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# Board Paper of Class 10 2017 Maths (SET 3) - Solutions

General Instructions :
(i) All questions are compulsory.
(ii) The question paper consists of 31 questions divided into four sections – A, B, C and D.
(iii) Section A contains 4 questions of 1 mark each, Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.
(iv) Use of calculated is not permitted.

• Question 1
A solid metallic cuboid of dimensions 9 m × 8 m × 2 m is melted and recast into solid cubes of edge 2 m. Find the number of cubes so formed. VIEW SOLUTION

• Question 2
PQ is a tangent drawn from an external point P to a circle with centre O, QOR is the diameter of the circle. If ∠POR = 120°, what is the measure of ∠OPQ? VIEW SOLUTION

• Question 3
A ladder 15 m long makes an angle of 60° with the wall. Find the height of the point where the ladder touches the wall. VIEW SOLUTION

• Question 4
If one root of the quadratic equation 6x2x – k = 0 is $\frac{2}{3},$ then find the value of k. VIEW SOLUTION

• Question 5
If two adjacent vertices of a parallelogram are (3, 2) and (−1, 0) and the diagonals intersect at (2, −5), then find the coordinates of the other two vertices. VIEW SOLUTION

• Question 6
In the given figure, if AB = AC, prove that BE = EC.

VIEW SOLUTION

• Question 7
Find the probability that in a leap year there will be 53 Tuesdays. VIEW SOLUTION

• Question 8
If seven times the 7th term of an A.P. is equal to eleven times the 11th term, then what will be its 18th term? VIEW SOLUTION

• Question 9
Two different dice are thrown together. Find the probability that the product of the numbers appeared is less than 18. VIEW SOLUTION

• Question 10
Solve for x:
$\sqrt{3}{x}^{2}-2x-8\sqrt{3}=0$ VIEW SOLUTION

• Question 11
Show that ∆ ABC with vertices A (–2, 0), B (0, 2) and C (2, 0) is similar to ∆ DEF with vertices D (–4, 0), F (4, 0) and E (0, 4). VIEW SOLUTION

• Question 12
In the given figure, ∆ABC is an equilateral triangle of side 3 units. Find the coordinates of the other two vertices.

VIEW SOLUTION

• Question 13
In the given figure, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and the distance between AB and AC is 14 cm. If arcs of equal radii 7 cm taking A, B, C and D as centres, have been drawn, then find the area of the shaded region.

VIEW SOLUTION

• Question 14
Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. VIEW SOLUTION

• Question 15
The shadow of a tower at a time is three times as long as its shadow when the angle of elevation of the sun is 60°. Find the angle of elevation of the sun at the time of the longer shadow. VIEW SOLUTION

• Question 16
In the given figure, PA and PB are tangents to a circle from an external point P such that PA = 4 cm and ∠BAC = 135°. Find the length of chord AB.

VIEW SOLUTION

• Question 17
Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4). VIEW SOLUTION

• Question 18
If the quadratic equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x, has equal roots, then show that either a = 0 or a3 + b3 + c3 = 3abc. VIEW SOLUTION

• Question 19
In an A.P. of 50 terms, the sum of the first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P. VIEW SOLUTION

• Question 20
A solid sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel? VIEW SOLUTION

• Question 21
Prove that the lengths of two tangents drawn from an external point to a circle are equal. VIEW SOLUTION

• Question 22
A child puts one five-rupee coin of her saving in the piggy bank on the first day. She increases her saving by one five-rupee coin daily. If the piggy bank can hold 190 coins of five rupees in all, find the number of days she can continue to put the five-rupee coins into it and find the total money she saved.

Write your views on the habit of saving. VIEW SOLUTION

• Question 23
A park is of the shape of a circle of diameter 7 m. It is surrounded by a path of width of 0·7 m. Find the expenditure of cementing the path, if its cost is Rs 110 per sq. m. VIEW SOLUTION

• Question 24
In a rectangular park of dimensions 50 m × 40 m, a rectangular pond is constructed so that the area of grass strip of uniform width surrounding the pond would be 1184 m2. Find the length and breadth of the pond. VIEW SOLUTION

• Question 25
Two circles touch internally. The sum of their areas is 116 π cm2 and the distance between their centres is 6 cm. Find the radii of the circles. VIEW SOLUTION

• Question 26
A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number, (ii) a number divisible by 5. VIEW SOLUTION

• Question 27
A well of diameter 3 m is dug 14 m deep. The soil taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment. VIEW SOLUTION

• Question 28
Solve for x:

4x2 + 4bx − (a2 − b2) = 0 VIEW SOLUTION

• Question 29
Draw a circle of radius of 3 cm. Take two points P and Q on one of its diameters extended on both sides, each at a distance of 7 cm on opposite sides of its centre. Draw tangents to the circle from these two points P and Q. VIEW SOLUTION

• Question 30
From the top of a hill, the angles of depression of two consecutive kilometer stones due east are found to be 45° and 30° respectivly. Find the height of the hill. VIEW SOLUTION

• Question 31
A right circular cone is divided into three parts by trisecting its height by two planes drawn parallel to the base. Show that the volumes of the three portions starting from the top are in the ratio 1 : 7 : 19. VIEW SOLUTION
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