## CBSE Previous Year Question Papers Class 10 Maths SA2  Outside Delhi – 2011

Time allowed: 3 hours                                                                                           Maximum marks: 90

GENERAL INSTRUCTIONS:

1. All questions are compulsory.
2. The Question Taper consists of 31 questions divided into four Sections A, B. C. and D.
3. 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.
4.  Use of calculators is not permitted.

### SET I

SECTION A
Questions number 1 to 4 carry one mark each.
Question.1 Find the roots of the equation x2  – 3x – m (m + 3) = 0, where m is a constant.
Solution.

Question.2 In Figure 1, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If âˆ POQ = 70 °, then calculate âˆ TPQ.

Solution.

Question.3 In Figure 2, AB and AC are tangents to the circle with centre O such thatâˆ BAC = 40 °. Then calculate âˆ BOC.

Solution.

Question.4 Find the perimeter (in cm) of a square circumscribing a circle of radius a cm.
Solution.

SECTION B
Questions number 5 to 10 carry 2 marks each.
Question.5 A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither an ace nor a king.
Solution.

Question.6 Find the area of the triangle whose vertices are (1, 2), (3, 7) and (5, 3).
Solution.

Question.7 Find the value of m so that the quadratic equation mx (x -7) + 49 = 0 has two equal roots.
Solution.

Question.8 Find how many two-digit numbers are divisible by 6?
Solution.

Question.9 In Figure 3, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm, BC = 9 cm and CD = 8 cm. Find the length of side AD.

Solution.

Question.10 Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that AP/AB =3/5.
Solution.

SECTION C
Questions number 11 to 20 carry 3 marks each.
Question.11 Find the perimeter of the shaded region in Figure 4, if ABCD is a square of side 14 cm arid APB and CPD are semicircles.
[Use Ï€ = 22/7]

Solution.

Question.12 Two cubes each of volume 27 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.
Or
A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.
Solution.

Question.13 Find the value of y for which the distance between the points A (3, -1) and B (11, y) is 10 units.
Solution.

Question.14 A ticket is drawn at random from a bag containing tickets numbered from 1 to 40. Find the probability that the selected ticket has a number which is a multiple of 5.
Solution.

Question.15. Find the roots of the following quadratic equation : x2  -3âˆš5x + 10 = 0
Solution.

Question.16 Find an A.P. whose fourth term is 9 and the sum of its sixth term and thirteenth term is 40.
Solution.

Question.17 In Figure 5, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contact T, are the lengths 12 cm and 9 cm respectively. If the area of Î”PQR = 189 cm2, then find the lengths of sides PQ and PR.

Solution.

Question.18 Draw a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of 60 °.
Or
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3
cm. Then construct another triangle whose sides are 3/5 times the corresponding sides of the given triangle.
Solution.

Question.19 A chord of a circle of radius 14 cm subtends an angle of 120 ° at the centre. Find the area of
the corresponding minor segment of the circle. [Use Ï€ = 22/7 and âˆš3 = 1.73]
Solution.

Question.20 An open metal bucket is in the shape of a frustum of a cone of height 21 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the cost of milk which can
completely fill the bucket at ?30 per litre. [Use Ï€ = 22/7 ]
Solution.

SECTION D
Questions number 21 to 31 carry 4 marks each.
Question. 21 Point P(x, 4) lies on the line segment joining the points A(- 5,8) and B(4, – 10). Find the ratio in which point P divides the line segment AB. Also find the value of x.
Solution.

Question.22. Find the area of the quadrilateral ABCD, whose vertices are A(- 3, – 1), B(- 2, – 4), C(4, -1) and D(3, 4).
Or
Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are A(2, 1), B(4, 3) and C(2, 5).
Solution.

Question.23 From the top of a vertical tower, the angles of depression of two cars, in the same straight line with the base of the tower, at an instant are found to be 45 ° and 60 °. If the cars are 100
m apart and are on the same side of the tower, find the height of the tower. [Use âˆš3 = 1.73]
Or
Two dice are rolled once. Find the probability of getting such numbers on the two dice, whose product is 12.
Solution.

Question.24 The probability of guessing the correct answer to a certain question is x/12. If the probability
of guessing the wrong answer is 3/4, find x.
If a student copies the answer, then its probability is 2/6 . If he doesn’t copy the answer, then
the probability is 2y/3. Find the value of y.
If he does not copy the answer, which moral value is depicted by him?
Solution.

Question.25 Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Solution.

Question. 26 The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
Or
How many multiples of 4 lie between 10 and 250? Also find their sum.
Solution.

Question.27 A train travels 180 km at a uniform speed. If the speed had been 9 km/hour more, it would have taken 1 hour less for the same joumev. Find the speed of the train.
Or
Find the roots of the equation 1/2x-3 + 1/x-5 = 1,x =/ 3/2, 5
Solultion.

Question.28 In Figure 6, three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed
between these three circles (shaded region). [Use Ï€= 22/7 ]

Solution.

Question.29 Water is flowing at the rate of 15 km/ hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?
Solution.

Question.30 The angle of elevation of the top of a vertical tower from a point on the ground is 60 °. From another point 10 m vertically above the first, its angle of elevation is 30 °. Find the height of the tower.
Solution.

Question.31 If pth, qth and rth terms of an A.P. are a, b, c respectively, then show that (a – b)r + (b – c)p + (c – a)q = 0.
Solution.

### SET II

Note:Except for the following questions, all the remaining questionr have been asked in Set I.
Question.5 Find 10th term from end of the A.F. 4, 9,14, …, 254.
Solution.

Question.6 Solve for x : 36  x2  – 12ax + (a2   – b2  ) = 0
Solution.

Question.13 Which term of the A.P. 3,14, 25, 36, … will be 99 more than its 25th term?
Solution.

Question.14 In Figure 7, a semi-circle is drawn with O as centre and AB as diameter. Semi-circles are drawn with AO and OB as diameters.
If AB = 28 m, find the perimeter of the shaded region.
[Use Ï€ = 22/7]

Solution.

Question.23 A chord of a circle of radius 21 cm subtends an angle of 60 ° at the centre. Find the area of
the corresponding minor segment of the circle. [Use Ï€ = 22/7  and âˆš3 = 1.73]
Solution.

Question.24 Point M(11, y) lies on the line segment joining the points P(15, 5) and Q(9, 20). Find the ratio in which point M divides the line segment PQ. Also find the value of y.
Solution.

Question.25 In Figure 8, an equilateral triangle has been inscribed in a circle of radius 6 cm. Find the area of the shaded region. [Use Ï€ = 3.14]

Solution.

Question.26A farmer connects a pipe of intemaTdiameter 20 cm, from a canal into a cylindrical tank in his field, which is 10 m in diameter and 4 m deep. If water flows through the pipe at the rate of 5 km/hour, in how much time will the tank be filled?
Solution.

Question.27 The angles of depression of the top and bottom of a 12 m tall building, from the top of a multi-storeyed building are 30 ° and 60 ° respectively. Find the height of the multi-storeyed building.
Solution.

### SET III

Note:Except for the following questions, all the remaining questions have been asked in Set I and Set II.
Question.1 In Figure 1, find the area of the shaded region.

Solution.

Question.2 If the perimeter of a semi-circular protractor is 36 cm, find the diameter of the protractor. (Take it = 22/7)
Solution.

Question.7 How many natural numbers are there between 200 and 500, which are divisible by 7?
Solution.

Question.14 In Fig. 9, ABC is a triangle right-angled at B, with AB = 14 cm and BC = 24 cm. With the vertices A, B and C as centres, arcs are drawn, each of radius 7 cm. Find the area of the shaded region.
[Use Ï€ = 22/7]

Solution.

Question.15 The point A(3, y) is equidistant from the points P(6, 5) and Q(0, – 3). Find the value of y.
Solution.

Question.16 Area of a sector of a circle of radius 14 cm is 154  cm2. Find the length of the corresponding
arc of the sector. [Use Ï€ = 22/7]
Solution.

Question.25 The angle of elevation of the top of a building from the foot of a tower is 30 ° and the angle of elevation of the top of the tower from the foot of the building is 60 °. If the tower is 50 m high, find the height of the building.
Solution.

Question.26 Water is flowing at the rate of 10 km/hour through a pipe of diameter 16 cm into a cuboidal tank of dimensions 22 m x  20 m x 16 m. How long will it take to fill the empty tank?
[Use Ï€ = 22/7]
Solution.

Question.27 Find the area of the shaded region in Figure 10, where ABCD is a square of side 28 cm.

Solution.