Match Column I with Column II

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

Match Column I with Column II.

Column I	Column II
(a) If the smallest positive integral value of $x$ for which $x^2-x-\sin^{-1}(\sin2)<0$ is $\lambda$ , then $3+\lambda$ is equal to	(p) $4$
(b) The number of solutions of $2\lfloor x\rfloor=x+2\{x\}$ , where $\lfloor\cdot\rfloor$ and $\{\cdot\}$ denote the greatest-integer and fractional-part functions, respectively	(q) $1$
(c) If $x^2+y^2=1$ and the maximum value of $x+y$ is $\frac{\sqrt{2}\lambda}{3}$ , then $\lambda$ is equal to	(r) $2$
(d) If $f\left(x+\frac12\right)+f\left(x-\frac12\right)=f(x)$ for all $x\in\mathbb{R}$ , then the period of $f(x)$ is	(s) $5$
	(t) $3$