JEE Advanced 2012 Paper 2 Mathematics Q15

Mathematics

Problem

For every integer

n

, let

a_n

and

b_n

be real numbers. Let function

f:\mathbb R\to\mathbb R

be given by

f(x)=\begin{cases}a_n+\sin\pi x,&x\in[2n,2n+1],\\b_n+\cos\pi x,&x\in(2n-1,2n),\end{cases}

for all integers

n

. If

f

is continuous, then which of the following hold(s) for all

n