The sum of first n terms of an A.P. is $3n^{2} +4n$. Find the $25^{th}$ term of this A.P.

The horizantol distance between two poles is 15 cm. The angle of depression of the top of first pole as seen from the top of second pole is 30$^{o}$. If the height of the second pole is 24 cm, find the height of the first pole. [use $\pi =\frac{22}{7}$] .

Find the ratio in which the y-axis divides line segment joining the points $( -4,\ -6)$ and $( 10,\ 12)$. Also find the coordinates of the point of division.

The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.

The area of two similar triangles are $25\ cm^2$ and $36\ cm^2$ respectively. If the altitude of the first triangle is $2.4\ cm$, find the corresponding altitude of the other.

The areas of two similar triangles are $169\ cm^2$ and $121\ cm^2$ respectively. If the longest side of the larger triangle is $26\ cm$, find the longest side of the smaller triangle.

The areas of two similar triangles are $81\ cm^2$ and $49\ cm^2$ respectively. Find the ration of their corresponding heights. What is the ratio of their corresponding medians?

In the figure below, $ΔACB\ ∼\ ΔAPQ$. If $BC\ =\ 10\ cm$, $PQ\ =\ 5\ cm$, $BA\ =\ 6.5\ cm$, $AP\ =\ 2.8\ cm$, find $CA$ and $AQ$. Also, find the $area\ (ΔACB)\ :\ area\ (ΔAPQ)$.

Triangles ABC and DEF are similar.

If $AB\ =\ 1.2\ cm$ and $DE\ =\ 1.4\ cm$, find the ratio of the area of two triangles.

Describe how the following expressions are obtained:$(i) 7 x y+5, (ii) x^{2} y, (iii) 4 x^{2}-5 x$.

We are really eager to clarify your doubts