$A$ conductor of resistance $3 \Omega$ is stretched uniformly until its length is doubled. The wire is now bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in ohms is

If $f(x) = x^3 - 6x^2 + 9x + 3$ is a decreasing function,then $x$ lies in

The densities of a liquid at $0^{\circ} C$ and $100^{\circ} C$ are respectively $1.0127$ and $1$. $A$ specific gravity bottle is filled with $300 \ g$ of the liquid at $0^{\circ} C$ up to the brim and it is heated to $100^{\circ} C$. Then,the mass of the liquid expelled in grams is: (Coefficient of linear expansion of glass $= 9 \times 10^{-6} /^{\circ} C$)

If the sum of the distances of a point $P$ from two perpendicular lines in a plane is $1$,then the locus of $P$ is a

The atomic numbers of elements $X, Y$ and $Z$ are $19, 21$ and $25$ respectively. The number of electrons present in the $M$-shell of these elements follow the order:

Two blocks of masses $1 \ kg$ and $2 \ kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{40}{3 \pi} \times 10^6 \ N m^{-2}$. What should be the minimum radius of the wire used if it should not break (in $mm$)? $\left(g = 10 \ m s^{-2}\right)$