acids and weak bases might be acidic, basic, or neutral.

Additional Information

• The pH is calculated as the negative logarithm of the concentration of H+ ions. So, the significance of pH as the power of hydrogen is validated.
• The pH scale has a 0–14 range. Materials can be identified as an acid or a base using litmus paper. To identify the type of chemical being tested, compare the colour of the paper to the pH scale values.
• Neutral solutions are those whose pH value on the pH scale is equal to 7.

The correct answer is Common salt, carbon dioxide and ammonia

Key Points

• The Solvay process is an industrial method for producing sodium carbonate (soda ash), from which baking soda can subsequently be obtained by a simple conversion process.
• The key raw materials for the Solvay process are:
• Sodium chloride (NaCl): Common salt, which serves as the source of sodium ions.
• Ammonia (NH₃): Ammonia is used to react with carbon dioxide and water to form ammonium bicarbonate.
• Carbon dioxide (CO₂): Introduced into the reaction, carbon dioxide reacts with the ammonium bicarbonate to precipitate out sodium bicarbonate.

Shortcut Trick

Total number of observations = 7

Total Sum = Mean × 7 = 30 × 7 = 210

Sum of numeric values = 22.5 + 56 + 42.5 + 1 − 2 + 36 = 156

Sum of variable terms = 2x + x + 3x = 6x

6x = 210 − 156 = 54 ⇒ x = 9

∴ The correct answer is 9.

Alternate Method

Given: Observations are 22.5, 56, 42.5, 2x+1, x−2, 3x, 36. Mean = 30.

Formula Used: Mean = (Sum of all observations) ÷ (Total number of observations)

⇒ Sum of observations = 22.5 + 56 + 42.5 + (2x + 1) + (x − 2) + 3x + 36

⇒ Sum = (22.5 + 56 + 42.5 + 1 − 2 + 36) + (2x + x + 3x)

⇒ Sum = 156 + 6x

⇒ 30 = (156 + 6x) ÷ 7

⇒ 30 × 7 = 156 + 6x

⇒ 210 = 156 + 6x

⇒ 6x = 210 − 156

⇒ 6x = 54

⇒ x = 54 ÷ 6

⇒ x = 9

∴ The correct answer is 9.

Additional Information

Sum of Deviations

The sum of deviations of all observations from their arithmetic mean is always zero, i.e., Σ(x_i − x̄) = 0.

Change of Origin and Scale

If a constant k is added to or subtracted from every observation, the new mean becomes Old Mean ± k. If every observation is multiplied by k, the new mean becomes Old Mean × k.

Combined Mean

If two groups have n₁ and n₂ observations with means x̄₁ and x̄₂ respectively, the combined mean is (n₁x̄₁ + n₂x̄₂) ÷ (n₁ + n₂).

The correct answer is 'Only Statement II is correct'.

Key Points

• The arrangement of chemical elements in rows and columns is called a periodic table.
• The atomic radius decreases as we move from left to right in a period as a result of an increase in effective nuclear charge.
• Atomic radius increases along the group as we move from top to bottom because the principal quantum number increases, increasing the number of shells and the shielding effect in the process.
• Ionic radii decrease along the periodic table from left to right and increase down the group from top to bottom.

The correct answer is 'Tuberculosis'.

Key Points

• The contagious diseases spread through sexual contact are known as sexually transmitted diseases or STDs.
• Some of the commonly found STDs are AIDS, gonorrhea, syphilis, genital herpes and warts, chlamydiosis, and hepatitis-B.
• STDs can be caused by disease causing bacterias, viruses, or parasites.
• Tuberculosis is a bacterial infection affecting the lungs and is transmitted to others through air.

The correct answer is HCl + KOH → KCl + H2O.

Key Points

• When two reactants exchange ions to create two new compounds, the reaction is referred to as a double displacement reaction.
• Typically, a precipitate is the end product of double displacement processes.
• The reactants may form covalent or ionic chemical bonds with one another.
• The general form of double displacement reaction is: AB + CD → AD + CB.

Given:

• Resistance of resistor is 6 Ω.
• Resistance of resistor is 12 Ω.
• Resistors A and B are connected in parallel to a battery to a battery of 3V.

​Formula Used:

• Equivalent Resistance (for parallel), ${ 1 \over R_{eq}} = {1 \over R_{1}} + {1 \over R_{2}}$
• Current,$I= {V \over R}$
• Energy, $E=VIt$

Calculations:

Equivalent Resistance,

${ 1 \over R_{eq}} = {1 \over A} + {1 \over B}\ \implies { 1 \over R_{eq}} = {1 \over 6} + {1 \over 12}\ \implies { 1 \over R_{eq}} =0.25\ \implies R_{eq}=4 \Omega$

Current,

$I= {V \over R}\ \implies I= {3 \over 4}\ \implies I=0.75A$

The total energy supplied by the battery to the circuit in 1 second can be given as,

$E=VIt\ \implies E=3\times 0.75 \times 1\ \implies E=2.25J$

Therefore, the total energy supplied by the battery to the circuit in 1 second is 2.25J.

The correct answer is "Mica". 

Key Points

The inorganic materials that are found naturally as minerals. They can be found in a variety of settings. Crystalline structures and specific chemical compositions are characteristics of minerals.

• Metallic minerals are those that contain metals in their natural state.
• Examples of metallic minerals include bauxite, gold, silver, copper, and iron.
• Minerals without any metal content are referred to as non-metallic minerals.
• When non-metallic minerals are liquefied, nothing new can be made from them, making them a unique class of chemical elements.
• Minerals like limestone, mica and gypsum, coal, and petroleum are examples of non-metallic minerals.
• Inorganic, non-metallic silicate makes up the majority of mica's chemical makeup.

The pattern followed here is:

Thus, the correct answer is 'JTA-36'.

Given: 

The circle represents girls, the triangle represents science students, and the rectangle represents PG students. The numbers in different sections indicate the number of persons. 

Here, PG students are girls who are Not science students are '13'.

Hence, the correct answer is Option (4).

The correct answer is Very reactive.

Key Points

• Non-metallic chemical element silicon (Si) is a member of the carbon family.
• The octahedral crystalline structure of pure silicon is a hard, dark grey solid with a metallic lustre.
• Since pure silicon is too reactive to be found in nature, it is instead mixed with other elements or oxygen to form silica, which is present in almost all rocks, sand, clays, and soils.
• the long chain compounds formed by silicon are very reactive.

Additional Information

• Reactivity is the ease with which one substance reacts chemically with another.
• The arrangement of metals in descending order of their reactivities is referred to as the "metal reactivity series", sometimes known as the "activity series".
• The susceptibility of an anion to become polarised by a cation is known as polarizability. When the degree of polarization is very low, an ionic bond is created, and when it is very high, a covalent bond is created.

Given: 

A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2, and so on till the topmost floor is numbered 6.

1.  E lives on the floor immediately below F's floor. D lives on the 2^nd  floor.

 2. C lives on the floor immediately below A's floor.

   Case 3 is eliminated, case 2 and case 1 are considered.

 3. F does not live on the 5^th floor.

 Case 1 is eliminated and case 2 will be considered.

4. On which floor does B live:

Thus, B lives on the '1^st  Floor'.

Given:

99.01 ÷ 10.93 + 6.987 × 16.01 = ?

Concept used:

This question will be solved by BODMAS rule.

Calculation:

99.01 ÷ 10.93 + 6.987 × 16.01 

Division will be solved first:

$={99.01\over10.93}+6.987\times16.01\={9901\over1093}+6.987\times16.01\=9.058+6.987\times16.01$

Now multiplication will be solved:

$=9.058+111.861\=120.919$

This is approximately equal to 121.

Thus the correct answer is 'Option 3' .

The correct answer is Cl, Br, I.

Key Points

• Johann Wolfgang Dobereiner, a German scientist, discovered Dobereiner's triads, which are collections of elements with related properties.
• He noticed that triads—groups of three elements—could develop in which all the components had comparable physical and chemical characteristics.
• According to  Dobereiner's law of triads, the atomic masses of the first and third elements in a triad will approximately equal the atomic masses of the second element in that triad.
• Halogens, chlrone (Cl), bromine (Br), and iodine (I) together form a triad and is an example of Dobereiner's triads.

Shortcut Trick

Using the effective percentage change formula: a + b + (a × b)/100

Here, a = −16% (decrease) and b = +25% (increase).

Net Change = −16 + 25 + (−16 × 25)/100

Net Change = 9 − 400/100 = 9 − 4 = 5%

∴ The correct answer is 5% increase.

Alternate Method

Given: Initial decrease = 16%, Subsequent increase = 25%.

Formula: Net Change % = [Final Value − Initial Value] / Initial Value × 100

⇒ Let Initial Salary be 100 units.

⇒ Salary after 16% decrease = 100 − 16 = 84 units.

⇒ Salary after 25% increase = 84 + (25% of 84)

⇒ 25% of 84 = 84 ÷ 4 = 21.

⇒ Final Salary = 84 + 21 = 105 units.

⇒ Net change = 105 − 100 = 5%.

∴ The correct answer is 5% increase.

Additional Information

Successive Percentage Change

When a value is changed by x% and then by y%, the net change is given by (x + y + xy/100)%. Use positive for increase and negative for decrease.

Ratio Method

Convert percentages to fractions. Final Ratio = (Initial Ratio) × (Multiplier 1) × (Multiplier 2). For 16% decrease, multiplier is 21/25; for 25% increase, multiplier is 5/4.

Base Change Rule

If salary increases by x%, to return to the original salary, it must decrease by [x/(100+x)] × 100%.

The correct answer is Gulzarilal Nanda.

Key Points

• The Planning Commission is a department of the Indian government, formed on March 15, 1950, to oversee the economic and social growth of the nation, primarily through the creation of five-year plans.
• The head of the serving government, the Prime Minister of India, also happen to be the chairman of the Planning Commission.
• The first Prime Minister of India, Jawaharlal Nehru was the Chairman of Planning Commission .
• Former Indian Prime Minister Gulzarilal Nanda served as the first deputy chairman of the planning commission from 17 February 1953 until 21 September 1963.
• Planning commission is currently abolished. Today, the Planning Commission is known as NITI Aayog.
• The Planning Commission of India's deputy chairperson is chosen by the central cabinet because the prime minister serves as the body's ex-officio chair.
• Mr Montek Singh Ahluwalia is the former and current deputy chairperson of the Planning Commission.

Additional Information

• Vallabhbhai Jhaverbhai Patel:
• ​Vallabhbhai Jhaverbhai Patel, also known as Sardar Patel, was an Indian lawyer, statesman, and powerful political figure.
• From 1947 until 1950, he held the positions of India's first Deputy Prime Minister and Home Minister.
• He was a lawyer and a prominent member of the Indian National Congress who led the country's independence movement and oversaw its fusion into a single, sovereign state.
• KC Neogy:
• ​Kshitish Chandra Neogy, popularly known as KC Neogy, was a politician from West Bengal, India.
• He served as the chairman of India's first finance commission and was a member of the country's first independent cabinet as well as the Indian Constituent Assembly.
• Neogy, an Indian National Congress member, was chosen to represent Bengal in the Central Legislative Assembly in 1920, 1923, 1926, and 1930.
• He was re-elected to the body in subsequent elections.
• Jawaharlal Nehru:
• ​Jawaharlal Nehru was a prominent figure in India around the middle of the 20^th century.
• He was an anti-colonial patriot, secular humanism, social democrat, statesman, and author.
• He was appointed India's first Prime Minister in 1947, taking power for 16 years.
• Nehru greatly influenced India's development into a modern nation in the 1950s by promoting parliamentary democracy, secularism, science, and technology.

The correct answer is "NABARD".

Key Points

• The beginning of the micro finance movement in India could be traced to the selfhelp group (SHG) - bank linkage programme (SBLP) started as a pilot project in 1992 by National Bank for Agricultural and Rural Development (NABARD).
• This programme not only proved to be very successful, but has also emerged as the most popular model of micro finance in India. \
• Other approaches like micro finance institutions (MFIs) also emerged subsequently in the country.

The logic followed here is:

 Hence, '228' is the correct answer.

Given:

• An object is placed in front of a concave mirror
• Focal length, f = -12 cm(since it is a concave mirror so f is negative)
• Object distance, u = -8 cm.

Formula Used:

Mirror Formula, ${1 \over f} = {1 \over v}+ {1 \over u}$

Calculations:

Using the mirror formula, we get

${1 \over f} = {1 \over v}+ {1 \over u}\ \implies {-1 \over 12} = {1 \over v}+ {-1 \over 8}\ \implies {1 \over v} = {-1 \over 12} +{1 \over 8}\ \implies {1 \over v} ={1 \over24} \ \implies v = 24 cm$

Therefore, the image of the concave mirror is formed at a distance (v) of 24 cm.

Shortcut Trick

Total Work (LCM of 12, 20) = 60 units.

Efficiency of (A + B) = 60 ÷ 12 = 5; Efficiency of A = 60 ÷ 20 = 3.

Efficiency of B = 5 − 3 = 2.

If B works half-day, his efficiency = 2 × 1/2 = 1.

New combined efficiency = 3 + 1 = 4 units/day.

Time taken = 60 ÷ 4 = 15 days.

∴ The correct answer is 15 days.

Alternate Method

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

⇒ Efficiency of B = 5 − 3 = 2 units/day

⇒ Given: B works only for half a day daily.

⇒ Effective Efficiency of B = 2 ÷ 2 = 1 unit/day

⇒ New combined efficiency of (A + B) = 3 (A's full) + 1 (B's half) = 4 units/day

⇒ Total Days = Total Work ÷ Combined Efficiency

⇒ Total Days = 60 ÷ 4 = 15 days

∴ The correct answer is 15 days.

Additional Information

Work and Efficiency Relationship

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

Partial Work Rule

When a person works for a fraction of a day, their effective efficiency for that day is multiplied by that same fraction (e.g., half day = 1/2 efficiency).

Pipes & Cisterns Connection

Similar logic applies to pipes where efficiency represents the rate of flow per unit time.

The correct answer is 5.0 Ω.

Key Points

• The obstruction to current flow in an electrical circuit is measured by resistance.
• The Greek letter omega (Ω) represents the unit of measurement for resistance, known as ohms.
• Georg Simon Ohm, a German physicist who investigated the connection between voltage, current, and resistance, is the subject of the name "Ohm."
• The formula for resistance is given as, $R = {V \over I}$, where R is the resistance in ohms, V is the potential difference in volts and I is the current in amperes.
• When the potential difference and current are found to be 2.0 V and 0.4 A respectively, then the resistance of the wire is given as,

$R = {V \over I}\ \implies R = {2 \over 0.4}\ \implies R = 5 \Omega$

Additional Information 

• A given object's resistance is mostly determined by its material and shape.
• The resistance for a particular material is inversely proportional to the cross-sectional area. Moreover, resistance is inversely proportional to material length.
• Electrical resistance, which is measured with an ohmmeter, is expressed in ohms. The resistance to be measured can be connected to the instrument in parallel or in series using the simplest ohmmeters.

BODMAS Table:

Decoding the information, 

 If '+' and '-' are interchanged and also '×'and '÷' 

Given equation: 10 + 152 × 19 - 2 ÷ 3 

After interchanging '+' and '-' and '×'and '÷' and using the BODMAS rule:

→ 10 - 152 ÷ 19 + 2 × 3

→ 10 - 8 + 2 × 3

 → 10 - 8 + 6

→ 16 - 8 = 8.

Thus, the correct answer is '8'.

Shortcut Trick

Apply the percentage change formula: Percentage more = [r ÷ (100 − r)] × 100

Given r = 20%

Required percentage = [20 ÷ (100 − 20)] × 100

⇒ [20 ÷ 80] × 100 = 1/4 × 100 = 25%

∴ The correct answer is 25%.

Alternate Method

Given: A's salary is 20% less than B's salary.

Let B's salary = 100

⇒ A's salary = 100 − 20% of 100 = 80

⇒ Difference in salary = 100 − 80 = 20

⇒ Required Percentage = (Difference ÷ A's Salary) × 100

⇒ (20 ÷ 80) × 100

⇒ 1/4 × 100 = 25%

∴ The correct answer is 25%.

Additional Information

Percentage Increase/Decrease Rule

If A is r% more than B, then B is [r ÷ (100 + r)] × 100% less than A.

Successive Percentage Change

The net change for two successive changes of x% and y% is given by [x + y + (xy/100)]%.

Fraction Equivalents

20% = 1/5. If value decreases by 1/5, it must increase by 1/(5-1) = 1/4 (which is 25%) to return to original.

The correct  answer is "EOS-04".

Key Points

• India's Polar Satellite Launch Vehicle PSLV-C52 injected Earth Observation Satellite EOS-04, into an intended sun synchronous polar orbit of 529 km altitude at 06:17 hours IST on February 14, 2022 from Satish Dhawan Space Centre, SHAR, Sriharikota
• PSLV C52 has been designed to orbit the 1,710 kg EOS-04 satellite in a 529 km sun-synchronous polar orbit. Two more small satellites will be installed in the PSLV-C52 mission. EOS-04 is a radar imaging satellite that will send high-quality all-weather images of agriculture, vegetation, soil moisture, and more.

The correct answer is People living in urban areas.

Key Points

• A stakeholder is a person with an interest in a particular business.
• Everyone uses forest resources in one form or the other.
• The stakeholders of forest resources include:
• People who live around the forest areas and depend upon the forest resources for sustenance,
• The Government Forest Department, which owns the forest land.
• The industrialists who use forest products for various industrial purposes.
• The enthusiasts for the conservation of wildlife and nature

Additional Information

• The people staying in nearby areas use firewood, thatch, and small timber from the forests.
• Bamboo is used in making huts, and baskets for collecting fruits and food materials.
• Forests are also the sites for hunting and fishing.
• The industries consider the forest as a source of raw materials for the factories.
• Industrialists are not concerned about sustainability.
• Before independence, the stakeholders were free to use forest resources. But after the British took over, access to forest resources was restricted to the forest dwellers. After independence, the government overtook forest departments, but the interest of the people staying in forests was still ignored. A few cultivation practices disturbed the whole biodiversity of the area.

The correct answer is μV > μG > μY.

Key Points

• Dispersion is the splitting of white light into its constituent colours when passed through a glass prism.
• Dispersion is the process by which white light divides into the colors that make up its spectrum, which are violet, indigo, blue, green, yellow, orange, and red (in order).
• The change in refractive index with wavelength is also measured by the dispersion.
• During dispersion of white light by a glass prism, the more a colour component is bent, the more is the refractive index of the glass for that colour component.
• Violet has the shortest wavelength and bent the most and its refractive index is more while red has the longest wavelength and bend the least and its refractive index is least.

The correct answer is "Prayagraj".

Key Points

• In Hinduism, Kumbh Mela is a major pilgrimage and festival. It is celebrated at four river-bank pilgrimage sites in a period of approximately 12 years: the Prayagraj (confluence of the Ganges-Yamuna Sarasvati rivers), Haridwar (Ganges), Nashik (Godavari), and Ujjain (Shipra).
• The festival is characterised by a ceremonial dip in the waters, but it is also a celebration of community exchange with various fairs, schooling, saintly religious discourses, monks or poor people's mass feedings, and entertainment displays.
• As part of his efforts to launch major Hindu gatherings for philosophical discussions and debates along with Hindu monasteries in the Indian subcontinent, the festival is historically attributed to the Hindu philosopher and Saint Adi Shankara of the 8^th century.
• There is, however, no historical literary evidence before the 19^th century of these mass pilgrimages called "Kumbha Mela".
• It has been inscribed on the UNESCO Official List of Humanity's Intangible Cultural Heritage.

The correct answer is (i), (ii), and (iv). 

Key Points

• Villi present in the small intestines of humans are finger-like projections having very thin walls with a rich supply of blood vessels.
• Villi provide a larger surface area in the inner lining of the small intestine and helps in larger absorption of nutrients with the increase in surface area.
• Villi is richly supplied with blood capillaries that helps in the absorption of digested food and carrying it to the blood stream.

The logic followed here is:

For, MGB : NTY

For, THK : GSP

Similarly, for QDF : JWU

Hence, the correct answer is 'Option 2'.

Shortcut Trick

Find individual remainders for each number when divided by 17.

Remainder of 171 ÷ 17 is 1.

Remainder of 172 ÷ 17 is 2.

Remainder of 173 ÷ 17 is 3.

Final Remainder = 1 × 2 × 3 = 6.

∴ The correct answer is 6.

Alternate Method

Given: Expression = 171 × 172 × 173, Divisor = 17.

Formula Used: Rem(A × B × C / K) = [Rem(A/K) × Rem(B/K) × Rem(C/K)] / K

Calculations:

⇒ 171 = (17 × 10) + 1

⇒ 172 = (17 × 10) + 2

⇒ 173 = (17 × 10) + 3

⇒ Required Remainder = (1 × 2 × 3) ÷ 17

⇒ Required Remainder = 6 ÷ 17

⇒ Since 6 is less than 17, the remainder is 6.

∴ The correct answer is 6.

Additional Information

Remainder Theorem

If a number is expressed as a product, the total remainder is the product of individual remainders divided by the divisor.

Negative Remainder Concept

Sometimes using a negative remainder (e.g., 16 ÷ 17 has a remainder of −1) simplifies calculations in large powers.

Property of Multiples

Any number in the form (n × k + r) when divided by k will always yield a remainder of r.

Shortcut Trick

Use the Quadrilateral Hierarchy: Square is the most specific shape.

A Square possesses all properties of a Rhombus (all sides equal) and a Rectangle (all angles 90°).

Therefore, Every Square is a Rhombus is a true statement.

Other statements are false because a Trapezium only needs one pair of parallel sides, and a Rectangle or Parallelogram does not require all sides to be equal.

∴ The correct answer is only d.

Alternate Method

Given Statements:

a) Trapezium → Parallelogram: False. A trapezium requires only one pair of parallel sides, while a parallelogram requires two.

b) Parallelogram → Square: False. A parallelogram does not necessarily have equal sides or 90° angles.

c) Rectangle → Square: False. A rectangle only requires 90° angles; its sides may not be equal.

d) Square → Rhombus: True. A square has four equal sides, which is the defining property of a rhombus.

Calculations:

⇒ A Rhombus is defined as a quadrilateral with all four sides equal.

⇒ A Square is defined as a quadrilateral with all four sides equal and all interior angles equal to 90°.

⇒ Since every Square must have four equal sides, it automatically satisfies the definition of a Rhombus.

⇒ Therefore, the statement Every square is a rhombus is mathematically true.

∴ The correct answer is only d.

Additional Information

Quadrilateral Hierarchy

The hierarchy flows from general to specific: Quadrilateral → Trapezium → Parallelogram → Rhombus/Rectangle → Square.

Properties of a Square

A Square is both a Rectangle (all angles 90°) and a Rhombus (all sides equal).

Trapezium Definition

A Trapezium is a quadrilateral with at least one pair of parallel sides. Every Parallelogram is a Trapezium, but not vice versa.

The correct answer is City councils.

Key Points

• States are required by Article 243Q to create the three types of municipalities listed below in each state.
• Nagar Panchayats (city councils) are for transitional areas, or areas that are changing from being rural to urban.
• Municipal council for a smaller urban area.
• Municipal corporation for a larger urban area.

Shortcut Trick

Effective rate for 2 years at 5% compound interest = 5 + 5 + (5 × 5)/100 = 10.25%.

Total amount percentage = 100% + 10.25% = 110.25%.

Amount = 110.25% of Rs 5,00,000.

Amount = 1.1025 × 5,00,000 = 5,51,250.

∴ The correct answer is Rs 5,51,250.

Alternate Method

Given: Principal (P) = Rs 5,00,000, Rate (R) = 5%, Current age = 16 years, Maturity age = 18 years.

Formula Used: Amount (A) = P(1 + R/100)ⁿ, where n = time period.

⇒ Time (n) = 18 − 16 = 2 years

⇒ A = 5,00,000 × (1 + 5/100)²

⇒ A = 5,00,000 × (105/100) × (105/100)

⇒ A = 5,00,000 × (21/20) × (21/20)

⇒ A = 5,00,000 × (441/400)

⇒ A = 1,250 × 441

⇒ A = 5,51,250

∴ The correct answer is Rs 5,51,250.

Additional Information

Effective Interest Rate for 2 Years

The net percentage change for compound interest over 2 years is calculated using the formula R_eff = x + y + (xy/100).

Difference between CI and SI for 2 Years

The difference between Compound Interest and Simple Interest for 2 years is given by D = P × (R/100)².

Compounding Annually vs Half-Yearly

If interest is compounded half-yearly, the rate is halved (R/2) and the time period is doubled (2n) in the standard formula.

Shortcut Trick

For a mixed recurring decimal, the numerator is the total number minus the non-recurring part.

The denominator consists of as many 9s as there are recurring digits, followed by as many 0s as there are non-recurring digits after the decimal.

Fraction = (13241 − 13) ÷ 99900

Fraction = 13228 ÷ 99900 = 3307 ÷ 24975

∴ The correct answer is 3307/24975.

Alternate Method

Given: x = 0.13241241241...

Formula Used: Conversion of Mixed Recurring Decimals to Vulgar Fractions.

⇒ Let x = 0.13241241...

⇒ Multiply by 100: 100x = 13.241241... (Equation 1)

⇒ Multiply Equation 1 by 1000: 100000x = 13241.241241... (Equation 2)

⇒ Subtract Equation 1 from Equation 2:

⇒ 100000x − 100x = 13241.241... − 13.241...

⇒ 99900x = 13228

⇒ x = 13228 ÷ 99900

⇒ Dividing numerator and denominator by 4:

⇒ x = 3307 ÷ 24975

∴ The correct answer is 3307/24975.

Additional Information

Pure Recurring Decimal

A decimal in which all digits after the decimal point repeat, e.g., 0.333... = 3/9 = 1/3.

Mixed Recurring Decimal

A decimal in which some digits do not repeat and some do, e.g., 0.1222... = (12 − 1)/90 = 11/90.

Rational Number Property

Every terminating or recurring decimal can be expressed in the form p/q and is thus a rational number.

The correct answer is Only (b).

Key Points

 The characteristics of the magnetic field produced by a straight conductor carrying current are:

• Magnetic field lines in the shape of concentric circles are created when electric current flows through a straight conductor.
• The strength of the magnetic field at any point is inversely proportional to the distance of the point from the straight conductor and directly proportional to the current magnitude.
• The direction of the magnetic field lines gets reversed if the direction of the current in the conductor is reversed.

The positions of letters according to the English alphabet series:

 The word can be represented as follows,

Clearly, we can see that 3 such pairs are there HI, ST and AH. 

Hence, the correct answer is Option (2).

The correct answer is "Anurag Thakur".

Key Points

• The passing of the bill, which was introduced by Union Sports Minister Anurag Thakur in December 2021,  in help of establishment of the National Board of Anti Doping in sports, with competent and independent personnel.
• Anti-doping Bill seeks to give NADA powers of 'investigation, levying sanctions for Anti-Doping Rule Violations, the disciplinary procedures to be adopted and the powers of inspection, sample collection and sharing and free flow of information.
• It is intended to provide a "statutory framework for the operation of the National Anti-Doping Agency (NADA), the National Dope Testing Laboratory (NDTL) and other dope testing laboratories and for creation of a National Board for Anti-Doping in Sports to strengthen anti-doping activities in sport.

Given: Six students, K, L, M, N, O and P.

1. M scores more marks than only three other students.

2) L scores more marks than M.

3) O scores more marks than L.

O > L > M > ___ >___ >___

4. K scores more marks than N. 5. P scores more marks than K.

P > K > N

6. P scores less marks than M.

O > L > M > P > K > N

Here, the highest mark scored among all six students is 'O'.

Hence, the correct answer is Option (2).

Given:

• The power of first lens is 8 D.
• The power of second lens is -4 D.

Formula Used:

• Net Power, $P_{net}=P_{1}+P_{2}$
• Focal length, $f={1 \over P}$

Calculations:

Net Power,

$P_{net}=8+(-4)\ \implies P_{net}=+4D$

Since, the net power is positive, the lens combination will act as converging or convex lens.

Focal length,

$f={1 \over P}\ \implies f={1 \over 4}\ \implies f = 0.25 m\ \implies f=25cm$

Therefore, the lens combination will act as a convex lens having focal length 25 cm.

Given: 63547981 

The digits is arranged in ascending order from left to right:

Here, 'Two' numbers 3 and 9 will remain unchanged.

Thus, the correct answer is 'Two'.

The correct answer is "Bombay".

Key Points

• Originally from India, the Indian National Congress is a political party.
• The party was established in 1885, making it the first modern nationalist movement to appear throughout Asia and Africa under the rule of the British Empire. Congress took the lead in the drive for Indian independence at the end of the 19^th century.
• Bombay hosted the Congress's inaugural meeting (Mumbai).

Additional Information

• The anti-colonial nationalist movements in the British Empire were greatly influenced by Congress, which also helped India win its independence from Britain.
• A well-known Bengali lawyer named Womesh Chandra Banerjee presided over the meeting. The meeting hosted 72 attendees from across the country.
• This gathering took place in December 1885, the same month that Calcutta hosted the All-India National Conference.

The correct answer is Diffusion.

Key Points

• Diffusion is the process of spontaneous movement of a substance from a high concentration to a low concentration area.
• There are two types of diffusion, simple diffusion and facilitated diffusion.
• Simple diffusion is the process by which a substance flows through a semipermeable membrane or in a solution without the aid of transport proteins.
• Facilitated diffusion occurs when molecules passively move from a location of higher concentration to a region of lower concentration through the cell membrane using a carrier molecule.
• Some of the factors affecting diffusion are temperature, particle size, region or area of interaction, and the steepness of concentration gradient.

Additional Information

• Gaseous exchange refers to the exchange or interchange of gases during respiration or other processses.
• Osmosis is the transfer of solvent molecules via a semipermeable membrane from an area of lower concentration to a region of higher concentration.
• Blood circulates continuously throughout the body as a result of the heart's pumping function and this process is known as circulation.

Shortcut Trick

For any regular polygon with n sides, the sum of all exterior angles is always 360°.

A regular octagon has n = 8 equal sides.

Measure of each exterior angle = 360° ÷ n = 360° ÷ 8 = 45°.

∴ The correct answer is 45⁰.

Alternate Method

Given: The polygon is a regular octagon.

Formula Used:

Measure of each exterior angle of a regular polygon = 360° ÷ n

Where n is the number of sides of the polygon.

Calculations:

⇒ For a regular octagon, number of sides (n) = 8

⇒ Measure of each exterior angle = 360° ÷ 8

⇒ Measure of each exterior angle = 45°

∴ The correct answer is 45⁰.

Additional Information

Interior Angle of a Regular Octagon

Each interior angle of a regular polygon is given by 180° − (Exterior Angle). For an octagon, it is 180° − 45° = 135°.

Sum of Interior Angles

The sum of interior angles of any polygon with n sides is (n − 2) × 180°. For an octagon, it is (8 − 2) × 180° = 1080°.

Regular Polygon Properties

In a regular polygon, all sides are equal in length and all interior (as well as exterior) angles are equal in measure.

Shortcut Trick

Total Work (LCM of 10, 12) = 60 units.

Efficiency: A = 6, B = 5. Combined (2 days) = 11 units.

In 10 days (5 pairs): 11 × 5 = 55 units. Remaining = 60 − 55 = 5 units.

On 11^th day, A works: Time taken = 5/6 days.

Total Time = 10 + 5/6 = 10(5)/(6) days.

∴ The correct answer is 10(5)/(6) days.

Alternate Method

Given: Time taken by A = 10 days, Time taken by B = 12 days.

Formula Used: Total Work = Time × Efficiency.

⇒ Work done in 1^st day (A) = 6 units

⇒ Work done in 2^nd day (B) = 5 units

⇒ Work done in 1 cycle (2 days) = 6 + 5 = 11 units

⇒ Work done in 5 cycles (10 days) = 11 × 5 = 55 units

⇒ Remaining work = 60 − 55 = 5 units

⇒ On 11^th day, it is A's turn. Time taken by A = 5/6 days

⇒ Total time = 10 + 5/6 = 10(5)/(6) days

∴ The correct answer is 10(5)/(6) days.

Additional Information

Alternate Day Concept

In alternate day work, identify the starting person and the work completed in one full cycle (sum of efficiencies of all participants).

Time and Work Relation

Efficiency is inversely proportional to the time taken to complete the work. Efficiency = Total Work ÷ Time.

Remaining Work Calculation

If the remaining work is less than the efficiency of the person whose turn it is, time taken = Remaining Work ÷ Efficiency.

Given:

• The resistance of A is 10 Ω.
• The resistance of B is 30 Ω.
• A and B are connected in series to a battery of 6V.

Formula Used:

• Equivalent Resistance (for series), $R_{eq}=R_{1}+R_{2}$
• Current, $I= {V \over R}$
• Heat Dissipated, $H=I^{2}Rt$

Calculations:

Equivalent resistance,

$R=A+B\ \implies R = 10 +30\ \implies R =40 \Omega$

Current,

$I={V \over R}\ \implies I = {6 \over 40}\ \implies I = 0.15 A$

Total heat dissipated in the resistors in 1 second,

$H=I^{2}Rt\ \implies H=0.15^{2} \times 40 \times 1\ \implies H = 0.9 J$

Therefore, the total heat dissipated in the resistors in 1 second is 0.90 J.

Shortcut Trick From the quadratic equation x2 − 5x − 14 = 0, identify sum and product of roots. Sum (a + b) = 5 and Product (ab) = −14. The expression a3b2 + a2b3 simplifies to a2b2(a + b) = (ab)2(a + b). Substitute the values: (−14)2 × 5 = 196 × 5 = 980. ∴ The correct answer is 980.

Alternate Method Given quadratic equation: x2 − 5x − 14 = 0 Comparing with standard form Ax2 + Bx + C = 0, we get A = 1, B = −5, C = −14. Using the relations between roots and coefficients: ⇒ Sum of roots (a + b) = −B/A = −(−5)/1 = 5 ⇒ Product of roots (ab) = C/A = −14/1 = −14 Now, we need to evaluate the expression: a3b2 + a2b3 ⇒ Factor out the common term a2b2: ⇒ a3b2 + a2b3 = a2b2(a + b) ⇒ (ab)2 × (a + b) ⇒ (−14)2 × 5 ⇒ 196 × 5 = 980 ∴ The correct answer is 980.

Additional Information Vieta's Formulas for Quadratic Equations For any quadratic equation ax2 + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a. Nature of Roots The nature of roots is determined by the Discriminant (D) = b2 − 4ac. If D > 0, roots are real and distinct; if D = 0, roots are real and equal; if D < 0, roots are complex/imaginary. Formation of Quadratic Equation If roots a and b are known, the equation is given by x2 − (a + b)x + (ab) = 0.

Given:

Conditions:

Given question: # 2264 % 33 & 37 @

Condition 1 → does not follows (the first element is a symbol, but the last element is not a number)

Condition 2 → does not follow (the second element is a number and the second last is not a symbol)

Condition 3 → follow (the question has an equal quantity of even and odd numbers)

So, # 2264 % 33 & 37 @ will be coded as H**A<F<S.

Hence, the correct answer is Option (3).

The correct answer is'Wrinkled, short and white'.

Key Points

• Mendel experiments of inheritance: 
• Pea plant was used by Mendel for this experiment.
• It was chosen because this plant has many contrasting characters like a dwarf and tall or wrinkled or round seeds.
• Gregor Mendel, through his experiments on pea plants, discovered the fundamental laws of inheritance.
• His breeding experiments in pea plants revealed that hereditary characteristics are determined by discrete factors (genes) that are transmitted to the next generation.
• He deduced three laws from his experiments and these laws are applicable when parents are pure breeding.
• The three laws of inheritance proposed by Mendel include:
• Law of Dominance
• Law of Segregation
• Law of Independent Assortment
• Mendel coined terms 'dominant' and 'recessive' in terms of the characters studied by him.
• A dominant trait is one that expresses itself in the presence of other contrasting trait and dominates it. eg: tallness.
• A recessive trait is one that is not expressed when present along with the contrasting trait in the hybrid. eg: dwarfness.​

• Wrinkled, short and white these are the recessive traits in the pea plant.

Shortcut Trick

Length (L) = 12 cm

Breadth (B) = 25% of 12 = 3 cm

Height (H) = 50% of 12 = 6 cm

Total Surface Area = 2 × (LB + BH + LH) = 2 × (36 + 18 + 72) = 2 × 126 = 252 cm²

∴ The correct answer is 252 cm².

Alternate Method

Given:

Length (L) = 12 cm

Breadth (B) = 25% of L = (1/4) × 12 = 3 cm

Height (H) = 50% of L = (1/2) × 12 = 6 cm

Formula Used:

Total Surface Area (TSA) of a cuboid = 2(lb + bh + hl)

Calculations:

⇒ TSA = 2 × (12 × 3 + 3 × 6 + 6 × 12)

⇒ TSA = 2 × (36 + 18 + 72)

⇒ TSA = 2 × 126

⇒ TSA = 252 cm²

∴ The correct answer is 252 cm².

Additional Information

Volume of Cuboid

The capacity of a cuboid is calculated as Volume = Length × Breadth × Height (V = L × B × H).

Lateral Surface Area

The area of the four side walls of a cuboid is LSA = 2 × Height × (Length + Breadth).

Diagonal of Cuboid

The longest rod that can be placed in a cuboid is given by √(L² + B² + H²).

The correct answer is "Tapi River".

 Key Points

• The Tapi River is a river in central India.
• It is one of the major rivers in peninsular India with a length of roughly 724 km and a flow direction from east to west.
• The Tapi River rises to a height of roughly 752 metres near Multai in the Betul district of Madhya Pradesh and flows for a distance of about 724 kilometres before emptying into the Arabian Sea through the Gulf of Cambay.

Additional Information

• There are just three rivers in peninsular India that flow from east to west, the other two being the Narmada River and the Mahi River.
• The second-largest interstate river basin that empties into the west is the Tapi.
• It includes a major portion of the state of Maharashtra as well as portions of Gujarat and Madhya Pradesh.

English alphabet and their positional value:

Given Word: TOMORROW 

Pairs in both forward and backward directions:

Here, 1 such pairs are there i.e. 'OR'.

Hence, the correct answer is Option (2).

The logic followed here is:

Logic: (1^st number × 5) + 3 = 2^nd number.

1) 6 : 33

​     

​2) 11 : 58

  ​

Similarly, for 18 : ?

   ​

​​Hence, the correct answer is '93' .

According to given information, we have the possible arrangements as follows:

1. P is older than only three other persons

• ​​___<<<  P  <<

2. ​ N is older than L.

• ​​L < N

3. ​O is younger than L.

• ​​O < L

4. ​Collectively (2) and (3) can be written as:

• ​​O < L < N

5. ​ M is older than K.

• ​​K <  M

6. ​ P is younger than K.

• ​​P < K

7. ​ Collectively (5) and (6) can be written as:

• ​​P < K < M

8. ​Final arrangement will be:

• ​​O < L < N < P < K < M
• L is second youngest among all 6 persons.

​​Thus the correct answer is 'Option 1' .

Shortcut Trick

The Gain % of 20% can be written in fraction form as 1/5.

This means for every 5 parts of weight given, 1 part is profit.

The ratio of False Weight to True Weight = 5 : (5 + 1) = 5 : 6.

Given that True Weight (6 units) = 1000 gm.

Therefore, False Weight (5 units) = (1000 ÷ 6) × 5 = 833.33 gm.

∴ The correct answer is 833.33 gm.

Alternate Method

Given:

Gain % = 20%

True Weight = 1 kg = 1000 gm

Let the False Weight used by the dealer be 'x' gm.

Formula Used:

Gain % = [(True Weight − False Weight) ÷ False Weight] × 100

Calculations:

⇒ 20 = [(1000 − x) ÷ x] × 100

⇒ 20 ÷ 100 = (1000 − x) ÷ x

⇒ 1 ÷ 5 = (1000 − x) ÷ x

⇒ x = 5 × (1000 − x)

⇒ x = 5000 − 5x

⇒ 6x = 5000

⇒ x = 5000 ÷ 6 = 833.33 gm

∴ The correct answer is 833.33 gm.

Additional Information

Dishonest Dealer Concept

When a dealer sells at Cost Price but uses less weight, the Gain % is calculated as [Error ÷ (True Weight − Error)] × 100.

Profit with Markup and False Weight

If a dealer marks up his goods by x% and uses a false weight of y% less, then Net Profit % = [(100 + x) ÷ (100 − y) × 100] − 100.

Profit with Discount and False Weight

If a dealer offers a discount of d% and uses a false weight, the profit is based on the ratio of the Selling Price of the claimed weight to the Cost Price of the actual weight given.

Shortcut Trick

Ratio of digits (hundreds : tens : units) = 3 : 2 : 1.

Possible number is 321 or 642 or 963.

Check 321: 321 + 123 = 444 (Incorrect).

Check 642: 642 + 246 = 888 (Incorrect).

Check 963: 963 + 369 = 1332 (Correct).

∴ The correct answer is 369.

Alternate Method

Given:

Ratio of Unit digit : Tens digit : Hundreds digit = 1 : 2 : 3.

Sum of number and its reversed number = 1332.

Calculations:

⇒ Let unit digit = x, tens digit = 2x, hundreds digit = 3x.

⇒ Original Number = 100(3x) + 10(2x) + x = 300x + 20x + x = 321x.

⇒ Reversed Number = 100(x) + 10(2x) + 3x = 100x + 20x + 3x = 123x.

⇒ Sum = 321x + 123x = 444x.

⇒ 444x = 1332

⇒ x = 1332 ÷ 444 = 3.

⇒ Reversed Number = 123 × 3 = 369.

∴ The correct answer is 369.

Additional Information

Place Value and Face Value

A number abc is represented as 100a + 10b + c, where a, b, c are the face values and 100, 10, 1 are place values.

Reversing Digits

The difference between a 3-digit number and its reverse is always a multiple of 99: (100a + 10b + c) − (100c + 10b + a) = 99(a − c).

Ratio Proportionality

When digits are in a ratio, they must be integers from 0 to 9. This limits the possible values for the multiplier x.

The correct answer is a.

Key Points

• Inspiration is the process of taking in atmospheric air.
• It is a dynamic process.
• Inspiration occurs when the air pressure drops and the thoracic cavity's volume rises.
• Thoracic cavity capacity increases as external intercostal muscles contract.
• The magnitude of the thoracic activity is further increased by diaphragmatic contraction. At the same time, the lungs expand.
• The internal air pressure of the lungs reduces as they expand.
• As the pressure equalises, the lungs are suddenly filled with atmospheric air.
• At the time of breathing in inhalation process, the air moves from the outside atmosphere into the lungs, the pressure in the lungs is required to be lower than atmospheric pressure.
• During inhalation, the ribs move outwards and the diaphragm lowers or contracts to enhance the volume of the thoracic cavity.

Additional Information

• During inhalation, when the chest expands air enters the lungs.
• This is because during inspiration the diaphragm contracts and moves downwards.
• This leads to an increase in the chest cavity, with the help of the intercostal muscles present between the ribs.
• The chest cavity expands, creating a small vacuum that draws air into the lungs and fills the enlarged alveoli.
• This space is taken up by the lungs when we inhale.

Shortcut Trick

Diameter (d) = 1/2 cm ⇒ Radius (r) = 1/4 cm.

Surface Area of sphere = 4πr².

Surface Area = 4 × π × (1/4)² = 4 × π × (1/16) = π/4 cm².

∴ The correct answer is π/4 cm².

Alternate Method

Given:

Diameter (d) = 1/2 cm

Formula Used:

Radius (r) = Diameter / 2

Surface Area (A) = 4πr²

Calculations:

⇒ Radius (r) = (1/2) ÷ 2 = 1/4 cm

⇒ Surface Area = 4 × π × (1/4)²

⇒ Surface Area = 4 × π × (1/16)

⇒ Surface Area = π/4 cm²

∴ The correct answer is π/4 cm².

Additional Information

Volume of a Sphere

The amount of space occupied by a sphere is given by Volume (V) = (4/3)πr³.

Surface Area of Hemisphere

The Curved Surface Area (CSA) is 2πr² and the Total Surface Area (TSA) is 3πr².

Relationship with Diameter

Surface area can also be expressed in terms of diameter (d) as Area = πd².

Given:

The ratio of adults to children in city A = 5 : 3

Total population of City A = 410400

Formula:

Difference = total population x (difference between ratio / sum of ratio)

Calculation:

Difference between the total number of adults and the total number of children in City A = $410400 \times \frac{5-3}{8}$

= 410400 x $\frac{1}{4}$

= 102,600

Hence, the correct answer is '1, 02, 600'.

Shortcut Trick

Identify the sum (S) and product (P) of the given values x and y.

S = x + y = (2 + √5) + (2 − √5) = 4

P = xy = (2 + √5)(2 − √5) = 2² − (√5)² = 4 − 5 = −1

Apply the algebraic identity: x² + y² = S² − 2P = 4² − 2(−1) = 16 + 2 = 18.

∴ The correct answer is 18.

Alternate Method

Given:

x = 2 + √5

y = 2 − √5

Formula used:

x² + y² = (x + y)² − 2xy

Alternatively, calculate x² and y² individually using (a ± b)² = a² + b² ± 2ab.

Calculations:

⇒ x² = (2 + √5)² = 2² + (√5)² + 2(2)(√5)

⇒ x² = 4 + 5 + 4√5 = 9 + 4√5

⇒ y² = (2 − √5)² = 2² + (√5)² − 2(2)(√5)

⇒ y² = 4 + 5 − 4√5 = 9 − 4√5

⇒ x² + y² = (9 + 4√5) + (9 − 4√5)

⇒ x² + y² = 9 + 9 + 4√5 − 4√5 = 18

∴ The correct answer is 18.

Additional Information

Algebraic Identity for Squares

The fundamental identities are (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Sum and Product relationship

For any two numbers, x² + y² = (x + y)² − 2xy and x² + y² = (x − y)² + 2xy.

Conjugate Surds

Expressions like (a + √b) and (a − √b) are conjugates; their product is always a rational number: a² − b.

The correct answer is "Gospels".

Key Points

• The first of the four New Testament Gospels, which detail the life and death of Jesus Christ, is the Gospel of Matthew.
• Along with the Gospels of Mark and Luke, it is one of the so-called Synoptic Gospels (i.e., those presenting a common view).
• The poem describes St. Matthew the Evangelist, one of the Twelve Apostles and a tax collector, as the author (10:3).

Additional Information

• It is obvious that the Gospel According to Mark, which came before it.
• It had an impact on the Gospel According to Matthew, which was written in Greek, most likely after 70 CE.
• Regarding the plausibility of an earlier Aramaic translation, there has been significant discussion. Several literary cues point to books.

The shadded area represents the Barrels that are only jugs:

Here, Only 4 barrels that are only jugs.

Hence, the correct answer is 'Option 3' .

The logic folloowed here is:

1. 18 : 63

​      

​2) 44 : 154

​     

​3) 54 : ?

​     

​​Thus, the correct option is '189'.

​The correct answer is Mitochondria.

Key Points 

• The majority of archaea, eukaryotes, and bacteria break down glucose using a process known as glycolysis.
• It is in charge of generating compounds that serve as precursors for the metabolic processes carried out inside cells as well as energy and reduced electron carriers.
• Pyruvate can go through either aerobic or anaerobic respiration after glycolysis to go through additional breakdown and release more energy.
• The breakdown of pyruvate using O2 takes place in the mitochondria matrix.
• When glucose gets converted to pyruvate by glycolysis, only a small fraction of the total free energy potentially available from the glucose is released.
• In mitochondria, when the metabolism of sugars is completed: the pyruvate is imported into the mitochondria and oxidized by O2 to CO2 and H2O.
• When oxygen is present, pyruvate enters the Krebs cycle in the mitochondria where it is broken down anaerobically.
• This allows 15 times more ATP to be made as compared to that produced by glycolysis alone.

Shortcut Trick The Empirical Relation is: Median = (Mode + 2 × Mean) ÷ 3 Substitute values: Median = (60 + 2 × 42) ÷ 3 Median = (60 + 84) ÷ 3 = 144 ÷ 3 Median = 48 ∴ The correct answer is 48. Alternate Method Given: Mean of the data = 42 Mode of the data = 60 Formula Used: Empirical Relationship: Mode = 3 × Median − 2 × Mean

Calculations: ⇒ 60 = 3 × Median − 2 × 42 ⇒ 60 = 3 × Median − 84 ⇒ 3 × Median = 60 + 84 ⇒ 3 × Median = 144 ⇒ Median = 144 ÷ 3 ⇒ Median = 48 ∴ The correct answer is 48. Additional Information Empirical Relationship For a moderately skewed distribution, the distance between the Mean and the Mode is approximately three times the distance between the Mean and the Median. Symmetric Distribution In a perfectly symmetrical distribution (like the Normal Distribution), the Mean, Median, and Mode are all equal: Mean = Median = Mode. Negatively Skewed Data When the distribution is negatively skewed (skewed to the left), the values generally follow the order: Mean < Median < Mode. Positively Skewed Data When the distribution is positively skewed (skewed to the right), the values generally follow the order: Mode < Median < Mean.

The correct answer is It increases the amount of waste going into landfills.

Key Points

• Landfills are places designated for the disposal of trash, garbage, and other types of solid waste.
• Historically, they have been the most often used technique of removing solid waste, which is either buried or allowed to accumulate in heaps.
• Due in major part to the increasing amount of waste generated by our homes, businesses, markets, and hospitals, landfills are a common occurrence around the world.

Additional Information

• Some of the landfills included in integrated waste management are well-managed and built.
• But the majority of towns neglect their landfills, causing land degradation and an unchecked buildup of various kinds of solid waste.
• Here are the causes, effects, and remedies of landfills.

Given: Eight students, 1 to 8, are sitting around a circular table facing the center.

1. 1 is the immediate neighbour of both 8 and 2.

​

​2. 3 is sitting second to the right of 1

​

3. ​1 is sitting second to the right of 7. 

​

​4. 5 is the immediate neighbour of 6 and 4.

• ​Two cases are possible here.

​

• In both the cases 3 students are there between 5 and 1.

Hence, the correct answer is Option (4) .

The correct answer is "14 years".

Key Points

• No kid under the age of fourteen may be employed to work in a factory, mine, or in any other hazardous occupation, according to Article 24.
• Children under the age of 14 are never allowed to work in any dangerous jobs, factories, or mines, per this article.
• Children may, however, be employed in non-hazardous jobs.

Additional Information

• Article 23(1): Traffic in human beings and the beggar and other similar forms of forced labour are prohibited and any contravention of this provision shall be an offence punishable in accordance with the law.
• Article 23(2): Nothing in this article shall prevent the State from imposing compulsory service for public purposes, and in imposing such service the State shall not make any discrimination on grounds only of religion, race, caste or class or any of them.

Given:

(Left) G B D F H & 8 * T % 7 D 4 @ 6 K & 2 R P Q T @ Y # 3 5 E * S (Right)

Logic:

Symbols immediately preceded by a letter and also immediately followed by a number is:

There are 4 such symbols in the series which are immediately preceded by a letter and also immediately followed by a number.

Hence, the correct answer is 'Option 2'.

The correct answer is "David Ricardo".

Key Points

• The first step in understanding economic rent is forgetting what you currently think of as rent.
• Economic rent has nothing to do with the more traditional definition of rent, which is a payment in exchange for the use of something for a set period of time.
• Economic rent is what the owner pays for additional services above what is expected.
• International free trade relies heavily on the idea of comparative advantage.
• According to David Ricardo's theory of international trade, which is partly based on Smith's concept of labour specialisation, countries should concentrate on doing whatever they can do more efficiently and then exchange their surplus for items they can't produce efficiently

Additional Information

• Like many of his contemporaries, David Ricardo was not a qualified economist. Although he didn't study economics, he did go to school to become a stock trader.
• He didn't start thinking and writing about economics until after a successful career in the financial markets, when he read Adam Smith's The Wealth of Nations.
• A family of moderate wealth gave birth to Ricardo in 1772; he was the third of seventeen children to be born into the family. Despite disowning David for choosing a non-Jewish spouse, David's father, a rich stockbroker, gave him the connections he needed to pursue a successful career.
• Ricardo built up his own riches and died at the age of 51, leaving three of his own kids.

The correct answer is "FICCI Ladies Organisation".

Key Points

• The industrial park owned by the FICCI Ladies Organization is the first of its kind in the nation.
• On 50 acres of land in Sultanpur, which is close to Patancheru, this park was constructed.
• It cost 250 crore rupees to produce. Already, female business owners are showing a great desire to establish and run their enterprises in this park.

Additional Information

• In his remarks at the park's opening, IT and Industries Minister KT Rama Rao urged business owners to set high goals and begin considering emerging technology.
• Additionally, he suggested that they focus on the manufacture of agricultural, defence, and aerospace products as well as establish international alliances.
• The minister agreed to add an additional 100 acres to the FLO Women's Industrial Park, subject to the park's viability.

Shortcut Trick

Express the base of each term as a prime number.

9⁶ → (3²)⁶ → Base is 3.

12⁴ → (2² × 3)⁴ → Bases are 2 and 3.

7⁷ → Base is 7.

The distinct prime factors are 2, 3, and 7.

Sum = 2 + 3 + 7 = 12.

∴ The correct answer is 12.

Alternate Method

Given: Expression = 9⁶ × 12⁴ × 7⁷

Step 1: Prime Factorization

⇒ 9 = 3²

⇒ 12 = 2² × 3¹

⇒ 7 = 7¹

Step 2: Substitute in the expression

⇒ (3²)⁶ × (2² × 3¹)⁴ × (7¹)⁷

⇒ 3¹² × 2⁸ × 3⁴ × 7⁷

⇒ 2⁸ × 3¹⁶ × 7⁷

Step 3: Identify distinct prime factors

⇒ The distinct prime factors are the bases of the prime powers: 2, 3, and 7.

Step 4: Calculate the sum

⇒ Sum = 2 + 3 + 7

⇒ Sum = 12

∴ The correct answer is 12.

Additional Information

Total Number of Prime Factors

If N = a^p × b^q × c^r where a, b, c are primes, total prime factors = p + q + r.

Distinct Prime Factors

These are the unique prime numbers that divide a given integer, regardless of their exponents in the factorization.

Number of Divisors

Total divisors of N = (p+1)(q+1)(r+1). This includes 1 and the number itself.

Shortcut Trick

Check the degree (highest power) of the variable x in the equation x³ − 3x + 6 = 0.

Highest power = 3 → This is a Cubic Equation.

A Quadratic Equation must have a degree of exactly 2.

Since the degree is 3, it cannot be a quadratic equation.

∴ The correct answer is not a quadratic equation.

Alternate Method

Given Equation: x³ − 3x + 6 = 0

Definition: A polynomial equation is called a quadratic equation if it can be written in the standard form ax² + bx + c = 0, where a ≠ 0 and the highest power of the variable is 2.

⇒ In the given equation x³ − 3x + 6 = 0, the variable is x.

⇒ The exponents of x are 3 and 1.

⇒ The highest exponent (degree) of the equation is 3.

⇒ An equation with degree 3 is known as a cubic equation.

⇒ Therefore, it does not satisfy the condition of being a quadratic equation.

∴ The correct answer is not a quadratic equation.

Additional Information

Linear Equation

An equation where the highest power of the variable is 1 (e.g., ax + b = 0).

Quadratic Equation

An equation where the highest power of the variable is 2 (e.g., ax² + bx + c = 0).

Cubic Equation

An equation where the highest power of the variable is 3 (e.g., ax³ + bx² + cx + d = 0).

Expression vs Equation

An expression does not contain an equality sign (=), whereas an equation always equates two expressions.

The correct answer is Anthracite.

Key Points

• The most metamorphosed variety of coal is anthracite, also referred to as hard coal.
• Its calorific values, which are close to 35 megajoules per kilogramme (15,000 British thermal units per pound), are equivalent to those of the bulk of bituminous coal.
• It possesses the most fixed carbon (86 percent or more) and the least volatile matter (14 percent or less on a dry, ash-free basis) of all the different forms of coal.
• The most uncommon type of coal is anthracite coal.
• Less than 2% of the US's total coal reserves are found in it, largely in northeastern Pennsylvania.
• South Africa, Australia, the eastern Ukraine, western Canada, China, and other areas have less anthracite.

Additional Information

• Bituminous:
• Up to 17 percent moisture can be found in bituminous coal.
• Nitrogen makes up between 0.5 and 2 percent of bituminous coal's weight.
• Up to 85% of its weight can be made up of fixed carbon, while up to 12% of it can be made up of ash.
• Lignite:
• Lignite, often known as brown coal is a soft, brown, flammable sedimentary rock that was created when peat was naturally compacted.
• Due to its relatively low heat content, it is regarded as the lowest rank of coal and has a carbon concentration of between 25 and 35 percent.
• It has a very high moisture content when taken out of the ground, which contributes to its low carbon content.
• Sub-bituminous:
• A lower grade of coal with a carbon content of 35–45% is called sub-bituminous coal.
• This form of coal has qualities that fall between between bituminous coal, the second-highest grade of coal, and lignite, the lowest grade.
• Sub-bituminous coal is primarily utilized as a fuel for the production of steam-electric power.

Shortcut Trick

Let the middle child be the average age.

Average age = Total Sum ÷ Number of children = 60 ÷ 5 = 12 years.

Since the interval is 3 years, the children ages are: (12 − 6), (12 − 3), 12, (12 + 3), (12 + 6).

Age of the youngest child = 12 − 6 = 6 years.

∴ The correct answer is 6 years.

Alternate Method

Given: Sum of ages = 60 years, Number of children = 5, Interval = 3 years.

Formula Used: Sum of an Arithmetic Progression (AP) = n/2 × [2a + (n − 1)d]

Let the age of the youngest child be x.

⇒ Ages are x, (x + 3), (x + 6), (x + 9), and (x + 12).

⇒ x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 60

⇒ 5x + 30 = 60

⇒ 5x = 60 − 30

⇒ 5x = 30

⇒ x = 30 ÷ 5 = 6

∴ The correct answer is 6 years.

Additional Information

Arithmetic Progression (AP) in Ages

When ages are at equal intervals, they form an AP where the middle term is the Average of the group.

Average of Odd Terms

For an odd number of terms (n), the Average is always the [(n+1)/2]^th term in the sequence.

Shortcut Trick

Let CP be 100.

MP = 100 + 18 = 118 (since Profit = 18% at MP).

Discount = 10% of 118 = 11.8.

Actual SP = 118 − 11.8 = 106.2.

Profit % = 106.2 − 100 = 6.2%.

∴ The correct answer is 6.2%.

Alternate Method

Given → Profit at MP = 18%, Discount = 10%. Formulas: SP = MP × (100 − D%) ÷ 100 | Profit% = (SP − CP) ÷ CP × 100.

⇒ Assume Cost Price (CP) = 100. ⇒ Marked Price (MP) = CP × (100 + 18) ÷ 100 = 118. ⇒ Selling Price (SP) = MP × (100 − 10) ÷ 100 = 118 × 0.9 = 106.2. ⇒ Actual Profit = SP − CP = 106.2 − 100 = 6.2. ⇒ Profit % = (6.2 ÷ 100) × 100 = 6.2%.

∴ The correct answer is 6.2%.

Additional Information

Relationship between CP and MP

The ratio of Marked Price to Cost Price is given by MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

Net Percentage Change

The actual profit can be viewed as the successive effect of Markup percentage (m) and Discount percentage (d): Net % = m − d − (m × d) ÷ 100.

Diagram is drawn as per the given information:

• Hisar is to the north of Bhiwani.
• ​Bhiwani is to the west of New Delhi.
• ​Rohtak is to the south of Panipat and to the east of New Delhi.

        ​

​

Therefore, Hisar is located at the west with respect to Panipat.

​Hence, the correct answer is 'West'.

Shortcut Trick

Age ratio (Now : Marriage) = 1(1/5) : 1 = 6 : 5

Difference in ratio parts = 6 − 5 = 1 unit

Actual time difference = 10 years ⇒ 1 unit = 10 years

Ramya present age (6 units) = 6 × 10 = 60 years

Daughter age = 1/10 × 60 = 6 years

∴ The correct answer is 6 years.

Alternate Method

Let Ramya age at the time of marriage be x years.

Given: Present Age = 1(1/5) × x = 6/5 × x

⇒ 6x/5 − x = 10

⇒ (6x − 5x)/5 = 10

⇒ x/5 = 10 ⇒ x = 50 years (Age at marriage)

⇒ Present Age = 50 + 10 = 60 years

⇒ Daughter age = 1/10 × 60

⇒ Daughter age = 6 years

∴ The correct answer is 6 years.

Additional Information

Ratio Method for Age Problems

When a multiplier like 1(1/5) is given, convert it to an improper fraction (6/5) to represent the ratio between two time periods directly.

Constant Difference Property

The difference between the ages of two people remains constant throughout their lives, regardless of the years passed.

Fractional Age Relations

If person A is 1/n of person B, then A = B/n. Always ensure to identify the reference person (usually the one mentioned with 'of').

The correct answer is Both (a) and (b).