**CBSE Previous Year Question Papers Class 10 Maths SA2 Delhi – 2013**

**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**

**Questions number 1 to 4 carry 1 mark each.**

** Question.1 Find the common difference of the Ap**

**Solution.**

**Question.2 In Fig.1, Calculate the area of triangle ABC (in sq.units).**

**Solution.**

**SECTION A**

**Question.3 In Fig. 2, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA PB, then find the length of each tangent.**

** **

** Solution.**

**Question.4 If the difference between the circumference and the radius of a circle is 37 cm, then using**

**π= 22/7, calculate the circumference (in cm) of the circle.**

** Solution.**

**SECTION B**

**Questions number 5 to 20 carry 2 marks each.**

** Question.5 Solve the following quadratic equation for x:**

** **

** Solution.**

**Question.6 How many three-digit natural numbers are divisible by 7?**

** Solution.**

**Question.7 In Fig. 3, a circle inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.**

** **

** Solution.**

**Question.8 Prove that the parallelogram circumscribing a circle is a rhombus.**

** Solution.**

**Question.9 A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is neither a king nor a queen.**

** Solution.**

**Question.10 Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm x 7 cm. Find the area of the remaining card**

** board. [Use π = 22/7 ]**

** Solution.**

**SECTION C**

**Questions number 11 to 20 carry 3 marks each.**

** Question.11 For what value of k, are the roots of the quadratic equation kx(x – 2) + 6 =0 equal?**

** Solution.**

**Question.12 Find the number of terms of the AP18,****15 ^{1/2}**

**, 13,…., -49**

^{1/2}and find the sum of all its terms.**Solution.**

**Question.13 Construct a triangle with sides 5 cm, 4 cm and 6 cm. Then construct another triangle whose**

** sides are 2/3 times the corresponding sides of first triangle.**

** Solution.**

**Question.14 The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30°. If the height of the second pole is 24 m, find the height of the first pole. [Use √3 = 1.732]**

** Solution.**

**Question.15 Prove that the points (7,10), (-2,5) and (3, -4) are the vertices of an isosceles right triangle.**

** Solution.**

**Question.16 Find the ratio in which the y-axis divides the line segment joining the points (-4, -6) and (10,12). Also find the coordinates of the point of division.**

** Solution.**

**Question.17 In Fig. 4, AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. QB is the diameter of the smaller**

** circle. If QA = 7 cm, find the area of the shaded region. [Useπ= 22/7]**

** **

** Solution.**

**Question.18 A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total (inner) suface area of the vessel. [Use π = 22/7 ]**

** Solution.**

**Question.19 A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy. [Use π = 22/7 ]**

** Solution.**

**Question.20 In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre.**

** Find: (i) the length of the arc (ii) area of the sector formed by the arc. [Use π = 22/7 ]**

** Solution.**

**SECTION D**

**Questions number 21 to 31 carry 4 marks each.**

** Question.21 Solve the following for x:**

**Solution.**

**Question.22 Sum of the areas of two squares is 400 ^{ }cm^{2}. If the difference of their perimeters is 16 cm, find the sides of the two squares.**

**Solution.**

**Question.23 If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289, find the sum of its first n terms.**

** Solution.**

**Question.24 Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.**

** Solution.**

**Question.25 In Fig. 5, l and m are two parallel tangents to a circle with centre O, touching the circle at A and B respectively. .Another tangent at C intersects the line / at D and m at E. Prove that ∠DOE = 90°.**

**Solution.**

**Question.26 The angle of elevation of the top of a building from the foot of the 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 60 m high, find the height of the building.**

** Solution.**

**Question.27 A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is**

** (i) extremely patient**

** (ii) extremely kind or honest.**

** Which of the above values you prefer more?**

** Solution.**

**Question.28 The three vertices of a parallelogram ABCD are A(3, -4), B(-l, -3) and C(-6, 2). Find the coordinates of vertex D and find the area of ABCD.**

** Solution.**

**Question.29 Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour.**

** Solution.**

**Question.30 A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 26 Cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs 10 per 100 cm2. [Use π = 3.14]**

** Solution.**

**Question.31 In Fig. 6, ABC is a right-angled triangle right angled at A.**

** Semicircles are drawn on AB, AC and BC as diametres. Find the area of the shaded region.**

**Solution.**

**SET II**

**Note: Except for the following questions, all the remaining questions have been asked in Set-1,**

** Question.4 Find the common difference of the A.P.**

** **

** Solution.**

**Question.10 A die is tossed once. Find the probability of getting an even number or a multiple of 3.**

** Solution.**

**Question.17 Prove that the points A(0, -1), B(-2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?**

** Solution.**

**Question.18 Draw a triangle PQR in which QR = 6 cm, PQ = 5 cm and ∠PQR = 60°. Then construct an-**

** other triangle whose sides are 3/5 times the corresponding sides of ΔPQR?**

** Solution.**

**Question.19 The «th term of an A.P. is given by (-4n + 15). Find the sum of first 20 terms of this A.P.**

** Solution.**

**Question.20 For what value of k, the roots of the quadratic equation kx(x – 2√5) + 10 = 0, are equal?**

** Solution.**

**Question.28 Find the value of x for which the points (x, -1), (2,1) and (4, 5) are collinear.**

** Solution.**

**Question.29 From a point P on the ground, the angle of elevation of the top of a 10m tall building is 30°. A flagstaff is fixed at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff and the distance of the building from the point P. (Take √3 = 1.73)**

** Solution.**

**Question.30 The 24 ^{th} term of an AP is twice its 10^{th} term. Show that its 72^{nd} term is 4 times its 15^{th }term.**

**Solution.**

**SET III**

**Note: Except for the following questions, all the remaining questions have been asked in Set-I and Set-II.**

** Question.4 Find the common difference of the A.P.**

** **

** Solution.**

**Question.10 A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is neither a jack nor an ace.**

** Solution.**

**Question.17 For what values of k, the roots of the quadratic equation (k + 4)x ^{2} + (k + 1)x + 1 = 0 are equal?**

**Solution.**

**Question.18 The sum of first n terms of an AP is 3n ^{2} + 4n . Find the 25^{th} term of this AP.**

**Solution.**

**Question.19 Construct a tangent to a circle of radius 4cm from a point on the concentric circle of radius 6 cm.**

** Solution.**

**Question.20 Show that the points (-2, 3), (8, 3) and (o, 7) are the vertices of a right triangle.**

** Solution.**

**Question.28 Find the number of terms of the A.P. -12, -9, -6,……,21. If 1 is added to each term of this**

** A.P., then find the sum of all terms of the A.P. thus obtained.**

** Solution.**

**Question.29 Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles and the distances of the point from the poles.**

** Solution.**

**Question.30 If the area of triangle ABC formed by A(x, y), B(1, 2) and C(2,1) is 6 square units, then prove that x + y = 15 or x + y = -9.**

** Solution.**