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A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:
A nucleus with Z = 92 emits the following in a sequence: $\alpha, \beta^-, \beta^-, \alpha, \alpha, \alpha, \alpha, \alpha, \beta^-, \beta^-, \alpha, \beta^+, \beta^+, \alpha$. The Z of the resulting nucleus is:
An automobile engine develops $100\text{ kW}$ when rotating at a speed of $1800\text{ rev/min}$. What torque does it deliver?
Given below are two statements: Statement-I: The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample. Statement-II: The half life of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time t=0. In the light of the above statements, choose the most appropriate answer from the options given below:
A nucleus of mass number 189 splits into two nuclei having mass numbers 125 and 64. The ratio of the radius of two daughter nuclei respectively is:
A light bulb and an inductor coil are connected to an AC source through a key as shown in the figure below. The key is closed and after some time an iron rod is inserted into the interior of the inductor. The glow of the light bulb:
The symbolic representations of four logic gates are given. The logic symbols for OR, NOT and NAND gates are respectively:
A spherical body of mass m and radius r is allowed to fall in a medium of viscosity η. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity (v) is called time constant (τ). Dimensionally τ can be represented by:
The distance covered by a particle undergoing SHM in one time period is: (amplitude = $A$)
To get output $1$ for the following circuit, the correct choice for the input is:
An excited heavy nucleus ${}_{Z}^{A}\mathrm{X}$ emits radiations in the following sequence: $${}_{Z}^{A}\mathrm{X} \rightarrow {}_{Z-2}^{A-4}\mathrm{D}_1 \rightarrow {}_{Z-1}^{A-4}\mathrm{D}_2 \rightarrow {}_{Z-3}^{A-8}\mathrm{D}_3 \rightarrow {}_{Z-4}^{A-8}\mathrm{D}_4 \rightarrow {}_{Z-4}^{A-8}\mathrm{D}_5$$ where $Z, A$ are the atomic and mass number of element $\mathrm{X}$, respectively. The possible emitted particles or radiations in the sequence, respectively are:
When an object is shot from the bottom of a long, smooth inclined plane kept at an angle of 60$^{\circ}$ with horizontal, it can travel a distance $x_1$ along the plane. But when the inclination is decreased to 30$^{\circ}$ and the same object is shot with the same velocity, it can travel $x_2$ distance. Then $x_1:x_2$ will be:
A spring of force constant $k$ is cut into lengths of ratio $1:2:3$. They are connected in series and the new force constant is $k'$. Then they are connected in parallel and the force constant is $k''$. Then $k':k''$ is:
Two cars moving in opposite directions approach each other with speed of $22 \text{ m/s}$ and $16.5 \text{ m/s}$ respectively. The driver of the first car blows a horn having a frequency $400 \text{ Hz}$. The frequency heard by the driver of the second car is [velocity of sound $340 \text{ m/s}$]
Find the value of the angle of emergence from the prism given below for the incidence ray shown. The refractive index of the glass is $\sqrt{3}$.
The rms value of potential difference V shown in the figure is
An intrinsic semiconductor is converted into an n-type extrinsic semiconductor by doping it with:
Two simple harmonic motions of angular frequencies $100$ and $1000 \text{ rad s}^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration is:
Two particles of masses $m_1, m_2$ move with initial velocities $u_1$ and $u_2$. On collision, one of the particles gets excited to a higher level, after absorbing energy $\varepsilon$. If the final velocities of the particles are $v_1$ and $v_2$, then we must have:
A second's pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket: