If $4ab = 3h^2$, then the ratio of the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is...

The equations of the tangent to the curve $x^2 + y^2 = 10$, where the tangent is parallel to the line $2x + y - 1 = 0$, are

If the line $y = 2x + \lambda$ is a tangent to the hyperbola $36x^2 - 25y^2 = 3600$, then $\lambda =$

$\displaystyle\lim_{x \to 0}\dfrac{(5^x - 1)^4\,\text{cosec}\,(x\log 5)}{\tan(x\log 5) \cdot \log(1 + x^2\log 25)} = \ldots\ldots$