Each of the roots of the equation $x^3-6x^2+6x-5=0$ is increased by $h$. If the new transformed equation does not contain the $x^2$ term,then $h$ is equal to:

Two steel wires of same length $L$ but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. $A$ force $F$ stretches the combination by $10 \ mm$. How far does the midpoint $A$ move in $mm$?

Two batteries,one of $emf$ $18 \, V$ and internal resistance $2 \, \Omega$ and the other of $emf$ $12 \, V$ and internal resistance $1 \, \Omega$,are connected in parallel as shown in the figure. The voltmeter $V$ will record a reading of ............. $V$.

$A$ fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self-inductance $L$ at $t=0$. The time at which the energy is stored equally between the electric and the magnetic field is

If ${x^y} = {y^x},$ then ${(x/y)^{(x/y)}} = {x^{(x/y) - k}},$ where $k = $

In majority of higher animals and plants, . . . . . . and . . . . . . are mutually exclusive events.