The probability of a student qualifying for $IITJEE$ and $EAMCET$ are $\frac{1}{5}$ and $\frac{3}{5}$ respectively. The probability that the student qualifies for at least one of these tests is:

The plank in the figure moves a distance $100\,mm$ to the right while the centre of mass of the sphere of radius $150\,mm$ moves a distance $75\,mm$ to the left. The angular displacement of the sphere (in radian) is (there is no slipping anywhere):-

An oxide of an element is a gas and dissolves in water to give an acidic solution. The element belongs to

$A$ telescope has an objective lens of focal length $200 \ cm$ and an eyepiece with focal length $2 \ cm$. If this telescope is used to see a $50 \ m$ tall building at a distance of $2 \ km$,what is the height of the image of the building formed by the objective lens in $cm$?

$A$ slit of width $a$ is illuminated by red light of wavelength $6500 \,\, \mathring{A}$. The first minimum will fall at $\theta = 30^{\circ}$ if $a$ is equal to:

Assertion : $NF_3$ is a weaker ligand than $N(CH_3)_3$.
Reason : $NF_3$ ionizes to give $F^-$ ions in aqueous solution.