$A$ thin rod of length $L$ is bent to form a semicircle. The mass of the rod is $M$. What will be the gravitational potential at the centre of the circle?

If the line $\vec{r} = (\hat{i} - 2\hat{j} - \hat{k}) + \lambda (2\hat{i} + \hat{j} + 2\hat{k})$ is parallel to the plane $\vec{r} \cdot (3\hat{i} - 2\hat{j} - m\hat{k}) = 14$,then the value of $m$ is:

In a $\triangle ABC$,if $3a = b + c$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

The vector $c \cdot (b+c) \times (a+b+c)$ is equal to

$A$ charge $+Q$ is moving upwards vertically. It enters a magnetic field directed to the north. The force on the charge will be towards

The steps of a plant breeding program are given below. Arrange them in the correct sequence.
$(a)$ Cross-hybridization among the selected parents
$(b)$ Testing,release,and commercialization of new cultivars
$(c)$ Collection of variability
$(d)$ Selection and testing of superior recombinants
$(e)$ Evaluation and selection of parents