Nishit K Sinha Solutions for Chapter: Measurement, Exercise 3: Practice Exercises

Find the centre of the circle ${\mathrm{x}}^2+{\mathrm{y}}^2-2\mathrm{x}-4\mathrm{y}-20=0$.

With rectangular axes of coordinates, the number of paths from $(1, 1)$ to $(8, 1 0)$ via $( 4, 6)$, where each step from any point $(\mathrm{x}, \mathrm{y})$ is either to$(\mathrm{x}, \mathrm{y} + 1)$ or to $(\mathrm{x} + 1, \mathrm{y})$, is (Fill in the blanks)

Let $\mathrm{T}$ be the triangle formed by the straight line $3 \mathrm{x}$ $+5 \mathrm{y}-45=0$ and the coordinate axes. Let the circumcircle of $\mathrm{T}$ have radius of length $\mathrm{L}$, measured in the same unit as the coordinate axes. Then, the integer closest to $\mathrm{L}$ is (Fill in the blanks) 

A triangle $\mathrm{ABC}$has area $32 \mathrm{sq} \mathrm{units}$ and its side $\mathrm{BC}$, of length$8 \mathrm{units}$, lies on the line $\mathrm{x} = 4 \mathrm{cm}$. Then the shortest possible distance between $\mathrm{A}$and the point $(0,0)$ is

Suppose the two sides of a square are along the straight lines $6\mathrm{x} - 8y = 15$ and $4\mathrm{y} - 3\mathrm{x} = 2$. Then the area of the square is

Consider a triangle drawn on the $\mathrm{X} - \mathrm{Y}$ plane with its three vertices of $(41, 0), (0, 41)$ and $(0, 0)$, each vertex being represented by its $(\mathrm{X}, \mathrm{Y})$ coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

In a general $\mathrm{X}-\mathrm{Y}$ plane, the area of the region bounded by the graph $|\mathrm{x}+\mathrm{y}|+|\mathrm{x}-\mathrm{y}|=4$ is 

The area bounded by the three curves $|\mathrm{x}+\mathrm{y}|=1$, $\left|\mathrm{x}\right|=1$, and $\left|\mathrm{y}\right|=1$ equal to