JEE Main - 4th April 2015

Electric field in a certain region is given by $\overrightarrow{E}=\left(\frac{A}{x^2}\hat{\mathrm{i}}+\frac{B}{y^3}\hat{\mathrm{j}}\right)$. The SI unit of $A$ and $B$ are :

In a screw gauge, there are $100$ divisions on the circular scale and the main scale moves by $0.5 \mathrm{mm}$ on a complete rotation of the circular scale. The zero of circular scale lies $6$ divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, $4$ linear scale divisions are clearly visible while 46^th division the circular scale coincide with the reference line. The diameter of the wire is ______ $\times {10}^{-2} \mathrm{mm}.$

Match List I with List II

Choose the correct answer from the options given below :

Match List I with List II

Choose the correct answer from the options given below :

$\left(P+\frac{a}{V^2}\right)\left(V-b\right)=RT$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$ , will be :

If the velocity of light $c$, universal gravitational constant $G$ and planck's constant $h$ are chosen as fundamental quantities. The dimensions of mass in the new system is:

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at $40 \mathrm{cm}$ from the pole of the mirror is formed at distance $120 \mathrm{cm}$ from the pole of the mirror. These distances are measured with a modified scale in which there are $20$ small divisions in $1 \mathrm{cm}$. The value of error in measurement of focal length of the mirror is $\frac{1}{K} \mathrm{cm}$. The value of $K$ is ______.

If $R, X_L \text{and} X_C$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless: