Physics — NDA General Ability Test PYQs

A pendulum of length $L$ oscillates with an angular amplitude of $\theta =60^{\circ }$ and time period $T$. Let $T_0=2\pi \sqrt{\frac{L}{g}}$ be the time period for small angle of oscillations, where $g$ is the acceleration due to gravity. If air resistance is negligibly small and the string remains straight, then which one of the following is correct?

Two forces of equal magnitude simultaneously act at a point. It is observed that the resultant force is equal in magnitude to the individual forces. Which of the following statements is/are correct?
I. The angle between one of the individual forces and the resultant force is $\pi /3$.
II. The angle between the individual forces is $2\pi /3$.
Select the answer using the code given below.

A solid of mass $m$ has temperature-dependent specific heat as $C(T)=C_0+\alpha T$, where $C_0$ and $\alpha$ are constants. The solid is heated from $T_1$ to $T_2$. Which one of the following is the correct expression for quantity of heat ($Q$) of the solid mass?

In a certain process, the relation between pressure ($P$) and volume ($V$), for an ideal gas, is given by $P{V}^2=\text{constant}$. If the initial temperature is $T_1$ and the final temperature is $T_2$; and the initial volume is $V_1$ and the final volume is $V_2$, then which one of the following is correct?

For an ideal gas, a process is described by $P=kT$, where $k$ is a constant. If the molar heat capacity for this process is $C$, then which one of the following is correct (where the symbols have their usual meanings)?

For an object in gravitational field, the gravitational potential is the same at two points $A$ and $B$, but the gravitational field is not the same at these two points. Which one of the following statements is correct?

The position vector of a particle is given by $\vec{r}=\sqrt{3}{t}^2\hat{i}+\sqrt{2}t\hat{j}+\sqrt{5}\hat{k}$. Which one of the following statements is correct?

A ball is dropped from rest from height $h$ above the ground in frame $S$ (the Earth's frame). Another frame $S^{\prime }$ is moving upwards with constant speed $u$ relative to the Earth. In frame $S^{\prime }$, the ball has initial downward speed $v$. Pertaining to the change in kinetic energy ($\Delta K$) of the ball from release to just before hitting the ground as measured in frames $S$ and $S^{\prime }$ separately, which one of the following is correct?

A floating body is in stable state. Which one of the following is correct?

A constant power machine pulls a block on a smooth horizontal surface. Which one of the following correctly describes the relation between speed of the block ($v$) and time ($t$)?