Embibe Multiple Choice

Let $f:\left[0, 2\right]\to ℝ$ be the function defined by

$f\left(x\right)=\left(3-\sin \left(2\pi x\right)\right)\sin \left(\pi x-\frac{\pi }{4}\right)-\sin \left(3\pi x+\frac{\pi }{4}\right)$.

If $\alpha , \beta \in \left[0, 2\right]$ are such that $\left\{x\in \left[0, 2\right] :f\left(x\right)\ge 0\right\}=\left[\alpha , \beta \right]$, then the value of $\beta -\alpha$ is _____

Rearrange the letters to form the name of one of the India's neighbours.
PLANE

Read the scale drawing and answer the questions given below.

In the scale drawing, the living room is ________ centimetres long.

Ismail’s Home On the phone Ismail told Srijata the route to his house from her house. The route map is shown here.

This is what Ismail told Srijata: “From your house, reach the milk-booth and then take a left turn. From the second crossing take a right turn and go over the bridge. Go straight and then take the first right turn. After about $100\mathrm{}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{s}$ you will see a big park. When you cross the park you will come to a side lane. My house is the first house in that lane.
Write the directions for going from Ismail’s house to Srijata’s house.

Read the scale drawing and answer the question given below.

In the scale drawing, the family room is ________ centimetres wide.