An aluminium (resistivity $\rho = 2.2 \times 10^{-8} \Omega \cdot m$) wire of a diameter $1.4 \text{ mm}$ is used to make a $4 \Omega$ resistor. The length of the wire is: (in $text{ m}$)

Which one of the following salts gives an acidic solution in water?

The refracting angle of a prism is $A$ and the refractive index of the material of the prism is $\cot(A/2)$. Then the angle of minimum deviation is

The length of an elastic string is $a$ metres when the longitudinal tension is $4 \ N$ and $b$ metres when the longitudinal tension is $5 \ N$. The length of the string in metres when the longitudinal tension is $9 \ N$ is

$A$ vehicle sounding a whistle of frequency $256 ~Hz$ is moving on a straight road towards a hill with a velocity of $10 ~ms^{-1}$. The number of beats per second observed by a person travelling in the vehicle is (velocity of sound $= 330 ~ms^{-1}$).

Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. If the first overtone of $A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B,$ the ratio of the lengths of the strings is