The velocity of a small ball of mass \(0.3\,g\) and density \(8\,g / cc\) when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \(1.3\,g / cc\), then the value of viscous force acting on the ball will be \(x \times 10^{-4}\,N\), the value of \(x\) is [use \(g=10\,m / s ^{2}\) ] 

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative \(z\)-axis and magnetic field is along the positive \(x\)-axis. Then the direction of propagation of electromagnetic wave is

A rod of length \(50\,cm\) is pivoted at one end. It is raised such that if makes an angle of \(30^o\) fro the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in \(rad\,s^{-1}\) ) will be \((g = 10\,ms^{-2})\)

A zener diode of power rating \(2\, {W}\) is to be used as a voltage regulator. If the zener diode has a breakdown of \(10 \,{V}\) and it has to regulate voltage fluctuated between \(6\, {V}\) and \(14\, {V}\), the value of \({R}_{{s}}\) for safe operation should be \(....\Omega\)

Given below are two statements: Statement \(I\) : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit \(\left( E _{1}\right)\) to higher energy orbit \(\left( E _{2}\right)\), is given as \(hf = E _{1}- E _{2}\). Statement \(II\) : The jumping of electron from higher energy orbit \(\left(E_{2}\right)\) to lower energy orbit \(\left(E_{1}\right)\) is associated with frequency of radiation given as \(f\) \(=\left( E _{2}- E _{1}\right) / h\) This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below

A beam of light has two wavelengths of \(4972\,\mathop A\limits^o \) and \(6216\,\mathop A\limits^o \) with a total intensity of \(3 .6 \times  10^{- 3}\,\,Wm^{-2}\) equally distributed among the two wavelengths. The beam falls normally on an area of \(1\,cm^2\) of a clean metallic surface of work function \( 2.3\,eV.\) Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photoelectrons liberated in \(2\,s\) is approximately

The voltage drop across \(15\, \Omega\) resistance in the given figure will be \(.....V.\)

A radioactive nucleus decays by two different process. The half life of the first process is \(5\) minutes and that of the second process is \(30\,s\). The effective half-life of the nucleus is calculated to be \(\frac{\alpha}{11}\,s\). The value of \(\alpha\) is \(..............\)

The foot of the perpendicular drawn from the origin, on the line, \(3x + y = \lambda \,\left( {\lambda  \ne 0} \right)\) is \(P\). If the line meets \(x-\) axis at \(A\) and \(y-\) axis at \(B\), then the ratio \(BP : PA\) is

Let \(A=\left[a_{i j}\right]\) be a matrix of order \(3 \times 3\), with \(a_{i j}=(\sqrt{2})^{i+j}\). If the sum of all the elements in the third row of \(A^2\) is \(\alpha+\beta \sqrt{2}, \alpha, \beta \in \mathbf{Z}\), then \(\alpha+\beta\) is equal to :

Let \(f\) be a polynomial function such that \(f(x^{2}+1)=x^{4}+5x^{2}+2,\) for all \(x\in\mathbb{R}.\) Then \(\int_{0}^{3}f(x)dx\) is equal to

Consider a frame that is made up of two thin massless rods \(AB\) and \(AC\) as shown in the figure. \(A\) vertical force \(\overrightarrow{ P }\) of magnitude \(100 \;N\) is applied at point \(A\) of the frame. Suppose the force is \(\overrightarrow{ P }\) resolved parallel to the arms \(AB\) and \(AC\) of the frame. The magnitude of the resolved component along the arm \(AC\) is \(xN\). The value of \(x\), to the nearest integer, is ............ [Given : \(\sin \left(35^{\circ}\right)=0.573, \cos \left(35^{\circ}\right)=0.819\) \(\left.\sin \left(110^{\circ}\right)=0.939, \cos \left(110^{\circ}\right)=-0.342\right]\)  

Let \(a _{ n }\) be the \(n ^{\text {th }}\) term of the series \(5+8+14+23\) \(+35+50+\ldots\) and \(S _{ n }=\sum \limits_{ k =1}^{ n } a _{ k }\). Then \(S _{30}- a _{40}\) is equal to