# Board Paper of Class 10 2015 Maths - Solutions

*Attempt all questions from Section A and any four questions from Section B.*

*All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer.*

*Omission of essential working will result in loss of marks.**The intended marks for questions or parts of questions are given in brackets [ ].*

*Mathematical tables are provided.*- Question 1
(a) 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) market price of the article.

(ii) price paid by a customer who buys the article.**[3]**(b) Solve the following inequation and write the solution set:

13*x*– 5 < 15*x*+ 4 < 7*x*+ 12,*x*∈ R

Represent the solution on a real number line.**[4]**(c) Without using trigonometric tables evaluate:

$\frac{\mathrm{sin}65\xb0}{\mathrm{cos}25\xb0}+\frac{\mathrm{cos}{\displaystyle}{\displaystyle 32}{\displaystyle \xb0}}{\mathrm{sin}{\displaystyle}{\displaystyle 58}{\displaystyle \xb0}}-\mathrm{sin}28\xb0.\mathrm{sec}62\xb0+{\mathrm{cosec}}^{2}30\xb0$**[3]**

- Question 2
(a) If $\mathrm{A}=\left[\begin{array}{cc}3& x\\ 0& 1\end{array}\right],\mathrm{B}=\left[\begin{array}{cc}9& 16\\ 0& -y\end{array}\right]$, find *x*and*y*where A^{2}= B.**[3]**(b) The present population of 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. **[3]**(c) Three vertices of parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2)

(i) the coordinate of the fourth vertex D

(ii) length of diagonal BD

(iii) equation of the side AD of the parallelogram ABCD**[4]**

- Question 3
(a) In the given figure, ABCD is the square of side 21 cm. AC and BD are two diagonals of the square. Two semicircles are drawn with AD and BC as diameters. Find the area of the shaded region. $\left(\mathrm{Take}\mathrm{\pi}=\frac{22}{7}\right)$

**[3]**(b) The marks obtained by 30 students in a class assignment of 5 marks are given below. **Marks**0 1 2 3 4 5 **Number of Students**1 3 6 10 5 5 **[3]**(c) In the figure given below, O is the centre of the circle and SP is a tangent.

If ∠SRT = 65°, find the value of*x, y*and*z.*

**[4]**

- Question 4
(a) Katrina opened a recurring deposit account with a Nationalised Bank for a period of 2 years. If the bank pays interest at the rate 6% per annum and the monthly instalment is Rs. 1,000, find the:

(i) Interest earned in 2 years.

(ii) Matured value**[3]**(b) Find the value of ‘ *k*’ for which*x*= 3 is a solution of the quadratic equation,

(*k*+ 2)*x*^{2}–*kx*+ 6 = 0.

Thus find the other root of the equation.**[3]**(c) Construct a regular hexagon of side 5 cm. Construct a circle circumscribing the hexagon.

All traces of construction must be clearly shown.**[4]**