The required amount of $KBr$ (molar mass $= 119 \, g/mol$) in grams to start the precipitation of $AgBr$ in $500 \, mL$ solution of $0.05 \, M \, AgNO_3$ will be ($K_{sp}$ of $AgBr = 5 \times 10^{-13}$)

$A$ pan balance has a container of water with an overflow spout on the right-hand pan as shown. It is full of water right up to the overflow spout. $A$ container on the left-hand pan is positioned to catch any water that overflows. The entire apparatus is adjusted so that it is balanced. $A$ brass weight on the end of a string is then lowered into the water,but not allowed to rest on the bottom of the container. What happens next?

$A$ simple harmonic oscillator consists of a particle of mass $m$ and an ideal spring with spring constant $k$. The particle oscillates with a time period $T$. The spring is cut into two equal parts. If one part oscillates with the same particle,the time period will be

$A$ ray of light refracts from medium $1$ into a thin layer of medium $2$,crosses the layer,and is incident at the critical angle on the interface between medium $2$ and $3$ as shown in the figure. If the angle of incidence of the ray is $\theta$,the value of $\theta$ is

The main objective of the production/use of herbicide-resistant $GM$ crops is to

If $f(t) = \int_{-t}^t \frac{e^{-|x|}}{2} dx$,then $\lim_{t \rightarrow \infty} f(t)$ is equal to: