Calculate simple and compound interest for the given values.

The amount $A = 13600$ টাকা.
The rate of simple interest $R = 6\%$.
The time $T = 6$ years.
Let the principal be $P$.

The formula for the amount $A$ is $A = P \left(1 + \frac{RT}{100}\right)$.

The principal is 10000 টাকা.

The correct option is (c).
$\boxed{\text{10000 টাকা}}$

1. (ii) Compound Interest

The principal $P = 100$ টাকা.
The amount $A = 144$ টাকা.
The time $T = 2$ years.
Let the rate of compound interest be $R$.

The formula for the amount $A$ is $A = P \left(1 + \frac{R}{100}\right)^T$.

Taking the square root of both sides:

The compound interest rate is $20\%$.

The correct option is (b).
$\boxed{20\%}$

1. (iii) Quadratic Equations

The given equation is $5x^2 + 2x - 3 = 0$.
Here, $a=5$, $b=2$, $c=-3$.

Sum of roots: $\alpha + \beta = -\frac{b}{a} = -\frac{2}{5}$
Product of roots: $\alpha\beta = \frac{c}{a} = \frac{-3}{5}$

We use the identity $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta$.
Substitute the values:

To add the fractions, find a common denominator:

The correct option is (a).
$\boxed{\frac{34}{25}}$

1. (iv) Mean Proportional

The two terms are $(x-y)^2$ and $(x+y)^2$.

The mean proportional of two numbers $a$ and $b$ is $\sqrt{ab}$.

Mean proportional $= \sqrt{(x-y)^2 (x+y)^2}$

Using the difference of squares formula, $(a-b)(a+b) = a^2 - b^2$:

The correct option is (d).
$\boxed{x^2 - y^2}$

1. (v) Cyclic Quadrilateral

In a cyclic quadrilateral, the sum of opposite angles is $180^\circ$.

Given that ABCD is a cyclic quadrilateral and $\angle A = 80^\circ$.
Therefore, $\angle A + \angle C = 180^\circ$.

The correct option is (b).
$\boxed{100^\circ}$

1. (vi) Angle in a Semicircle

An angle subtended by the diameter at any point on the circumference of a circle (i.e., an angle in a semicircle) is always a right angle.

A right angle is $90^\circ$.