Let A be a symmetric matrix such that $$\mathrm{|A|=2}$$ and $$\left[ {\matrix{ 2 & 1 \cr 3 & {{3 \over 2}} \cr } } \right]A = \left[ {\matrix{ 1 & 2 \cr \alpha & \beta \cr } } \right]$$. If the sum of the diagonal elements of A is $$s$$, then $$\frac{\beta s}{\alpha^2}$$ is equal to __________.
With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is
(A) directly proportional to the length of the potentiometer wire
(B) directly proportional to the potential gradient of the wire
(C) inversely proportional to the potential gradient of the wire
(D) inversely proportional to the length of the potentiometer wire
Choose the correct option for the above statements :
The ratio of de-Broglie wavelength of an $$\alpha$$ particle and a proton accelerated from rest by the same potential is $$\frac{1}{\sqrt m}$$, the value of m is -
A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be: