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# Board Paper of Class 10 2017 Maths (SET 1) - 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
What is the common difference of an A.P. in which a21 – a7 = 84? VIEW SOLUTION

• Question 2
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 3
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 4
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 5
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 6
Which term of the progression is the first negative term? VIEW SOLUTION

• Question 7
Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord. VIEW SOLUTION

• Question 8
A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA. VIEW SOLUTION

• Question 9
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 10
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 11
If ad ≠ bc, then prove that the equation (a2 + b2) x2 + 2 (ac + bd) x + (c2 + d2) = 0 has no real roots. VIEW SOLUTION

• Question 12
The first term of an A.P. is 5, the last term is 45 and the sum of all its terms is 400. Find the number of terms and the common difference of the A.P. VIEW SOLUTION

• Question 13
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 14
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 15
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 16
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 17
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 18
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 19
The slant height of a frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum. VIEW SOLUTION

• Question 20
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 22
Two taps running together can fill a tank in $3\frac{1}{13}$ hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank? VIEW SOLUTION

• Question 23
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 24
Prove that the lengths of two tangents drawn from an external point to a circle are equal. VIEW SOLUTION

• Question 25
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 26
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 27
An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are 45° and 60° respectively. Find the width of the river. [Use $\sqrt{3}=1·732$] VIEW SOLUTION

• Question 28
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 29
Two different dice are thrown together. Find the probability that the numbers obtained have

(i) even sum, and
(ii) even product. VIEW SOLUTION

• Question 30
In the given figure, ABCD is  rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure. VIEW SOLUTION

• Question 31
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
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