A drop of liquid of density ρ is floating half immersed in a liquid of density σ and surface tension 7.5×10−4 Ncm−1. The radius of drop in cm will be : ( Take : g=10 m/s2)
Electron beam used in an electron microscope, when accelerated by a voltage of $20 kV$, has a de-Broglie wavelength of $\lambda_0$. If the voltage is increased to $40 kV$, then the de-Broglie wavelength associated with the electron beam would be:
As shown in the figure a block of mass \(10\, kg\) lying on a horizontal surface is pulled by a force \(F\)acting at an angle \(30^{\circ}\), with horizontal For \(\mu_{ s }=0.25\), the block will just start to move for the value of \(F\) : [Given g=10ms-2]
For the system of linear equations\(\alpha x+y+z=1, x+\alpha y+z=1, x+y+\alpha z=\beta\) which one of the following statements is NOT correct ?
Let αx=exp(xβyγ) be the solution of the differential equation 2x2ydy−(1−xy2) dx = 0, x>0 , y(2)=\(\sqrt {log_e2}\). Then α+β−γ equals :
If \(A=\frac{1}{2}\begin{bmatrix}1 & \sqrt{3} \\ -\sqrt{3} & 1\end{bmatrix}\), then :
An organic compound $[ A ]\left( C _4 H _{11} N \right)$, shows optical activity and gives $N _2$ gas on treatment with The structure of $A$ is :
The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is:
