List of practice Questions

An insulated cylinder of volume $60\,\text{cm}^3$ is filled with a gas at $27^\circ\text{C}$ and $2$ atmospheric pressure. The gas is then compressed making the final volume $20\,\text{cm}^3$ while allowing the temperature to rise to $77^\circ\text{C}$. The final pressure is ____________ atmospheric pressure.

A wire of uniform resistance $\lambda$ $\Omega$/m is bent into a circle of radius r and another piece of wire with length 2r is connected between points A and B (ACB) as shown in figure. The equivalent resistance between points A and B is_______ $\Omega$.

Give the output of the following program segment:
\texttt{String S = "GRACIOUS".substring(4);}
\texttt{System.out.println(S);}
\texttt{System.out.println("GLAMOROUS".endsWith(S));}

The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?

Given below are two statements:
Statement I: Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.
In the light of the above statements, choose the correct answer from the options given below

A chord of a circle, of radius 14 cm, subtends an angle of $60^{\circ}$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

A bead P sliding on a frictionless semi-circular string... bead Q ejected... relation between $t_P$ and $t_Q$ is

In case of vertical circular motion of a particle by a thread of length $ r $, if the tension in the thread is zero at an angle $30^\circ$ as shown in the figure, the velocity at the bottom point (A) of the vertical circular path is ( $ g $ = gravitational acceleration ).

The correct order of C, N, O and F in terms of second ionisation potential is

For the series LCR circuit connected with $220\,\text{V},\,50\,\text{Hz}$ a.c. source as shown in the figure, the power factor is $\dfrac{\alpha}{10}$. The value of $\alpha$ is ___.

The electrostatic potential in a charged spherical region of radius $r$ varies as $V = ar^{3} + b$, where $a$ and $b$ are constants. The total charge in the sphere of unit radius is $a \times \pi \varepsilon_{0}$. The value of $a$ is ___.
(Permittivity of vacuum is $\varepsilon_{0}$)

A spherical body of radius $r$ and density $\sigma$ falls freely through a viscous liquid having density $\rho$ and viscosity $\eta$ and attains a terminal velocity $v_0$. Estimated maximum error in the quantity $\eta$ is : (Ignore errors associated with $\sigma$, $\rho$ and $g$, gravitational acceleration)

A moving coil galvanometer of resistance $100\,\Omega$ shows a full scale deflection for a current of $1\,\text{mA}$. The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of $5\,\text{mA}$, is ________ $\Omega$.

A brass wire of length $2\,\text{m}$ and radius $1\,\text{mm}$ at $27^\circ\text{C}$ is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^\circ\text{C}$ creating a tension $T$ in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to $1.4T$ is ___$^\circ$C.

If $\varepsilon_0$, $E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of \[ \frac{\varepsilon_0 E}{t} \] will be

Number of photons of equal energy emitted per second by a 6 mW laser source
operating at wavelength 663 nm is _______.

(Given: h = 6.63 × 10^-34 J·s and c = 3 × 10^8 m/s)