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Given:

An average of 40 numbers = 36

average of the first 25 numbers = 31

Average of last 16 numbers = 43

Calculation:

⇒ {(31 × 25) + (16 × 43)} – (40 × 36)

⇒ {775 + 688} – 1440

⇒ 1463 – 1440

⇒ 23

∴ The 25^th number is 23.  

Shortcut Trick 

GIven average = 36 

Missing number. = average + (higher avg. - avg ) × carry a higher average of candidate - (avg - lower avg) × carry a lower average of the candidate 

So, the 25^th number. =  36 + (43 - 36) 16 - (36 - 31) 25

⇒ 36 + 112 - 125 = 23

From the given figure, we can tell that

‘6’ is facing opposite to ‘3’.

‘2’ is opposite to ‘5’.

And,

‘4’ is opposite to the side having ‘1’.

Hence, “4” is the correct answer.

The correct answer is C₂H₅OH

Explanation:

• Alcohols are organic compounds in which a hydroxyl group (-OH) is attached to a carbon atom. The general formula for alcohols is R-OH, where R represents an alkyl group.
• Ethanol (C₂H₅OH) is the most common type of alcohol, and it is widely used in beverages, as a solvent, and in the pharmaceutical industry.
• The molecular formula of ethanol is C₂H₅OH, which indicates it consists of two carbon atoms, six hydrogen atoms, and one oxygen atom, with the hydroxyl group attached to one of the carbon atoms.

Other Options:

• C₂H₅: This formula represents an ethyl group, which is an alkyl group derived from ethane (C₂H₆) by removing one hydrogen atom.
• C₂H₅COOH: This is the chemical formula for propanoic acid, a carboxylic acid. It contains a carboxyl group (-COOH) instead of a hydroxyl group.

The correct answer is option 1

Key Points

• Kuno National Park (Madhya Pradesh) is the primary site for the cheetah reintroduction project.
• Ranthambore National Park (Rajasthan) is being considered as a potential site for additional cheetah relocation.
• The panel is working on addressing issues of cheetah dispersal and establishing sustainable habitats in Rajasthan.
• The joint corridor management committee was formed to handle issues related to cheetahs straying from Kuno National Park (Madhya Pradesh) into Rajasthan.
• This initiative ensures better wildlife management and explores suitable relocation areas for cheetahs in Rajasthan.

Additional Information

• Cheetahs were declared extinct in India in 1952, primarily due to overhunting and habitat destruction.
• Project Cheetah, launched in 2022, aims to restore the species by bringing cheetahs from Namibia and South Africa.
• The reintroduction effort is expected to boost biodiversity and restore ecological balance in grassland ecosystems.
• Kuno National Park (MP) is currently the primary site for Project Cheetah, where cheetahs from Namibia and South Africa were reintroduced in 2022.

Given :

Sum of Rs. 7560 is divided among A,B and C

If Rs 400, 300 and 260 is taken from A,B and C respectively then their shares  ratio is 4 ∶ 2 ∶ 5

Calculation :

Shares of A,B and C is diminished by Rs. 400, Rs. 300 and Rs. 260 respectively

Diminished sum = Rs.7560 - (400 + 300 +260)

⇒ Rs.6600

The new ratio is 4 ∶ 2 ∶ 5 = 11 units 

⇒ 11 units = Rs. 6600

⇒ 1 unit = Rs. 600

⇒ Share of B after diminishing  = 2 × 600

⇒ Rs. 1200

 B was diminished by Rs. 300

∴ Original share of B is Rs. 1500

The logic followed here is:

Logic: The series follows Step 1 and Step 2 on alternative basis to get the subsequent images of the series.

Hence, the correct answer is "Option 4".

The correct answer is Sunlight.

Key Points

• Sunlight is the most natural and cost-free source of Vitamin D. Ultraviolet B (UVB) rays from sunlight trigger Vitamin D synthesis in the skin.
• Vitamin D produced from sunlight exposure is stored in the liver and fat tissue, where it can be utilized by the body when required.
• Regular exposure to sunlight for about 10-30 minutes (depending on skin type, geographic location, and time of day) is sufficient to meet the daily Vitamin D requirement for most individuals.
• Unlike dietary sources, sunlight does not involve any monetary cost, making it the cheapest and most accessible source of Vitamin D.
• Deficiency of Vitamin D is common in regions with limited sunlight exposure or during winter months, underscoring the importance of sunlight for maintaining optimal levels.

Additional Information

• Vitamin D:
• Vitamin D is a fat-soluble vitamin essential for calcium absorption, bone health, and immune function.
• The two main forms are Vitamin D2 (ergocalciferol) and Vitamin D3 (cholecalciferol), with D3 being more effective in raising blood levels of the vitamin.
• Sources of Vitamin D:
• Natural sources include sunlight, fatty fish (like salmon, mackerel, and sardines), egg yolks, and fortified foods such as milk, cereals, and orange juice.
• Vitamin D supplements are widely available for individuals unable to meet their requirements through sunlight or diet.
• Health Benefits of Vitamin D:
• Supports strong and healthy bones by promoting calcium and phosphorus absorption.
• Plays a critical role in immune system regulation and reducing inflammation.
• May help reduce the risk of chronic diseases such as osteoporosis, cardiovascular issues, and certain cancers.
• Risk Factors for Deficiency:
• Limited sunlight exposure, use of sunscreen, darker skin pigmentation, and aging reduce the skin’s ability to synthesize Vitamin D.
• Individuals with malabsorption conditions (e.g., Crohn’s disease) or those following strict vegetarian/vegan diets may also be at risk.

The correct answer is Bhopal.

In News

• Bhopal is hosting the 22^nd All India Annual TDS Conference, organised by the Central Board of Direct Taxes (CBDT).

Key Points

• The 22^nd TDS Conference is being held in Bhopal, Madhya Pradesh.
• Senior CBDT officials, including the Chairman, are inaugurating the event.
• Key focus areas include amendments in the Income Tax Act, 2025, especially revised TDS provisions.
• The conference also highlights digital tools like automated TDS tracking and analytics dashboards.

Additional Information

• CBDT
• Apex body administering direct taxes in India.
• Responsible for policy formulation, implementation, and enforcement.
• Organises annual TDS conferences to review compliance and strengthen systems.
• TDS (Tax Deducted at Source)
• Mechanism ensuring tax collection at the time of income generation.
• Recent amendments aim to simplify compliance and reduce litigation.
• Critical for transparency and voluntary tax culture.
• Digital Initiatives
• Automated TDS monitoring systems under implementation.
• Data-driven analytics to identify mismatches and compliance gaps.
• Online platforms designed for faster grievance redressal.
• Key Participants
• Principal Chief Commissioners, Chief Commissioners, DGs, and senior TDS officers.
• Provide policy inputs and discuss nationwide compliance challenges.
• Focus on implementing new compounding guidelines effectively.

Shortcut Trick

If the expression is in the form x − a/x = n, then the value of x² + a²/x² = n² + 2a.

Given: k − 3/k = 5. Here, x = k, a = 3, and n = 5.

Applying the shortcut: k² + 9/k² = 5² + 2(3) = 25 + 6 = 31.

∴ The correct answer is 31.

Alternate Method

Given:

k − 3/k = 5

Formula Used:

(a − b)² = a² + b² − 2ab

Calculations:

⇒ k − 3/k = 5

Squaring both sides of the equation:

⇒ (k − 3/k)² = 5²

⇒ k² + (3/k)² − 2 × k × (3/k) = 25

⇒ k² + 9/k² − 2 × 3 = 25

⇒ k² + 9/k² − 6 = 25

⇒ k² + 9/k² = 25 + 6

⇒ k² + 9/k² = 31

∴ The correct answer is 31.

Additional Information

Algebraic Identity for Square of a Sum

(x + y)² = x² + y² + 2xy. If x + a/x = n, then x² + a²/x² = n² − 2a.

Algebraic Identity for Square of a Difference

(x − y)² = x² + y² − 2xy. This is used to derive relations between linear and quadratic terms.

Difference of Two Squares

x² − y² = (x − y)(x + y). Useful for simplifying products of conjugate algebraic terms.

Decoding the information, 

Given:

15 C 7 B (24 D 8) A 16 C 4 B 21 D 3

After replacing the signs from left to right and using the BODMAS rule,

15 × 7 - (24 ÷ 8) + 16 × 4 - 21 ÷ 3

= 15 × 7 - 3 + 16 × 4 - 7

= 105 - 3 + 64 - 7

= 169 - 10

= 159

Hence, “159” is the correct answer.