CBSE Board Paper 2011 (Set-3) Class X

Transcription

1 L.K.Gupta (Mathematic Classes) Ph: , CBSE Board Paper 11 (Set-3) Class X General Instructions 1. All questions are compulsory.. The question paper consists of 34 questions divided into four sections A, B, C and D. 3. Section A contains 1 questions of 1 mark each, which are multiple choice type question, Section B contains 8 questions of marks each, Section C contains 1 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 marks. 3 questions of 3 marks and two questions of 4 marks. 5. Use of calculators is not permitted. SECTION A Question number 1 to 1 carry 1 mark each. For each of the question numbers 1 to 1, four alternative choices have been provided, of which only one is correct. Select the correct choice. 1. A solid sphere or radius r is melted and recast into the shape of a solid cone of height 4r. The radius of the base of the cone is (a) r (b) r (c) 3r (d) 4r. A card is drawn from a well-shuffled deck of 5 playing cards. The probability that it is not a face card is (a) 1 5 (b) 16 5 (c) 1 13 (d) If A and B are the points ( 6,) and ( 1, 5) respectively, then the distance AB is equal to (a) 13 (b) 6 (c) 169 (d) 38 PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 3, SECT 4 D, CHANDIGARH 1

2 L.K.Gupta (Mathematic Classes) Ph: , a 4. If P,4 B(,3), then the value of a is is the mid-point of the line-segment joining the points A ( 6,5) and (a) 8 (b) 3 (c) 4 (d) 4 5. A tower stands vertically on the ground. From a point on the ground which is 5 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 45. Then the height (in meters ) of the tower is (a) 5 (b) 5 3 (c) 5 (d) The perimeter (in cm) of a square circumscribing a circle or radius a cm is (a) 8a (b) 4a (c) a (d) 16 a. In figure, AB and AC are tangent to the circle with centre O such that Then BOC is equal to BAC = 4. (a) 4 (b) 5 (c) 14 (d) In Figure,O is the centre of a circle, PQ is a chord and PT is the tangent at P. If POQ =, then TPQ is equal to PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 3, SECT 4 D, CHANDIGARH

3 L.K.Gupta (Mathematic Classes) Ph: , (a) 55 (b) (c) 9. If the common difference of an A.P. is 3, then a a15 is 45 (d) (a) 5 (b) 3 (c) 15 (d) 1. The roots of the equation (a) m,m + 3 (b) m,m + 3 (c) m, (m + 3) (d) m, (m + 3) 35 x 3x m(m + 3) =, where m is a constant, are SECTION B Question numbers 11 to18 carry marks each 11. How many natural numbers are there between and 5, which are divisible by. 1. A ticket is drawn at random from a bag containing tickets numbered from 1 to 4. Find the probability that the selected ticket has a number which is a multiple of Find the value of y for which the distance between the points A(3, 1) and B (11,y) is 1 units. 14. Two cubes each of volume surface area of the resulting cuboid. 3 cm are joined end to end to form a solid. Find the Or PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 3, SECT 4 D, CHANDIGARH 3

4 L.K.Gupta (Mathematic Classes) Ph: , A cone of height 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. 15. Draw a line segment AB of length cm. Using ruler and compasses, find a point P on AB such that AP = 3. AB In Figure, a circel 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. 1. Find the value of m so that the quadratic equation mx (x ) + 49 = has two equal roots. 18. In figure, ABC is a triangle right-angled at B, with AB = 14 cm and BC = 4 cm. With the vertices A,B and C as centers, arcs are drawn, each of radius cm. Find the area of the shaded region. [Use π = ] PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 3, SECT 4 D, CHANDIGARH 4

5 L.K.Gupta (Mathematic Classes) Ph: , SECTION C Questions numbers 19 to 8 carry 3 marks each 19. The point A (3,y) is equidistant from the points P (6,5)and Q (, 3). Find the value of y.. Area of a sector of a circle of radius 14 cm is 154 corresponding arc of the sector. [Use π = ] cm. Find the length of the 1. Two dice are rolled once. Find the probability of getting such numbers on the two dice, whose product is 1. A box contains 8 discs which are numbered from 1 to 8. If one disc is drawn at random from the box, find the probability that it bears a perfect square.. 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 6. If the cars are 1 m apart and are on the same side of the tower, find the height of the tower. [Use 3 = 1.3] 3. Find the area of the quadrilateral ABCD, whose vertices are A ( 3, 1),B(, 4), C(4, 1) and D (3,4). Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are A (,1),B(4,3) and C (,5). 4. Draw a pair of tangents to a circle of radius to a cirlce of radius 3 cm, which are inclined to each other at an angle of 6 Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 3, SECT 4 D, CHANDIGARH 5

6 L.K.Gupta (Mathematic Classes) Ph: , cm. Then construct another triangle whose sides are 3 5 times the corresponding sides of the given triangle. 5. In Figure, 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 of lengths 1 cm and 9 cm respectively. If the area of PQR = 189 sides PQ and PR cm, then find the lengths of 6. Find an A.P. whose fourth term is 9 and the sum of its sixth term and thirteenth term is 4.. Find the roots of the following quadratic equation : x 3 5x + 1 = 8. An open metal bucket is in the shape of a frustum of a cone of height 1 cm with radii of its lower and upper ends as 1 cm and cm respectively. Find the cost of milk which can completely fill the bucket at Rs. 3 per litre. [Use π = ] SECTION D Question numbers 9 to 34 carry 4 marks each. 9. The angle of elevation of the top of a building from the foot of a tower is the angle of elevation of the top of the tower from the foot of the building is tower is 5 m high, find the height of the building. 3 and 6. If the PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 3, SECT 4 D, CHANDIGARH 6

7 L.K.Gupta (Mathematic Classes) Ph: , Water is flowing at the rate of 1 km/hour through a pipe of diameter 16 cm into a cuboidal tank of dimensions m m 16m. How long will it take to fill the empty tank? [Use π = ] 31. Find the area of the shaded region in Figure, where ABCD is a square of side 8 cm. 3. A train travels 18 km at a uniform speed. If the speed had been 9 km/ hour more, it would have taken 1 hour less for the same journey. Find the speed of the train Find the roots of the equation 1,x,5. x 3 + x 5 = 33. The first and the last terms of an A.P. are 8 and 35 respectively. If its common difference is 9, how many terms are there and what is their sum How many multiples of 4 lie between 1 and 5? Also find their sum. 34. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 3, SECT 4 D, CHANDIGARH