A force \(\overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{b} \hat{j}+\hat{k}\) is applied on a particle and it undergoes a displacement \(\hat{i}-2 \hat{j}-\hat{k}\). What will be the value of \(b\), if work done on the particle is zero.

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by \(y=\left(10 \cos \pi x \sin \frac{2 \pi t}{T}\right)\, cm\) The amplitude of the particle at \(x =\frac{4}{3} \,cm\) will be........ \(cm\).

A parallel plate capacitor with air between the plate has a capacitance of \(15 pF\). The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant \(3.5.\) Then the capacitance becomes \(\frac{ x }{4}\,pF\).The value of \(x\) is \(............\)

A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature \(50^{\circ} C\). The gas is now heated to double its temperature. The modified pressure is _________ Pa .

A car accelerates from rest to \(u\,m / s\). The energy spent in this process is \(E\,J\). The energy required to accelerate the car from \(u\,m / s\) to \(2u\,m / s\) is \(nE\,J\). The value of \(n\) is ..............

A wire of resistance \(R\) and radius \(r\) is stretched till its radius became \(r / 2\). If new resistance of the stretched wire is \(xR\), then value of \(x\) is _______.

The kinetic energy of an electron, \(\alpha\)-particle and a proton are given as \(4K,2K\) and \(K\) respectively. The de-Broglie wavelength associated with electron ( \(\lambda e), \alpha\)-particle \((\lambda \alpha)\) and the proton \((\lambda p)\) are as follows:

A capacitor of capacitance \(150.0\,\mu F\) is connected to an alternating source of \(emf\) given by \(E =36\) \(\sin (120 \pi t ) V\). The maximum value of current in the circuit is approximately equal to \(......\,A\)

Let a total charge \(2Q\) be distributed in a sphere of radius \(R\), with the charge density given by \(\rho(r) = kr\), where \(r\) is the distance from the centre. Two charges \(A\) and \(B\), of \(-Q\) each, are placed on diametrically opposite points, at equal distance, \(a\), from the centre. If \(A\) and \(B\) do not experience any force, then

Paramagnetic substances: \(A\). align themselves along the directions of external magnetic field. \(B\). attract strongly towards external magnetic field. \(C\). has susceptibility little more than zero. \(D\). move from a region of strong magnetic field to weak magnetic field. Choose the most appropriate answer from the options given below:

The electric field in an electromagnetic wave is given by \(\overrightarrow{\mathrm{E}}=\hat{\mathrm{i}} 40 \cos \omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right) N \mathrm{NC}^{-1}\). The magnetic field induction of this wave is (in SI unit) _______.