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Given:

The ratio of two numbers is 3 ∶ 4

LCM is 72

Calculation:

Let the HCF of two numbers be x

So, Two numbers are 3x and 4x

⇒ The LCM of 3x and 4x = 12x

Now, According to the question

⇒ 12x = 72

⇒ x = 6

So, 

Two numbers = 6 × 3, 6 × 4 

∴ The two numbers are 18 and 24.

Given:

Length of the rectangle = 15 cm

Breadth of the rectangle = 14 cm

Formula Used:

Perimeter of a rectangle = 2 × (Length + Breadth)

Calculation: 

Perimeter = 2 × (15 cm + 14 cm)

Perimeter = 2 ×  29 cm

Perimeter = 58 cm

So, the correct answer is: B) 58 cm

Given,

Height of the equilateral triangle = 10√3 cm

Formula:

Area of the equilateral triangle = (√3/4) × a²

Height of the equilateral triangle = (√3/2) × a

Calculation:

According to the question

(√3/2) × a = 10 √3

⇒ a = 10√3 × (2/√3)

⇒ a = 20 cm

∴ Area of equilateral triangle = (√3/4) × 20 × 20 = 100√3

Given:

\(\frac{1.15}{0.23}\) \(÷\) \(\frac{0.23}{1.15}\) 

Concept used:

Calculation:

\(\frac{1.15}{0.23}\) ÷ \(\frac{0.23}{1.15}\)

⇒ \(\frac{1.15}{0.23}\) × \(\frac{1.15}{0.23}\)

⇒ 5 × 5

⇒ 25

∴ The value of \(\frac{1.15}{0.23}\) ÷ \(\frac{0.23}{1.15}\) is 25.

Given:

The cost of leveling a square field at the rate of ₹ 52/m² = Rs. 1,30,000

Formula used:

Area of square = (side)²

Perimeter of the square = 4 × side

Calculation:

Area of the square field leveled = (1,30,000/52)

⇒ 2500

(Side)² = 2500 m²

⇒ side = 50 m

Now,

Perimeter of the square = (4 × 50) = 200 m

Now,

The cost of fencing its boundary at the rate of ₹35/m = Rs. (200 × 35)

⇒ Rs. 7,000

∴ The required cost is Rs. 7,000

The correct answer is Convex Mirror.

Key Points

• Convex mirrors have a positive focal length and produce virtual, upright, and diminished images.
• They are commonly used in applications where a wide field of view is needed, such as in automobile side mirrors and security mirrors.
• The magnifying power of a convex mirror is positive, indicating that it forms diminished images compared to the actual object size.
• Convex mirrors are also known as diverging mirrors because they diverge light rays that strike them.

Explanation:

States of matter

• Matter exists in nature in different forms, the three basic states of matter are Solid, Liquid and Gas.
• Apart from these three, there are two more states of matter exist which we do not see in our everyday life. They are Plasma & Bose-Einstein condensate.

​Properties of Solid -

• In solids, the particles are closely packed and the gaps between the particles are tiny and hence it is tough to compress them.
• Solid has a fixed shape and volume.

Properties of Liquid -

• In a liquid, particles are less tightly packed as compared to solids and less difficult to compress as compare to solid because particles have less space between them to move but more than the that of solid.
• Liquids take the shape of the container in which they are kept.

Properties of Gas -

• In gases, particles are far apart from each other, the force of attraction between the particles is negligible and they can move freely.
• The gaseous state has the highest compressibility as compared to solids and liquids.
• Gases have neither a fixed volume nor a fixed shape.

So, A substance has a definite shape as well as definite volume. This substance is Solid.

option (1)

CONCEPT:

• Conduction is the mechanism of transfer of heat between two adjacent parts of a body because of their temperature difference.
• Conduction is mostly seen in solids and liquids because the particles are very close within them than in gases where particles are further apart.

EXPLANATION:

• Conduction is majorly takes place in solids.
• Heat transfer is maximum in solids because their atoms and molecules are located very closely together as compared to liquid and gas.\
• Hence option 1 is correct.
• Solids are hard and have higher conductivity, which is also named good conductors.

​

Additional Information 

• Convection: The process of heat transfer by the physical movement of molecules such as gases and liquids.
• Radiation: The energy that comes from a source and travels through space at the rate of speed of light.
• Radiation contains both an electric field and a magnetic field associated with it,
• Radiation is also named EM Wave( Electromagnetic wave).
• Radiation is mainly three types:
• alpha rays
• beta rays
• gamma rays

The correct answer is frequency.

Key Points

• The Pitch of a sound depends on its frequency.
• Pitch can be defined as the quality of sound based on the rate of vibrations that produced it.
• The faster the vibration of source, the higher is the frequency and hence higher the pitch.
• If the frequency is lower, then pitch also decreases.

The correct answer is option 4) i.e. all of the above

CONCEPT:

• Mass is the measure of the amount of matter present in an object.
• It is the basic property of matter around us.
• The SI unit of mass is the kilogram (kg).
• Not all mass can be represented in kilograms.
• A few common units of mass and their conversions are given in the table:

EXPLANATION:

• The gram, kilogram, and tonne are all different units of mass.