C++ | MCQs

Explanation

When a wire is stretched to double its length, its resistance becomes:

R' = ρ × (2L) / (A/2) = 4 × R

So, the new resistance is 4r ohms

Explanation

 If the temperature of the source of heat increases, the efficiency of a Carnot engine will increase.

The efficiency of a Carnot engine is directly related to the temperature difference between the hot and cold reservoirs.

A higher source temperature leads to a greater temperature difference and thus, a higher efficiency. 

Explanation

The magnitude of i · (j × k) is:

This is a scalar triple product, and for standard unit vectors:

i · (j × k) = 1

Explanation

Explanation

• One parallel to the field (causes straight motion)
• One perpendicular to the field (causes circular motion)

Explanation

The electrostatic force between two charges is given by Coulomb’s Law:

F = k * q₁ * q₂ / R²

If a total charge Q is divided into two parts: q and Q−q, the force becomes:

F = k * q * (Q − q) / R²

To maximize F, differentiate F with respect to q and set dF/dq = 0:

dF/dq = k/R² * [Q − 2q] = 0  

⇒ Q − 2q = 0  

⇒ q = Q/2

Explanation

The correct answer is:  All of the above

A complete revolution corresponds to an angular displacement of:

• 360°

• $2\pi$ radians

So, for 2 complete revolutions:

• Degrees: $2\times 360°=720°$

• Radians: $2 times 2pi = 4pi$ radians

• Approximate radians:

  $$4\pi \approx 4\times 3.14=12.56\text{ radians (rounded to 12.6)}$$

Explanation

A cell counter is a device specifically designed to count the number of cells in a suspension.

This is crucial in cell culture experiments, as researchers need to know the cell concentration before seeding or performing other procedures. 

Explanation

In a reversible reaction, a catalyst reduces the time to reach equilibrium by increasing the rate of both forward and reverse reactions. 

Explanation

A crystal can only have one center of symmetry. 

A center of symmetry is a point within a crystal where, if a line is drawn through that point and extended an equal distance on the other side, it intersects an identical point on the crystal.

Since this is a single, specific point within the crystal, there can only be one center of symmetry per crystal.