# Board Paper of Class 10 2014 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) Ranbir borrows Rs. 20,000 at 12% per annum compound interest. If he repays Rs. 8400 at the end of the first year and Rs. 9680 at the end of the second year, find the amount of loan outstanding at the beginning of the third year. **[3]**(b) Find the values of *x*, which satisfy the in-equation $-2\frac{5}{6}<\frac{1}{2}-\frac{2x}{3}\le 2,x\in \mathrm{W}$. Graph the solution set on the number line.**[3]**(c) A die has 6 faces marked by the given numbers as shown below:

$\begin{array}{cccccc}\overline{)1}& \overline{)2}& \overline{)3}& \overline{)\u20131}& \overline{)-2}& \overline{)-3}\end{array}$

The die is thrown once. What is the probability of getting:

(i) a positive integer.

(ii) an integer greater than –3.

(iii) the smallest integer.**[4]**

- Question 2
(a) Find *x, y*if $\left[\begin{array}{cc}-2& 0\\ 3& 1\end{array}\right]\left[\begin{array}{c}-1\\ 2x\end{array}\right]+3\left[\begin{array}{c}-2\\ 1\end{array}\right]=2\left[\begin{array}{c}y\\ 3\end{array}\right]$.**[3]**(b) Shahrukh opened a ‘Recurring Deposit’ account in a bank and deposited Rs. 800 per month for $1\frac{1}{2}$ years. If he received Rs. 15,084 at the time of maturity, find the rate of interest per annum. **[3]**(c) Calculate the ratio in which the line joining A(–4, 2) and B(3, 6) is divided by a point P( *x*, 3). Also find (i)*x*(ii) Length of AP.**[4]**

- Question 3
(a) Without using trigonometric tables, evaluate

sin^{2}34° + sin^{2}56° + 2tan18° tan72° – cot^{2}30°**[3]**(b) Using the Remainder and Factor Theorem, factorise the following polynomial:

*x*^{3}+ 10*x*^{2 }– 37*x*+ 26**[3]**(c) In the figure given below, ABCD is a rectangle. AB = 14 cm, BC = 7 cm.

From the rectangle, a quarter circle BFEC and a semicircle DGE are removed.

Calculate the area of the remaining piece of the rectangle.(Take π = 22/7)

**[4]**

- Question 4
(a) The numbers 6, 8, 10, 12, 13 and *x*are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of*x***[3]**(b) In the figure, m∠DBC = 58°. BD is the diameter of the circle. Calculate:

(i) m∠BDC

(ii) m∠BEC

(iii) m∠BAC

**[3]**(c) Use graph paper to answer the following questions. (Take 2 cm = 1 unit on both axes)

(i) Plot the points A(–4, 2) and B(2, 4)

(ii) A' is the image of A when reflected at the*y*-axis.Plot it on the graph paper and write the co-ordinates of A'.(iii) B' is the image of B when reflected on the line AA'. Write the co-ordinates of B'.

(iv) Write the geometric name of the figure ABA'B'.

(v) Name a line of symmetry of the figure formed.**[4]**