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.
(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
The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap? VIEW SOLUTION
 Question 2
If a tower 30 m high, casts a shadow $10\sqrt{3}$ m long on the ground, then what is the angle of elevation of the sun? VIEW SOLUTION
 Question 3
If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP. VIEW SOLUTION
 Question 4
What is the common difference of an A.P. in which a_{21} – a_{7} = 84? VIEW SOLUTION
 Question 5
A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA. VIEW SOLUTION
 Question 6
Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord. VIEW SOLUTION
 Question 7
A line intersects the yaxis and xaxis at the points P and Q respectively. If (2, –5) is the midpoint of PQ, then find the coordinates of P and Q. VIEW SOLUTION
 Question 8
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y. VIEW SOLUTION
 Question 9
Find the value of p, for which one root of the quadratic equation px^{2} – 14x + 8 = 0 is 6 times the other. VIEW SOLUTION
 Question 10
For what value of n, are the n^{th} terms of two A.Ps 63, 65, 67,... and 3, 10, 17,... equal ? VIEW SOLUTION
 Question 11
On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower. VIEW SOLUTION
 Question 12
A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag. VIEW SOLUTION
 Question 13
Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.
VIEW SOLUTION
 Question 14
In what ratio does the point $\left(\frac{24}{11},\mathrm{y}\right)$ divide the line segment joining the points P(2, –2) and Q(3, 7)? Also find the value of y. VIEW SOLUTION
 Question 15
Water in a canal, 5·4 m wide and 1·8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation? VIEW SOLUTION
 Question 16
In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region. $\left[\mathrm{Use}\mathrm{\pi}=\frac{22}{7}\right]$
VIEW SOLUTION
 Question 17
The dimensions of a solid iron cuboid are 4·4 m × 2·6 m × 1·0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe. VIEW SOLUTION
 Question 18
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy. VIEW SOLUTION
 Question 19
How many terms of an A.P. 9, 17, 25, ... must be taken to give a sum of 636? VIEW SOLUTION
 Question 20
If the roots of the equation (a^{2} + b^{2}) x^{2} – 2(ac + bd) x + (c^{2} + d^{2}) = 0 are equal, prove that $\frac{\mathrm{a}}{\mathrm{b}}=\frac{\mathrm{c}}{\mathrm{d}}.$ VIEW SOLUTION
 Question 21
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k. VIEW SOLUTION
 Question 22
Construct a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are $\frac{3}{4}$ times the corresponding sides of the ∆ABC. VIEW SOLUTION
 Question 23
Two different dice are thrown together. Find the probability that the numbers obtained have
(i) even sum, and
(ii) even product. VIEW SOLUTION
 Question 24
In the given figure, XY and X'Y' are two parallel tangents to circle with centre O and another tangent AB with point of contact C, is intersecting XY at A and X'Y' at B. Prove that ∠AOB = 90°.
VIEW SOLUTION
 Question 25
In a rainwater harvesting system, the rainwater from a roof of 22 m × 20 m drains into a cylindrical tank having diameter of base 2 m and height 3·5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation. VIEW SOLUTION
 Question 26
Prove that the lengths of two tangents drawn from an external point to a circle are equal. VIEW SOLUTION
 Question 27
If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9^{th} terms. VIEW SOLUTION
 Question 28
Solve for x :
$\frac{\mathrm{x}1}{2\mathrm{x}+1}+\frac{2\mathrm{x}+1}{\mathrm{x}1}=2,\mathrm{where}\mathrm{x}\ne \frac{1}{2},1$ VIEW SOLUTION
 Question 29
A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days, how many days will B take to finish it? VIEW SOLUTION
 Question 30
From the top of a tower, 100, high, a man observes two cars on the opposite sides of the tower and in same straight line with its base, with angles of depression 30° and 45°. Find the distance between the cars. [Take $\sqrt{3}$ = 1.732] VIEW SOLUTION
 Question 31
In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region.
VIEW SOLUTION
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