Manipal Entrance Test 2020 Math Paper

Given, f(x)=[sin‌x+cos‌x]
=[√2(‌

1

√2

‌sin‌x+‌

1

√2

‌cos‌x)]
=[√2‌sin(x+‌

π

4

)]
We know that, greatest integer function is discontinuous on integer values.
Function √2‌sin(x+‌

π

4

) will gives integer values at x=90∘,135∘,180∘,270∘,315∘
Hence, there are five points in the given interval, in which f(x) is not continuous.