# Board Paper of Class 10 2017 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) If b is the mean proportion between a and c, show that $\frac{{\mathrm{a}}^{4}+{\mathrm{a}}^{2}{\mathrm{b}}^{2}+{\mathrm{b}}^{4}}{{\mathrm{b}}^{4}+{\mathrm{b}}^{2}{\mathrm{c}}^{2}+{\mathrm{c}}^{4}}=\frac{{\mathrm{a}}^{2}}{{\mathrm{c}}^{2}}$.

(b) Solve the equation 4*x*^{2}– 5*x*– 3 = 0 and give your answer correct to two decimal places.

(c) AB and CD are two parallel chords of a circle such that AB = 24 cm and CD = 10 cm.If the radius of the circle is 13 cm, find the distance between the two chords.

VIEW SOLUTION

- Question 2
(a) Evaluate without using trigonometric tables, sin
^{2}28° + sin^{2}62° + tan^{2}38° – cot^{2}52° + $\frac{1}{4}$ sec^{2}30°

(b) If $\mathrm{A}=\left[\begin{array}{cc}1& 3\\ 3& 4\end{array}\right]\mathrm{and}\mathrm{B}=\left[\begin{array}{cc}-2& 1\\ -3& 2\end{array}\right]\mathrm{and}{\mathrm{A}}^{2}-5{\mathrm{B}}^{2}=5\mathrm{C}$. Find matrix C where C is a 2 by 2 matrix.

(c) Jaya borrowed Rs. 50,000 for 2 years. The rates of interest for two successive years are 12% and 15% respectively.She repays 33,000 at the end of the first year. Find the amount she must pay at the end of the second year to clear her debt.VIEW SOLUTION

- Question 3
(a) The catalogue price of a computer set is Rs. 42,000. The shopkeeper gives a discount of 10% on the listed price. He further gives an off-season discount of 5% on the discounted price. However, sales tax at 8% is charged on the remaining price after the two successive discounts.

(b) P(1, –2) is a point on the line segment A(3, –6) and B(

Find:

(i) the amount of sales tax a customer has to pay

(ii) the total price to be paid by the customer for the computer set.

*x, y*) such that AP : PB is equal to 2 : 3. Find the coordinates of B.

(c) The marks of 10 students of a class in an examination arranged in ascending order is as follows:13, 35, 43, 46,VIEW SOLUTION*x*,*x*+ 4, 55, 61, 71, 80

If the median marks is 48, find the value of*x*. Hence find the mode of the given data.

- Question 4
(a) What must be subtracted from 16
*x*^{3}– 8*x*^{2}+ 4*x*+ 7 so that the resulting expression has 2*x*+ 1 as a factor?

(b) In the given figure ABCD is a rectangle. It consists of a circle and two semi-circles each of which are of radius 5 cm.

Find the area of the shaded region. Give your answer correct to three significant figures.

(c) Solve the following in-equation and represent the solution set on a number line.VIEW SOLUTION

$-8\frac{1}{2}<-\frac{1}{2}-4x\le 7\frac{1}{2},x\in \mathrm{I}$