Mathematics Tes...

$\text{If}\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$is the A.M between a and b. Then, find the value of \(n\)

Find the condition that the point (x, y) may lie on the line joining (3, 4) and (–5, 6).

The equivalent discount with respect to two successive discounts 30% and 40% will be?

If the 8th term of an A.P is 31 and the 15th term is 16 more than the 11th term, find the A.P.

$\text{If}(1+x{)}^n=C_0+C_{1}x+C_2{x}^2+\dots .+C_n{x}^n,C_0+\frac{c_2}{2}+\frac{c_2}{3}+\dots \dots .+\frac{C_n}{n+1}\text{is equal to}$?

Direction : If f (–x) = –f (x), then f (x) is an odd function & if f (–x) = f (x) then f (x) is an even function.

$\text{Also}{\int }_{-a}^{a}f\left(x\right)dx=\left\{\begin{array}{cl}2{\int }_0^{a}f\left(x\right),& \text{if}f\left(x\right)\text{is even}\\ 0& \text{if}f\left(x\right)\text{is odd}\end{array}\right.$

In the given figure, there are three semicircles A, B and C having diameter 3 cm each and another semi circle E having a circle D with diameter 4.5 cm are shown. Calculate the area of the shaded region.