Correct Answer is: 135 ohm

Explanation:

The resistance R of a wire is given by the formula:

Where:

• R = Resistance
• ρ​ = Resistivity (same for both wires as they are of the same material)
• L = Length of the wire
• A = Cross-sectional area of the wire

Since the cross-sectional area A of a wire is given by:

Since resistance is inversely proportional to the cross-sectional area:

Information Booster:

Factors Affecting Resistance:

1. Material of the Wire: Different materials have different resistivities ρ.
2. Length of the Wire (L): Resistance is directly proportional to the length:

Cross-sectional Area (A): Resistance is inversely proportional to the area:

1. Temperature: Resistance increases with temperature in conductors.

The Correct Answer is: (a) n > 1

Explanation:

From the figure, the light ray bends towards the normal as it travels from medium A into medium B. According to Snell’s Law:

Where:

• iii is the angle of incidence (in Medium A)
• rrr is the angle of refraction (in Medium B)

Since the ray bends towards the normal, this indicates:

Hence, medium B is optically denser than medium A, and the refractive index of B with respect to A is greater than 1.

Information Booster:

• Light slows down when entering an optically denser medium (B), causing it to bend towards the normal.

• A higher refractive index means greater optical density.

• Refractive index (n) is a ratio of the speed of light in vacuum to that in the medium:

• This principle is the basis of lenses, prisms, and fiber optics.

• The amount of bending depends on the angle of incidence and difference in optical density.

• Snell’s Law governs the relationship between angles and refractive indices:

Correct Answer is: 5000000

Given:

Present population = 6,838,155

Annual growth rate = 11%

Time period = 3 years

Formula Used:

​​The population of the city 3 years ago was 5,000,000

Correct Answer is: 48 km

Let the actual distance travelled be d km.

Let the time taken to travel this distance be t hours.

When walking at 12 km/hr, the distance travelled

12t = d

When walking at 18 km/hr, the distance travelled

18t = d+24

d= 18t -24

Equate both

18t -24 = 12t

6t = 24

t = 4

Distance = 12t = 12×4 = 48km

Correct Answer is: The ratio of the speed of light in vacuum to its speed in a specific medium is called the refractive index.

Explanation:

The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v). It determines how much light slows down when entering a medium. The formula is:

where:

• c = Speed of light in vacuum (3 × 10⁸ m/s)
• v = Speed of light in the medium

A higher refractive index means light slows down more when passing through the medium.

Information Booster:

• Higher refractive index → More bending of light.
• Common values:
  • Vacuum: 1
  • Air: ~1.0003
  • Water: 1.33
  • Glass: 1.5
  • Diamond: 2.42
• Used in optics, lenses, and fiber optics technology.
• Explains phenomena like total internal reflection (TIR).

Additional Information:

• A (Incorrect): Refractive index is NOT the sum of the angles of incidence and refraction; it is a ratio of speeds.
• C (Incorrect): Refractive index and reflection are different; reflection involves light bouncing off a surface, while refraction is light bending when passing through a medium.
• D (Incorrect): The statement is reversed; refractive index is the ratio of the speed of light in vacuum to its speed in the medium, not vice versa.

Correct Answer is: Delivery of nutrients to the fetus

​The correct answer is (b) - Delivery of nutrients to the fetus

Explanation:

• The placenta is an organ that develops in the uterus during pregnancy and plays a crucial role in supporting fetal growth.
• Its primary function is to deliver oxygen and nutrients from the mother's blood to the developing fetus through the umbilical cord.

Information Booster:

Key Functions of the Placenta:

Nutrient Transfer: Transports glucose, amino acids, and vitamins from the mother to the fetus.
Gas Exchange: Supplies oxygen to the fetus and removes carbon dioxide.
Waste Removal: Helps eliminate fetal metabolic waste through the maternal bloodstream.
Hormone Production: Secretes progesterone, estrogen, and hCG (human chorionic gonadotropin) to support pregnancy.
Immune Protection: Transfers maternal antibodies to protect the baby from infections.

Additional Knowledge:

• Placenta produces hormones like progesterone and hCG.
• Egg maturation occurs in the ovaries.
• Placenta protects the fetus, not the uterus. The uterus itself is responsible for holding and supporting the pregnancy.

Correct Answer is: 108°

Total distribution of constituents = 100% = 360°

Distribution of Constituents on protein and Other items = 16 + 14 = 30%

Central angle of the sector showing the distribution of protein and other constituents

Correct Answer is: South – west

Given,

​One morning Yogesh started from his home to visit his sister in another city.

He first drove for 10 km towards the north and then turned towards the east and further drove for 10 km After this he turned towards the north and drove for 30 km.

Finally he turned towards the east and drove for 20 km to reach his sister’s home

From the given information possible Direction will be:

So, the direction of his home from his sister’s home south-west.

Thus, the correct option is: (a) south-west

Correct Answer is: Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA)

Explanation:

• The Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) is a government scheme that guarantees at least 100 days of wage employment per year to rural households.
• The primary goal of the scheme is to provide livelihood security in rural areas by offering employment opportunities through public works projects.
• MGNREGA aims to reduce poverty, enhance livelihoods, and create sustainable assets in rural India.
• It was launched in 2005 and has become one of the largest workfare programs in the world.

Information Booster:

Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) – Overview

Additional Knowledge:

• Pradhan Mantri Kaushal Vikas Yojana, launched in 2015, is a skill development program aimed at providing training and certification to youth in various skills, enabling them to gain employment.
• Pradhan Mantri Rozgar Protsahan Yojana, launched in 2016 is aimed at encouraging employers to hire unemployed youth, providing them with financial incentives. It focuses on promoting employment in the organized sector.
• National Rural Livelihood Mission (NRLM), launched in 2011 is focused on promoting self-employment and livelihoods among rural women through the formation of self-help groups (SHGs).

Correct Answer: B) CH₃OH

Explanation:

When carbon monoxide (CO) reacts with hydrogen gas (H₂) under high pressure and in the presence of a catalyst (like Cu/ZnO/Cr₂O₃), the product formed is methanol (CH₃OH). This process is known as the catalytic hydrogenation of CO or the synthesis of methanol.

Chemical Reaction:

Information Booster:

• The process is carried out at 50–100 atm pressure and 250–300°C.

• It is an example of industrial synthesis of methanol.

• Methanol is used as a solvent, antifreeze, fuel, and as a feedstock for many chemicals.

• The reaction is exothermic and reversible.

• Catalysts used: Cu-ZnO-Al₂O₃.

Additional Information:

• (A) C₂H₅OH – Ethanol, not formed from CO and H₂.

• (C) HCHO – Formaldehyde, an oxidation product of methanol.

• (D) HCOOH – Formic acid, not formed directly from CO and H₂.