UPSC NDA I 2015 Mathematics Solved Paper

Consider statement 1
f(x)=[x]
f(x)

lim

x→n−

≠f(x)

lim

x→n+

‌∀n∊Z
Hence f(x) is discontinuous at all integral points.
Therefore, statement 1 is true.
Considering statement 2
f(x)=cot(x)=

cos(x)

sin(x)

∀x=nπ→sin(x)=0
∴ The graph of cot( ) will be discontinuous at x=nπ
Hence f(x) is discontinuous at all integral multiples of π
Therefore statement 2 is also correct.