A body of mass \(2\, kg\) moves under a force of \((2 \hat{ i }+3 \hat{ j }+5 \hat{ k }) \,N\). It starts from rest and was at the origin initially. After \(4 \,s\), its new coordinates are \((8, b, 20)\). The value of \(b\) is ........ . (Round off to the Nearest Integer)

If \(B\) is magnetic field and \(\mu_0\) is permeability of free space, then the dimensions of \(\left(B / \mu_0\right)\) is

Identify the semiconductor devices whose characteristics are given below, in the order \((a),(b),(c),(d) \) 

A Spherical ball of radius \(1 mm\) and density \(10.5 g / cc\) is dropped in glycerine of coefficient of viscosity \(9.8\) poise and density \(1.5 g / cc\). Viscous force on the ball when it attains constant velocity is \(3696 \times 10^{-x} N\). The value of \(x\) is \(\text { (Given, } g =9.8 m / s ^2 \text { and } \pi=\frac{22}{7} \text { ) }\)

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, \(\mathrm{T}_{1}\) and \(\mathrm{T}_{2} .\) The temperature of the hot reservoir of the first engine is \(\mathrm{T}_{1}\) and the temperature of the cold reservoir of the second engine is \(\mathrm{T}_{2} . T\) is temperature of the sink of first engine which is also the source for the second engine. How is \(T\) related to \(\mathrm{T}_{1}\) and \(\mathrm{T}_{2}\), if both the engines perform equal amount of work?

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.
Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet.
In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements:
Statement I: For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles.
Statement II: The total kinetic energy can be the sum of kinetic energy of the center of mass w.r.t. to the origin and the kinetic energy of all the particles w.r.t. the center of mass as the reference.
In the light of the above statements,choose the correct answer from the options given below:

All resistances in figure are \(1\,\Omega\) each. The value of current ' \(I\) ' is \(\frac{a}{5}\,A\). The value of \(a\) is

In the following circuit, the battery has an emf of \(2\mathrm{V}\) and an internal resistance of \(\frac{2}{3}\  \Omega\). The power consumption in the entire circuit is _______ \(W\).