Two waves $Y_{1} = 0.25 \sin(316 t)$ and $Y_{2} = 0.25 \sin(310 t)$ are propagating along the same direction. The number of beats produced per second is:

Suppose $\overrightarrow{a}=\lambda \hat{i}-7 \hat{j}+3 \hat{k}$ and $\overrightarrow{b}=\lambda \hat{i}+\hat{j}+2 \lambda \hat{k}$. If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is greater than $90^{\circ}$,then $\lambda$ satisfies the inequality

$A$ wire has a resistance of $12 \, \Omega$. It is bent in the form of an equilateral triangle. The effective resistance between any two corners of the triangle is:

The plates of a parallel plate capacitor are charged up to $100 \, V$. $A$ $2 \, mm$ thick dielectric plate is inserted between the plates. To maintain the same potential difference,the distance between the capacitor plates is increased by $1.6 \, mm$. The dielectric constant of the plate is:

What are the algal components of a lichen called?

Which plant group exhibits a haplodiplontic life cycle pattern?