# 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) Given $A=\left[\begin{array}{cc}2& -6\\ 2& 0\end{array}\right],B=\left[\begin{array}{cc}-3& 2\\ 4& 0\end{array}\right],C=\left[\begin{array}{cc}4& 0\\ 0& 2\end{array}\right]$

Find the matrix*X*such that*A*+ 2*X*= 2*B + C*.**[3]**(b) At what rate % p.a. will a sum of Rs 4000 yield Rs 1324 as compound interest in 3 years? **[3]**(c) The median of the following observations

11, 12, 14, (*x*– 2), (*x*+ 4), (*x*+ 9), 32, 38, 47 arranged in ascending order is 24.

Find the value of*x*and hence find the mean.**[4]**

- Question 2
(a) What number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional? **[3]**(b) If ( *x*– 2) is a factor of the expression 2*x*^{3}+*ax*^{2 }+*bx*– 14 and when the expression is divided by (*x*– 3), it leaves a remainder 52, find the values of*a*and*b*.**[3]**(c) Draw a histogram from the following frequency distribution and find the mode from the graph: Class 0–5 5–10 10–15 15–20 20–25 25–30 Frequency 2 5 18 14 8 5 **[4]**

- Question 3
(a) Without using tables evaluate:

3 cos 80°. cosec 10° + 2 sin 59° sec 31°.**[3]**(b) In the given figure, ∠BAD = 65°, ∠ABD = 70°and ∠BDC = 45°.

(i) Prove that AC is a diameter of the circle.

(ii) Find ∠ACB**[3]**(c) AB is a diameter of a circle with centre C = (–2, 5). If A = (3, –7). Find

(i) the length of radius AC

(ii) the coordinates of B.**[4]**

- Question 4
(a) Solve the following equation and calculate the answer correct to two decimal places:

*x*^{2}– 5*x*– 10 = 0**[3]**(b) (b) In the given figure, AB and DE are perpendicular to BC.

(i) Prove that ΔABC ~ ΔDEC

(ii) If AB = 6 cm; DE = 4 cm and AC = 15 cm. Calculate CD.

(iii) Find the ratio of area of ΔABC: area of ΔDEC.**[3]**(c) Using a graph paper, plot the points A(6, 4) and B(0, 4).

(i) Reflect A and B in the origin to get the images A' and B'.

(ii) Write the co-ordinates of A' and B'.

(iii) State the geometrical name for the figure ABA' B'.

(iv) Find its perimeter.**[4]**