Mean Deviation about Mean

Q. If $x^2+y^2=1$ and $p=(3x-4x^3{)}^2+(3y-4y^3{)}^2$ then $P$ is equal to

Q. The mean deviation from the mean of the series $a,a+d,a+2d,....a+2nd$, is

1. $n(n+1)d$
2. $\frac{n(n+1)d}{2n}$
3. $\frac{n(n-1)d}{2n+1}$
4. $\frac{n(n+1)d}{2n+1}$

Q.

If the mean deviation of the numbers $1,1+d,1+2d,\cdot ,1+100d$ from their mean is 255, then $d$ is equal to:

1. 20.2

2. 10.0

3. 20.0

4. 10.1

Q. Solve the equations $\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=\frac{10}{3},x+y=10$ simultaneously for $x$ and $y$.

Q. Simplify:
$\frac{x^2-5x-24}{\left(x+3\right)\left(x+8\right)}\times \frac{x^2-64}{{\left(x-8\right)}^2}$

Q. Let $G_{1}and{G}_2$ be the geometric means of two series $x_1,x_2,.....x_{n}and{y}_1,y_2.....,y_n$ respectively. If G is the geometric mean of series $x_i/y_i$, $i=1,2,....,n$, then G is equal to

1. $G_1-G_2$
2. $\log G_1/\log G_2$
3. $\log \left(G_1/G_2\right)$
4. $G_1/G_2$