$A$ cup of tea cools from $80^{\circ}C$ to $60^{\circ}C$ in $1$ minute. The ambient temperature is $30^{\circ}C$. How many seconds will it take to cool from $60^{\circ}C$ to $50^{\circ}C$?

$100$ cells each of e.m.f. $5 \ V$ and internal resistance $1 \ \Omega$ are to be arranged so as to produce maximum current in a $25 \ \Omega$ resistance. Each row is to contain equal number of cells. The number of rows should be

If $2x + 3y + 12 = 0$ and $x - y + 4\lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $\lambda$ is equal to

In a biprism experiment,if the $5^{\text{th}}$ bright band with wavelength $\lambda_1$ coincides with the $6^{\text{th}}$ dark band with wavelength $\lambda_2$,then the ratio $\left(\frac{\lambda_2}{\lambda_1}\right)$ is:

If the chord $y=mx+1$ of the circle $x^2+y^2=1$ subtends an angle of $45^{\circ}$ at the major segment of the circle,then the value of $m$ is:

$A$ straight conductor of length $4 ~m$ moves at a speed of $10 ~m/s$. When the conductor makes an angle of $30^{\circ}$ with the direction of the magnetic field of induction $0.1 ~Wb/m^2$,the induced emf is: (in $~V$)