The sum of the numbers between $100$ and $1000$ which are divisible by $9$ is:

If the $m^{th}$ terms of the series $63 + 65 + 67 + 69 + \dots$ and $3 + 10 + 17 + 24 + \dots$ are equal,then $m = $

Let $f(x)$ be a quadratic polynomial. If $f(1) = f(-1)$ and $a, b, c$ are in arithmetic progression,then $f'(a), f'(b), f'(c)$ are in..... progression.

For three positive integers $p, q, r$,$x^{pq p^2} = y^{qr} = z^{p^2 r}$ and $r = pq + 1$ such that $3, 3 \log_y x, 3 \log_z y, 7 \log_x z$ are in $A$.$P$. with common difference $\frac{1}{2}$. Then $r - p - q$ is equal to

The number of terms in an $A.P.$ is even. The sum of the odd terms is $24$ and the sum of the even terms is $30$. If the last term exceeds the first term by $10\frac{1}{2}$,then the number of terms in the $A.P.$ is:

The interior angles of a polygon are in $A.P.$ If the smallest angle is $120^o$ and the common difference is $5^o$,then the number of sides is