Given:

A car covers a distance of 350 km in 5 hours and covers another 450 km at a speed of 90 km/h

Formula used:

Average speed = Total distance/ Total time

Calculation:

Total distance covered = 350 km + 450 km = 800 km

Total time = 5 hour + 5 hour = 10 hours

Average speed = Total distance/ Total time

Average speed = 800/10 = 80 km/hr

His average speed for the whole journey is 80 km/hr.

• By presenting the highlights of the film, the producer team expects the media to understand the concept of the film and then create the right hype, that is the right advertisement. Thus, conclusion I logically follows the statement.
• Since the producer team is promoting the film, it is obvious that they expect it to be successful. thus, conclusion II also follows.

Hence the correct answer is option 4.

Concept:

• Magnetic field lines, also known as magnetic lines of force, represent the strength and direction of a magnetic field. They are used to illustrate how the magnetic field behaves in a certain region.
• Here are some fundamental properties of magnetic lines of force:
  •  Magnetic field lines never intersect each other.
  •  They are continuous lines emanating from the north pole and merging at the south pole.
  •  The direction of the magnetic field is always from the North pole to the South pole outside the magnet, and from the South pole to the North pole inside the magnet.
  •  The density of magnetic lines of force is more near the poles where the magnetic field is the strongest.

Explanation:

•  The statement "Magnetic lines of force do not intersect each other" is correct. If they did intersect, they would have two different directions of the magnetic field at the point of intersection, which is not possible.
• The statement "Each line is a closed and continuous curve" is correct. Magnetic field lines form continuous loops from the North pole to the South pole outside the magnet and from South to North inside.
• The statement "The direction of field lines outside the magnet is from the South pole to the North pole" is incorrect.
• The statement "They are crowded near the poles, where the magnetic field is strong" is also correct. The density of magnetic field lines is a measure of the strength of the magnetic field; therefore, it is more concentrated near the poles, which are the strongest parts of the magnet.

All statements provided are correct with regard to the properties of magnetic lines of force, so none of them are correct.

Additional Information

• Remember that while we often visualize magnetic field lines as starting at the North pole and ending at the South pole, this is a simplification. In reality, magnetic field lines form continuous loops, and the concept of them "starting" or "ending" is just a convention used for simplicity. Magnetic field lines are also a visualization tool; they do not exist physically in the way that electric field lines do.

Given:

Height of tent (H) = 10 m

Base diameter (D) = 48 m

Formula used:

The curved surface area of the cone = π × R × l

Where, l = √(H² + R²) 

R = radius ; l = slant height

Calculation:

Base diameter (D) = 48 m

Base radius (R) = 48/2 = 24 m

Slant height (l) = √(H² + R²)

⇒ √{(10)² + (24)²}

⇒ √{100 + 576} = √676

⇒ 26 m

The curved surface area of the cone = π × R × l

⇒ π × 24 × 26 = 624 π m² 

∴ The correct answer is 624 π m².

Logic : (2nd number × 2) = (3rd number + 1st number)

Given:

• (18, 39, 60)

39 × 2 = 60 + 18

78 = 78 (LHS = RHS)

• (27, 48, 69)

48 × 2 = 69 + 27 

96 = 96 (LHS = RHS)

So,

• Option - (1) : (24, 64,96)

​56 × 2 = 96 + 24

112 ≠ 120 (LHS ≠ RHS)

• Option - (2) : (35, 56, 77)

​56 × 2 = 77 + 35

112 = 112 (LHS = RHS)

• Option - (3) : (31, 52, 84)

​52 × 2 = 84 + 31

104 ≠ 115 (LHS ≠ RHS)

• Option - (4) : (17, 28, 49)

​28 × 2 = 49 + 17

56 ≠ 66 (LHS ≠ RHS)

Hence, "Option - (2)" is the correct answer.

The correct answer is 1924.

Key Points

• Bose-Einstein Condensate is called the Fifth state of matter.
• It is formed when a gas of bosons having low densities is cooled to an absolute zero temperature.
• At this temperature, the atoms stop moving.
• They thus clump to each other acting like a single atom with the whole group having identical physical properties.
• Plasma is a subset of gas which, unlike ordinary gases, is made up of atoms where some or all the electrons are stripped and positively charged protons roam freely.
• Albert Einstein predicts it in the year 1924.

Additional Information

• States of Matter: There are five states of matter.
  • Solid
  • Liquid
  • Gas
  • Plasma
  • Bose-Eienstein Condensate(BEC)

Given:

A six-digit number Is divisible by 33

Formula used:

Dividend = divisor × quotient + remainder

Calculation:

Dividend = divisor × quotient + remainder

⇒ 33 × q + 0 = 33q

If 54 is added to the dividend then,

New number = 33q + 54

⇒ 3 × (11q + 18)

So, we can clearly say that the new number is divisible by 3.

∴ The correct option is 1.

The logic followed here is:

Logic: Number of sides = Number of figures inside

We get that, in figure (C): Number of sides (3) ≠ Number of figures inside (4)

Hence, the correct answer is "Option (2)".

The correct answer is Gallium.

Key Points

• The chemical element gallium has the atomic number 31 and the symbol Ga.
• Group 13 of the periodic table contains gallium.
• Gallium is an element that is soft and silvery at ordinary pressure and temperature.
• It turns silvery white when it's liquid.
• Gallium may fracture conchoidally if excessive force is used.
• Gallium has been commonly utilized to create alloys with low melting points.
• As a dopant on semiconductor substrates, it is also utilized in semiconductors.
• The temperature reference point is gallium's melting point.
• Most people are familiar with gallium and cesium as metals that melt when held in the palm.
• Because gallium has a relatively low melting point and is quickly melted by the heat from our palms, it essentially dissolves when held in the palm.

Additional Information

• Germanium:
  • The chemical element germanium has the atomic number 32 and the symbol Ge.
  • It resembles silicon in appearance and is hard, brittle, and glossy.
• Indium:
  • With the atomic number 49 and the symbol In, indium is a chemical element.
  • The softest metal that is not an alkali metal is indium.
• Copper:
  • The chemical element copper has the atomic number 29 and the symbol Cu.
  • It is an extremely high thermal and electrical conductivity metal that is soft, malleable, and ductile.

Given:

The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. 

Calculation:

Let the numbers are x and y

(x - y)² = 324

So, x - y = 18, xy = 144

(x + y)² = (18)² + 4× 144

⇒ 900

⇒ x + y = 30

Then, x is (30 + 18) / 2 = 24 and y = 6

So , x² - y² = 24² - 6²

⇒ 576 - 36 = 540

∴ The correct  option is 2