A vector in $x-y$ plane makes an angle of $30^{\circ}$ with $y$-axis. The magnitude of $\mathrm{y}$-component of vector is $2 \sqrt{3}$. The magnitude of $x$-component of the vector will be :

The speed of a wave produced in water is given by $v=\lambda^{a} g^{b} \rho^{c}$. Where $\lambda, g$ and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a, b$ and $c$ respectively, are :

The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is:

For designing a voltmeter of range $50 \mathrm{~V}$ and an ammeter of range $10 \mathrm{~mA}$ using a galvanometer which has a coil of resistance $54 \Omega$ showing a full scale deflection for $1 \mathrm{~mA}$ as in figure.



(A) for voltmeter $R \approx 50 \mathrm{k} \Omega$

(B) for ammeter $\mathrm{r} \approx 0.2 \Omega$

(C) for ammeter $\mathrm{r}=6 \Omega$

(D) for voltmeter $R \approx 5 \mathrm{k} \Omega$

(E) for voltmeter $R \approx 500 \Omega$

Choose the correct answer from the options given below: