Nishit K Sinha Solutions for Chapter: X+2 Maths, Exercise 5: Practice Exercises

A truck is to be driven for $300 \mathrm{km}$ on a highway at a constant speed of $\mathrm{x} \mathrm{km}/\mathrm{h}$. The speed rules of the highway require $30\le \mathrm{x}\le 60$. The fuel costs $₹ 10$ per litre and is consumed at the rate of $2+\frac{{\mathrm{x}}^2}{600}$ liters per hour. The wages of the driver are $₹ 200$ per hour. The most economical speed to drive the truck, in km/h, is:

How many integral points are there within the graph of $\left|x\right|+\left|y\right|\le 4$?

The sides of a rectangle of the greatest area that can be inscribed into an ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ is:

The sets

$\left\{\right[x,y]:|y-1|-x\ge 1\}$

$\left\{\right[x,y]:|x|-y\ge 1\}$

$\left\{\right[x,y]:|x-1|+y\ge 0\}$

$\left\{\right[x,y]:y-|x-1\mid \ge 0\}$

are represented by the shaded regions in the figures given below in some order.

From a square tin sheet of side $12$ feet, a box with its top open is made by cutting equal squares at the four corners and then bending the tin sheet so as to form the sides of the box. The side of the removed square for which the box has the maximum possible volume in feet is:

From a circular sheet of paper of radius $a$, a sector with a central angle is cut out and folded into the shape of a conical funnel. The volume of this funnel is maximum when $\mathrm{\theta }$ equals:

Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as:

Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as: