Let $f$ and $g$ be continuous functions on $[0, a]$ such that $f(x) = f(a - x)$ and $g(x) + g(a - x) = 4$. Then $\int_{0}^{a} f(x)g(x) dx$ is equal to

The solution of $\frac{dy}{dx} = \frac{y^2}{xy - x^2}$ is

Which of the following statements is correct?

Which of the following oxides of nitrogen is a blue solid?

$\sec ^2(\tan ^{-1} 2) + \operatorname{cosec}^2(\cot ^{-1} 3)$ is equal to

If $10000\, V$ is applied across an $X$-ray tube, what will be the ratio of the de-Broglie wavelength of the incident electrons to the shortest wavelength of the $X$-rays produced? (Given: $\frac{e}{m}$ for an electron is $1.8 \times 10^{11}\, C\, kg^{-1}$)