RRB Group D Previous Year Paper (Held on: 30 Sept 2022 Shift 3)

The correct answer is Young Bengal Movement.

Key Points

• Henry Vivian Derozio was an Indian poet and teacher of Anglo-Indian descent, and he is known for his influential role in the Young Bengal Movement.
• Derozio was a radical thinker, poet, and a teacher at Hindu College in Calcutta (now Kolkata) who inspired his students to question traditional societal norms and values.
• The Young Bengal Movement, initiated by Derozio, was characterized by its emphasis on rational thinking, freedom of expression, and the advocacy for social reforms.
• Derozio's followers, known as Derozians, played a significant role in spreading progressive ideas and promoting the spirit of nationalism among the youth of Bengal during the early 19th century.

Additional Information

• Young Bengal Movement:
• The Young Bengal Movement was a group of radical Bengali free thinkers emerging from Hindu College, Calcutta, in the early 19th century.
• They were inspired by the teachings of Henry Vivian Derozio, who encouraged them to challenge conventional practices, caste distinctions, and social injustices.
• The movement was marked by its emphasis on rationalism, secularism, and scientific thought.
• Despite facing opposition from conservative sections of society, the movement significantly influenced the intellectual and social landscape of Bengal.
• Henry Vivian Derozio:
• Derozio was born in 1809 in Kolkata to an Indo-Portuguese father and an English mother.
• He was a brilliant student and later became a teacher at Hindu College, where his progressive ideas left a lasting impact on his students.
• Derozio's poetry reflected his passion for freedom and reform, with notable works including "To India - My Native Land" and "The Harp of India".
• He passed away at a young age of 22 in 1831, but his legacy continued to inspire future generations of reformers and intellectuals in Bengal.
• Hindu College (now Presidency University):
• Hindu College was established in 1817 in Kolkata and became a leading center for Western education in India.
• The college played a pivotal role in the Bengal Renaissance, a period of cultural, social, and intellectual awakening in Bengal.
• It produced many notable alumni who went on to become prominent figures in various fields, including literature, science, and politics.
• In 1855, the college was renamed Presidency College and later achieved university status in 2010, becoming Presidency University.

Shortcut Trick

The least number is calculated as LCM(12, 16, 18) + Remainder.

LCM of 12, 16, and 18 → 12 = 2² × 3, 16 = 2⁴, 18 = 2 × 3².

LCM = 2⁴ × 3² = 16 × 9 = 144.

Required Number = 144 + 5 = 149.

∴ The correct answer is 149.

Alternate Method

Given: Divisors are 12, 16, and 18. Common remainder is 5.

Formula Used: Required Number = LCM(Divisors) + Common Remainder

⇒ Prime factorization of 12 = 2 × 2 × 3

⇒ Prime factorization of 16 = 2 × 2 × 2 × 2

⇒ Prime factorization of 18 = 2 × 3 × 3

⇒ LCM = 2⁴ × 3² = 16 × 9 = 144

⇒ Required Number = 144 + 5

⇒ Required Number = 149

∴ The correct answer is 149.

Additional Information

LCM (Least Common Multiple)

It is the smallest positive integer that is divisible by each of the given numbers without leaving a remainder.

Case of Different Remainders

If remainders are different such that (Divisor − Remainder) = k (constant), then Number = LCM(Divisors) − k.

HCF (Highest Common Factor)

The largest number that divides two or more numbers. Relationship: LCM × HCF = Product of two numbers.

The logic followed here is:

Logic: (1st number + 3rd number) ÷ 4 = 2nd number.

Here,

For, (8, 5, 12)

→ (8 + 12) ÷ 4

⇒ 20 ÷ 4 = 5.

For, (2, 6, 22)

→ (2 + 22) ÷ 4

⇒ 24 ÷ 4 = 6.

Now, checking the options:

Option 1: (1, 6, 23)

→ (1 + 23) ÷ 4

⇒ 24 ÷ 4 = 6.

Option 2: (17, 8, 11)

→ (17 + 11) ÷ 4

⇒ 28 ÷ 4 = 7 ≠ 8.

Option 3: (5, 9, 19)

→ (5 + 19) ÷ 4

⇒ 24 ÷ 4 = 6 ≠ 9.

Option 4: (9, 12, 23)

→ (9 + 23) ÷ 4

⇒ 32 ÷ 4 = 8 ≠ 12.

Hence, the correct answer is "Option 1".

Given:

Sneha starts walking 5 m towards the east.

She turns right and walks 5 m.

Then she takes a left, walks 4 m.

and again takes a left and walks 2 m.

and then again takes a left and walks 3 m.

and then takes a right and walks 2 m. 

again, takes a right again and walks 3 m.

So, Sneha is facing at the 'East' direction now.

Hence, the correct answer is "Option 2".

Shortcut Trick

Total volume of cuboid = 9 × 32 × 48 = 13824 cm³.

Volume of one cube = 13824 ÷ 8 = 1728 cm³.

Edge of the cube (a) = ³√1728 = 12 cm.

Lateral Surface Area (LSA) of 5 cubes = 5 × (4a²) = 20 × 12² = 20 × 144 = 2880 cm².

∴ The correct answer is 2880 cm².

Alternate Method

Given: Dimensions of cuboid = 9 cm × 32 cm × 48 cm. Number of cubes = 8.

Formula: Volume of cuboid = l × b × h; Volume of cube = a³; LSA of cube = 4a².

⇒ Volume of cuboid = 9 × 32 × 48 = 13824 cm³

⇒ 8 × (a³) = 13824

⇒ a³ = 13824 ÷ 8 = 1728

⇒ a = ³√1728 = 12 cm

⇒ LSA of 1 cube = 4 × (12)² = 4 × 144 = 576 cm²

⇒ LSA of 5 cubes = 5 × 576 = 2880 cm²

∴ The correct answer is 2880 cm².

Additional Information

Total Surface Area of Cube

The total area of all six faces of a cube is given by the formula TSA = 6a².

Diagonal of a Cube

The longest distance between any two corners of a cube is d = a√3.

Surface Area of Cuboid

The Total Surface Area of a cuboid is 2(lb + bh + hl) and its Lateral Surface Area is 2h(l + b).

The correct answer is Gold.

Key Points

• Gold (Au)
• Atomic Number: 79
• Atomic Mass: 196.96657 u
• Electron Configuration: [Xe] 4f14 5d10 6s1
• Melting Point: 1064.18 °C (1337.33 K)
• Boiling Point: 2808 °C (3081 K)
• Density: 19.32 g/cm³
• Reactivity: Extremely low, resists corrosion and tarnish.

Additional Information

• Sodium (Na)
• Atomic Number: 11
• Atomic Mass: 22.98976928 u
• Electron Configuration: [Ne] 3s1
• Melting Point: 97.72 °C (370.87 K)
• Boiling Point: 883 °C (1156 K)
• Density: 0.968 g/cm³
• Reactivity: Highly reactive, reacts vigorously with water and air.
• Silver (Ag)
• Atomic Number: 47
• Atomic Mass: 107.8682 u
• Electron Configuration: [Kr] 4d10 5s1
• Melting Point: 961.78 °C (1234.93 K)
• Boiling Point: 2162 °C (2435 K)
• Density: 10.49 g/cm³
• Reactivity: Moderately reactive, tarnishes in air due to sulfur compounds.
• Mercury (Hg)
• Atomic Number: 80
• Atomic Mass: 200.59 u
• Electron Configuration: [Xe] 4f14 5d10 6s2
• Melting Point: -38.83 °C (234.32 K)
• Boiling Point: 356.73 °C (630.08 K)
• Density: 13.534 g/cm³
• Reactivity: Relatively low, forms amalgams with other metals.

According to the given Venn diagram:

The shaded area shows the children who like music but NOT sports.

So, there are '42' children who like music but NOT sports.

Hence, the correct answer is "42".

The correct answer is Palk Strait.

Key Points

• The Palk Strait is a strait between India and Srilanka.
• It connects the Bay of Bengal in the northeast with the Gulf of Mannar in the southwest.
• This chain extends between Dhanushkodi on Pamban (Rameswaram) Island in Tamil Nadu and Mannar Island in Sri Lanka.

Important Points

• Palk Strait is a water body that separates India and Sri Lanka.
• Palk strait is a water body between the Jaffna district of Sri Lanka and the Tamil Nadu state of India. The Palk strait connects the Bay of Bengal in the northeast with Palk Bay in the southwest.
• The Palk strait is named after the Governor of Madras Robert Palk, during the Company Raj period.
• Vaigai River of Tamil Nadu flows into the Palk Strait.

Additional Information

• The Radcliffe Line is the boundary line between India and Pakistan.
• The McMahon Line is the boundary line between northeastern India and China.

The correct answer is SAMRIDH.

Key Points

• The Union government has launched a program to support 300 IT start-ups.
• The government would provide seed funding and market access with a view to creating 100 unicorns out of the selected start-ups.
• The concept of the Startup Accelerator of MeitY for Product Innovation, Development & Growth (SAMRIDH) has been developed on the lines of silicon valley based accelerator YCombinator.
• Under the programme, Meity will provide seed funds of up to Rs 40 lakh for the selected start-ups and mentorship for six months.
• The government wants to scale up the networks of incubators and startups to 10x, 20x and more.

​ 

Additional Information

ASPIRE: A Scheme for promotion of Innovation, Entrepreneurship and Agro-Industry

• The main objective of the schemes are:
• Create new jobs and reduce unemployment
• Promote entrepreneurship culture in India
• Grassroots economic development at the district level
• Facilitate innovative business solution for unmet social needs
• Promote innovation to further strengthen the competitiveness of the MSME sector.
• This scheme was launched in 2015 by Ministry of MSME (Ministry of Micro, Small and Medium Enterprises).
• The union minister of MSME is Nitin Gadkari.
• Multiplier Grant Scheme: 
• MGS aims to encourage collaborative R&D between industry and academics/ R&D institutions for development of products and packages.
• Startup India Seed Fund
• Minister of Railways, Commerce and Industry, Consumer Affairs, and Food and Public Distribution Piyush Goyal launched the Startup India Seed Fund Scheme (SISFS) on 19 April 2021.
• The fund aims to provide financial assistance to startups for proof of concept, prototype development, product trials, market entry, and commercialization.
• It was announced by PM Narendra Modi on 16th January 2021.

Shortcut Trick

Directly substitute standard values: sin 30° = 1/2, cos 60° = 1/2, tan 45° = 1, cosec 60° = 2/√3.

Expression = 1/2 − 1/2 + 1 + 2/√3

⇒ 1 + 2/√3 = (1 × √3 + 2) / √3 = (√3 + 2) / √3

Rationalizing: [(√3 + 2) × √3] / [√3 × √3] = (3 + 2√3) / 3

∴ The correct answer is (3 + 2√3) / 3.

Alternate Method

Given: sin 30° − cos 60° + tan 45° + cosec 60°

Formula Used: Standard trigonometric ratios of specific angles.

⇒ Substituting values: (1/2) − (1/2) + 1 + (2/√3)

⇒ 0 + 1 + 2/√3

⇒ 1 + 2/√3

⇒ (√3 + 2) / √3

⇒ Multiply numerator and denominator by √3 to rationalize:

⇒ [(√3 + 2) × √3] / 3

⇒ (3 + 2√3) / 3

∴ The correct answer is (3 + 2√3) / 3.

Additional Information

Trigonometric Complementary Ratios

Note that sin θ = cos (90° − θ). Thus, sin 30° = cos 60°, which results in their subtraction becoming zero.

Reciprocal Identities

cosec θ is the reciprocal of sin θ. Since sin 60° = √3/2, cosec 60° = 2/√3.

Rationalization Rule

To remove a radical from the denominator, multiply both numerator and denominator by the same radical: a/√b = (a×√b)/b.

The correct answer is Soil → root hairs → root cortex → xylem of roots → xylem of stem → xylem of leaf.

Key Points

• The provided data outlines the pathway of water transport in plants, starting from the soil and culminating in the leaves. Here's a breakdown of the process:
• Soil: Water is absorbed from the soil by the plant's root hairs.
• Root Hairs: These tiny, hair-like extensions of root epidermal cells significantly increase the surface area for water absorption.
• Root Cortex: Water absorbed by the root hairs moves through the cortex, a layer of cells that lies beneath the epidermis.
• Xylem of Roots: From the cortex, water enters the xylem, a specialized tissue for water and mineral transport.
• Xylem of Stem: The xylem tissue forms a continuous network throughout the plant, extending from the roots to the stem. Water is transported upward through the xylem of the stem.
• Xylem of Leaf: The xylem vessels reach the leaves, delivering water to the various cells within the leaf.
• Transpiration: Water is lost from the leaves through tiny pores called stomata in a process called transpiration.
• Water Potential Gradient: Transpiration creates a water potential gradient, pulling water upward from the roots through the xylem.
• Cohesion-Tension Theory: Water molecules are cohesive (stick together) due to hydrogen bonds. This cohesion, combined with the tension created by transpiration, helps to move water up the xylem.
• Root Pressure: In some plants, root pressure can also contribute to water movement. This pressure is generated by the active transport of minerals into the root xylem, which draws water in by osmosis.

Given word: 'PROUDLY'

Now, arranging in Alphabetical order:

Here, after arranged in alphabetical order 'Two' letters will remain unchanged i.e. 'O' and 'Y'.

Hence, the correct answer is "Option 1".

Given:

19.99 - 10.01 + 24.99 × 10.01

Formula Used:

Expression evaluation

Calculation:

Approximate the values:

19.99 ≈ 20

10.01 ≈ 10

24.99 ≈ 25

Substitute the approximate values into the expression:

⇒ 20 - 10 + 25 × 10

First, perform the multiplication:

⇒ 20 - 10 + 250

Next, perform the addition and subtraction:

⇒ 10 + 250

⇒ 260

The correct answer is option 2.

The correct answer is ₹10 crore.

Key Points

• As of April 2022, to avail the scheme of Permanent Residency Status to Foreign Investors, the investment amount required was INR 10 Crore within 18 months.
• Here's a breakdown of the scheme and its requirements:
• Permanent Residency Status (PRS) for Foreign Investors: This scheme aimed to attract foreign investment and boost economic growth in India. It offered a pathway to permanent residency for eligible foreign investors who met specific criteria.
• Investment Threshold: The key requirement was a substantial investment in India. In April 2022, the threshold for obtaining PRS was set at INR 10 Crore within 18 months.
• This investment had to be made under the Foreign Direct Investment (FDI) route.
• Employment Generation: The scheme also stipulated that the investment should result in employment for at least 20 resident Indians in every financial year.
• Eligibility: The scheme was applicable to foreign nationals, excluding citizens of Pakistan or third-country nationals of Pakistani origin.
• Benefits of PRS: Obtaining PRS granted several advantages to foreign investors, including:
• Long-term Stay: PRS holders were allowed to stay in India for an extended period without restrictions on each visit.
• Multiple Entry: PRS provided for multiple entries into India.
• No Registration Requirements: PRS holders were exempted from registration requirements with the Foreigners Regional Registration Office (FRRO) or Foreigners Registration Office (FRO).
• Property Ownership: PRS holders were permitted to purchase one residential property for dwelling purposes.

Additional InformationRs. 25 crore in 36 months to secure a Permanent Residency Status. The foreign investment should result in generating employment to at least 20 resident Indians. The PRS will serve as a multiple entry visa without any stay stipulation.

The correct answer is Bay of Bengal branch.

Key Points

• The Bay of Bengal branch of the southwest monsoon is one of the two branches of the monsoon winds that affect the Indian subcontinent.
• Originating from the warm, moist air over the Bay of Bengal, this branch is driven towards the Indian subcontinent by the Southwest Monsoon winds.
• After making landfall, it splits into two branches, one moving northwest towards the Indo-Gangetic Plain and the other northeast towards the Eastern Himalayas.
• The Bay of Bengal branch is responsible for bringing substantial rainfall to the eastern and northeastern parts of India, including West Bengal, Northeastern states, and as far west as Uttar Pradesh and Bihar. It is crucial for the agriculture of these regions.
• The progress of the Bay of Bengal branch can experience "monsoon breaks," where rainfall diminishes for several days or weeks.

Additional Information

• Western Disturbances:
• The interior region of Asia and Europe gets extremely cold during Winters, this creates a high-pressure zone especially along the Mediterranean region.
• Compared to those regions, the Indian subcontinent is a low-pressure zone, hence winds blow from the Mediterranean region towards India, causing rainfall mainly in parts of Punjab and Haryana
• Returning Monsoon
• The returning monsoon winds, also known as the northeast monsoon, bring rain to the states of Tamil Nadu and Andhra Pradesh.
• These winds are part of the larger pattern of seasonal winds that include the southwest monsoon, which brings rain to most of India during the summer.
• The northeast monsoon typically occurs from October to December and is crucial for the winter crops in Tamil Nadu and Andhra Pradesh.
• This monsoon is characterized by relatively stable and dry conditions in most parts of India, except for the southeastern region, which receives significant rainfall.
• Arabian Sea branch
• Arabian Sea monsoon makes landfall on the coast north of Mumbai.
• These winds, which move over the Narmada and Tapi River basins, generate rain in large parts of central India. This section of the branch brings 15 cm of rain to the Chotanagpur plateau.
• Following that, they enter the Ganga plains and mix with the Bay of Bengal branch.

Shortcut Trick Rewrite the equation in standard form ax2 + bx + c = 0: 2x2 + 9x − 5 = 0. Identify a = 2, b = 9, c = −5. Apply the Discriminant formula: D = b2 − 4ac. D = 92 − 4 × 2 × (−5) = 81 + 40 = 121. ∴ The correct answer is 121.Alternate Method Given: Equation: 9x + 2x2 = 5 Formula Used: For a quadratic equation of the form ax2 + bx + c = 0, the Discriminant (D) is given by: D = b2 − 4ac Calculations: ⇒ Rearranging 9x + 2x2 = 5 to the standard form: ⇒ 2x2 + 9x − 5 = 0 ⇒ Comparing with ax2 + bx + c = 0, we get: ⇒ a = 2, b = 9, c = −5 ⇒ D = (9)2 − 4 × 2 × (−5) ⇒ D = 81 − (−40) ⇒ D = 81 + 40 ⇒ D = 121 ∴ The correct answer is 121.Additional Information Nature of Roots If D > 0, roots are real and distinct. If D = 0, roots are real and equal. If D < 0, roots are imaginary. Quadratic Formula The roots of the equation are calculated as x = (−b ± √D) ÷ 2a. Perfect Square Discriminant If D is a perfect square and a, b, c are rational, then the roots of the quadratic equation are rational.

Given Numbers: '7639482 '

Now, arranging in ascending order from right to left:

Here, after arranged in ascending order from right to left 'Two' numbers will remain unchanged i.e. '4' and '2'.

Hence, the correct answer is "Option 3".

Mistake Points Ascending order from right to left means Descending order.

The correct answer is Litmus solution is a purple dye, which is extracted from lichen.

Key Points

• Litmus solution is a common pH indicator used in laboratories.
• When the pH is neutral, litmus solution turns Purple.
• Litmus paper can be either red or blue; red litmus paper turns blue in basic conditions, and blue litmus paper turns red in acidic conditions.
• Neutral pH is considered to be 7, which is the pH of pure water.
• Litmus solution is derived from lichens, primarily Roccella tinctoria.

Additional Information

• Litmus solution is often used in educational settings to teach students about acids and bases.
• Other pH indicators include phenolphthalein, bromothymol blue, and methyl orange, each changing color at different pH levels.
• Understanding pH is crucial in various fields, including chemistry, biology, environmental science, and medicine.

The correct answer is The change in total cost per unit of change in output.

Key Points

• Long Run Marginal Cost (LRMC) represents the extra cost incurred by a firm to produce one additional unit of output in the long run. Unlike the short run where some inputs are fixed, the long run allows a firm to adjust all its inputs (labor, capital, technology) to achieve optimal production levels.

Additional Information

• Derived from Long Run Total Cost (LRTC): LRMC is the slope of the LRTC curve at any given level of output.
• Relationship with Long Run Average Cost (LRAC):
• When LRMC is below LRAC, LRAC is falling.
• When LRMC is above LRAC, LRAC is rising.
• When LRMC intersects LRAC, LRAC is at its minimum point.
• Reflects Returns to Scale: LRMC is closely linked to returns to scale.
• Increasing Returns to Scale: If output more than doubles when inputs double, LRMC is falling.
• Constant Returns to Scale: If output doubles when inputs double, LRMC is constant.
• Decreasing Returns to Scale: If output less than doubles when inputs double, LRMC is rising.
• Production Decisions: Firms use LRMC to determine the optimal level of output to maximize profits. They compare LRMC to the long-run marginal revenue (LRMR) and produce where LRMC equals LRMR.
• Long-Run Planning: LRMC helps firms make long-term decisions about plant size, technology adoption, and resource allocation.
• Understanding Industry Structure: The shape of the LRMC curve can provide insights into the competitive structure of an industry.

Shortcut Trick

For four numbers a, b, c, and d in proportion: Product of extremes = Product of means.

20 × x = 38 × 40

x = (38 × 40) ÷ 20

x = 38 × 2 = 76

∴ The correct answer is 76.

Alternate Method

Given: Numbers 20, 38, 40 and x are in proportion.

Formula Used: If a, b, c, d are in proportion, then a/b = c/d.

⇒ 20 ÷ 38 = 40 ÷ x

⇒ 20 × x = 38 × 40

⇒ x = (38 × 40) ÷ 20

⇒ x = 38 × 2

⇒ x = 76

∴ The correct answer is 76.

Additional Information

Mean Proportional

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

Third Proportional

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

Fourth Proportional

In the proportion a : b :: c : d, the term d is called the fourth proportional, calculated as d = (b × c) ÷ a.

Shortcut Trick

Condition 1: Neither number should be prime (both must be composite).

Condition 2: They must be co-prime (HCF = 1).

Check pairs: (19, 27) → 19 is prime. (11, 17) → Both are prime. (21, 35) → HCF is 7. (8, 25) → Both composite and HCF is 1.

∴ The correct answer is (8, 25).

Alternate Method

Given: Pairs of numbers to test for non-prime status and co-prime property.

Step-by-step Evaluation:

⇒ Option (1): (8, 25). Factors of 8: 1, 2, 4, 8 (Composite). Factors of 25: 1, 5, 25 (Composite). HCF(8, 25) = 1. (Valid)

⇒ Option (2): (19, 27). 19 is a Prime Number. (Invalid based on first condition)

⇒ Option (3): (11, 17). Both 11 and 17 are Prime Numbers. (Invalid based on first condition)

⇒ Option (4): (21, 35). Factors of 21: 1, 3, 7, 21. Factors of 35: 1, 5, 7, 35. HCF is 7. (Invalid based on co-prime condition)

∴ The correct answer is (8, 25).

Additional Information

Prime and Composite Numbers

A Prime number has exactly two factors (1 and itself), while a Composite number has more than two factors.

Co-prime Numbers

Two numbers are co-prime if their Highest Common Factor (HCF) is 1. They do not need to be prime individually.

Twin Primes

A pair of prime numbers that have a difference of 2, such as (11, 13) or (17, 19).

Given: Six colleagues are sitting around a circular table facing the centre.

1. Amrita is sitting second to the left of Kavita.

2) Rohan is an immediate neighbour of both Kavita and Amrita.

3. Meagan is sitting second to the right of Sabina.

4. Rochelle is an immediate neighbour of both Meagan and Sabina.

So, 'Amrita' is sitting to the immediate right of Meagan.

Hence, the correct answer is "Option 2".

The correct answer is Fleming’s Left Hand Rule, electrical, mechanical.

Key Points 

Fleming's left-hand rule:

Fleming’s left-hand rule states that when current flows through a conducting wire (let it be along with middle finger of a left hand) and an external magnetic field applied in the perpendicular direction (along with index finger) then the thrust of the motor is the mutually perpendicular direction (along with thumb finger) to both current and magnetic field.

Fleming’s left hand is a visual mnemonic for electric motors to represent the direction of thrust of motor w.r.t to the direction of the current and magnetic field.

Additional Information

• Fleming's left-hand rule is used for electric motors, while Fleming's right-hand rule is used for electric generators.
• In an electric motor, the electric current and magnetic field exist (which are the causes), and they lead to the force that creates the motion (which is the effect), and so the left-hand rule is used.

The logic followed here is:

So, 'AI17' will complete the series.

Hence, the correct answer is "Option 1".

The correct answer is Li(6.9), Na(23.0), K(39.1).

Key Points

• Dobereiner's Triads:
• ​ In the early 19th century, German chemist Johann Wolfgang Dobereiner observed a pattern in the properties of certain groups of elements. He noticed that some elements could be grouped into sets of three, called triads, based on their similar chemical and physical properties.

 Additional Information

• Similar Properties: The elements within a triad exhibited striking similarities in their chemical behavior. For example, chlorine, bromine, and iodine are all halogens, a group of highly reactive non-metals.
• Atomic Mass Relationship: The most significant observation was that the atomic mass of the middle element in the triad was approximately the average of the atomic masses of the other two elements.
• In the case of chlorine, bromine, and iodine:
• Atomic mass of chlorine: 35.45
• Atomic mass of bromine: 79.90
• Atomic mass of iodine: 126.90
• Average of chlorine and iodine: (35.45 + 126.90) / 2 = 81.17
• Limitations: While Dobereiner's triads provided an early attempt at classifying elements, they had limitations. Not all elements could be neatly organized into triads, and the concept didn't fully explain the periodic trends observed in elemental properties.

The correct answer is Gujarat Titans.

Key Points

• Gujrat Titans(GT) won the Tata Indian Premier League (IPL) 2022.
• GT won IPL 2022 by 7 wickets from Rajasthan Royals under the captaincy of Hardik Pandya.
• GT played 14 matches and won 10 of them to become the leading team of the year.

 Additional Information

• 2022 was the debut year of Gujrat Titans.
• IPL is a mega cricket event which is organized annually in India on a very large scale
• Here is a look at various award winners after the final match in Ahmedabad: ​

The correct answer is Goods and Services Tax.

Key Points

• Indirect tax -
• The tax which is not taken directly from the public but reaches the government indirectly is called indirect tax.
• Indirect taxes are excise duties on goods manufactured in the country, customs duties on goods to be imported or exported.
• E.g. Service Tax, Central Excise Duty, Customs Duty, etc.

Additional Information

• The tax levied on all services is called Service Tax.
• The tax levied on the sale of goods under indirect tax is called sales tax.
• The tax levied on the products made in the country is called Excise Duty.
• Types of Indirect Taxes -
• Sales Tax
• Service Tax
• Excise Duty
• Professional Tax
• Dividend Distribution Tax
• Entertainment Tax
• Property Tax
• Stamp Duty
• VAT Tax (VAT)
• Toll Tax

The logic followed here is:

For, BOOK ∶ YLLP

For, 

Similarly, for WORD: ?

Hence, the correct answer is "Option 4".

Given:

Total students in the school = 47,500

Survey conducted on 80% of students

Percentage of students reading mystery = 15%

Percentage of students reading horror = 20%

Formula used:

1. Total students surveyed = Total students × (80/100)
2. Students reading a genre = Total surveyed students × (percentage of the genre/100)
3. Total students reading mystery and horror = Students reading mystery + Students reading horror

Calculations:

Step 1: Calculate total students surveyed:

Total surveyed students = 47,500 × (80/100) = 38,000

Step 2: Calculate students reading mystery:

Students reading mystery = 38,000 × (15/100) = 5,700

Step 3: Calculate students reading horror:

Students reading horror = 38,000 × (20/100) = 7,600

Step 4: Calculate total students reading mystery and horror:

Total students = 5,700 + 7,600 = 13,300

The number of students who read mystery and horror books is 13,300.

Shortcut Trick

Ratio of Young members to Old members = 70 : 30 = 7 : 3.

Average age of Young = 20 years, Average age of Old = 40 years.

Weighted Average = [(7 × 20) + (3 × 40)] ÷ (7 + 3)

⇒ (140 + 120) ÷ 10 = 260 ÷ 10 = 26 years.

∴ The correct answer is 26 years.

Alternate Method

Given:

Total members (assumed) = 100

Young members = 70% of 100 = 70

Old members = 30% of 100 = 30

Average age of Young = 20 years

Average age of Old = 40 years

Formula: Average = Sum of all observations ÷ Total number of observations

⇒ Total age of Young members = 70 × 20 = 1400 years

⇒ Total age of Old members = 30 × 40 = 1200 years

⇒ Total age of all members = 1400 + 1200 = 2600 years

⇒ Average age of all members = 2600 ÷ 100

⇒ Average age = 26 years

∴ The correct answer is 26 years.

Additional Information

Weighted Average Formula

It is used when two or more groups are combined: A_avg = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Alligation Method

Ratio of quantities = (Higher Value − Mean) : (Mean − Lower Value). This can be used to find the mean age directly.

Combined Average Properties

The combined average always lies between the lowest and the highest individual averages of the constituent groups.

The correct answer is 2014.

Key Points

• Namami Gange Programme:
• ​It was started in 2014.
• Namami Gange Programme is an Integrated Conservation Mission, approved by the Government of India.
• It was started with a budget outlay of Rs.20,000 Crore to accomplish the twin objectives of effective abatement of pollution, conservation, and rejuvenation of National River Ganga.
• The River Ganga is important not only for its cultural and spiritual significance but also because it hosts more than 40% of the country’s population.
• 8 states are covered under the project including Uttar Pradesh, West Bengal, and Jharkhand.
• The main pillars of this programme include Biodiversity, Riverfront Development, Sewage Treatment Infrastructure, River Surface Cleaning, Public Awareness, Afforestation, Ganga Gram and Industrial Effluent Monitoring.

 Additional Information

• Namami Gange Programme has been started in order to protect and clean the Ganga. The programme is 100% centrally funded. It intends to ramp up the progress of the Ganga clean-up mission.
• 8 states are covered under the project including Uttar Pradesh, West Bengal, and Jharkhand. The main pillars of this programme include Biodiversity, Riverfront Development, Sewage Treatment Infrastructure, River Surface Cleaning, Public Awareness, Afforestation, Ganga Gram and Industrial Effluent Monitoring.

Shortcut Trick

Let the daughter’s age one year ago be 1 unit. Then Praveena’s age was 4 units.

Present ages: Praveena = 4x + 1, Daughter = x + 1.

Condition 6 years hence: (4x + 7) = 2(x + 7) + 7 ⇒ 4x + 7 = 2x + 14 + 7 ⇒ 2x = 14 ⇒ x = 7.

Sum of present ages = (4x + 1) + (x + 1) = 5x + 2 = 5(7) + 2 = 37 years.

∴ The correct answer is 37 years.

Alternate Method

Given:

Ratio of Praveena to Daughter (1 year ago) = 4 : 1

Calculations:

⇒ Let Praveena’s age (1 yr ago) = 4x and Daughter’s age (1 yr ago) = x

⇒ Present age of Praveena = 4x + 1

⇒ Present age of Daughter = x + 1

⇒ Age 6 years hence: Praveena = (4x + 1) + 6 = 4x + 7

⇒ Age 6 years hence: Daughter = (x + 1) + 6 = x + 7

⇒ According to the question: (4x + 7) = 2(x + 7) + 7

⇒ 4x + 7 = 2x + 14 + 7

⇒ 4x − 2x = 21 − 7

⇒ 2x = 14 ⇒ x = 7

⇒ Present Praveena = 4(7) + 1 = 29 years

⇒ Present Daughter = 7 + 1 = 8 years

⇒ Sum = 29 + 8 = 37 years

∴ The correct answer is 37 years.

Additional Information

Problems on Ages

Age difference between two people always remains constant regardless of the number of years passed.

Ratio Method

If the ratio of ages is given for two different time periods, equate the difference in ratio units to the actual time gap.

Future and Past Calculations

For 'n' years hence, add 'n' to present age. For 'n' years ago, subtract 'n' from present age.

The logic followed here is:

‘FAR’ is written as ‘SARF’.

‘PICK’ is written as ‘SICKP’.

Similarly, for ‘BLACK’

So, 'BLACJ' will be written as 'SLACKB'.

Hence, the correct answer is "Option 4".

The correct answer is One.

Key Points

• India achieved its highest ranking in over four decades, finishing 48th on the medal tally in Tokyo.
• The nation competed at the 2020 Summer Olympics in Tokyo, Japan.
• Originally slated for July 24 to August 9, 2020, the games were rescheduled to July 23 to August 8, 2021, due to the COVID-19 pandemic.
• India has participated in every edition of the Summer Olympics since 1920, making its official debut at the 1900 Summer Olympics in Paris.
• The country fielded its largest-ever contingent of 126 competitors at the 2020 Games.
• The 2020 Summer Olympics marked India's most successful Games since its inaugural regular Olympics appearance in 1920, with Indian athletes securing 7 medals (1 gold, 2 silver, and 4 bronze).

Additional Information

• The 2020 Summer Olympics, officially known as the Games of the XXXII Olympiad and branded as Tokyo 2020, were a global multi-sport event conducted from July 23 to August 8, 2021, in Tokyo, Japan, with some preliminary events commencing on July 21, 2021.
• Tokyo was chosen as the host city during the 125th IOC Session in Buenos Aires, Argentina, on September 7, 2013.
• These Games marked the fourth time that Japan hosted the Olympics, following the 1964 Summer Olympics (Tokyo), 1972 Winter Olympics (Sapporo), and 1998 Winter Olympics (Nagano).
• Tokyo became the first Asian city to host the Summer Olympic Games twice.
• The 2020 Games were part of a series of three consecutive Olympics held in East Asia, preceded by the 2018 Winter Olympics in Pyeongchang, South Korea, and followed by the 2022 Winter Olympics in Beijing, China.

Shortcut Trick In the quadratic equation 6x2 − 11x + 3 = 0, the product of a × c is 6 × 3 = 18 and the sum b is −11. Identify two numbers that multiply to 18 and add up to −11: these are −9 and −2. The roots are obtained by changing the signs of these factors and dividing by the coefficient of x2 (6). Roots = 9/6 and 2/6 ⇒ 3/2 and 1/3. ∴ The correct answer is 1/3, 3/2. Alternate Method Given: The quadratic equation is 6x2 − 11x + 3 = 0. Method: Factorization by splitting the middle term. ⇒ 6x2 − 9x − 2x + 3 = 0 ⇒ 3x(2x − 3) − 1(2x − 3) = 0 ⇒ (3x − 1)(2x − 3) = 0 For the product to be zero, either: ⇒ 3x − 1 = 0 ⇒ 3x = 1 ⇒ x = 1/3 OR ⇒ 2x − 3 = 0 ⇒ 2x = 3 ⇒ x = 3/2 Comparing these roots with the options, we find they match the values 1/3 and 3/2. ∴ The correct answer is 1/3, 3/2. Additional Information Quadratic Formula The roots of ax2 + bx + c = 0 can also be found using x = [−b ± √(b2 − 4ac)] / 2a. Nature of Roots The Discriminant (D) = b2 − 4ac. If D > 0 and a perfect square, the roots are rational and distinct. Sum and Product of Roots For any quadratic equation, Sum of roots (α + β) = −b/a and Product of roots (αβ) = c/a.

Given:

Number of cars sold:

2015: 15 thousand

2017: 30 thousand

2019: 35 thousand

2021: 40 thousand

Formula used:

1. Total cars sold in specified years = Sum of cars sold in those years
2. Ratio = Total cars sold in 2015 and 2017 : Total cars sold in 2019 and 2021

Calculations:

Step 1: Calculate total cars sold in 2015 and 2017:

Total = 15 + 30 = 45 thousand

Step 2: Calculate total cars sold in 2019 and 2021:

Total = 35 + 40 = 75 thousand

Step 3: Find the ratio:

Ratio = 45 : 75

Ratio = 3 : 5 (after simplification)

The respective ratio of the total cars sold in 2015 and 2017 to the total cars sold in 2019 and 2021 is 3:5.

Shortcut Trick

Effective % for Amount (Case 1) = 100% + (8 × 3.5)% = 128%

Effective % for Simple Interest (Case 2) = (10.5 × 12)% = 126%

Difference in percentage = 128% − 126% = 2%

Given, 2% of Sum = ₹156

∴ 100% (Sum) = 156 ÷ 2 × 100 = ₹7,800

∴ The correct answer is ₹7,800.

Alternate Method

Given:

Case 1: Rate (R₁) = 8%, Time (T₁) = 3.5 years

Case 2: Rate (R₂) = 10.5%, Time (T₂) = 12 years

Difference between Amount₁ and SI₂ = ₹156

Formula Used:

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

Amount (A) = P + SI

Calculations:

Let the Sum be P.

⇒ SI₁ = (P × 8 × 3.5) ÷ 100 = 0.28P

⇒ Amount₁ = P + 0.28P = 1.28P

⇒ SI₂ = (P × 10.5 × 12) ÷ 100 = 1.26P

According to the question:

⇒ 1.28P − 1.26P = 156

⇒ 0.02P = 156

⇒ P = 156 ÷ 0.02

⇒ P = 15600 ÷ 2 = 7800

∴ The correct answer is ₹7,800.

Additional Information

Simple Interest Concept

Simple interest is calculated only on the Principal amount for the entire duration. Formula: SI = P × R × T / 100.

Maturity Amount

The total amount payable at maturity is the sum of the initial principal and the total interest earned: A = P × (1 + RT/100).

Effective Interest Rate

For multiple periods at SI, the effective rate is simply the product of Rate and Time (R × T)%.

The correct answer is voltaic cell.

Key Points

• Voltaic Cell:
• A voltaic cell, also known as a galvanic cell, is an electrochemical device that converts chemical energy directly into electrical energy.
• It does this through a spontaneous redox reaction, where oxidation and reduction occur at separate electrodes.
• Chemical Energy:
• Within the voltaic cell, chemical energy is stored in the form of potential energy within the chemical bonds of the reactants.
• This potential energy arises from the tendency of the reactants to undergo a spontaneous redox reaction.

Additional Information

• Electrical Energy:
• When the circuit is closed, the chemical energy is converted into electrical energy.
• Electrons flow from the anode (where oxidation occurs) to the cathode (where reduction occurs) through an external wire, creating an electric current.
• Voltmeter:
• A voltmeter is a device used to measure the potential difference (voltage) between two points in an electrical circuit.
• In a voltaic cell, it measures the electromotive force (EMF) generated by the cell, which is the maximum potential difference it can provide.
• Resistor:
• A resistor is an electrical component that resists the flow of electric current.
• It converts some of the electrical energy into heat energy, reducing the amount of electrical energy available to other components in the circuit.
• Ammeter:
• An ammeter is a device used to measure the electric current flowing through a conductor.
• In a voltaic cell circuit, it measures the amount of electrical current produced by the cell.

 Important Points

• Energy Conversion:
• the voltaic cell converts chemical energy into electrical energy.
• The voltmeter measures the potential difference (voltage) of this electrical energy.
• The resistor converts some of the electrical energy into heat energy.
• And the ammeter measures the flow of electrical current through the circuit.

Statement:

Some Baskets are Canes.

Some Canes are Woods.

All Woods are Forests.

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

Conclusions:

(i) All Canes are Forests - False (Some canes are forests, but All canes are forest can be possible, not definite).

(ii) Some Baskets are Woods - False (Because no direct relation given between Baskets and Woods, so it can be possible only).

Here, Neither conclusion (I) nor (II) follows..

Hence, the correct answer is "Option 1".

Shortcut Trick

Total distance = Train length + Tunnel length = 150 + 100 = 250 m.

Speed in m/s = 25 × (5/18) = 125/18 m/s.

Time = Distance ÷ Speed = 250 ÷ (125/18) = 2 × 18 = 36 sec.

∴ The correct answer is 36 sec.

Alternate Method

Given:

Length of train (L₁) = 150 m

Length of tunnel (L₂) = 100 m

Speed of train (v) = 25 km/h

Formula Used:

Time = Total Distance ÷ Speed

To convert km/h to m/s, multiply by 5/18.

Calculations:

⇒ Total Distance = 150 m + 100 m = 250 m

⇒ Speed in m/s = 25 × (5/18) m/s

⇒ Time = 250 ÷ (25 × 5 / 18)

⇒ Time = (250 × 18) ÷ 125

⇒ Time = 2 × 18

⇒ Time = 36 sec

∴ The correct answer is 36 sec.

Additional Information

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Relative Speed

When two objects move in the same direction, relative speed is S₁ − S₂. In opposite directions, it is S₁ + S₂.

Crossing Objects

To cross a point object (pole, man), distance = length of train. To cross a platform or tunnel, distance = train length + platform/tunnel length.

Given:

Now, the group of numbers and symbols is: 7 2 π 3 @ 6

Here, Second conditions followed in the given group,

So, First and last elements are to be coded as ©.

Then, the code for **'**7 2 π 3 @ 6' is → '© M E V L ©'.

Hence, the correct answer is "Option 3".

The correct answer is Part A only.

Key Points

• A zygote is a diploid cell formed by the fusion of female and male gametes.

Explanation:

Zygote:

• It is a eukaryotic cell.
• Once the zygote is formed embryo formation occur.
• Zygote formation occurs in the first weeks of fertilization.
• In each gamete, the genome of the zygote is a combination of DNA.
• In an individual, it contains required genetic information.

Thus, the zygote is a new cell.

Additional Information

Sperm:

• It is a male reproductive cell or gametes.
• The sperm is divided into a head middle piece and tail.
• It creates from the testis.
• When it's fertilised the ovum creates a zygote.

Ovum:

• Ova is released from the ovaries (ovum plural form, ova singular form).
• Ovum contains a central nucleus, cytoplasm, and first polar body covered with vitelline membrane, zona pellucida and corona radiate.
• For an embryo, the ovum provides half of the genetic material.

Chromosome:

• In animal and plant cells inside the nucleus, there is a thread-like structure present called a chromosome.
• Chromosomes are made up of protein.
• It contains the genetic material, DNA.

Given: Four friends R, S, T and U.

1. R is sitting to the immediate right of S.

2. T is sitting to the immediate left of U.

Here, from the arrangement the pair 'R - U' is sitting opposite to each other.

Hence, the correct answer is "Option 1".

Shortcut Trick

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

Given angle = 108°

a = 180° − 108°

a = 72°

∴ The correct answer is 72°.

Alternate Method

Given: A pair of parallel lines intersected by a transversal. The angles shown in the figure are consecutive interior angles.

Formula Used: Sum of consecutive interior angles = 180°

⇒ a + 108° = 180° (Consecutive interior angles are supplementary)

⇒ a = 180° − 108°

⇒ a = 72°

∴ The correct answer is 72°.

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, corresponding angles are equal.

Alternate Interior Angles

When two parallel lines are intersected by a transversal, the alternate interior angles (Z-shape) are equal.

Linear Pair

A pair of adjacent angles formed by intersecting lines. The

The correct answer is 2H2(g) + O2(g) → 2H2O(l).

Key Points

• A combination reaction occurs when two or more reactants combine to form a single product.
• However, when calcium carbonate is heated, it undergoes thermal decomposition to form calcium oxide and carbon dioxide.
• Examples of combination reactions
• Formation of water from hydrogen gas and oxygen gas
• Formation of calcium oxide by the combination of calcium and oxygen
• Formation of calcium hydroxide by adding water to quicklime

 Additional Information

• Combination reaction
• ​A combination reaction is when two or more reactants combine to form a single product.
• The three types of combination reactions are between two elements, two compounds, or between an element and a compound.
• Displacement reaction:
• The reaction in which an ion (or an atom) in a compound is replaced by an ion (or an atom) of another element is known as a displacement reaction.
• It is denoted by X + YZ  → XZ+Y
• Fe (s) + CuSO4 (aq) → FeSO4 (aq) + Cu (s)
• In the above reaction, iron is more reactive than copper, it displaces copper, resulting in the formation of ferrous sulphate.
• Fe2O3 (s) + 2Al (s) → Al2O3 (s) + 2F3 (s)
• In the above reaction, aluminium is more reactive than iron, it displaces iron, resulting in the formation of aluminium oxide.
• Decomposition reaction:
• In a Decomposition reaction, a compound breaks down into two or more components, in which one component must be in the elemental state.
• Decomposition reaction is the opposite reaction of the combination reaction.
• CaCO3 (s) → CaO (s) + CO2 (g)

The logic followed here is:

Logic: 1st number × 3rd number × 3 = 2nd number.

For, (5, 315, 21)

→ 5 × 21 × 3 = 315.

For, (9, 486, 18)

→ 9 × 18 × 3 = 486.

Now, checking the options:

Option 1: (10, 480, 16)

→ 10 × 16 × 3 = 480.

Option 2: (7, 294, 21)

→ 7 × 21 × 3 = 441 ≠ 294.

Option 3: (8, 368, 23)

→ 8 × 23 × 3 = 552 ≠ 368.

Option 4: (12, 560, 11)

→ 12 × 11 × 3 = 396 ≠ 560.

Hence, the correct answer is "Option 1".

Shortcut Trick

Ratio of Hema to Deeksha (10 years ago) = 3 : 1 (Difference = 2 units)

Ratio of Hema to Deeksha (10 years later) = 2 : 1 → 4 : 2 (Difference = 2 units)

Increase in ratio (1 to 2 or 3 to 4) = 1 unit → 20 years (10 ago + 10 later)

Deeksha age 10 years ago = 1 unit = 20 years.

Present age of Deeksha = 20 + 10 = 30 years.

∴ The correct answer is 30 years.

Alternate Method

Given: 10 years ago, Hema was 3 times as old as Deeksha. After 10 years, Hema will be twice as old as Deeksha.

Formula Used: Age difference between two people remains constant over time.

⇒ Let Deeksha's age 10 years ago be x.

⇒ Hema's age 10 years ago = 3x.

⇒ Present ages: Deeksha = x + 10, Hema = 3x + 10.

⇒ After 10 years: (3x + 10) + 10 = 2 × [(x + 10) + 10]

⇒ 3x + 20 = 2(x + 20)

⇒ 3x + 20 = 2x + 40

⇒ x = 20.

⇒ Present age of Deeksha = 20 + 10 = 30 years.

∴ The correct answer is 30 years.

Additional Information

Ratio Balancing Method

To solve age problems quickly, ensure the difference between ratio parts remains same. If 3:1 (diff 2) and 2:1 (diff 1), multiply the second ratio by 2 to get 4:2 (diff 2).

Concept of Age Difference

The numerical difference between the ages of two persons is constant and does not change with time. If A is 5 years older than B today, A will still be 5 years older than B after 50 years.

Given numbers: 4 7 2 1 8 6 9 1 2 5 3 1 9 4 7 1 8 3 5 6 8 2 7 1 8 5 6 9

Even digits immediately preceded by a perfect square and immediately followed by an odd digit,

So, the pattern needed is: 

Now,

So, there are four pairs i.e.: 125, 947, 183, 185.

Hence, the correct answer is "Option 1".

Given: A, B, C, D, E and F live on Six different floors of the same building.

1) D lives on an odd numbered floor but not on floor number 3.

2. Only two people live between D and A.

Case I:

Case II:

3. C lives immediately above A.

4. Only two people live between C and B.

Case I:

Case II:

5. F lives on one of the floors below B but not on the lowermost floor (This statement cancel Case II).

And, 'E' will sit on the remaining floor.

So, from Case I:

So, from the arrangement 'F' lives on floor number 4.

Hence, the correct answer is "Option 2".

The correct answer is Padho Pardesh.

Key Points

• Padho Pardesh
• Scheme for providing 'interest subsidy' for minority students for overseas studies.
• Meritorious students from economically weaker sections of notified minority communities.
• The loan for overseas studies for specific courses should have been sanctioned by the bank.
• The annual income of the parents should be less than 6 lakhs.
• The scheme provides an interest subsidy on education loans for students pursuing master’s, M.Phil, or Ph.D. degrees abroad.
• A wide range of fields, including arts, sciences, engineering, technology, and more.​

Additional Information

• Benefits
• Financial assistance:
• The scheme provides an interest subsidy on education loans, which can help to reduce the cost of overseas education for minority students.
• Increased access to education:
• The scheme makes overseas education more accessible to minority students from all backgrounds, regardless of their financial situation.
• Improved employability:
• ​ Studying abroad can give students a competitive edge in the job market, and the Padho Pardesh scheme can help minority students to achieve their career goals.
• Personal and professional development:
• Studying abroad can be a transformative experience, and the Padho Pardesh scheme can help minority students to develop their skills and knowledge in a global context.

The correct answer is 22.

Key Points

• The constitution contained 395 articles divided into 22 parts and 12 schedules.
• Indian Constitution originally had eight schedules. Four more schedules were added by different amendments, now making a total tally of twelve.

 Additional Information 

• Parts of the Indian Constitution

Important Points 

• Indian Constitution Schedules 1 to 12

Given:

Sudesh starts from point A and drives 9 km towards North,

takes a left turn and drives for 4 km,

then turns right and drives for 2 km,

then turns right and drives for 9 km.

takes a final right turn and drives for 11 km to reach point M.

So, the distance between points A and M is '5 km'.

Hence, the correct answer is "Option 2".

The correct answer is 1986.

Key Points

• Nairobi is the headquarter of the United Nations Environment Programme (UNEP). 
• The United Nations Environment Programme (UNEP) is responsible for coordinating responses to environmental issues within the United Nations system.
• It was established by Maurice Strong, its first director, after the United Nations Conference on the Human Environment in Stockholm in June 1972.
• Its mandate is to provide leadership, deliver science and develop solutions on a wide range of issues, including climate change, the management of marine and terrestrial ecosystems, and green economic development.
• As a member of the United Nations Development Group, UNEP aims to help the world meet the 17 Sustainable Development Goals.

 Additional Information

• The UNEP's mission is to provide leadership and encourage partnership in caring for the environment by inspiring, informing, and enabling nations and peoples to improve their quality of life without compromising that of future generations.
• The UNEP is the coordinating body for the United Nations' environmental activities.
• It assesses environmental conditions and trends at the global, regional and national levels
• it develops international agreements and national environmental instruments
• It strengthens institutions for wise environmental management.

The correct answer is 6 amp.

Key Points

• Joule's Law: The heat generated in a conductor is directly proportional to the square of the current flowing through it, the resistance of the conductor, and the time for which the current flows.
• Mathematical Representation:
• H = I² * R * t
• Where:
• H is the heat generated (in Joules)
• I is the current flowing through the resistor (in Amperes)
• R is the resistance of the resistor (in Ohms)
• t is the time for which the current flows (in seconds)
• Given:
• H = 360 J (energy produced per second)
• R = 10 ohms
• t = 1 second
• Rearranging the formula to find the current (I):
• I² = H / (R * t)
• I = √(H / (R * t))
• Substituting the given values:
• I = √(360 J / (10 ohms * 1 second))
• I = √(36)
• I = 6 Amperes

Given:

Simplify (3^-1 × 6^-1)-1 ÷ 3^-1

Formula Used:

Use the rules of exponents and order of operations (PEMDAS/BODMAS).

Calculation:

First, simplify the exponents:

3^-1 = 1/3

6^-1 = 1/6

Next, simplify within the parentheses:

(1/3 × 1/6) = 1/18

Now, handle the exponent -1:

(1/18)^-1 = 18

Finally, divide by 3^-1:

18 ÷ (1/3)

⇒ 18 × 3

⇒ 54

The correct answer is option 1.

Shortcut Trick

Monthly Savings = 50000 × (100−25)/100 × (100−30)/100 × (100−10)/100

Monthly Savings = 50000 × 0.75 × 0.70 × 0.90 = ₹23,625

Annual Savings = 23625 × 12 = ₹2,83,500

∴ The correct answer is ₹2,83,500.

Alternate Method

Given: Monthly Income = ₹50,000 | Tax = 25% | Household = 30% of remaining | Entertainment = 10% of remaining

Step-by-step Calculation:

⇒ Income after Tax = 50000 − (25% of 50000) = 50000 − 12500 = ₹37,500

⇒ Income after Household = 37500 − (30% of 37500) = 37500 − 11250 = ₹26,250

⇒ Monthly Savings = 26250 − (10% of 26250) = 26250 − 2625 = ₹23,625

⇒ Annual Savings = Monthly Savings × 12 months

⇒ Annual Savings = 23625 × 12 = ₹2,83,500

∴ The correct answer is ₹2,83,500.

Additional Information

Successive Percentage Change

When changes are applied on the remaining value, the final value = Initial × (100−r₁)/100 × (100−r₂)/100.

Base Change vs. Direct Percentage

Always identify if the percentage is of the Original Total or the Remaining Balance before calculating.

Annual Conversion

To find annual values from monthly data, multiply the final monthly result by 12.

Shortcut Trick

In a parallelogram, sum of adjacent angles is 180°.

(3x + 16) + (2x + 24) = 180 ⇒ 5x + 40 = 180 ⇒ 5x = 140 ⇒ x = 28.

Opposite angles are equal, so m∠C = m∠A = 3(28) + 16 = 84 + 16 = 100°.

∴ The correct answer is 100°.

Alternate Method

Given: m∠A = (3x + 16)°, m∠B = (2x + 24)° in parallelogram ABCD.

Formula: Sum of interior angles on the same side of the transversal (adjacent angles) is 180°.

⇒ m∠A + m∠B = 180°

⇒ (3x + 16) + (2x + 24) = 180

⇒ 5x + 40 = 180

⇒ 5x = 140

⇒ x = 28

Since opposite angles of a parallelogram are equal:

⇒ m∠C = m∠A

⇒ m∠C = 3(28) + 16

⇒ m∠C = 84 + 16 = 100°

∴ The correct answer is 100°.

Additional Information

Properties of Parallelogram

Opposite sides are parallel and equal. Diagonals bisect each other but are not necessarily equal.

Angle Relationships

Opposite angles are congruent (equal). Consecutive angles are supplementary (sum = 180°).

Area and Perimeter

Area = base × height. Perimeter = 2(a + b), where a and b are adjacent sides.

The correct answer is Milk.

Key Points

• Adolescence is a period of rapid growth and development, making a balanced diet crucial.
• Fueling Growth Spurts: Teenagers experience significant growth spurts, requiring increased energy and nutrients. A balanced diet provides the necessary fuel for bone growth, muscle development, and overall physical development.
• Supporting Brain Development: The adolescent brain is still developing rapidly. Nutrients like omega-3 fatty acids (found in fish, nuts, and seeds) are essential for brain function, cognitive development, and mood regulation.

Additional Information

• Providing Essential Nutrients:
• Calcium and Vitamin D: Crucial for strong bones and teeth, especially important for girls during puberty. Dairy products, leafy greens, and fortified foods are good sources.
• Iron: Essential for the production of red blood cells, particularly important for girls due to menstrual blood loss. Red meat, poultry, beans, and leafy greens are good sources.
• Protein: Needed for tissue growth and repair, hormone production, and immune function. Lean meats, fish, beans, eggs, and dairy products are good sources.
• Complex Carbohydrates: Provide sustained energy and fiber, essential for digestion and overall health. Whole grains, fruits, and vegetables are excellent sources.
• Maintaining a Healthy Weight: A balanced diet helps adolescents maintain a healthy weight, reducing the risk of obesity and related health problems such as type 2 diabetes and heart disease.
• Boosting the Immune System: A diet rich in fruits, vegetables, and whole grains provides essential vitamins and antioxidants, strengthening the immune system and helping adolescents fight off infections.
• Improving Mood and Mental Health: Some nutrients, such as omega-3 fatty acids and B vitamins, play a crucial role in mood regulation and mental well-being.

Additional Information

• Key Components of a Balanced Diet for Adolescents:
• Fruits and Vegetables: Aim for at least 5 servings per day. Include a variety of colors for a wide range of nutrients.
• Whole Grains: Choose whole-grain bread, pasta, rice, and cereals over refined grains.
• Lean Protein: Include lean meats, poultry, fish, beans, lentils, eggs, and nuts in your diet.
• Dairy or Dairy Alternatives: Choose low-fat or non-fat options for calcium and vitamin D.
• Healthy Fats: Include sources like avocados, nuts, seeds, and olive oil in moderation.

Given: P, Q, R, S, T and U are six different cars, each of a different weight.

1. Q is heavier than only one car.

__ > __ > __ > __ > Q > __

2. S is heavier than Q.

S > Q

3. T is heavier than S.

T > S

4. P is heavier than T.

P > T

5) R is heavier than P.

R > P

After combining all the statements:

R > P > T > S > Q

So, the final arrangement will be:

R > P > T > S > Q > U

Here, 'R' is the six heaviest car.

Hence, the correct answer is "Option 4".

The logic followed here is:

So, '30000' will complete the series.

Hence, the correct answer is "Option 2".

The correct answer is -2/5.

Key Points

• Formula for Magnification:
• The magnification (m) produced by a mirror is given by the formula:
• m = -v/u
• where:
• v is the image distance
• u is the object distance
• Given:
• Object distance (u) = 5 cm (negative sign convention)
• Image distance (v) = 2 cm
• Calculation:
• m = -v/u
• m = -2  / 5

The correct answer is Agriculture.

Key Points

• On the eve of India's independence in 1947, the principal source and sector of occupation was agriculture.   
• Agriculture-Dominated Economy: A vast majority of the Indian population, estimated around 70-80%, was directly or indirectly involved in agriculture. This included farmers, landless laborers, and those engaged in allied activities like livestock rearing and fishing.
• Low Productivity: Agricultural practices were largely traditional, with low levels of mechanization and reliance on monsoon rains. This resulted in low productivity and frequent crop failures, leading to widespread poverty and food insecurity.
• Subsistence Farming: A significant portion of agricultural production was for subsistence, meaning farmers primarily grew crops to feed their families rather than for commercial purposes.
• Limited Industrial Development: While some industries existed, their development was hampered by British colonial policies that favored raw material exports and discouraged industrial growth within India. This limited alternative employment opportunities outside of agriculture.
• Social and Economic Inequalities: The agrarian economy was characterized by significant social and economic inequalities. Land ownership was concentrated in the hands of a small elite, while the majority of farmers were landless or had small, fragmented landholdings.

The correct answer is Article 343.

 Key Points

• Article 343
• Article 343 (1) of the Constitution, states that the official language of the Union shall be Hindi in Devanagari script.
• Hindi written in Devanagari script is to be the official language of the Union.
• But, the form of numerals to be used for the official purposes of the Union has to be the international form of Indian numerals and not the Devanagari form of numerals.

Additional Information

• Article 351
• The Indian constitution in its article 351 has laid down provisions for promoting and developing Hindi as the national official language.
• This also directed the educational system of India to take initiatives and functions to facilitate the article to increase student and teacher communication and to spread awareness of national integrity and unity.
• Article 351 enjoins the Union to promote the spread of the Hindi language and to develop it so that it may serve as a medium of expression of all elements of the composite culture of India.
• Thus, it is concluded that  Article 351 of the Indian constitution lays down a provision for the promotion of the Hindi language as the national and official language of India.
• ​Article 336
• Article 336 of the Indian Constitution provides Special provisions to Anglo Indian community in certain services.
• An Anglo Indian community means a person whose father was a European descent but who is domiciled within the territory of India.
• ​Article 347
• States about the Special provision related to the language spoken by the section of the population of the state.

The correct answer is for** concave mirror f is negative, R is negative**.

Key Points

• When dealing with spherical mirrors, a consistent set of sign conventions is crucial for accurate calculations and understanding of image formation. These conventions help determine the nature (real/virtual, erect/inverted), size, and position of the image.
• Sign Conventions:
• Object Distance (u):
• Negative: When the object is placed in front of the mirror (the usual case).
• Positive: When the object is placed behind the mirror (rarely encountered).
• Image Distance (v):
• Positive: When the image is formed in front of the mirror (real image).
• Negative: When the image is formed behind the mirror (virtual image).
• Focal Length (f):
• Positive: For concave mirrors.
• Negative: For convex mirrors.
• Radius of Curvature (R):
• Positive: For concave mirrors.
• Negative: For convex mirrors.

Additional Information

• Relationship Between Focal Length and Radius of Curvature:
• The focal length (f) of a spherical mirror is related to its radius of curvature (R) by the following equation:
• f = R/2
• Significance of Sign Conventions:
• Accurate Calculations: By adhering to these sign conventions, you can correctly apply the mirror formula (1/f = 1/v + 1/u) and magnification formula (m = -v/u) to determine the image characteristics.
• Understanding Image Formation: The signs of image distance and magnification provide valuable information about the nature of the image (real/virtual, erect/inverted).
• Consistency: Consistent use of sign conventions ensures that calculations are accurate and reliable, regardless of the type of mirror or the object's position.

The correct answer is Sattva. 

Key Points

• Certainly, let's explore how Hinduism encourages full participation in life through the Purusharthas:
• Purusharthas: These are the four primary goals or aims of human life in Hinduism: Dharma, Artha, Kama, and Moksha.
• Dharma: This encompasses righteousness, duty, and moral conduct. It involves fulfilling one's social and religious obligations, acting ethically, and living a virtuous life.
• Artha: This refers to prosperity, wealth, and material success. It encourages individuals to pursue legitimate means of earning a living, building a family, and contributing to society.
• Kama: This signifies pleasure, love, and fulfillment of desires. It emphasizes the importance of enjoying life, pursuing relationships, and experiencing happiness.
• Moksha: This is the ultimate goal of liberation or enlightenment, transcending the cycle of birth and death. It involves realizing one's true nature and attaining spiritual freedom.

Additional Information

• Full Participation in Life:
• Holistic Approach: Hinduism doesn't view these goals as mutually exclusive. It encourages a balanced pursuit of all four Purusharthas, recognizing that a fulfilling life encompasses both material and spiritual dimensions.
• Dharma as Foundation: Dharma acts as the foundation for all other Purusharthas. It provides ethical guidelines for pursuing wealth and pleasure responsibly.
• Importance of Artha and Kama: Hinduism acknowledges the importance of material well-being and fulfilling desires. It encourages individuals to work hard, build a comfortable life, and enjoy the pleasures of life within the framework of Dharma.
• Moksha as the Ultimate Goal: While material pursuits and worldly enjoyments are valued, Hinduism ultimately emphasizes the importance of striving for Moksha. It encourages individuals to use their material and worldly experiences as stepping stones towards spiritual growth and liberation.

Given equation: 3 × 5 + 20 ÷ 8 - 17 = 11.

BODMAS Table: 

Let's check each option one by one.

Option 1) 5 and 8 

Given: 3 × 5 + 20 ÷ 8 - 17 = 11

After interchanging the numbers we get;

⇒ 3 × 8 + 20 ÷ 5 - 17 = 11

⇒ 3 × 8 + 4 - 17 = 11

⇒ 24 + 4 - 17 = 11

⇒ 28 - 17 = 11

⇒ 11 = 11

⇒ LHS = RHS

Option 2) 17 and 3 

Given: 3 × 5 + 20 ÷ 8 - 17 = 11

After interchanging the numbers we get;

⇒ 17 × 5 + 20 ÷ 8 - 3 = 11

⇒ 17 × 5 + 2.5 - 3 = 11

⇒ 85 + 2.5 - 3 = 11

⇒ 87.5 - 3 = 11

⇒ 84.5 ≠ 11

⇒ LHS ≠ RHS

Option 3) 5 and 17

Given: 3 × 5 + 20 ÷ 8 - 17 = 11

After interchanging the numbers we get;

⇒ 3 × 17 + 20 ÷ 8 - 5 = 11

⇒ 3 × 17 + 2.5 - 5 = 11

⇒ 51 + 2.5 - 5 = 11

⇒ 53.5 - 5 = 11

⇒ 48.5 ≠ 11

⇒ LHS ≠ RHS

Option 4) 8 and 17

Given: 3 × 5 + 20 ÷ 8 - 17 = 11

After interchanging the numbers we get;

⇒ 3 × 5 + 20 ÷ 17 - 8 = 11

⇒ 3 × 5 + 1.18 - 8 = 11

⇒ 15 + 1.18 - 8 = 11

⇒ 16.18 - 8 = 11

⇒ 8.18 ≠ 11

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 1".

The correct answer is (current)2 .

Key Points 

• Joule's Law of Heating
• The amount of heat produced in a conductor is directly proportional to:
• The square of the current (I²) flowing through it.
• The resistance (R) of the conductor.
• The time (t) for which the current flows.
• This relationship is mathematically expressed as:
• H = I²Rt   
• where:
• H is the heat produced in joules (J)
• I is the current flowing through the conductor in amperes (A)
• R is the resistance of the conductor in ohms (Ω)
• t is the time for which the current flows in seconds (s)

Additional Information

• Heat Produced in an Electric Circuit
• When an electric current flows through a conductor, it encounters resistance.
• This resistance hinders the free flow of electrons, causing them to collide with the atoms of the conductor.
• These collisions result in the conversion of electrical energy into heat energy.
• This phenomenon is known as the heating effect of electric current.

Shortcut Trick

Apply the M₁D₁/W₁ = M₂D₂/W₂ formula directly.

(10 × 8) / 50 = (M₂ × 10) / 100

80 / 50 = 10M₂ / 100

1.6 = M₂ / 10 ⇒ M₂ = 16 men.

∴ The correct answer is 16 men.

Alternate Method

Given:

Initial men (M₁) = 10, Initial days (D₁) = 8, Initial depth (W₁) = 50 feet

Final days (D₂) = 10, Final depth (W₂) = 100 feet, Final men (M₂) = ?

Formula Used:

Chain Rule: (M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂

Calculations:

⇒ (10 × 8) / 50 = (M₂ × 10) / 100

⇒ 80 / 50 = 10M₂ / 100

⇒ 8 / 5 = M₂ / 10

⇒ M₂ = (8 × 10) / 5

⇒ M₂ = 80 / 5

⇒ M₂ = 16 men

∴ The correct answer is 16 men.

Additional Information

Chain Rule Property

The relationship between men, days, hours, and work is given by (M × D × H) / W = Constant, where work is always in the denominator.

Direct and Inverse Proportion

Men and Days are inversely proportional (more men, fewer days), while Men and Work are directly proportional (more men, more work).

I. Babies born before 37 weeks of pregnancy have issues in adjusting properly in the world outside their mother’s womb and need to be in a Neonatal Intensive Care Unit for durations varying from a few days to several weeks - False (There is nothing mention about issues caused by before 37 weeks of pregnancy).

II. Infants born after 37 weeks of pregnancy are called full term babies and are completely healthy - False (Nothing mention about after 37 weeks of pregnancy in the statement).

So, Neither conclusion I nor II follows.

Hence, the correct answer is "Option 3".

Given word: 'ACQUIRE'

After arranged in alphabetical order:

After arranged in alphabetical order,

Fifth alphabet from the left end is: Q,

First alphabet from the right end is: U,

Now,

there are 3 letters between Q and U.

Hence, the correct answer is "Option 2".

The correct answer is reduction.

Key Points

• Reduction:
• Reduction is a chemical reaction where a substance gains electrons.
• This gain of electrons leads to a decrease in the oxidation state of the substance.
• A classic example is the reduction of iron ore (Fe2O3) to iron metal (Fe) in a blast furnace.

Additional Information

• Oxidation:
• Oxidation is the opposite of reduction.
• It involves the loss of electrons by a substance.
• This loss of electrons results in an increase in the oxidation state of the substance.
• A common example is the rusting of iron, where iron metal (Fe) reacts with oxygen (O2) to form iron oxide (Fe2O3), which is rust.
• Chlorination:
• Chlorination is a chemical reaction where chlorine (Cl2) is added to a substance.
• It often involves the substitution of hydrogen atoms with chlorine atoms.
• Chlorination is used to purify water by killing harmful bacteria and is also used in the production of various chemicals.
• Bromination:
• Bromination is a chemical reaction where bromine (Br2) is added to a substance.
• Similar to chlorination, it often involves the substitution of hydrogen atoms with bromine atoms.
• Bromination is used in the production of various organic compounds and in some industrial processes.

The correct answer is 60.

Key Points

• Fullerene consists of 60 carbon atoms.
• Fullerene, an allotrope of carbon, is rarely found in nature. It is found in soot and in interstellar space.
• The first example of fullerene is Buckminsterfullerene (C60). This allotrope of carbon is named fullerene after the architect Richard Buckminster Fuller because the structure of C60 resembles the structure of the geodesic dome he designed.
• It was discovered by Richard Smalley in 1985.
• Harold Kroto, Robert Curl, and Richard Smalley were given the Nobel prize in chemistry 1996, for the discovery of this carbon allotrope, fullerene C60.

The correct answer is Technology Based Entrepreneurship Development Programme.

Key Points

• The full form of TEDP is Technology Based Entrepreneurship Development Programme.
• About TEDP:
• Initiated by the Department of Science and Technology (DST), Government of India: This program aims to nurture and support aspiring entrepreneurs with a focus on science and technology.
• Structured Training: TEDP provides comprehensive training to individuals, equipping them with the necessary skills and knowledge to launch and successfully run technology-based businesses.
• Focus on Innovation: The program emphasizes the development and commercialization of innovative products, technologies, and processes.

Additional Information

• TEDP typically covers a wide range of topics, including:
• Business Planning: Developing detailed business plans, including market research, financial projections, and go-to-market strategies.
• Technology Commercialization: Understanding intellectual property rights (IPR), technology transfer mechanisms, and strategies for bringing innovative technologies to the market.
• Entrepreneurial Skills: Developing essential skills such as leadership, teamwork, communication, problem-solving, and financial management.
• Mentorship and Networking: Providing access to mentors, industry experts, and potential investors to guide and support entrepreneurs.

Given: A certain number of people are sitting in a row, facing north.

1. R sits third to the right of P.

2. Q is an immediate neighbour of both R and M.

3. M is not an immediate neighbour of P.

4. Exactly four people sit between M and T.

If no other person is sitting in the row, then '11' people seated in the row.

Hence, the correct answer is "Option 3".

Shortcut Trick Total Cost Price (CP) = 25,000 + 2,750 = 27,750. Selling Price (SP) = 26,085. Loss = CP − SP = 27,750 − 26,085 = 1,665. Loss% = (Loss ÷ CP) × 100 = (1,665 ÷ 27,750) × 100. Calculation: 166,500 ÷ 27,750 = 6%. ∴ The correct answer is 6%.

Alternate Method Given → Camera Price = 25,000, Leather Case Price = 2,750, Total SP = 26,085. Formulas: Loss = CP − SP | Loss% = (Loss ÷ CP) × 100.

⇒ Total Cost Price (CP) = Cost of Camera + Cost of Leather Case = 25,000 + 2,750 = 27,750. ⇒ Total Selling Price (SP) = 26,085. ⇒ Since CP > SP, there is a loss. ⇒ Loss = 27,750 − 26,085 = 1,665. ⇒ Loss% = (1,665 ÷ 27,750) × 100 = 6%. ∴ The correct answer is 6%.

Additional Information Total Cost Price Calculation When multiple items are bought together or overhead expenses (repair, transport) are incurred, they must be added to the initial price to find the Effective Cost Price. Loss and Profit Condition If SP < CP, it is a loss. If SP > CP, it is a profit. Both are always calculated on the Cost Price (CP) unless stated otherwise.

The correct answer is three lakh.

Key Points

Under Article-243 Definitions.-

• In this section, unless the context requires otherwise,-
• (a) 'District' shall mean a district within a State;
• (b) 'Gram Sabha' means an agency composed of persons registered in the electoral rolls relating to a village within the Panchayat district at the level of the village;
• (c) 'Intermediate level' means the intermediate level between the level of the village and the level of the district defined by the Governor of a State for the purposes of this Part by public notification;
• (d) 'Panchayat' means, for rural areas, an agency (by whatever name) of self-government, constituted under Article 243B;
• (e) 'Panchayat area' means the Panchayat territorial area;
• (f) 'Population' means the population of which the related figures have been published, as determined in the last preceding census;
• (g) 'Village' means a village appointed by the Governor to be a village for the purposes of this Part by public notice and includes a collection of villages so designated.

 Additional Information

Given: Six friends A, B, C, D, E and F.

1. Only two people are shorter than B.

2. Only one person is taller than A.

__ > A > __ > B > __ > __

3. C is shorter than E but taller than F.

4.  E is neither the tallest nor the shortest. 

__ > A > E > B > C > F

So, D is the tallest (because only person and place left).

D > A > E > B > C > F

From the arrangement, 'E' is the taller than B but shorter than A.

Hence, the correct answer is "Option 2".

Given Alphabets: M O V E O I F V A S K C O S D V I N S D I N I S

Consonants are immediately preceded by a vowel and also immediately followed by a vowel,

So, the pattern should be: 

Now,

So, there are Two pairs i.e.: 'OVE' and 'INI'.

Hence, the correct answer is "Option 1".

Shortcut Trick Identify the maximum frequency from the given distribution table. The frequencies provided are 3, 4, 6, and 7. The highest frequency is 7, which corresponds to the mark 40. ∴ The correct answer is 40. Alternate Method Given: A frequency distribution of marks where Marks (xi) and Frequency (fi) are provided. Formula: Mode is the value of the observation that has the maximum frequency in the data set.

⇒ Frequency of 51 = 3 ⇒ Frequency of 29 = 4 ⇒ Frequency of 85 = 6 ⇒ Frequency of 40 = 7 ⇒ Comparing all frequencies: 7 > 6 > 4 > 3 ⇒ Since 7 is the highest frequency, the corresponding mark is the Mode. ⇒ Mode = 40 ∴ The correct answer is 40.

Statement:

Some Dogs are Barks.

Some Barks are Trees.

All Trees are Woods.

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

Conclusions:

(i) Some Dogs are Trees - False (Because No definite relation given between Dogs and Cats, so it can be possible only).

(ii) Some Woods are Barks - True (Those Barks which is Trees is also Woods).

Here, Only conclusion (II) follows..

Hence, the correct answer is "Option 2".

Shortcut Trick

Let the smallest side be x.

Sides are x, (2x + 7), and (3x + 5).

Sum of sides = 6x + 12 = 90.

6x = 78 ⇒ x = 13.

∴ The correct answer is 13 m.

Alternate Method

Given:

Smallest side = x m

Second side = (2x + 7) m

Third side = (3x + 5) m

Formula Used:

Perimeter of a triangle = Sum of all three sides

Calculations:

⇒ x + (2x + 7) + (3x + 5) = 90

⇒ 6x + 12 = 90

⇒ 6x = 90 − 12

⇒ 6x = 78

⇒ x = 78 ÷ 6

⇒ x = 13 m

∴ The correct answer is 13 m.

Additional Information

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Types of Triangles by Sides

Scalene: All sides different. Isosceles: Two sides equal. Equilateral: All sides equal.

Heron's Formula for Area

Area = √[s(s−a)(s−b)(s−c)], where s is the semi-perimeter (a+b+c)/2.

The correct answer is -0.1 m.

Key Points

• Power of a lens (P) is the reciprocal of its focal length (f) in meters.

• P = 1 / f

• Given:

• Power of the concave lens (P) = -10 D (Concave lenses have negative power)

• Calculation:

• f = 1 / P

• f = 1 / (-10 D)

• f = -0.1 meters

• Therefore, the focal length of the concave lens is -0.1 meters.

Given:

1/12 + 1/16 - 1/8

Solution:

Step 1: Find the LCM of the denominators 12, 16, and 8:

LCM(12, 16, 8) = 48

Step 2: Rewrite each fraction with a denominator of 48:

1/12 = 4/48, 1/16 = 3/48, 1/8 = 6/48

Step 3: Combine the fractions:

1/12 + 1/16 - 1/8 = 4/48 + 3/48 - 6/48

= (4 + 3 - 6)/48

= 1/48

The simplified value is 1/48.