$A$ solution of $Na_2SO_4$ in water is electrolysed using inert electrodes. The products at cathode and anode are respectively:

If $x = \log \left[ \cot \left( \frac{\pi}{4} + \theta \right) \right]$,then the value of $\sinh x$ is

Let $a \neq 0$ and $p(x)$ be a polynomial of degree greater than $2$. If $p(x)$ leaves remainders $a$ and $-a$ when divided respectively by $x+a$ and $x-a$,then the remainder when $p(x)$ is divided by $x^2-a^2$ is:

Identify $A$ and $B$ in the following reactions:

Three rods made of the same material and having the same cross-section are joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at $0^{\circ}C$ and $90^{\circ}C$ respectively. The temperature of the junction of the three rods will be ...... $^{\circ}C$.

If the difference between the roots of the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ is the same,and $a \neq b$,then: