Thermite is a mixture of $X$ parts of ferric oxide and $Y$ parts of aluminium powder. What are $X$ and $Y$ respectively?

If the circle $x^2+y^2=a^2$ intersects the hyperbola $xy=c^2$ in four points $(x_i, y_i)$,for $i=1, 2, 3, 4$,then $y_1+y_2+y_3+y_4$ equals

Observe the following statements:
$A$. Integrating factor of $\frac{dy}{dx} + y = x^2$ is $e^x$.
$R$. Integrating factor of $\frac{dy}{dx} + P(x)y = Q(x)$ is $e^{\int P(x) dx}$.
Then,the true statement among the following is:

If $\sin A + \sin B = \sqrt{3}(\cos B - \cos A)$,then $\sin 3A + \sin 3B$ is equal to:

Which has the maximum number of molecules among the following?

The number of common tangent$(s)$ to the circles $x^2 + y^2 + 2x + 8y - 23 = 0$ and $x^2 + y^2 - 4x - 10y + 19 = 0$ is: