The length of an elastic string is $a \, m$ when the longitudinal tension is $4 \, N$ and $b \, m$ when the longitudinal tension is $5 \, N$. The length of the string in metres when the longitudinal tension is $9 \, N$ is

$A$ metallic frame moves with constant velocity $v$ near an infinitely long current-carrying wire. At any instant,the induced electromotive forces (emf) in sides $AD$ and $BC$ are $5\,V$ and $2\,V$ respectively. If the resistance of the frame is $6\,\Omega$,find the magnitude and direction of the induced current in it.

If $f:[-6,6] \rightarrow R$ is defined by $f(x)=x^2-3$ for $x \in R$,then $(f \circ f \circ f)(-1)+(f \circ f \circ f)(0)+(f \circ f \circ f)(1)$ is equal to

The perimeter of the triangle with vertices at $(1,0,0), (0,1,0)$ and $(0,0,1)$ is

In a thermodynamic process,the pressure of a fixed mass of a gas is changed in such a manner that the gas releases $20 \, J$ of heat when $8 \, J$ of work is done on the gas. If the initial internal energy of the gas was $30 \, J$,then the final internal energy will be ........ $J$.

When light of wavelength $\lambda$ is incident on a photosensitive surface,the stopping potential is $V$. When light of wavelength $3 \lambda$ is incident on the same surface,the stopping potential is $\frac{V}{6}$. The threshold wavelength for the surface is: