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The ratio of nuclear densities and nuclear volumes of ${}_{26}^{56}\mathrm{Fe}$ and ${}_{2}^{4}\mathrm{He}$ are, respectively:
At any instant, two elements $X_1$ and $X_2$ have the same number of radioactive atoms. If the decay constants of $X_1$ and $X_2$ are $10\lambda$ and $\lambda$ respectively, then the time when the ratio of their atoms becomes $1/e$ will be:
Which of the following gate is called the universal gate?
Which one of the following equations of motion represents simple harmonic motion? (where $k, k_0, k_1$ and $a$ are all positive.)
A rectangular block of mass $m$ and area of cross-section $A$ floats in a liquid of density $\rho$. If it is given a small vertical displacement from equilibrium, it undergoes oscillation with a time period $T$. Then:
A particle of mass $m$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time?
The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is:
The average velocity of a particle executing SHM in one complete vibration is:
If in a p-n junction, a square input signal of $10\text{ V}$ is applied as shown, then the output across $R_L$ will be:
The given graph represents the $V$-$I$ characteristics of a semiconductor device. Which of the following statements is correct?
The amount of energy required to form a soap bubble of radius $2 \text{cm}$ from a soap solution is nearly (surface tension of soap solution $= 0.03 \text{N m}^{-1}$)
A Carnot engine has an efficiency of $50\%$ when its source is at a temperature $327^\circ\text{C}$. The temperature of the sink is
The displacement of a particle along the x-axis is given by $x = a \sin^2 \omega t$. The motion of the particle corresponds to:
Candela is the unit of
If a body is executing simple harmonic motion with frequency $n$, then the frequency of its potential energy is:
A spring is stretched by $5 \text{ cm}$ by a force $10 \text{ N}$. The time period of the oscillations when a mass of $2 \text{ kg}$ is suspended by it is:
Identify the function which represents a non-periodic motion?
A cylinder of $500 \text{ g}$ and radius $10 \text{ cm}$ has moment of inertia (about its natural axis):
The circuit diagram shown here corresponds to the logic gate:
An object is placed on the principal axis of a concave mirror at a distance of $1.5f$ ($f$ is the focal length). The image will be at: