NDA / CDS / AFCAT - MCQ Practice Questions

Understanding:

We need to find the maximum height reached by a ball thrown vertically upward.

Formula:

Using the third equation of motion:

Step 1: Substitute known values

Step 2: Solve for $H$

Answer:

The maximum height reached by the ball is $20\text{m}$.

Quick Tip:

At maximum height, the velocity becomes zero. Always set $v=0$ when finding maximum height in vertical projectile problems.

Understanding:

We need to find the retarding force that brings a moving body to rest.

Formula:

First find acceleration using:

Then apply Newton's second law:

Step 1: Calculate acceleration

Step 2: Calculate force

Answer:

The magnitude of the force applied is $5\text{N}$.

Quick Tip:

The negative sign of acceleration indicates deceleration. The question asks for magnitude, so always take the absolute value of $a$ before computing $F$.

Understanding:

A wire of total resistance $12\Omega$ is bent into a circle. We need to find the resistance between the two ends of a diameter.

Formula:

When the wire is bent into a circle and connected at two diametrically opposite points, the wire is divided into two equal halves, each of resistance $\frac{R}{2}$, connected in parallel:

Step 1: Find resistance of each half

Step 2: Calculate parallel combination

Answer:

The effective resistance between the two ends of a diameter is $3\Omega$.

Quick Tip:

For a wire of resistance $R$ bent into a circle, the resistance between diametrically opposite points is always $\frac{R}{4}$. Here $\frac{12}{4}=3\Omega$.

Understanding:

We need to find the length of a simple pendulum given its time period.

Formula:

The time period of a simple pendulum is:

Step 1: Square both sides

Step 2: Solve for $L$

Answer:

The length of the pendulum is $1\text{m}$.

Quick Tip:

A pendulum with $T=2\text{s}$ is called a "seconds pendulum" and always has length $\approx 1\text{m}$ on Earth. This is a frequently tested fact.

Understanding:

Two resistors are in parallel across a battery. We need to find the total current.

Formula:

In a parallel circuit, the same voltage appears across each resistor. The total current is:

Step 1: Calculate individual currents

Step 2: Find total current

Verification:

Equivalent resistance $R_{\text{eq}}=\frac{4\times 6}{4+6}=\frac{24}{10}=2.4\Omega$, so $I=\frac{12}{2.4}=5\text{A}$. ✓

Answer:

The total current drawn from the battery is $5\text{A}$.

Understanding:

We need to find the time period of a body moving uniformly in a circular path.

Formula:

The time period is the time taken to complete one full revolution. The circumference of the circle is $2\pi r$:

Step 1: Substitute values

Answer:

The time period of revolution is $1\text{s}$.

Quick Tip:

Notice how choosing $v=\pi \text{m/s}$ causes $\pi$ to cancel neatly. In MCQs, look for such cancellations before doing heavy arithmetic.

Understanding:

We need to compare the resistances of two bulbs rated for the same voltage but different wattages.

Formula:

The resistance of a bulb at rated conditions is:

Step 1: Find individual resistances

Step 2: Compute the ratio

So $R_{60}:R_{100}=5:3$, meaning the $60\text{W}$ bulb has the higher resistance.

Answer:

The $60\text{W}$ bulb has higher resistance and the ratio is $5:3$.

Quick Tip:

Since $R=V^2/P$ and $V$ is the same, resistance is inversely proportional to power. Lower wattage $\Rightarrow$ higher resistance.

Understanding:

We must find the stopping distance of a train under a braking force.

Formula:

First find deceleration using Newton's second law:

Then use the equation of motion:

Step 1: Calculate deceleration

Step 2: Find stopping distance

Answer:

The train travels $200\text{m}$ before stopping.

Quick Tip:

Always convert $\text{km/h}$ to $\text{m/s}$ by multiplying by $\frac{5}{18}$. Here $72\times \frac{5}{18}=20\text{m/s}$.

Understanding:

We need to find the speed of sound using its wavelength and frequency.

Formula:

The wave speed relation is:

Step 1: Substitute values

Answer:

The speed of sound in air is $340\text{m/s}$.

Quick Tip:

The speed of sound in air at $0°\text{C}$ is approximately $332\text{m/s}$ and at room temperature ($\approx 25°\text{C}$) is about $346\text{m/s}$. The standard value $340\text{m/s}$ is widely used in competitive exams.

Understanding:

We need to find the potential energy at height $h$ and the kinetic energy just before impact, using energy conservation.

Formula:

Potential energy:

By conservation of mechanical energy (no air resistance), all PE converts to KE:

Step 1: Calculate potential energy

Step 2: Apply energy conservation

Just before hitting the ground, height $=0$, so all potential energy converts to kinetic energy:

Answer:

The potential energy at $5\text{m}$ is $100\text{J}$ and the kinetic energy just before impact is also $100\text{J}$.

Quick Tip:

By the law of conservation of mechanical energy, in the absence of friction or air resistance, the total mechanical energy remains constant. Therefore $K{E}_{\text{bottom}}=P{E}_{\text{top}}$.