If $[x]$ denotes the greatest integer not exceeding $x$ and if the function $f$ defined by $f(x)= \begin{cases} \frac{a+2 \cos x}{x^2} & , x < 0 \\ b \tan \frac{\pi}{[x+4]} & , x \geq 0 \end{cases}$ is continuous at $x=0$,then the ordered pair $(a, b)$ is equal to

If $m$ and $n$ are respectively the order and degree of the differential equation of the family of parabolas with origin as its focus and $X$-axis as its axis, then $mn-m+n=$

How many corners of $SiO_4$ units are shared in the formation of three-dimensional silicates?

Different conformations of the same molecule are called

The equation of the line passing through the point of intersection of the lines $x-3y+2=0$ and $2x+5y-7=0$ and perpendicular to the line $3x+2y+5=0$ is:

$A$ person lives in a high-rise building at a height of $30 \, m$ on the bank of a river. Across the river is a well-lit tower of height $60 \, m$. When the person looks through a polarizer at an appropriate angle at the light from the top of the tower reflecting from the river surface,he finds the intensity of light is least. If the refractive index of water is $\frac{4}{3}$,the width of the river is......$m$.