Five very long,straight wires are bound together to form a small cable. Currents carried by the wires are $I_1 = 20\ A, I_2 = -6\ A, I_3 = 12\ A, I_4 = -7\ A, I_5 = 18\ A$. The magnetic induction at a distance of $10\ cm$ from the cable is

$A$ gaseous mixture consists of $16\,g$ of helium and $16\,g$ of oxygen. The ratio $(C_p/C_v)$ of the mixture is

$A$ stretched wire of length $110 \ cm$ is divided into three segments whose frequencies are in the ratio $1 : 2 : 3$. Their lengths must be

Given $\lambda \in [0, 20]$,find the number of integral values of $\lambda$ for which the function $f(x) = x^3 - 12x + \lambda$ has a point of local maxima.

If $P_1, P_2, P_3$ are the perimeters of the three circles $x^2+y^2+8x-6y=0$,$4x^2+4y^2-4x-12y-186=0$,and $x^2+y^2-6x+6y-9=0$ respectively,then

Two concentric coils each of radius equal to $2\pi \, cm$ are placed at right angles to each other. $3\, A$ and $4\, A$ are the currents flowing in each coil respectively. The magnetic induction in $Wb/m^2$ at the centre of the coils will be $(\mu_0 = 4\pi \times 10^{-7} \, Wb/A \cdot m)$.