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Question 3 :
To save on helium costs, a balloon is inflated with both helium and nitrogen gas. Between the two gases, the balloon can be inflated up to $8$ liters in volume. The density of helium is $0.20$ grams per liter, and the density of nitrogen is $1.30$ grams per liter. The balloon must be filled so that the volumetric average density of the balloon is lower than that of air, which has a density of $1.20$ grams per liter. Which of the following system of inequalities best describes how the balloon will be filled, if $x$ represents the number of liters of helium and $y$ represents the number of liters of nitrogen ?
Question 4 :
What is the value of $x$ for the following equations: $x - 5y = 10$ and $x + y =4$? (Use cross multiplication method).<br/>
Question 5 :
Find the Quotient and the Remainder when the first polynomial is divided by the second.$-6x^4 + 5x^2 + 111$ by $2x^2+1$
Question 6 :
The difference of two natural numbers is $4$ and the difference of their reciprocals is $\dfrac{1}{3}$. Find the numbers.
Question 9 :
Slope of the line $AB$ is $-\dfrac {4}{3}$. Co-ordinates of points $A$ and $B$ are $(x, -5)$ and $(-5, 3)$ respectively. What is the value of $x$
Question 10 :
A kite is flying with the string inclined at$\displaystyle 45^{\circ}$ to the horizontal If the string is straight and 50 m long the height at which the kite is flying is
Question 11 :
<br>On the level ground the angle of elevation of the top of a tower is $30^{0 }$ On moving 20 metres nearer tower, the angle of elevation is found to be $60^{0}$ The height of the towerin metres is<br>
Question 12 :
Two boats are sailing in the sea on either side of a lighthouse. At a particular time the angles of depression of the two boats, as observed from the top of the lighthouse are 45$^{\circ}$ and 30$^{\circ}$ respectively. If the lighthouse is 100m high, find the distance between the two boats.<br>
Question 13 :
Simplest form of $\displaystyle \dfrac{1}{\sqrt{2 + \sqrt{2 + \sqrt{2 + 2 cos 4x}}}}$ is
