List of practice Questions

An ideal gas is placed in a container at \( (P_1, V_1, T_1) \) and another ideal gas is placed in a different container at \( (P_2, V_2, T_2) \) are mixed at final pressure of \( P \) and final volume of \( V \). Calculate the final temperature.

Statement-1: Heat capacity at constant volume is always greater than heat capacity at constant pressure.
Statement-2: At constant volume as work done is zero, heat given to the chaotic motion is reflected by increase in temperature.

Statement-1: Under certain conditions, the covalency of oxygen can be up to 4. In \( \text{SO}_2 \), the oxidation state of oxygen is \( -2 \) and in \( \text{OF}_2 \), the oxidation state of oxygen is \( +2 \). Statement-2: The anomalous behaviour of oxygen in the 16th group is due to its small size and high electronegativity.

Anion \( X^- \) contains 45 neutrons and 36 electrons. The atomic mass, period number, and state in which "X" exists is:

Two forces are acting on a body: \[ \vec{F}_1 = 3\hat{i} -5\hat{j} +2\hat{k} \] \[ \vec{F}_2 = 8\hat{i} +2\hat{j} -3\hat{k} \] The displacement of the body is \(25\,\text{m\) along the direction \(3\hat{i}-4\hat{j}\). Find the work done.}

Each diode in the circuit has \(10\Omega\) resistance in forward bias and infinite resistance in reverse bias. Find the time constant of the circuit. Given: \(R=100\Omega\), \(C=0.2\,\mu F\).

A particle is moving along the \(x\)-axis where the speed varies as \[ v^2 = 100 - x^2 \] Determine the time period.

The reaction follows 1st order reaction \( \text{R} \rightarrow \text{P} \) Find the fraction of molecules dissociated in time \( t \). \([k_1 = \text{Rate constant}]\)

In a screw gauge, when the circular scale is given five complete rotations, it moves linearly by \(2.5\,\text{mm\). If the circular scale has 100 divisions, the least count of the screw gauge is:}

There is a spiral which has \(r_i=3\,\text{cm\), \(r_{ext}=6\,\text{cm}\), \(I=20\,\text{mA}\) and \(N=200\), where \(r_i\) : internal radius \(r_{ext}\) : external radius \(N\) : number of turns \(I\) : current. Find the magnetic moment of the spiral.}

If the right plate of a parallel plate capacitor is pulled with constant velocity as shown in the figure, find how the rate of change of energy stored in the capacitor depends on the separation \(x\).

A solid sphere of mass \(M\) and radius \(R\) is split into two pieces of masses \( \frac{7M{8} \) and \( \frac{M}{8} \). The piece of mass \( \frac{7M}{8} \) is converted into a disc of radius \(2R\) and thickness \(t\) whose moment of inertia is \(I_1\). The other piece is made into a solid sphere with moment of inertia \(I_2\). Find \( \frac{I_1}{I_2} \).}

Length of rods are \( \ell \) and \(2\ell\) respectively and their Young's modulus are \( \gamma \) and \(2\gamma\) respectively. Given: \[ \ell = 0.314\,\text{m}, \quad R = 0.2\,\text{mm} \,(\text{same}), \quad \gamma = 2\times10^9 \]

Find the total extension \( \Delta \ell \).

Find the work done in expanding a soap bubble from radius \(1\,\text{cm}\) to \(2\,\text{cm}\). Surface tension is \( \gamma = 7.2 \times 10^{-2}\,\text{N/m} \).

Refer the given image carefully:

Explain any two measures that can be taken by the Central Bank to control the indicated macroeconomic problem.

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is picked from B and put in A. Then a ball is drawn from A. Probability it is white is $p/q$. Find $p+q$.

If the domain of the function $f(x)=\sin^{-1}\!\left(\dfrac{1}{x^2-2x-2}\right)$ is $(-\infty,\alpha)\cup[\beta,\gamma]\cup[\delta,\infty)$, then $\alpha+\beta+\gamma+\delta$ is equal to