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

**Time allowed: 3 hours Maximum marks: 90**

**GENERAL INSTRUCTIONS:**

**All questions are compulsory.****The Question Taper consists of 31 questions divided into four Sections A, B. C. and D.****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.****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 x ^{2} – 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 ∠POQ = 70°, then calculate ∠TPQ.**

**Solution.**

**Question.3 In Figure 2, AB and AC are tangents to the circle with centre O such that∠BAC = 40°. Then calculate ∠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 π = 22/7]**

**Solution.**

**Question.12 Two cubes each of volume 27 cm ^{3} 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 : x ^{2} -3√5x + 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 ΔPQR = 189 cm ^{2}, 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 π = 22/7 and √3 = 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 π = 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 √3 = 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 π= 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 x ^{2} – 12ax + (a^{2} – b^{2} ) = 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 π = 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 π = 22/7 and √3 = 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 π = 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 π = 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 cm ^{2}. Find the length of the corresponding**

**arc of the sector. [Use π = 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 π = 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.**