The main span of the Howrah bridge in Kolkata, West Bengal is about $194 \mathrm{m}$ long. The height of the towers is $26.2 \mathrm{m}$. The supporting cable for the main span of the bridge touches the road deck at the centre of the span. The parabola shown in the graph models the supporting cable of the main span of the Howrah Bridge and the green line segment represents the towers. Write down the values of $m, n, p$.

   

A tour bus in jaipur serves $400$ customers in a day. The charge is $₹50$ per person. The owner of bus service estimates that the company would lose $10$ passengers a day for each $₹5$ fare increase.

How much should the fare be in order to maximise the income for the company and find the maximum income for the company.

The diagram shows the graph of the function $y=A{x}^2+Bx+C$.

Complete the table below to show whether each expression is positive, negative or zero.

$\begin{array}{|llll|}\hline \text{ Expression }& \text{ positive }& \text{ negative }& \text{ zero }\\ A& & & \\ C& & & \\ B^2-4AC& & & \\ B& & & \\ \hline\end{array}$

Consider a person throwing a basketball $10 \text{m}$ above the ground. The basketball will reach its peak height and fall back to the ground. At time $t$, the height $h$ from the ground is given by $h=-2t^2+8t+10$. Calculate the time taken by the basketball to reach the ground.

When buying Embibe T-shirts, Raju determines that the total cost of buying $X$ T-shirts is given by the function,

$F\left(X\right)=0.04X^2-36X+9000$

If he wants to minimize the total cost of buying the T-shirts, how many shirts should he buy?

What is the maximum possible area for the rectangle shown?

There is a square field whose side is $44 \mathrm{m}$. A square flower bed is prepared in its centre leaving a gravel path all around the flower bed. The total cost of laying the flower bed and gravelling the path at $₹2.75$ and $₹1.50$ per square metre, respectively, is $₹4904$. Find the width of the gravel path in $\mathrm{m}$.

Alia and Ranbir went to Varanasi during their holidays. Alia wanted to visit all the ghats of Varanasi. So, they hired a motor boat for this purpose. While riding, Ranbir observed that the speed of motor boat was $20 \mathrm{km}/\mathrm{h}$. He was curious to know the speed of river Ganga. So, he noted the time taken by the boat to travel upstream and downstream in the river. He noticed that the boat took $1$ hour more to travel upstream than downstream to cover a distance of $15 \mathrm{km}$. Find the speed of the river Ganga in $\mathrm{km}/\mathrm{h}$.