Questions

1. Question 1

   Solve the following equations:

   (i)

   $\\dfrac{1}{3x}+\\dfrac{4x}{6}=1,\\; x\\ne 0$

   (ii)

   $\\dfrac{x}{x+1}+\\dfrac{x+1}{x}=\\dfrac{5}{2},\\; x\\ne -1,0$

   (iii)

   $\\dfrac{1}{x+1}+\\dfrac{2}{x+2}=\\dfrac{7}{x+5},\\; x\\ne -1,-2,-5$

   (iv)

   $\\dfrac{a}{ax-1}+\\dfrac{b}{bx-1}=a+b,\\; x\\ne \\dfrac{1}{a},\\dfrac{1}{b}$

   (v)

   $3x^2+15x-2\\sqrt{x^2+5x+1}=2$

   (vi)

   $\\sqrt{2x+8}+\\sqrt{x+5}=7$

   (vii)

   $\\sqrt{3x+4}=2+\\sqrt{2x-4}$

   (viii)

   $\\sqrt{x+5}-\\sqrt{x-3}=2$

   SolutionTheory
2. Question 2

   A farmer bought some sheep for Rs. 9000. If he had paid Rs. 100 less for each, he would have got 3 sheep more for the same money. How many sheep did he buy, when the rate in each case is uniform?

   SolutionTheory
3. Question 3

   A man sold his stock of eggs for Rs. 2400. If he had 2 dozen more, he would have got the same money by selling the whole for Rs. 0.50 per dozen cheaper. How many dozen eggs did he sell?

   SolutionTheory
4. Question 4

   A cyclist travelled 48 km at a uniform speed. If he had travelled 2 km/hour slower, he would have taken 2 hours more to perform the journey. How long did he take to cover 48 km?

   SolutionTheory
5. Question 5

   To do a piece of work, Abdullah takes 10 days more than Abdul Hadi. Together they finish the work in 12 days. How long would Abdul Hadi take to finish it alone?

   SolutionTheory
6. Question 6

   The braking distance (in metres) of a car is modeled by $d(s)=0.02s^2+0.1s$, where $s$ is the speed of car in km/h. If the maximum safe braking distance is 50 metres, find the range of speed where braking is safe.

   SolutionTheory
7. Question 7

   A rocket follows the height function $h(t)=-5t^2+20t+30$, where $h(t)$ is the height in metres and $t$ is the time in seconds. Find the time interval during which the rocket is at least 40 metres above the ground.

   SolutionTheory