Consider the inequations 5x - 4y + 12 < 0, x + y < 2, x < 0 and y > 0. Which one of the following points lies in the common region?

Consider the following statements in respect of the function y = [x], x ∈ (-1, 1) where [.] is the greatest integer function:

1. Its derivative is 0 at x = 0.5

2. It is continuous at x = 0

Which of the above statements is/are correct?

What is the degree of the differential equation? $1+\left(\frac{dy}{dx}\right)^2 =\left(\frac{d^2y}{dx^2}\right)^{\frac{4}{3}}?$

A radioactive substance decays at a rate proportional to the amount of substance present. If half of the substance decays in 100 years, then what is the decay constant (proportionality constant) ?