$A$ long solenoid of length $L$ has a mean diameter $D$. It has $n$ layers of windings of $N$ turns each. If it carries a current $i$,the magnetic field at its centre will be

In the conversion of limestone to lime,$CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$,the values of $\Delta H^o$ and $\Delta S^o$ are $+179.1 \ kJ \ mol^{-1}$ and $160.2 \ J \ K^{-1} \ mol^{-1}$ respectively at $298 \ K$ and $1 \ bar$. Assuming that $\Delta H^o$ and $\Delta S^o$ do not change with temperature,the temperature above which the conversion of limestone to lime will be spontaneous is ............. $K$.

The complex formed by a pair of synapsed homologous chromosomes is called:

Let $PQR$ be a right-angled isosceles triangle,with the right angle at $P(2, 1)$. If the equation of the line $QR$ is $2x + y = 3$,then the equation representing the pair of lines $PQ$ and $PR$ is:

Two simple harmonic motions are represented by the equations $y_1 = 0.1 \sin(100\pi t + \frac{\pi}{3})$ and $y_2 = 0.1 \cos(100\pi t)$. The phase difference of the velocity of particle $1$ with respect to the velocity of particle $2$ is

Helium mixed with oxygen is used in the treatment of