$A$ particle is tied to a $20\, cm$ long string. It performs circular motion in a vertical plane. What is the angular velocity of the string when the tension in the string at the top is zero? (Take $g = 9.8\, m/s^2$)

If $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k}$,$\overrightarrow{b}=\hat{i}+\hat{j}$,$\overrightarrow{c}=\hat{i}$ and $(\overrightarrow{a} \times \overrightarrow{b}) \times \overrightarrow{c}=\lambda \overrightarrow{a}+\mu \overrightarrow{b}$,then $\lambda+\mu$ is equal to:

The moment of inertia of a thin circular lamina of mass $1\,kg$ and diameter $0.2\,m$ rotating about one of its diameters is:

Which tissue provides mechanical support to the young stem and petiole of leaves?

The number of nuclei of a radioactive substance at time $t = 0$ is $1000$,and at time $t = 2 \ s$,it is $900$. Then,the number of nuclei at time $t = 4 \ s$ will be:

$A$ ray of light passes through an equilateral prism such that the angle of incidence is equal to the angle of emergence and each one is equal to $3/4$th the angle of the prism. The angle of deviation is (in $^{\circ}$)