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A body is released from a great height and falls freely towards the earth. Another body is released from the same height exactly one second later. The separation between the two bodies, two seconds after the release of the second body is:
A closely wound solenoid of 2000 turns and area of cross-section $1.5 \times 10^{-4} \text{ m}^2$ carries a current of $2.0 \text{ A}$. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field $5 \times 10^{-2} \text{ T}$ making an angle of $30^{\circ}$ with the axis of the solenoid. The torque on the solenoid will be
A metallic rod of mass per unit length of 0.5 kg m⁻¹ is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction of 0.25 T is acting on it in the vertical direction. What is the current flowing through the rod to keep it stationary?
In the nuclear reaction $X(n, \alpha){}_{3}^{7}\mathrm{Li}$, the term $X$ will be:
The interference pattern is obtained with two coherent light sources of intensity ratio $n$. In the interference pattern, the ratio $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$ will be
A voltmeter has a resistance of $G$ ohms and range $V$ volts. The value of resistance used in series to convert it into a voltmeter of range $nV$ volts is:
The current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is:
A long solenoid of radius $1 \text{ mm}$ has $100$ turns per mm. If $1 \text{ A}$ current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:
A square loop ABCD carrying a current $i$ is placed near and coplanar with a long straight conductor XY carrying a current $I$. The net force on the loop will be:
In the following figure, the diodes which are forward biased, are (I) (II) (III) (IV). Choose the correct option from the given ones:
An electron moving in a circular orbit of radius $r$ makes $n$ rotations per second. The magnetic field produced at the centre has magnitude:
From Ampere's circuital law, for a long straight wire of circular cross-section carrying a steady current, the variation of the magnetic field inside and outside the region of the wire is:
The half-life of a radioactive sample undergoing $\alpha$-decay is $1.4 \times 10^{17}\text{ s}$. If the number of nuclei in the sample is $2.0 \times 10^{21}$, the activity of the sample is nearly equal to:
If the nuclear radius of $^{27}\text{Al}$ is 3.6 Fermi, the approximate nuclear radius of $^{64}\text{Cu}$ in Fermi is:
The half-life of a radioactive substance is 30 minutes. The time (in minute) taken between 40% decay and 85% decay of the same radioactive substance is:
An n-p-n transistor is connected in the common base configuration in a given amplifier. A load resistance of $800\, \Omega$ is connected in the collector circuit and the voltage drop across it is $0.8\text{ V}$. If the current amplification factor is $0.96$ and the input resistance of the circuit is $192\, \Omega$, the voltage gain and the power gain of the amplifier will respectively be:
A simple pendulum performs simple harmonic motion about $x = 0$ with an amplitude $a$ and time period $T$. The speed of the pendulum at $x = rac{a}{2}$ will be:
The mean free path l for a gas molecule depends upon the diameter, d of the molecule as:
The value $\gamma = \frac{C_P}{C_V}$ for hydrogen, helium, and another ideal diatomic gas $X$ (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to:
In a common-emitter transistor amplifier, the audio signal voltage across the collector is $3\text{ V}$. The resistance of the collector is $3\text{ k}\Omega$. If the current gain is $100$ and the base resistance is $2\text{ k}\Omega$, the voltage and power gain of the amplifier are: