Flux $\phi$ (in weber) in a closed circuit of resistance $10\,\Omega$ varies with time $t$ (in sec) according to the equation $\phi = 6t^2 - 5t + 1$. What is the magnitude of the induced current at $t = 0.25\,s$ (in $,A$)?

For the Bohr's first orbit of circumference $2\pi r$,the de-Broglie wavelength of the revolving electron will be

While a collector to emitter voltage is constant in a transistor,the collector current changes by $8.2 ~mA$ when the emitter current changes by $8.3 ~mA$. The value of forward current ratio is

If $(a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y)=a^{2}-b^{2}$ where $a>b>0,$ then $\frac{dx}{dy}$ at $\left(\frac{\pi}{4}, \frac{\pi}{4}\right)$ is

In order to eliminate the first degree terms from the equation $2x^2+4xy+5y^2-4x-22y+7=0$,the point to which the origin is to be shifted is

$A$ particle of mass $10\, g$ is kept on the surface of a uniform sphere of mass $100\, kg$ and radius $10\, cm$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $G = 6.67 \times 10^{-11}\, N m^2/kg^2$).