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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
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 a21 – a7 = 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 y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point 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 px2 – 14x + 8 = 0 is 6 times the other.           VIEW SOLUTION

• Question 10
For what value of n, are the nth 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 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. 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 (a2 + b2) x2 – 2(ac + bd) x + (c2 + d2) = 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 rain-water harvesting system, the rain-water 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 9th terms. 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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