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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
If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k? VIEW SOLUTION

• Question 2
The ratio of the height of a tower and the length of its shadow on the ground is $\sqrt{3}:1$. What is the angle of elevation of the sun? VIEW SOLUTION

• Question 3
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere? VIEW SOLUTION

• Question 4
A number is chosen at random from the number –3, –2, –1, 0, 1, 2, 3. What will be the probability that square of this number is less then or equal to 1? VIEW SOLUTION

• Question 5
In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD. VIEW SOLUTION

• Question 6
Draw a line segment of length 8 cm and divide it internally in the ratio 4:5. VIEW SOLUTION

• Question 7
Find the roots of the quadratic equation $\sqrt{2}{x}^{2}+7x+5\sqrt{2}=0$. VIEW SOLUTION

• Question 8
Find how many integers between 200 and 500 are divisible by 8. VIEW SOLUTION

• Question 9
Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots. VIEW SOLUTION

• Question 10
In the figure, AB and CD are common tangents to two circles of unequal radi. Prove that AB = CD. VIEW SOLUTION

• Question 11
Two different dice are thrown together. Find the probability that the numbers obtained

(i) have a sum less than 7

(ii) have a product less than 16

(iii) is a doublet of odd numbers. VIEW SOLUTION

• Question 12
Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2 ∠OPQ. VIEW SOLUTION

• Question 13
The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, –2). If the third vertex is find the value of y. VIEW SOLUTION

• Question 14
Find the sum of n terms of the series $\left(4-\frac{1}{n}\right)+\left(4-\frac{2}{n}\right)+\left(4-\frac{3}{n}\right)+..........$ VIEW SOLUTION

• Question 15
Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles. VIEW SOLUTION

• Question 16
In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region. VIEW SOLUTION

• Question 17
If the equation (1 + m2) x2 + 2mcx + c2a2 = 0 has equal roots then show that c2 = a2 (1 + m2). VIEW SOLUTION

• Question 18
If the pth term of an A. P. is q and qth term is p, prove that its nth term is (p + qn). VIEW SOLUTION

• Question 19
A solid metallic sphere of diamter 16 cm is melted and recasted into smaller solid cones, each of radius 4 cm and height 8 cm. Find the number of cones so formed. VIEW SOLUTION

• Question 20
The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If height of the tower is 50 m, find the height of the hill. VIEW SOLUTION

• Question 21
In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O' are centres of the circles. Find the area of shaded region. VIEW SOLUTION

• Question 22
In a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If tank is filled completely then what will be the height of standing water used for irrigating the park. Write your views on recycling of water. VIEW SOLUTION

• Question 23
A chord PQ of a circle of radius 10 cm substends an angle of 60° at the centre of circle. Find the area of major and minor segments of the circle. VIEW SOLUTION

• Question 24
Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number 25. VIEW SOLUTION

• Question 25
Prove that the lengths of tangents drawn from an external point to a circle are equal. VIEW SOLUTION

• Question 26
Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream. VIEW SOLUTION

• Question 27
If $a\ne b\ne 0$, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear. VIEW SOLUTION

• Question 28
Construct a triangle ABC with sides BC = 7 cm, ∠B = 45° and ∠A = 105°. Then construct a triangle whose sides are $\frac{3}{4}$ times the corresponding sides of ∆ABC. VIEW SOLUTION

• Question 29
If the pth term of an A. P. is $\frac{1}{q}$ and qth term is $\frac{1}{p}$, prove that the sum of first pq terms of the A. P. is $\left(\frac{pq+1}{2}\right).$ VIEW SOLUTION

• Question 30
An observer finds the angle of elevation of the top of the tower from a certain point on the ground as 30°. If the observe moves 20 m towards the base of the tower, the angle of elevation of the top increases by 15°, find the height of the tower. VIEW SOLUTION

• Question 31
A cone of radius 10 cm is divided into two parts by a plane parallel to its base through the mid-point of its height. Compare the volumes of the two parts. VIEW SOLUTION
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