The electric potential $V$ at any point $(x, y, z)$ (all in $m$) in space is given by $V = 4x^2 \, V$. The electric field at the point $(1 \, m, 0, 2 \, m)$ in $V/m$ is:

The rate constant,$k$,of a zero order reaction $2 NH_3(g) \xrightarrow[1130 \ K]{Pt} N_2(g) + 3 H_2(g)$ is $y \times 10^{-4} \ mol \ L^{-1} \ s^{-1}$. The rate of formation of hydrogen (in $mol \ L^{-1} \ s^{-1}$) is

$A$ particle of mass $5 \times 10^{-5} \ kg$ is placed at the lowest point of a smooth parabola $x^2 = 40y$ (where $x$ and $y$ are in $m$). If it is displaced slightly such that it is constrained to move along the parabola,the angular frequency of oscillation (in $rad/s$) will be approximately:

In the following common emitter circuit,if $\beta = 100$,$V_{CE} = 7\,V$,$V_{BE} = 0\,V$ (negligible),and $R_C = 2\,k\Omega$,then the value of $I_B$ is.......$mA$.

In a $CE$ transistor amplifier,the audio signal voltage across the collector resistance of $2\, k\Omega$ is $2\, V$. If the base resistance is $1\, k\Omega$ and the current amplification factor $(\beta)$ of the transistor is $100$,the input signal voltage is:

$2 \pi - (\sin^{-1} \frac{4}{5} + \sin^{-1} \frac{5}{13} + \sin^{-1} \frac{16}{65})$ is equal to