Board Paper of Class 10 2011 Maths (SET 3)  Solutions
1. All questions are compulsory.
2. The question paper consists of 34 questions divided into four sections A, B, C and
D.
3. Section A contains 10 questions of 1 mark each, which are multiple choices type
questions, Section B contains 8 questions of 2 marks each, Section C contains 10
questions of 3 marks each, Section D contains 6 questions of 4 marks each.
4. There is no overall choice in the paper. However, internal choice is provided in one
question of 2 marks, 3 questions of 3 marks each and two questions of 4 marks each.
5. Use of calculators is not permitted.
 Question 1
Which of the following can not be the probability of an event?
A. 1.5
B.
C. 25%
D. 0.3
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 Question 2
The midpoint of segment AB is the point P (0, 4). If the coordinates of B are (−2, 3) then the coordinates of A are
A. (2, 5)
B. (−2, −5)
C. (2, 9)
D. (−2, 11)
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 Question 3
The point P which divides the line segment joining the points A (2, −5) and B (5, 2) in the ratio 2:3 lies in the quadrant.
A. I
B. II
C. III
D. IV
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 Question 4
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 45°. The height of the tower (in metres) is
A. 15
B. 30
C.
D.
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 Question 5
A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises (in cm) by
A. 3
B. 4
C. 5
D. 6
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 Question 6
In figure 1, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to
A. 100°
B. 40°
C. 50°
D. 90°
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 Question 7
In figure 2, PA and PB are tangents to the circle with centre O. If ∠APB = 60°, then ∠OAB is
A. 30°
B. 60°
C. 90°
D. 15°
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 Question 8
The roots of the equation x^{2} + x − p (p + 1) = 0, where p is a constant, are
A. p, p + 1
B. −p, p + 1
C. p, − (p + 1)
D. −p, − (p + 1)
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 Question 9
In an AP, if a = 15, d = −3 and a_{n} = 0, then the value of n is
A. 5
B. 6
C. 19
D. 4
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 Question 10
The radii of two circles are 8 cm and 6 cm respectively. The diameter of the circle having area equal to the sum of the areas of the two circles (in cm) is
A. 10
B. 14
C. 20
D. 28
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 Question 11
A coin is tossed two times. Find the probability of getting both heads or both tails.
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 Question 12
Find the value of m so that the quadratic equation mx (5x − 6) + 9 = 0 has two equal roots.
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 Question 13
Find the values(s) of x for which the distance between the points P(x, 4) and Q(9, 10) is 10 units.
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 Question 14
Two cubes, each of side 4 cm are joined end to end. Find the surface area of the resulting cuboid.
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 Question 15
Draw a line segment of length 6 cm. Using compasses and ruler, find a point P on it which divides it in the ratio 3:4.
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 Question 16
Two concentric circles are of radii 7 cm and r cm respectively, where r > 7. A chord of the larger circle, of length 48 cm, touches the smaller circle. Find the value of r.
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 Question 17
Find whether − 150 is a term of the AP 17, 12, 7, 2,…?
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 Question 18
In figure 3, APB and CQD are semicircles of diameter 7 cm each, while ARC and BSD are semicircles of diameter 14 cm each. Find the perimeter of the shaded region.
OR
Find the area of a quadrant of a circle, where the circumference of circle is 44 cm.
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 Question 19
If two vertices of an equilateral triangle are (3, 0) and (6, 0), find the third vertex.
OR
Find the value of k, if the points P(5, 4), Q(7, k) and R (9, −2) are collinear.
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 Question 20
From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30° and 45° respectively. Find the distance between the cars.
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 Question 21
Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is a perfect square.
OR
A game consists of tossing a coin 3 times and noting its outcome each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
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 Question 22
The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14 cm). If the volume of bucket is 5390 cm^{3}, then find the value of r.
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 Question 23
In fig. 4, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively. If area of ΔABC = 21 cm^{2}, then find the lengths of sides AB and AC.
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 Question 24
Find the value of the middle term of the following AP:
−6, −2, 2, ……, 58.
OR
Determine the AP whose fourth term is 18 and the differences of the ninth term from the fifteenth term is 30.
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 Question 25
Find the roots of the following quadratic equation:
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 Question 26
Find the area of the major segment APB, in Fig 5, of a circle of radius 35 cm and ∠AOB = 90°.
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 Question 27
Draw a triangle PQR such that PQ = 5 cm, ∠P = 120° and PR = 6 cm. Construct another triangle whose sides are times the corresponding sides of ΔPQR.
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 Question 28
Find the point of yaxis which is equidistant from the points (−5, −2) and (3, 2).
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 Question 29
From a solid cylinder of height 20 cm and diameter 12 cm, a conical cavity of height 8 cm and radius 6 cm is hollowed out. Find the total surface area of the remaining solid.
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 Question 30
The length and breadth of a rectangular piece of paper are 28 cm and 14 cm respectively. A semicircular portion is cut off from the breadth’s side and a semicircular portion is added on length’s side, as shown in Fig. 6. Find the area of the shaded region.
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 Question 31
From the top of a 15 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Determine the height of the tower.
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 Question 32
A motor boat whose speed is 20 km/h in still water, takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the stream.
OR
Find the roots of the equation
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 Question 33
Prove that the lengths of tangents drawn from an external point to a circle are equal.
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 Question 34
If the sum of first 4 terms of an AP is 40 and that of first 14 terms is 280, find the sum of its first n terms.
OR
Find the sum of the first 30 positive integers divisible by 6.
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