RRB Group D Previous Year Paper (Held on: 30 Aug 2022 Shift 2)

The correct answer is He was unable to make more than three triads of the elements.

Key Points

• Johann Wolfgang Döbereiner was a German chemist who attempted to classify elements into groups of three, known as triads.
• The main drawback of Döbereiner's triads was that he was unable to make more than three triads of the elements.
• Döbereiner's triads were an early attempt to classify elements, which later paved the way for the development of the periodic table.
• Although his model showed some periodicity in properties, it was limited by the small number of triads he could identify.

Additional Information

• Döbereiner's work highlighted the need for a more comprehensive system of classification of elements.
• His observations contributed to the development of the periodic law and the modern periodic table.
• The periodic table as we know it today was developed by Dmitri Mendeleev, who arranged elements by increasing atomic mass and grouped them based on similar chemical properties.

Shortcut Trick

Total Work = LCM(15, 12, 20, 8) = 120 units.

Efficiencies: A = 8, B = 10, C = 6, D = 15.

Team Efficiency: SUN (A+D) = 23, MOON (B+C) = 16, RED (A+C) = 14.

The team with the highest efficiency takes the least time.

∴ The correct answer is Team SUN.

Alternate Method

Given: A = 15 days, B = 12 days, C = 20 days, D = 8 days.

Formula: Time = Total Work ÷ Efficiency

⇒ Efficiency of Team SUN (A + D) = 8 + 15 = 23 units/day

⇒ Efficiency of Team MOON (B + C) = 10 + 6 = 16 units/day

⇒ Efficiency of Team RED (A + C) = 8 + 6 = 14 units/day

⇒ Time taken by SUN = 120 ÷ 23 ≈ 5.21 days

⇒ Time taken by MOON = 120 ÷ 16 = 7.5 days

⇒ Time taken by RED = 120 ÷ 14 ≈ 8.57 days

∴ The correct answer is Team SUN.

Additional Information

Inverse Proportion of Time and Efficiency

Time is inversely proportional to Efficiency (T ∝ 1/E). A higher combined efficiency always results in shorter project duration.

Total Work Concept

Total Work is usually taken as the Least Common Multiple (LCM) of the individual time periods to keep efficiency values as integers.

The correct answer is neutralisation reaction

Key Points

• Neutralisation reaction is the chemical reaction where an acid reacts with a base to form salt and water.
• In this reaction, the H⁺ ion from the acid combines with the OH^- ion from the base to produce water (H₂O).
• The general form of the neutralisation reaction is: Acid + Base → Salt + Water.
• This reaction is important in various industrial and laboratory processes, including titrations in chemistry.

Additional Information

• Acids are substances that release H⁺ ions in solution, while bases release OH^- ions.
• Common examples of acids include hydrochloric acid (HCl) and sulfuric acid (H₂SO₄).
• Common examples of bases include sodium hydroxide (NaOH) and potassium hydroxide (KOH).
• The pH scale is used to measure the acidity or basicity of a solution, with 7 being neutral, below 7 being acidic, and above 7 being basic.

The logic followed here is:

So, the missing term of the series is '961'

Hence, the correct answer is "Option 3".

The correct answer is 1961

Key Points

• The Third Five Year Plan of India was launched in 1961.
• The plan aimed at making India a self-reliant and self-generating economy.
• It focused on agriculture and improving the production of wheat, with an emphasis on long-term development.
• During this plan, India faced economic challenges due to conflicts with China in 1962 and Pakistan in 1965, which impacted its implementation.
• The Third Five Year Plan also aimed to address issues related to poverty, unemployment, and improving living standards.

Additional Information

• India's Five Year Plans were centralized and integrated national economic programs.
• The concept was borrowed from the Soviet Union and aimed at planned economic development.
• The First Five Year Plan was launched in 1951, focusing primarily on the agricultural sector.
• The Second Five Year Plan (1956-1961) emphasized industrialization.
• Due to the Indo-China war in 1962 and the Indo-Pakistan war in 1965, the Third Five Year Plan could not achieve all its targets and objectives.
• After the Third Plan, there was a period of three annual plans before the Fourth Five Year Plan was implemented in 1969.

The correct answer is Tamil

Key Points

• Tamil was accorded the classical language status in 2004 by the Union Government of India.
• The status of a classical language is given to languages that have a rich heritage and independent nature.
• Tamil is one of the oldest languages in the world, with a recorded history spanning over 2000 years.
• This recognition highlights the cultural and historical significance of the Tamil language.
• Tamil literature, with its ancient texts and poetry, is a testament to the language's classical status.

Additional Information

• Kannada and Telugu were later accorded the classical language status in 2008.
• Malayalam received the classical language status in 2013.
• The criteria for declaring a language as classical include its antiquity, a body of ancient literature or texts, and its original literary tradition.
• The classical language status is a recognition of the language's historical and cultural significance.

The correct answer is Mangrove

Key Points

• Mangrove forests are unique ecosystems found in coastal intertidal zones.
• These forests consist of hardy shrubs and trees that thrive in saltwater environments.
• Mangroves have specialized adaptations, such as pneumatophores (breathing roots) and salt-filtering mechanisms, to survive the volatile energies of intertidal zones.
• They play a crucial role in protecting coastlines from erosion and provide habitat for a diverse range of marine and terrestrial species.

Additional Information

• Mangrove ecosystems are found in tropical and subtropical regions around the world.
• They are highly productive and provide numerous ecosystem services, including carbon sequestration, water filtration, and serving as nurseries for fish and other aquatic organisms.
• Conservation of mangrove forests is essential for maintaining biodiversity and supporting the livelihoods of local communities who depend on these ecosystems for resources.

The correct answer is Smell

Key Points

• Olfactory receptors are specialized cells responsible for detecting odors and are essential for the sense of smell.
• These receptors are located in the olfactory epithelium in the nasal cavity.
• When odor molecules bind to these receptors, they send signals to the brain, which interprets them as distinct smells.
• The sense of smell plays a critical role in flavor perception, environmental awareness, and memory.

Additional Information

• The olfactory system is one of the oldest sensory systems in evolutionary history.
• Humans have approximately 400 types of olfactory receptors, enabling the detection of a wide range of odors.
• Olfactory receptors are part of the chemosensory system, which also includes taste receptors.
• Damage to the olfactory receptors or the olfactory nerve can lead to loss of smell (anosmia), which can affect the quality of life and safety.
• Olfaction is closely linked to the limbic system, which is involved in emotion and memory, explaining why certain smells can trigger strong emotional responses and memories.

The correct answer is CH₄, C₂H₆, C₃H₆

Key Points

• Option 1: CH₄, C₂H₆, C₃H₆ - Methane (CH₄) and Ethane (C₂H₆) belong to the alkane series (C_nH_₂n+₂), while Propene (C₃H₆) belongs to the alkene series (C_nH_₂n).
• Option 2: C₃H₆, C₅H₁₀, C₇H₁₄ - All these hydrocarbons belong to the alkene series (C_nH_₂n).
• Option 3: C₂H₄, C₃H₆, C₄H₈ - All three follow the general formula for alkenes (C_nH_2n).
• Option 4: C₂H₂, C₃H₄, C₄H₆ - All these hydrocarbons belong to the alkyne series (CnH2n-2).

Additional Information

• A homologous series is a group of organic compounds with a similar general formula, possessing similar chemical properties due to the presence of the same functional group.
• Alkanes have the general formula C_nH_₂n+₂, alkenes have C_nH_₂n, and alkynes have C_nH_₂n-₂.
• Understanding the homologous series helps in predicting the properties and reactions of organic compounds.

The correct answer is Small Industries Development Bank of India (SIDBI)

Key Points

• The Small Industries Development Bank of India (SIDBI) has launched the 'Waste to Wealth Creation' programme for women in the Sundarbans in West Bengal.
• This initiative aims to empower women by providing them with opportunities to create sustainable income through waste management and recycling activities.
• Sundarbans, a UNESCO World Heritage Site, is known for its unique biodiversity and the programme seeks to address environmental concerns while promoting economic development.
• The programme is expected to enhance the livelihoods of women by involving them in the production of eco-friendly products from waste materials.

Additional Information

• SIDBI was established in 1990 and is headquartered in Lucknow, Uttar Pradesh.
• It serves as the principal financial institution for the promotion, financing, and development of the Micro, Small, and Medium Enterprise (MSME) sector in India.
• The bank provides various financial and non-financial services to support the growth and development of MSMEs across the country.
• SIDBI also plays a crucial role in implementing government schemes aimed at fostering entrepreneurship and innovation in the MSME sector.

Shortcut Trick

Volume of Cylinder = πr²h

Given radius (r) = 5 cm and height (h) = 7 cm

Volume = π × 5² × 7 = π × 25 × 7 = 175π cm³

∴ The correct answer is 175π cm³.

Alternate Method

Given:

Radius (r) of the cylinder = 5 cm

Height (h) of the cylinder = 7 cm

Formula Used:

Volume (V) = π × r² × h

Calculations:

⇒ Volume = π × (5)² × 7

⇒ Volume = π × 25 × 7

⇒ Volume = 175π cm³

∴ The correct answer is 175π cm³.

Additional Information

Curved Surface Area (CSA)

The area of the curved surface of a cylinder is given by 2πrh.

Total Surface Area (TSA)

The total surface area includes the curved surface and the two circular bases: 2πr(h + r).

Base Area

The area of the circular base is πr².

Shortcut Trick

When two parallel lines are intersected by a transversal, the alternate interior angles are always equal.

⇒ m∠2 = m∠1

⇒ m∠2 = 35°

∴ The correct answer is 35°.

Alternate Method

Given:

Measure of ∠1 = 35°

∠1 and ∠2 are alternate interior angles formed by a transversal intersecting parallel lines.

Property Used:

If two parallel lines are cut by a transversal, then each pair of alternate interior angles is equal in measure.

Calculations:

⇒ m∠1 = 35°

⇒ m∠2 = m∠1 (Since alternate interior angles are equal for parallel lines)

⇒ m∠2 = 35°

∴ The correct answer is 35°.

Additional Information

Corresponding Angles

Angles in the same relative position at each intersection where a straight line crosses two others. If the lines are parallel, these angles are equal.

Consecutive Interior Angles

The pairs of angles on one side of the transversal and between the two parallel lines. These angles are supplementary (sum = 180°).

The correct answer is Only (a)

Key Points

• Only (a) is correct because electromagnetic induction occurs when there is a change in the magnetic flux linked with the coil.
• During the time the key is closed, the current in coil A changes from zero to a certain value, causing a change in magnetic flux, which induces a current in coil B.
• Two minutes after the key is closed, the current in coil A becomes steady, and there is no change in the magnetic flux linked with coil B, hence no electromagnetic induction occurs.

Additional Information

• Electromagnetic induction is governed by Faraday's law, which states that the induced electromotive force (EMF) in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit.
• Lenz's Law further states that the direction of the induced current will be such that it opposes the change in magnetic flux that produced it.
• This principle is widely used in various applications such as transformers, electric generators, and induction cooktops.

Given word: PACKED

According to the question:

1. Each vowel is changed to the letter following it in the English alphabetical order.

2. Each consonant is changed to the letter preceding it in the English alphabetical order. 

Word formed after arrangement → OBBJFC

Thus, B appeared twice in the group of letters thus formed.

Hence, "Option 2" is the correct answer.

Given:

17.89 - 0.0123 + 2.21 × 3.63 = ?

Formula used:

Basic arithmetic operations

Calculation:

17.89 - 0.0123 + 2.21 × 3.63 = ?

⇒ 2.21 × 3.63 = 8.0223

⇒ 17.89 - 0.0123 + 8.0223

⇒ 17.8777 + 8.0223

⇒ 26

∴ The correct answer is option 3 (26).

The logic followed here is:

So, the missing term of the series is '513'

Hence, the correct answer is "Option 3".

Given:

Find the value of 7834 + 213 ÷ 3 - 51.

Formula used:

Use the order of operations (BODMAS/BIDMAS):

Brackets, Orders (i.e., powers and square roots, etc.), Division and Multiplication (left-to-right), Addition and Subtraction (left-to-right)

Calculation:

7834 + 213 ÷ 3 - 51

⇒ 7834 + 71 - 51

⇒ 7905 - 51

⇒ 7854

∴ The correct answer is option (2).

Given:  Six persons, A, B, C, D, E and F have birthdays in different months of the same year viz. February, April, June, August, September and December 

1. F has a birthday in a month immediately before September.

2. D has a birthday in December. 

3. Only one person has a birthday between B and A, in the same order.

4. Only two people have birthdays between C and E, in the same order.

So, B has his birthday in February

Hence, the correct answer is "Option 1"

The logic followed here is:

 'we prefer green' is coded as 'yo ha ni,

'green peas grow' Is coded as 'ki mi yo',

 'we grow herbs' is coded as 'zu ha mi'

Here, code for 'we' is 'ha'

code for 'green' is 'yo'

code for 'prefer' is 'ni'

code for 'grow' is 'mi'

code for 'peas' is 'ki'

code for 'herbs' is 'zu'

hence the correct answer is "Option 2".

The correct answer is Numerous waste products from plants are stored in centrioles.

Key Points

• Numerous waste products from plants are stored in centrioles is a false statement.
• Centrioles are organelles involved in cell division and are not associated with storing waste products in plants.
• Waste products in plants are typically stored in vacuoles, resins, gums, or excreted through processes like transpiration.
• Transpiration is the mechanism by which a plant eliminates surplus water.
• Photosynthesis produces oxygen as a by-product.
• Gum is an excretory product of plants.

Additional Information

• Centrioles are cylindrical structures found in animal cells and some lower plant forms, playing a key role in cell division.
• In higher plants, cell division occurs without centrioles.
• Plant cells typically store waste products in the central vacuole or secrete them into the surrounding environment.

Given:

$\dfrac{(0.5 \times 10.6 - 0.2 \times 1.4)}{0.4}$

Formula used:

$\dfrac{a \times b - c \times d}{e}$

Calculation:

$\dfrac{(0.5 \times 10.6 - 0.2 \times 1.4)}{0.4}$

⇒ $\dfrac{(5.3 - 0.28)}{0.4}$

⇒ $\dfrac{5.02}{0.4}$

⇒ 12.55

∴ The correct answer is option 2.

The logic followed here is:

So, the missing term of the series is "DWL 66".

Hence the correct answer is "Option 2".

The correct answer is Vaisheshika

Key Points

• Vaisheshika is one of the six orthodox schools of Hindu philosophy (Astika).
• It was founded by the sage Kanada and is known for its naturalism.
• The Vaisheshika system postulates an atomic pluralism and is closely related to the Nyaya school of philosophy.
• It identifies six categories of existence: substance, quality, activity, generality, particularity, and inherence.
• Vaisheshika emphasizes the analysis of the physical world and metaphysics through logic and reason.

Additional Information

• The other main schools of Hindu philosophy include Nyaya, Samkhya, Yoga, Mimamsa, and Vedanta.
• Hindu philosophy is diverse and has a rich history of debate and dialogue between different schools of thought.
• Philosophical teachings in Hinduism cover various aspects such as metaphysics, epistemology, ethics, and logic.
• Each school of Hindu philosophy offers unique perspectives and methods for understanding the nature of reality and the self.

Shortcut Trick

Teacher's Age = New Average + (Initial Count × Change in Average)

New Average = 15 + 1 = 16 years

Initial Count of students = 35

Teacher's Age = 16 + (35 × 1) = 51 years

∴ The correct answer is 51 years.

Alternate Method

Given:

Number of students = 35

Average age of students = 15 years

Total count including teacher = 35 + 1 = 36

New average age = 15 + 1 = 16 years

Formula Used:

Sum of ages = Average × Number of persons

Calculations:

⇒ Total age of 35 students = 35 × 15 = 525 years

⇒ Total age including teacher = 36 × 16 = 576 years

⇒ Age of teacher = Total age with teacher − Total age of students

⇒ Age of teacher = 576 − 525 = 51 years

∴ The correct answer is 51 years.

Additional Information

Inclusion Rule in Average

When a new person joins and the average increases, the new person's age = New Average + (Old Count × Increase in Average).

Exclusion Rule in Average

When a person leaves and the average increases, the age of the person who left = Old Average − (New Count × Increase in Average).

Replacement Rule

New person age = Age of replaced person + (Total persons × Increase in Average).

The correct answer is Sex is not genetically determined

Key Points

• In some animals, such as snails, individuals have the ability to change their sex.
• This phenomenon suggests that sex is not genetically determined in these species.
• Instead, sex determination in these animals can be influenced by various factors, including environmental conditions.
• This flexibility in sex determination allows these animals to adapt to their surroundings and optimize their reproductive success.

Additional Information

• In contrast, in many other species, sex is determined genetically, typically by specific chromosomes (e.g., XX for females and XY for males in mammals).
• The ability to change sex can be advantageous in certain environments, particularly where the population sex ratio is skewed or where there are changes in social structure.
• Examples of other animals that can change sex include some species of fish and reptiles.

The correct answer is -20 cm

Key Points

• Focal length (f) is the distance over which parallel rays of light either converge or diverge.
• The formula to find the focal length in meters when the power (P) of the lens is given in diopters (D) is:
  

f = 1 / P

• Given the power of the lens P = -5 D, the focal length can be calculated as:
  

f = 1 / -5 = -0.2 meters

• To convert meters to centimeters, multiply by 100:
  

f = -0.2 * 100 = -20 cm

• Therefore, the focal length of the lens is -20 cm.

Additional Information

• Lens power is measured in diopters (D), which is the reciprocal of the focal length in meters.
• A positive focal length indicates a converging lens, while a negative focal length indicates a diverging lens.
• Diopters are commonly used in optometry and ophthalmology to prescribe corrective lenses for vision correction.

Shortcut Trick

Ratio of students in Section A and Section B = 40 : 50 = 4 : 5.

Using weighted average logic with ratio parts:

Combined Average = [(4 × 36) + (5 × 45)] ÷ (4 + 5)

Combined Average = (144 + 225) ÷ 9 = 369 ÷ 9 = 41 kg.

∴ The correct answer is 41 kg.

Alternate Method

Given:

Students in Section A (n₁) = 40, Average weight (w₁) = 36 kg

Students in Section B (n₂) = 50, Average weight (w₂) = 45 kg

Formula Used: Combined Average = (Total Weight) ÷ (Total Students)

⇒ Total weight of Section A = 40 × 36 = 1440 kg

⇒ Total weight of Section B = 50 × 45 = 2250 kg

⇒ Total weight of the whole class = 1440 + 2250 = 3690 kg

⇒ Total number of students in the class = 40 + 50 = 90

⇒ Average weight of the whole class = 3690 ÷ 90

⇒ Average weight = 41 kg

∴ The correct answer is 41 kg.

Additional Information

Weighted Average Concept

When groups have different sizes, the combined mean is the weighted average: X_avg = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Deviation Method

Assume a provisional average (e.g., 36) and calculate the net deviation divided by total students to find the adjustment to the assumed average.

Property of Averages

The combined average of two groups must always lie between the smallest and largest individual averages (36 kg < 41 kg < 45 kg).

Shortcut Trick

Rate for 1st year = 7.5%. For remaining 4 months, rate = 7.5% × (4/12) = 2.5%.

Net percentage rate for CI = a + b + (ab/100) ⇒ 7.5 + 2.5 + (7.5 × 2.5 / 100).

Net CI % = 10 + 0.1875 = 10.1875%.

CI = 10.1875% of ₹20,000 = 20,000 × (10.1875/100) = 200 × 10.1875 = ₹2,037.50.

∴ The correct answer is ₹2,037.50.

Alternate Method

Given: Principal (P) = ₹20,000, Time (T) = 1 year 4 months, Rate (R) = 7.5% per annum.

Formula Used: Amount (A) = P(1 + R/100)ⁿ[1 + (R × t/12)/100], where n is complete years and t is remaining months.

⇒ Interest for 1st year = 20,000 × 7.5 / 100 = ₹1,500.

⇒ Principal for the next 4 months = ₹20,000 + ₹1,500 = ₹21,500.

⇒ Interest for the next 4 months = 21,500 × (7.5 × 4/12) / 100 = 21,500 × 2.5 / 100.

⇒ Interest for the next 4 months = 215 × 2.5 = ₹537.50.

⇒ Total Compound Interest = 1,500 + 537.50 = ₹2,037.50.

∴ The correct answer is ₹2,037.50.

Additional Information

Compound Interest for Fractional Time

When time is given in parts like T = n (a/b) years, Amount = P(1 + R/100)ⁿ × [1 + (R × a/b)/100].

Effective Rate of Interest

For two successive rates r₁ and r₂, the net effective rate is r₁ + r₂ + (r₁r₂/100)%.

SI vs CI for First Year

For the first year (or first compounding period), Simple Interest and Compound Interest are always equal on the same principal and rate.

The correct answer is CSIR Jigyasa

Key Points

• CSIR Jigyasa is the program that launched India's first virtual science lab for children in November 2021.
• The initiative aims to connect students with scientists across the country.
• It is a significant step in promoting scientific curiosity and knowledge among young students.
• This virtual lab platform provides an opportunity for students to engage in scientific experiments and activities remotely.

Additional Information

• The CSIR Jigyasa program is an initiative by the Council of Scientific and Industrial Research (CSIR) in collaboration with Kendriya Vidyalaya Sangathan (KVS).
• It aims to extend classroom learning with well-planned research laboratory-based learning.
• The program is designed to inculcate scientific temper among school students and to ignite inquiring minds.
• It also seeks to promote science and technology by providing a platform for students to interact with scientists and gain hands-on experience in scientific research.

Shortcut Trick

Ratio of interior angles = 3 : 7 ⇒ Sum = 10 units.

Sum of consecutive interior angles = 180°.

10 units = 180° ⇒ 1 unit = 18°.

Difference between angles = 7 − 3 = 4 units.

Positive difference = 4 × 18° = 72°.

∴ The correct answer is 72°.

Alternate Method

Given:

Ratio of two interior angles on the same side of a transversal = 3 : 7.

The lines are parallel.

Formula Used:

When two parallel lines are intersected by a transversal, the interior angles on the same side are supplementary (their sum is 180°).

Calculations:

⇒ Let the measures of the two interior angles be 3x and 7x.

⇒ 3x + 7x = 180°

⇒ 10x = 180°

⇒ x = 18°

⇒ First angle = 3 × 18° = 54°

⇒ Second angle = 7 × 18° = 126°

⇒ Positive difference = 126° − 54° = 72°

∴ The correct answer is 72°.

Additional Information

Consecutive Interior Angles

Shortcut Trick

In cases where a number is multiplied, the remainder follows the same operation.

New Remainder = (n × Original Remainder) − Divisor

Divisor = (2 × 16) − 3

Divisor = 32 − 3 = 29

∴ The correct answer is 29.

Alternate Method

Given: First remainder (R₁) = 16. Second remainder (R₂) = 3. Multiplier (n) = 2.

Formula: N = Dq + R

⇒ Let the number be N and divisor be D.

⇒ N = Dq + 16

⇒ 2N = 2(Dq + 16) = 2Dq + 32

⇒ Since 2N divided by D leaves remainder 3, then 32 divided by D must leave remainder 3.

⇒ 32 − 3 = 29 must be exactly divisible by D.

⇒ Since the original remainder was 16, D must be greater than 16.

⇒ D = 29.

∴ The correct answer is 29.

Additional Information

Remainder Theorem Property

If a number N leaves remainder R when divided by D, then kN leaves the same remainder as kR divided by D.

Divisor Constraint

The divisor must always be greater than the remainder. In this problem, D > 16.

Sum of Remainders Rule

If N₁ and N₂ leave R₁ and R₂, then (N₁+N₂) leaves the same remainder as (R₁+R₂) divided by D.

The logic followed here is:

Logic: (3rd number - 1st number)² = 2nd number.

Now,

For, 14, 25, 19

⇒ (19 - 14)² = 25

For, 12, 16, 16

⇒ (16 - 12)² = 16

Similarly, 18, 16, 14

⇒ (14 - 18)² = (-4)² = 16

Hence, the correct answer is "Option 3".

Shortcut Trick

For mean proportion x between a and b, x = √(a × b).

x = √(49 × 81) = 7 × 9 = 63.

y = √(64 × 169) = 8 × 13 = 104.

Value = 2(63) + 3(104) = 126 + 312 = 438.

∴ The correct answer is 438.

Alternate Method

Given:

49 ÷ x = x ÷ 81

64 ÷ y = y ÷ 169

Formula Used:

If a, b, c are in continued proportion, then b² = ac.

Calculations:

⇒ x² = 49 × 81

⇒ x = √(49 × 81) = 7 × 9 = 63

⇒ y² = 64 × 169

⇒ y = √(64 × 169) = 8 × 13 = 104

⇒ Required Value = 2x + 3y

⇒ 2(63) + 3(104)

⇒ 126 + 312 = 438

∴ The correct answer is 438.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(ab).

Third Proportional

If a, b, and c are in continued proportion, then c is the third proportional where c = b²/a.

Fourth Proportional

If a : b :: c : d, then d is the fourth proportional given by d = (b × c) / a.

The logic followed here is:

Reptiles, Amphibians, Aves all have double circulation,

Whereas,

Pisces have single circulation.

Hence, the correct answer is "Pisces".

Given: T, U, V, W, X, Y, Z and A were eight family members sitting around a square table, facing the centre.

1. Only one person was sitting between W and X.

2. V was sitting fourth to the left of U.

3. Only A was sitting between Z and X.

4. Y was not sitting at any of the corner positions.

5. X was sitting at one of the corners.

6. V was sitting to the immediate let of Z

So, 'T' was sitting at the corner position of the table.

Hence the correct answer is "Option 4".

Shortcut Trick Convert the equation 5 × Number1 = 4 × Number2 into a ratio. The ratio of the numbers is Number1 : Number2 = 4 : 5. Total ratio units = 4 + 5 = 9 units. Given total sum = 27, so 9 units = 27 ⇒ 1 unit = 3. Smaller number = 4 units × 3 = 12. ∴ The correct answer is 12.

Alternate Method Given: Sum of two numbers = 27. Relation: 5 × (One number) = 4 × (Other number).

Let the two numbers be x and y. ⇒ x + y = 27 --- (Equation 1) ⇒ 5x = 4y ⇒ x = 4y / 5 --- (Equation 2) Substitute Equation 2 into Equation 1: ⇒ 4y / 5 + y = 27 ⇒ (4y + 5y) / 5 = 27 ⇒ 9y / 5 = 27 ⇒ y = (27 × 5) / 9 ⇒ y = 3 × 5 = 15 Now, find x: ⇒ x = 27 − 15 = 12 Comparing 12 and 15, the smaller number is 12. ∴ The correct answer is 12.

Additional Information Ratio Conversion Rule When ax = by, the ratio of the variables is always the inverse of their coefficients: x : y = b : a. Unitary Method in Ratios To find individual values when the sum is known, divide the total sum by the sum of ratio parts to find the value of one unit. Comparing Numbers In a ratio a : b, if a < b, then the term corresponding to a is the smaller number.

The correct answer is ∠ABN and ∠EOD

Key Points

• The angle of incidence and angle of deviation in the path of a ray of light through a triangular glass prism are ∠ABN and ∠EOD respectively.
• In the given options, Option 3 correctly identifies these angles.
• The angle of incidence is where the ray enters the prism, and the angle of deviation is the angle between the incident ray and the emergent ray.

Additional Information

• When light enters a prism, it bends towards the normal due to refraction.
• Upon exiting the prism, the light bends away from the normal, causing a deviation from its original path.
• The amount of deviation depends on the angle of incidence, the angle of the prism, and the refractive index of the material of the prism.

The correct answer is Next-Gen Technologies for Digital Government

Key Points

• The theme of Tech Conclave 2022, organised by the National Informatics Centre (NIC) in March 2022, was Next-Gen Technologies for Digital Government.
• The conclave focused on the application of emerging technologies in e-Governance.
• The event aimed to showcase the advancements and potential of next-generation technologies to enhance digital governance.
• Topics discussed included artificial intelligence, machine learning, blockchain, and other cutting-edge technologies relevant to the digital transformation of government services.
• The conclave served as a platform for experts, policymakers, and stakeholders to share insights and experiences on leveraging technology for efficient governance.

Additional Information

• The National Informatics Centre (NIC) is a premier technology advisor and ICT solution provider to the Government of India.
• NIC plays a crucial role in implementing and managing e-Governance initiatives across various government departments and agencies.
• Tech Conclave 2022 provided a platform to demonstrate NIC's ongoing efforts and future plans to integrate emerging technologies into government operations.
• The conclave also aimed to foster collaboration between the government and technology industry leaders to drive digital transformation.

The correct answer is Preserve the natural resources for the needs of the future generation

Key Points

• Sustainable development aims to balance the fulfillment of human needs with the protection of the natural environment.
• It ensures that natural resources are available for future generations by promoting responsible and efficient use.
• The concept emphasizes the importance of intergenerational equity, which means that the current generation should meet its needs without compromising the ability of future generations to meet theirs.
• Sustainable development also involves the integration of economic, social, and environmental policies to create a more stable and equitable society.

Additional Information

• The concept of sustainable development was popularized by the Brundtland Report in 1987, which defined it as "development that meets the needs of the present without compromising the ability of future generations to meet their own needs."
• Sustainable development is a key principle in international environmental agreements and policies, including the United Nations' Sustainable Development Goals (SDGs).
• There are 17 SDGs that address global challenges such as poverty, inequality, climate change, environmental degradation, and peace and justice, with the aim of achieving a better and more sustainable future for all by 2030.
• Businesses, governments, and individuals all have roles to play in promoting sustainable development through practices such as reducing waste, conserving energy, and supporting sustainable products and services.

Shortcut Trick

If x + 1/x = k, then x³ + 1/x³ = k³ − 3k.

Here, the value of k = 42.

Substituting the value: 42³ − 3 × 42

74088 − 126 = 73962.

∴ The correct answer is 73962.

Alternate Method

Given: x + 1/x = 42

Formula Used: (a + b)³ = a³ + b³ + 3ab(a + b)

⇒ Cube both sides of the equation x + 1/x = 42:

⇒ (x + 1/x)³ = (42)³

⇒ x³ + (1/x)³ + 3 × x × (1/x) × (x + 1/x) = 74088

⇒ x³ + 1/x³ + 3 × (x + 1/x) = 74088

⇒ x³ + 1/x³ + 3 × (42) = 74088

⇒ x³ + 1/x³ + 126 = 74088

⇒ x³ + 1/x³ = 74088 − 126

⇒ x³ + 1/x³ = 73962

∴ The correct answer is 73962.

Additional Information

Fundamental Algebraic Cube Identity

The expansion of (a + b)³ is given by a³ + b³ + 3a²b + 3ab², which can be rearranged as a³ + b³ + 3ab(a + b).

Reciprocal Square Relation

If x + 1/x = k, then the squared value is x² + 1/x² = k² − 2.

Negative Reciprocal Cube

If x − 1/x = k, then the value of x³ − 1/x³ = k³ + 3k.

To reach point L from M Narendra should walk

100 m towards the north

He then takes a right turn and walks 900 m.

He takes a right turn again and walks 750 m.

Again, he takes a right turn and walks 900 m to reach point M.

So, he is 650 m south 

Hence the correct answer is "option 2".

According to the given Venn diagram:

The shaded area shows the number of space scientists who earn equal to or more than 50K a month

So, the number of space scientists who earn equal to or more than 50K a month are '46'.

Hence, the correct answer is "Option 2".

The correct answer is Alkaline KMnO4 and Acidified K2Cr2O7

Key Points

• Alkaline KMnO4 and Acidified K2Cr2O7 are commonly used oxidizing agents in organic chemistry.
• These reagents are effective in converting ethanol (a primary alcohol) to ethanoic acid (a carboxylic acid).
• Acidified K2Cr2O7 (Potassium dichromate) in acidic medium acts as a powerful oxidizing agent.
• Alkaline KMnO4 (Potassium permanganate) in basic medium also acts as a strong oxidizing agent.
• The oxidation process involves the removal of hydrogen from the ethanol molecule and the addition of oxygen to form ethanoic acid.

Additional Information

• In the oxidation of ethanol to ethanoic acid, ethanol is first oxidized to acetaldehyde, and then further oxidized to ethanoic acid.
• Both alkaline KMnO4 and acidified K2Cr2O7 are strong oxidants that can facilitate the complete oxidation of ethanol.
• This reaction is an example of an oxidation-reduction (redox) reaction where ethanol loses electrons (is oxidized) and the oxidizing agent gains electrons (is reduced).
• These reagents are widely used in organic synthesis and analytical chemistry for various oxidation reactions.

The correct answer is Jair Bolsonaro

Key Points

• Jair Bolsonaro was the Chief Guest of Republic Day celebration of India in 2020.
• Jair Bolsonaro is the President of Brazil, and his visit to India marked an important event in strengthening bilateral relations between the two countries.
• He was invited as the Chief Guest to witness the grand parade and celebrations held on January 26th, 2020, which is a significant day marking the adoption of the Indian Constitution.
• The Republic Day celebrations in India include a grand parade showcasing India's defense capabilities, cultural heritage, and various achievements.

Additional Information

• The Republic Day of India is celebrated on 26th January every year to commemorate the day when the Constitution of India came into effect in 1950.
• The event is marked by a grand parade held at Rajpath, New Delhi, which includes a display of India's military might, cultural diversity, and various achievements.
• Each year, a Head of State or Government of another country is invited as the Chief Guest, which is a significant diplomatic honor reflecting India's international relations.
• The invitation to the Chief Guest is a strategic move by the Indian government to strengthen ties with the respective country.

The correct answer is Sports

Key Points

• Sumit Antil received the Padma Shri 2022 award in the field of Sports.
• He is an Indian Paralympic javelin thrower who has made significant contributions to the field of athletics.
• Sumit Antil won a gold medal in the men's javelin throw F64 category at the Tokyo 2020 Paralympic Games, setting a new world record.
• His achievements have brought immense pride to the nation and have been recognized with one of India's highest civilian honors.

Additional Information

• The Padma Shri is the fourth highest civilian award in India, after the Bharat Ratna, the Padma Vibhushan, and the Padma Bhushan.
• It is awarded to Indian citizens in recognition of their distinguished contribution in various spheres of activity including the arts, education, industry, literature, science, sports, medicine, social service, and public affairs.
• The awards are announced every year on Republic Day (26th January).
• Recipients of the Padma Shri award are recommended by the Padma Awards Committee, which is constituted by the Prime Minister of India.

The correct answer is 0.3 A and 0.15 A.

Key Points

• In a parallel circuit, the voltage across each branch is the same; hence V_A=V_B=6 V.
• By Ohm’s law (I = V/R): I_A = 6/20 = 0.30 A, I_B = 6/40 = 0.15 A → matches option 3.
• Currents in parallel branches are inversely proportional to resistances; here I_A/I_B = R_B/R_A = 40/20 = 2, consistent with 0.30 A vs 0.15 A.
• Check: R_eq = (R₁R₂)/(R₁+R₂) = 13.33 Ω, so total current = 6/13.33 ≈ 0.45 A = 0.30 + 0.15 A.

Additional Information

• Ohm’s law forms: V = IR, I = V/R, R = V/I—fundamental for branch-current calculations.
• In parallel, the total current equals the sum of branch currents (Kirchhoff’s Current Law).
• Equivalent resistance in parallel is always less than the smallest branch; for two resistors use product-over-sum.
• Power in a resistor: P = VI = I²R = V²/R; at 6 V, P_A=1.8 W and P_B=0.9 W, so the lower resistance dissipates more power.

Given: Some students are standing in a queue.

Only Radhika is standing between Sonia and Sujata.

Divya is standing immediately ahead of Sonia.

Divya > Sonia > Radhika > Sujata

Exactly two girls are standing behind Sujata and only one girl is standing exactly ahead of Divya

______ > Divya > Sonia  >  Radhika  >  Sujata > _____ > ______

So, '7' students are standing in a queue.

Hence the correct answer is "Option 4".

The least possible Venn diagram for the given statement is as follows:

Conclusions:

I : Some angles are thumbs - FALSE (Because no direct relation is given between angles and thumbs, so it may be a possibility but not definite)

II : Some trees are fingers - FALSE (Because some thumbs are tress and all fingers are thumbs, but some tress are also angles so it may be a possibility but not definite).

So, Neither conclusion I nor II follows.

Hence, the correct answer is "Option 2".

Given:

Production of company C in various years is compared with company A to find the minimum percentage.

Formula used:

Percentage = (Production of C / Production of A) × 100

Calculations:

For 2016:

⇒ (45 / 60) × 100 = 75%

For 2017:

⇒ (45 / 55) × 100 = 81.81%

For 2018:

⇒ (50 / 40) × 100 = 125%

For 2019:

⇒ (40 / 50) × 100 = 80%

For 2020:

⇒ (30 / 39) × 100 = 76.92%

∴ The minimum percentage is in 2016: 75%

The correct answer is option (2): 2016

The correct answer is Halving of chromosomes during gamete formation

Key Points

• Halving of chromosomes during gamete formation is crucial for maintaining the chromosome number from one generation to another in sexually reproducing organisms.
• This process occurs during meiosis, where the chromosome number is halved in the gametes (sperm and egg cells).
• When fertilization occurs, the fusion of two gametes restores the diploid chromosome number in the zygote.
• This ensures genetic continuity and stability across generations.

Additional Information

• Meiosis is a specialized type of cell division that reduces the chromosome number by half, resulting in four haploid cells.
• These haploid cells develop into gametes, which are essential for sexual reproduction.
• During fertilization, the haploid sperm and egg combine to form a diploid zygote.
• This diploid zygote undergoes multiple rounds of mitosis to develop into a multicellular organism with the same chromosome number as its parents.
• This process is fundamental to the genetic diversity and evolution of sexually reproducing species.

Shortcut Trick

When three numbers a, b, c are in continued proportion, b is the mean proportional.

Formula: b² = a × c

⇒ b = √(144 × 36)

⇒ b = 12 × 6 = 72

∴ The correct answer is 72.

Alternate Method

Given: 144 : b :: b : 36 and 0**.**

Formula Used:** In a proportion a : b :: c : d, the product of means equals the product of extremes (b × c = a × d).**

⇒ 144 / b = b / 36

⇒ b × b = 144 × 36

⇒ b² = 5184

⇒ b = √5184

⇒ b = 72

∴ The correct answer is 72.

Additional Information

Mean Proportional

The mean proportional between two numbers a and c is a number b such that a/b = b/c, which implies b = √(ac).

Third Proportional

If a : b :: b : c, then c is called the third proportional to a and b, calculated as c = b²/a.

Fourth Proportional

In the ratio a : b :: c : d, d is the fourth proportional and is calculated as d = (b × c) / a.

Given equation - 7A3C6D2E30B14

BODMAS Rule

Decoding the given information:

Now replacing the sign from left to right using BODMAS Rule, we get:

⇒ 7 + 3 x 6 ÷ 2 = 30 - 14

⇒ 7 + 3 x 3 = 30 - 14

⇒ 7 + 9 = 30 - 14

⇒ 16 = 16

⇒LHS = RHS

Hence, the correct answer is "Option 3".

The correct answer is Two

Key Points

• India won two silver medals at the Tokyo Olympic 2020.
• The silver medals were won in the following events:
• Weightlifting - Mirabai Chanu in Women's 49 kg category.
• Wrestling - Ravi Kumar Dahiya in Men's Freestyle 57 kg category.
• The Tokyo Olympics 2020 was originally scheduled to take place in 2020 but was postponed to 2021 due to the COVID-19 pandemic.
• India had a total of seven medals in the Tokyo Olympics 2020, which is the country's best performance in an Olympic event.

Additional Information

• The Tokyo 2020 Olympics took place from 23rd July to 8th August 2021.
• Neeraj Chopra won India's first-ever gold medal in athletics (javelin throw) at the Tokyo Olympics 2020.
• The Indian men's hockey team won a bronze medal, ending a 41-year medal drought in hockey at the Olympics.
• Other medalists for India included PV Sindhu (badminton), Lovlina Borgohain (boxing), and Bajrang Punia (wrestling).

The correct answer is Lord William Bentinck

Key Points

• The first medical college in India, Calcutta Medical College, was established during the period of Lord William Bentinck.
• Calcutta Medical College was established in 1835 and was the first institution in Asia to teach modern medicine.
• Lord William Bentinck was the Governor-General of India from 1828 to 1835.
• His tenure is notable for several reforms, including the abolition of Sati and the introduction of English education in India.

Additional Information

• Lord Cornwallis was Governor-General of India from 1786 to 1793 and is known for the Cornwallis Code and the Permanent Settlement of Bengal.
• Lord Mayo served as Viceroy of India from 1869 to 1872 and was assassinated in the Andaman Islands.
• Lord Curzon was Viceroy of India from 1899 to 1905 and is known for the partition of Bengal in 1905.
• The establishment of Calcutta Medical College marked the beginning of formal medical education in India and paved the way for the development of modern medical practices in the country.

The correct answer is 3 km

Key Points

• 3 km is the distance covered by the man.
• To find the distance, we use the formula: Distance = Speed × Time.
• Given the speed is 5 km/h and the time taken is 36 minutes.
• First, convert the time from minutes to hours: 36 minutes = 36/60 hours = 0.6 hours.
• Then, calculate the distance: Distance = 5 km/h × 0.6 hours = 3 km.

The correct answer is -48 cm

Key Points

• The focal length of a concave mirror is given as 24 cm, following the New Cartesian Sign Convention.
• According to the sign convention, the focal length (f) of a concave mirror is negative, so f = -24 cm.
• The centre of curvature (C) of a concave mirror is located at a distance equal to twice the focal length from the pole of the mirror.
• Thus, the distance to the centre of curvature is 2f = 2(-24 cm) = -48 cm.
• Therefore, the centre of curvature is located at -48 cm.

Additional Information

• The New Cartesian Sign Convention is used to determine the signs of the distances measured along the principal axis of the mirror.
• Distances measured in the direction of the incident light (towards the mirror) are considered negative.
• Distances measured against the direction of the incident light (away from the mirror) are considered positive.
• The focal length of concave mirrors is always negative, while that of convex mirrors is positive.

Shortcut Trick

Ratio of two parts = 4 : 3

Difference in ratio parts = 4 − 3 = 1 unit

Given difference = 10 ⇒ 1 unit = 10

Total value = (4 + 3) units = 7 units = 7 × 10 = 70

∴ The correct answer is 70.

Alternate Method

Given:

Ratio of two parts = 4 : 3

Difference between parts = 10

Calculations:

⇒ Let the two parts be 4x and 3x.

⇒ According to the problem: 4x − 3x = 10

⇒ x = 10

⇒ First part = 4 × 10 = 40

⇒ Second part = 3 × 10 = 30

⇒ Initial number = First part + Second part

⇒ Initial number = 40 + 30 = 70

∴ The correct answer is 70.

Additional Information

Ratio and Proportion

If a number A is divided into two parts in the ratio m : n, the parts are (m/(m+n)) × A and (n/(m+n)) × A.

Difference Rule

If the difference between two parts in ratio m : n is D, then the value of 1 unit is D / |m − n|.

Direct Sum calculation

Initial Number = (Sum of Ratios / Difference of Ratios) × Given Difference = (7 / 1) × 10 = 70.

Given Statement: Since Movie X has spent Rs. 3.6 crores in its promotion as against Movie R that spent only Rs. 1.3 crores, Movie X will definitely earn more at the box office.

Now, 

Assumptions:

I. A movie that spends less than ₹1 crore on its promotion cannot do well at the box office - Not Implicit (The statement does not provide information about the performance of movies spending less than ₹1 crore on promotion.)

II. Movie X may win more awards than Movie R - Not Implicit (The statement only discusses box office earnings and not awards.)

Here, Neither assumption I nor II is implicit.

Hence, the correct answer is "Option 3".

The correct answer is Article 22

Key Points

• Article 22 of the Indian Constitution deals with preventive detention and the rights of individuals who are detained.
• Under this article, certain safeguards are provided to individuals who are arrested or detained, including the right to be informed of the grounds of arrest and the right to consult and be defended by a legal practitioner of their choice.
• Article 22 also includes provisions for the establishment of advisory boards to review cases of preventive detention.
• The article ensures that no person can be detained for more than three months without the recommendation of an advisory board.
• Preventive detention is a measure to prevent individuals from committing future crimes or acting in a manner that could threaten public order or national security.

Additional Information

• The Constitution of India was adopted by the Constituent Assembly on 26th November 1949 and came into effect on 26th January 1950.
• It lays down the framework defining fundamental political principles, establishes the structure, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• The Constitution of India is the longest written constitution of any country in the world.
• It declares India a sovereign, socialist, secular, and democratic republic, assuring its citizens justice, equality, and liberty, and endeavors to promote fraternity.
• The Seventh Schedule of the Constitution contains three lists which delineate the subjects under the Union, State, and Concurrent lists.
• Amendments to the Constitution can be made through a process outlined in Article 368.

The correct answer is 0.4 J

Key Points

• The heat produced (H) in a resistor can be calculated using the formula: H = I²Rt, where I is the current, R is the resistance, and t is the time.
• Given: Current (I) = 0.2 A, Resistance (R) = 10 Ω, Time (t) = 1 second.
• Substituting the given values into the formula: H = (0.2)² × 10 × 1 = 0.04 × 10 = 0.4 J.
• Therefore, the heat produced in the resistor in 1 second is 0.4 J.

Additional Information

• The formula H = I²Rt is derived from Joule's law of heating, which states that the heat produced in a resistor is proportional to the square of the current, the resistance, and the time for which the current flows.
• This principle is widely used in electrical heating appliances such as electric heaters, toasters, and irons.
• Understanding this concept is fundamental in the field of electrical engineering and physics.

Given: 1 April 2017 was Saturday.

Now,

From 1 April 2017 to 12 May 2017, we need to count the number of days.

April has 30 days, so the days in April after 1 April = 30 - 1 = 29 days.

In May, up to 12 May, there are 12 days.

Total days from 1 April 2017 to 12 May 2017 = 29 (April) + 12 (May) = 41 days.

41 days → 41/7 = 5 weeks and 6 odd days.

So, 12 May 2017 will be Saturday + 6 = Friday.

Hence, the correct answer is "Option 1".

Given Statement: O > L ≥ E = P > S < A

Now,

Conclusions:

Option 1: P < A → False (P > S < A No definite relation can be possible between P and A)

Option 2: O < E → False (O > L ≥ E It gives O > E)

So, Neither conclusion I nor II is true.

Hence, the correct answer is "Option 4".

Given number: '684912753'

After arranging in ascending order:

After arranging the digits in ascending order,

we can see that only the digit '7' remains in its original position.

Hence, the correct answer is "Option 1".

The correct answer is i, ii and iii

Key Points

• Bleaching powder is used for disinfecting drinking water supply.
• It is also used in the manufacture of chloroform.
• Additionally, bleaching powder can be used for making wool unshrinkable.
• Therefore, the correct options are i, ii, and iii.

Additional Information

• Bleaching powder is chemically known as calcium hypochlorite.
• It is widely used in water treatment plants to ensure the supply of clean and safe drinking water.
• Bleaching powder is also used in the textile industry to bleach fabrics and make them less prone to shrinking.
• In addition to these uses, it is also an important chemical in organic synthesis, such as in the production of chloroform.

Shortcut Trick Sum of roots = (2 + √3) + (4 − 2√3) = 6 − √3 Product of roots = (2 + √3)(4 − 2√3) = 8 − 4√3 + 4√3 − 2(3) = 2 The Quadratic Equation is x2 − (Sum of roots)x + (Product of roots) = 0 Placing values: x2 − (6 − √3)x + 2 = 0 ∴ The correct answer is x2 − (6 − √3)x + 2 = 0.

Alternate Method Given: Roots are α = 2 + √3 and β = 4 − 2√3 Formula Used: A quadratic equation with roots α and β is formed as: x2 − (α + β)x + αβ = 0 ⇒ Step 1: Calculate the Sum of the roots (α + β) ⇒ α + β = (2 + √3) + (4 − 2√3) ⇒ α + β = 2 + 4 + √3 − 2√3 = 6 − √3 ⇒ Step 2: Calculate the Product of the roots (αβ) ⇒ αβ = (2 + √3) × (4 − 2√3) ⇒ αβ = 2(4) − 2(2√3) + 4(√3) − √3(2√3) ⇒ αβ = 8 − 4√3 + 4√3 − 2(3) = 8 − 6 = 2 ⇒ Step 3: Form the Equation ⇒ x2 − (6 − √3)x + 2 = 0 ∴ The correct answer is x2 − (6 − √3)x + 2 = 0.

Additional Information Nature of Roots For a quadratic equation ax2 + bx + c = 0, 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 imaginary. Relation between Roots and Coefficients Sum of roots (α + β) = −b/a and Product of roots (αβ) = c/a. This allows for constructing the equation directly from its roots. Irrational Roots If a quadratic equation has rational coefficients and one root is of the form p + √q, then the other root must be its conjugate p − √q. Note that this rule only applies if the coefficients are rational numbers.

Given:

Marks obtained by Punit in all subjects:

Chemistry = 80

Physics = 60

Mathematics = 70

Biology = 75

Accounting = 80

Computer Science = 60

Formula used:

Mean aggregate percentage = (Total marks obtained / Total maximum marks) × 100

Calculations:

Total marks obtained by Punit = 80 + 60 + 70 + 75 + 80 + 60

⇒ Total marks = 425

Total maximum marks = 600

⇒ Mean aggregate percentage = (425 / 600) × 100

⇒ Mean aggregate percentage = 70.8%

∴ The correct answer is option (2): 70.8%

The correct answer is Grass, wood, orange peels

Key Points

• Option 4 includes grass, wood, and orange peels, all of which are biodegradable substances.
• Biodegradable substances are those that can be broken down by natural processes involving microorganisms into simpler, non-toxic substances.
• Grass decomposes quickly and returns nutrients to the soil.
• Wood is a natural material that decomposes over time, especially when exposed to environmental elements.
• Orange peels are organic waste that decomposes and enriches the soil with nutrients.
• Thus, this group consists of items that are environmentally friendly and can be naturally recycled.

Additional Information

• Option 1 includes batteries, which are not biodegradable.
• Option 2 includes rubber, which is not biodegradable.
• Option 3 includes plastic, which is not biodegradable.
• Biodegradable waste is crucial for composting and reducing landfill use, thereby helping in sustainable waste management.
• Using biodegradable substances reduces pollution and supports ecological balance.

The correct answer is AD = C + I + G

Key Points

• Aggregate Demand (AD) is the total demand for goods and services in an economy at a given overall price level and in a given time period.
• It is represented by the formula AD = C + I + G, where:
• C stands for consumption expenditure.
• I stands for investment expenditure.
• G stands for government expenditure.
• This formula indicates that AD is the sum of consumption, investment, and government spending.
• Other options given in the question do not correctly represent the components of Aggregate Demand.

Additional Information

• Aggregate Demand plays a crucial role in the analysis of economic fluctuations and policy-making.
• Changes in AD can lead to economic growth or recession, depending on whether the demand is increasing or decreasing.
• Factors influencing AD include changes in consumer confidence, interest rates, government policies, and global economic conditions.

Shortcut Trick

Identify the sum and product of the given roots (15 and −16).

Sum = 15 + (−16) = −1

Product = 15 × (−16) = −240

Equation: x² − (Sum)x + Product = 0 ⇒ x² − (−1)x + (−240) = 0

∴ The correct answer is x² + x − 240 = 0.

Alternate Method

Given:

First root (α) = 15

Second root (β) = −16

Formula Used:

A quadratic equation with roots α and β is given by: x² − (α + β)x + αβ = 0

Calculations:

⇒ Sum of roots (α + β) = 15 + (−16) = −1

⇒ Product of roots (αβ) = 15 × (−16) = −240

⇒ Substituting these values into the standard equation form:

⇒ x² − (−1)x + (−240) = 0

⇒ x² + x − 240 = 0

∴ The correct answer is x² + x − 240 = 0.

Additional Information

Standard Form of Quadratic Equation

The general form is ax² + bx + c = 0, where α + β = −b/a and αβ = c/a.

Nature of Roots

Determined by the Discriminant (D) = b² − 4ac. If D > 0, roots are real and distinct; if D = 0, roots are real and equal.

Factor Theorem

If k is a root of the equation, then (x − k) is a factor of the quadratic polynomial.

Given: K, L, M, N, O and P live on six different floors of the same building. 

1. L does not live on floor number 5.

2. O and P live on even numbered floors, but not on floor number 6.

3. N lives on floor number 3.

4. K lives immediately below L.

5. O lives immediately above M, but not on floor number 4. 

CASE1, will not be a possible case and gets eliminated. We have the final arrangement in CASE 2

So, K lives on floor number 5

Hence, the correct answer is "Option 1".

The correct answer is SMILE

Key Points

• SMILE (Support for Marginalized Individuals for Livelihood and Enterprise) is a Central Sector Scheme launched in February 2022.
• The scheme aims to provide welfare measures to the transgender community and people engaged in acts of begging.
• It includes comprehensive measures for their rehabilitation, medical care, counseling, education, skill development, and economic linkages.
• The scheme is designed to ensure that these marginalized groups are brought into the mainstream and can live with dignity and respect.

Additional Information

• The Ministry of Social Justice and Empowerment is the nodal ministry for the implementation of the SMILE scheme.
• It is part of the government's broader vision to provide social security and inclusion to the most vulnerable sections of society.
• Other initiatives under the ministry also focus on the welfare of senior citizens, persons with disabilities, and other disadvantaged groups.

Shortcut Trick

Net discount for 10% and 20% = 10 + 20 − (10 × 20) ÷ 100 = 28%.

Net discount for 28% and 15% = 28 + 15 − (28 × 15) ÷ 100.

Calculation: 43 − 4.2 = 38.8%.

Alternatively, using Multipliers: 1 − (0.9 × 0.85 × 0.8) = 1 − 0.612 = 0.388.

Percentage = 0.388 × 100 = 38.8%.

∴ The correct answer is 38.8%.

Alternate Method

Given → Successive Discounts of 10%, 15%, and 20%. Formulas: Successive Discount = a + b − (a × b) ÷ 100

⇒ Let the Marked Price (MP) be 100. ⇒ Price after 10% discount = 100 − 10 = 90. ⇒ Price after 15% discount on 90 = 90 − (15% of 90) = 90 − 13.5 = 76.5. ⇒ Price after 20% discount on 76.5 = 76.5 − (20% of 76.5) = 76.5 − 15.3 = 61.2. ⇒ Total Single Equivalent Discount = 100 − 61.2 = 38.8.

∴ The correct answer is 38.8%.

Additional Information

Successive Discounts

When multiple discounts are applied one after another, the base value for each subsequent discount is the value obtained after the previous discount.

Effective Discount Rate

The order of applying successive discounts does not change the final Selling Price (SP) or the net discount percentage.

Shortcut Trick

When the Sum (S) and Difference (D) of two quantities are given:

Larger Quantity = (Sum + Difference) ÷ 2

Radha is older, so her age = (26 + 6) ÷ 2

Radha's age = 32 ÷ 2 = 16 years.

∴ The correct answer is 16 years.

Alternate Method

Given:

Sum of ages of Radha and Rama = 26

Difference of ages of Radha and Rama = 6

Let Radha's age be x and Rama's age be y.

⇒ x + y = 26 ----(i)

⇒ x − y = 6 ----(ii)

Adding equations (i) and (ii):

⇒ (x + y) + (x − y) = 26 + 6

⇒ 2x = 32

⇒ x = 32 ÷ 2

⇒ x = 16

∴ The correct answer is 16 years.

Additional Information

Linear Equations in Two Variables

When solving for two variables with sum and difference, the smaller value is (Sum − Difference) ÷ 2.

Age Problems

The difference between the ages of two people remains constant regardless of the number of years passed.

Ratio of Ages

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

The correct answer is 14-45 years

Key Points

• 14-45 years is the age bracket for trainees under the Seekho aur Kamao (Learn and Earn) Scheme as of July 2022.
• The Seekho aur Kamao Scheme aims to provide skill development training to minority communities to enhance their employability and entrepreneurial skills.
• The scheme focuses on modern trades and ensures placements for at least 75% of the trained candidates, out of which 50% should be in the organized sector.
• The scheme is implemented through selected Project Implementing Agencies (PIAs) across the country.

Additional Information

• The Seekho aur Kamao Scheme is an initiative of the Ministry of Minority Affairs, Government of India.
• The scheme also aims to preserve and update the traditional skills of minorities and establish their linkages with the market.
• It includes soft skills, IT, and English language training as part of the curriculum.
• Special focus is given to women, with 33% of the total beneficiaries being female candidates.
• The scheme also includes a post-placement support system to ensure the sustainability of the employment provided.

Given: Six friends, A. B, C, D, E and F, are comparing their heights

Each has a different height.

1. D is taller than only two other friends.

2. C is shorter than B

   >      >      >   D   >      >       > 

3. F is taller than E.

4. D is shorter than A

   >      >   A   >   D   >      >       > 

5. E is taller than A.

 F  >   E   >  A    >   D   >  B    >  C     > 

So, F is the tallest person

Hence the correct answer is "Option 3".

The correct answer is remains constant

Key Points

• Valence electrons are the outermost electrons of an atom and are crucial for determining how the atom interacts with other atoms.
• In a group of the periodic table, the number of valence electrons remains constant as you move down from one element to the next.
• This is because elements in the same group have similar chemical properties and the same number of electrons in their outermost shell.
• For example, all elements in Group 1 (alkali metals) have one valence electron.

Additional Information

• The periodic table is arranged in such a way that elements with similar properties fall into the same vertical columns, known as groups.
• While the number of valence electrons remains constant within a group, the number of electron shells increases as you move down the group, leading to larger atomic radii.
• This constancy in the number of valence electrons is a key reason why elements in the same group exhibit similar chemical behavior.
• Understanding the behavior of valence electrons is essential for predicting the chemical reactivity and bonding characteristics of elements.

The correct answer is 73rd amendment

Key Points

• The 73rd amendment to the Constitution of India is related to the establishment and empowerment of Panchayati Raj institutions.
• This amendment was enacted in 1992 and came into force on 24th April 1993.
• It added a new Part IX to the Constitution titled "The Panchayats" and also added a new Eleventh Schedule covering 29 subjects within the functions of Panchayats.
• The amendment mandates the creation of Panchayats at the village, intermediate, and district levels.
• It aims to decentralize power and ensure local self-governance, providing a greater degree of participation by people at the grassroots level in decision-making processes.
• The act also includes provisions for the reservation of seats for Scheduled Castes, Scheduled Tribes, and women.

Additional Information

• The Constitution of India was adopted by the Constituent Assembly on 26th November 1949 and came into effect on 26th January 1950.
• It lays down the framework defining fundamental political principles, establishes the structure, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• The Constitution of India is the longest written constitution of any country in the world.
• It declares India a sovereign, socialist, secular, and democratic republic, assuring its citizens justice, equality, and liberty, and endeavors to promote fraternity.
• The Seventh Schedule of the Constitution contains three lists which delineate the subjects under the Union, State, and Concurrent lists.
• Amendments to the Constitution can be made through a process outlined in Article 368.
• The 73rd Amendment has played a crucial role in strengthening the democratic fabric of rural India by empowering local governance structures.

Shortcut Trick

Area of triangle = 1/2 |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|

8 = 1/2 |3(−3 − (−4)) + 2(−4 − (−2)) + P(−2 − (−3))|

16 = |3(1) + 2(−2) + P(1)| ⇒ 16 = |3 − 4 + P| ⇒ 16 = |P − 1|

P − 1 = 16 or P − 1 = −16 ⇒ P = 17 or P = −15

∴ The correct answer is 17.

Alternate Method

Given: Vertices (x₁, y₁) = (3, −2), (x₂, y₂) = (2, −3), (x₃, y₃) = (P, −4). Area = 8 sq units.

Formula: Area = 1/2 |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|

⇒ 8 = 1/2 |3(−3 − (−4)) + 2(−4 − (−2)) + P(−2 − (−3))|

⇒ 16 = |3(1) + 2(−2) + P(1)|

⇒ 16 = |3 − 4 + P|

⇒ 16 = |P − 1|

⇒ P − 1 = 16 or P − 1 = −16

⇒ P = 17 or P = −15

From the options provided, the value of P is 17.

∴ The correct answer is 17.

Additional Information

Collinear Points

If three points are collinear, the area of the triangle formed by them is zero.

Area using Determinant

Area can also be calculated as 1/2 |det([[x₁, y₁, 1], [x₂, y₂, 1], [x₃, y₃, 1]])|.

Centroid of a Triangle

The centroid G(x, y) of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) is given by ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3).

The correct answer is No flexibility of constitution

Key Points

• No flexibility of constitution is a false statement regarding the unitary features of the Indian Constitution.
• The Indian Constitution is known for its flexibility as well as rigidity. While certain provisions can be amended by a simple majority, others require a special majority.
• The Constitution of India allows for amendments to adapt to changing needs and circumstances, thereby providing a balance between flexibility and rigidity.
• All India Services, Strong Centre, and No equality of representation are indeed unitary features of the Indian Constitution, as they centralize power and authority.

Additional Information

• All India Services such as IAS, IPS, and IFS are designed to maintain uniform standards of administration across the country.
• A Strong Centre ensures that the Union government holds significant power over states, especially in times of emergency.
• No equality of representation is reflected in the Rajya Sabha, where states have unequal representation based on population.
• The Indian Constitution is a blend of federal and unitary features, allowing it to function effectively in a diverse and populous country like India.

The correct answer is basic

Key Points

• Washing soda, also known as sodium carbonate (Na₂CO₃), is a chemical compound that is basic in nature.
• It is commonly used in laundry detergents and cleaning products due to its ability to remove dirt and grease.
• Washing soda is an alkaline substance, which means it has a high pH level and can neutralize acids.
• It is also used in various industrial processes, such as glass manufacturing and water treatment.

Additional Information

• Sodium carbonate should be handled with care as it can cause irritation to the skin, eyes, and respiratory system.
• In addition to its cleaning properties, washing soda is also used in cooking, particularly in the preparation of certain types of noodles and pretzels.
• It is important to store washing soda in a dry place as it can absorb moisture from the air and form clumps.
• Washing soda can be used as an eco-friendly alternative to many harsh chemical cleaners.

The least possible Venn diagram for the given statements is as follows:

Conclusions:

(i) Some goggles are caps - TRUE (Because all hat are caps and some googles are hat, it indicates some goggles are caps too)

(ii) Some gloves are goggles - TRUE (Because all hat and caps are glove, it indicates some gloves are goggles too)

(iii) No goggle is a glove - FALSE (Because all hat and caps are glove, so some part of googles is glove is definitely true, so the conclusion dose not follows).

So, only conclusion I and II follows

Hence, the correct answer is "Option 1".

Given word: COMPANY

Operation 1: Each consonant in the word is changed to the letter following it in the English alphabetical order

Operation 2: Each vowel is changed to the letter preceding it in the English alphabetical order and is arranged in alphabetical order

New word : DNNQZOZ

Arranging the letters in alphabetical order

So, O is fourth from the right.

Hence, the correct answer is "Option 2".

Given: Eight girls Q, R, S, T, U, V, W and X were sitting around a square table, facing the centre. 

S is sitting at one of the corners

1. Only V was sitting between R and S.

2. Q and T were immediate neighbours.

3. Only X was sitting between T and S.

4. U was sitting to the immediate right of Q.

5. S was sitting fourth to the left of U.

So, W sits fourth to the left of X

Hence the correct answer is "Option 3".

Concept:

Resistance:

• Resistance (R) is the property of a material to oppose the flow of electric current through it.
• It depends on the length (L), cross-sectional area (A), and resistivity (ρ) of the material.
• The formula for resistance is: $R = \rho \frac{L}{A}$
• SI Unit: Ohm (Ω)
• Dimensional Formula: $[ML^2T^{-3}I^{-2}]$
• When the length of a wire changes, its cross-sectional area adjusts to keep the volume constant.
• The volume of the wire remains constant: $L_1A_1 = L_2A_2$
• New resistance $R_2$ after deformation is proportional to the square of the new length: $R_2 = R_1 \left(\frac{L_2}{L_1}\right)^2$