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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:
A body performs simple harmonic motion about $x=0$ with an amplitude $a$ and a time period $T$. The speed of the body at $x=\frac{a}{2}$ will be:
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:
The fraction of the original number of radioactive atoms that disintegrates (decays) during the average lifetime of a radioactive substance will be:
An n-p-n transistor is connected in a common emitter configuration (see figure) in which collector voltage drop across load resistance ($800\ \Omega$) connected to the collector circuit is $0.8\text{ V}$. The collector current is:
The half-life of a radioactive isotope $X$ is 20 years. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio 1:7 in a sample of a given rock. The age of the rock is estimated to be:
Two simple harmonic motions of angular frequency $100\text{ rad s}^{-1}$ and $1000\text{ rad s}^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration will 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 decay constant of a radio isotope is $\lambda$. If $A_1$ and $A_2$ are its activities at times $t_1$ and $t_2$ respectively, the number of nuclei which have decayed during the time $(t_1 - t_2)$ is:
The activity of a radioactive sample is measured as $N_0$ counts per minute at $t=0$ and $N_0/e$ counts per minute at $t=5$ min. The time (in minute) at which the activity reduces to half its value is:
A radioisotope X with a half-life 1.4 × 10^9 yr decays into Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1:7. The age of the rock is:
The mass of a ${}_{3}^{7}\mathrm{Li}$ nucleus is 0.042 u less than the sum of the masses of its nucleons. The binding energy per nucleon of ${}_{3}^{7}\mathrm{Li}$ nucleus is nearly:
Which one of the following equations of motion represents simple harmonic motion where $k$, $k_0$, $k_1$, and $a$ are all positive?
A particle is executing SHM along a straight line. Its velocities at distances $x_1$ and $x_2$ from the mean position are $v_1$ and $v_2$, respectively. Its time period is:
A person can see objects clearly only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be:
A radioactive nucleus ${}_{Z}^{A}\mathrm{X}$ undergoes spontaneous decay in the sequence ${}_{Z}\mathrm{X} \rightarrow {}_{Z-1}\mathrm{B} \rightarrow {}_{Z-3}\mathrm{C} \rightarrow {}_{Z-2}\mathrm{D}$, where $Z$ is the atomic number of element $\mathrm{X}$. The possible decay particles in the sequence are:
In the given figure, a diode D is connected to an external resistance $R = 100 \, \Omega$ and an e.m.f of $3.5\text{ V}$. If the barrier potential developed across the diode is $0.5\text{ V}$, the current in the circuit will be:
The unit of permittivity of free space $\varepsilon_0$ is
If $T_1, T_2, T_3, T_4$ and $T_5$ represent the tension in the string of a simple pendulum when the bob is at the left extreme, right extreme, mean, any intermediate left and any intermediate right positions, respectively. Then, which of the following relations are correct? (A) $T_1 = T_2$ (B) $T_3 > T_2$ (C) $T_4 > T_3$ (D) $T_3 = T_4$ (E) $T_5 > T_2$ Choose the most appropriate answer from the options given below:
An automobile engine develops $100\text{ kW}$ when rotating at a speed of $1800\text{ rev/min}$. What torque does it deliver?