11.

The horizontal distance between two towers is 120 m. The angle of elevation of the top and angle of depression of the bottom of the first tower as observed from the second tower is ${30}^{°}$and ${24}^{°}$respectively.

Find the height of the two towers. Give your answer correct to 3 significant figures.

A wholesaler buys a TV from the manufacturer for Rs. 25,000. He marks the price of TV 20% above his cost price and sells it to a retailer at a 10% discount on the market price. If the rate of VAT is 8%, find the :

(i) Market price

(ii) Retailer’s cost price inclusive of tax.

(iii) VAT paid by the wholesaler.

If $\mathrm{A} = \left[\begin{array}{cc}3& 7\\ 2& 4\end{array}\right] , \mathrm{B} = \left[\begin{array}{cc}0& 2\\ 5& 3\end{array}\right] \mathrm{and} \mathrm{C} = \left[\begin{array}{cc}1& - 5\\ - 4& 6\end{array}\right]$

Find AB - 5C.

Sum of two natural numbers is 8 and the difference of their reciprocal is $\frac{2}{15}$.
Find the numbers.

Given, $\frac{{\mathrm{x}}^3 + 12\mathrm{x}}{6{\mathrm{x}}^2} = \frac{{\mathrm{y}}^3 + 27}{9{\mathrm{y}}^2 + 27}$. Using componendo and dividendo find x:y.

Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and $\angle \mathrm{BAC} = {105}^{°}$. Hence:

(i) Construct the locus of points equidistant from BA and BC.

(ii) Construct the locus of points equidistant from B and C.

(iii) Mark the point which satisfies the above two loci as P. Measure and write the length of PC.

A shopkeeper bought an article for Rs. 3,450. He marks the price of the article 16% above the cost price. The rate of sales tax charged on the article is 10%. Find the (i) marked price of the article. (ii) price paid by a customer who buys the article.

Without using trigonometric tables evaluate:

$\frac{\sin \left({65}^{°}\right)}{\cos \left({25}^{°}\right)} + \frac{\cos ({\displaystyle {32}^{°})}}{\sin ({\displaystyle {58}^{°})}} - \sin (28°).\sec \left(62{ }^{°}\right) + {\mathrm{cosec}}^2\left({30}^{°}\right)$

If A = $\left[\begin{array}{cc}3& \mathrm{x}\\ 0& 1\end{array}\right]$ , B = $\left[\begin{array}{cc}9& 16\\ 0& -\mathrm{y}\end{array}\right]$ ,find x and y where A² = B.

The present population of a town is 2,00,000. The population is increased by 10% in the first year and 15% in the second year. Find the population of the town at the end of two years.