# Board Paper of Class 10 2016 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) Using remainder theorem, find the value of *k*if on dividing 2*x*^{3}+ 3*x*^{2}–*kx*+ 5 by*x*– 2, leaves a remainder 7.**[3]**(b) Given *A*= $\left[\begin{array}{cc}2& 0\\ -1& 7\end{array}\right]\mathrm{and}\mathrm{I}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ and*A*^{2}= 9*A*+*mI*. Find*m*.**[4]**(c) The mean of following number is 68. Find the value of ‘ *x*’

45, 52, 60,*x*, 69, 70, 26, 81 and 94

Hence estimate the median.**[3]**

- Question 2
(a) The slope of a line joining P (6, *k*) and Q (1 – 3*k*, 3) is $\frac{1}{2}$. Find

(i)*k*

(ii) Midpoint of PQ, using the value of ‘*k*’ found in (i).

**[3]**(b) Without using trigonometrical tables, evaluate:

${\mathrm{cosec}}^{2}57\xb0-{\mathrm{tan}}^{2}33\xb0+\mathrm{cos}44\xb0\mathrm{cosec}46\xb0-\sqrt{2}\mathrm{cos}45\xb0-{\mathrm{tan}}^{2}60\xb0$**[4]**(c) A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number

of cones.**[3]**

- Question 3
(a) Solve the following inequation, write the solution set and represent it on

the number line.

$-3\left(x-7\right)\ge 15-7x>\frac{x+1}{3},x\in \mathrm{R}$**[3]**(b) In the figure given below, AD is a diameter. O is the centre of the circle.

AD is parallel to BC and ∠CBD = 32°. Find:

(i) ∠OBD

(ii) ∠AOB

(iii) ∠BED

**[4]**(c) If (3 *a*+ 2*b*): (5*a*+ 3*b*) = 18 : 29. Find*a*:*b*.**[3]**

- Question 4
(a) A game of numbers has cards marked with 11, 12, 13,..., 40. A card is drawn

at random. Find the Probability that the number on the card drawn is:

(i) A perfect square

(ii) Divisible by 7**[3]**(b) Use graph paper for this question. (Take 2 cm = 1 unit along both *x*and*y*

axis.) Plot the points O (0, 0), A (–4, 4), B (–3, 0) and C (0, –3)

(i) Reflect points A and B on the*y*-axis and name them A' and B' respectively.Write down their coordinates.(ii) Name the figure OABCB'A'.

(iii) State the line of symmetry of this figure**[4]**(c) Mr. Lalit invested Rs. 5000 at a certain rate of interest, compounded annually

for two years. At the end of first year it amounts to Rs. 5325. Calculate

(i) The rate of interest

(ii) The amount at the end of second year, to the nearest rupee.**[3]**