Which one of the following aqueous solutions will exhibit the highest boiling point?

Let $P = \{\theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta\}$ and $Q = \{\theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta\}$ be two sets,then:

If $X = \{ 8^n - 7n - 1 : n \in N \}$ and $Y = \{ 49(n - 1) : n \in N \}$,then

$A$ hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids $L_1$ or $L_2$ having refractive indices $n_1$ and $n_2$ respectively $(n_2 > n_1 > 1)$. The lens will diverge a parallel beam of light if it is filled with

There are $n$ distinct points on the circumference of a circle. The number of pentagons that can be formed with these points as vertices is equal to the number of possible triangles. Then the value of $n$ is

The magnitude of maximum acceleration is $\pi$ times that of maximum velocity of a simple harmonic oscillator. The time period of the oscillator in seconds is