What is the concentration of nitrate ions if equal volumes of $0.1 \ M$ $AgNO_3$ and $0.1 \ M$ $NaCl$ are mixed together (in $M$)?

All capacitors used in the diagram are identical and each is of capacitance $C$. Then the effective capacitance between the points $A$ and $B$ is

The incentre of the triangle with vertices $(1, \sqrt{3})$,$(0, 0)$ and $(2, 0)$ is

$A$ black body has a maximum wavelength ${\lambda _m}$ at a temperature of $2000 \; K$. Its corresponding wavelength at a temperature of $3000 \; K$ will be:

If $(a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y)=a^{2}-b^{2}$ where $a>b>0,$ then $\frac{dx}{dy}$ at $\left(\frac{\pi}{4}, \frac{\pi}{4}\right)$ is

$A$ and $B$ are two radioactive substances whose half-lives are $1$ and $2$ years respectively. Initially, $10 \, g$ of $A$ and $1 \, g$ of $B$ are taken. The time (approximate) after which they will have the same quantity remaining is ........... $years$.