2008 sample paper of maths for cbse 9 Question paper
Sample Paper 2008 Class  X Mathematics
Time: 3 hrs Marks: 80
General Instructions: ( i ) All questions are compulsory. ( ii ) The question paper consists of 30 questions divided into four sections –A, B, C and D. Section A contains 10 questions of 1 mark each, Section B is of 5 questions of 2 marks each, Section C is of 10 questions of 3 marks each and section D is of 5 questions of 6 marks each. ( iii ) There is no overall choice. However, an internal choice has been provided in one question of two marks each, three questions of three marks each and two questions of six marks each. ( iv ) In question on construction, the drawing should be neat and exactly as per the given measurements. ( v ) Use of calculator is not permitted.
SECTION A ( Qns 1 – 10 carry 1 mark each )
1. Find the discriminant of the quadratic equation by factorization: 2x2 + x – 6= 0 2. Given H.C.F ( 96, 404 ) = 4, find L.C.M (96, 404 ) 3. Write the condition for which the given pair of equations has unique solutions. ax + by + c = 0 Ax + By + d = 0 4. Find the 10th term of the AP: 2,7,12… 5. Evaluate Cos 700 + Cos550 cosec350 Sin200 tan50 tan250 tan450 tan650 tan850 6. In fig. DE // BC. Find EC. A 3cm 2cm D E 6cm B C 7.The length of a tangent from a point A at a distance of 5 cm from the center of the circle is 4 cm. What will be the radius of the circle? 8. A card is drawn at random from a wellshuffled deck of 52 cards. Find the probability that it is neither an ace nor a queen. 9. The minute hand of a clock is 10 cm. long. Find the area on the face of the clock described by the minute hand in 10 minutes.
10. Find the value of ‘f’, if the mean of the following distribution is 18
Class 1113 1315 1517 1921 2123 2325 Frequency 7 6 9 f 5 4
SECTION B ( Qns 11 – 15 carry 2 marks each ) 11.Factorise p3(q – r)3 + q3(r – p)3 + r3(p – q)3 12.If tan ? = 3 Sin? , Find The value of sin2 ?  Cos2?. Or Prove that sec A.(1 – sin A).( sec A + tan A) = 1. 13. Prove that (a,0), (0,b) and (1,10 are collinear if 1/a + 1/b =1 14. D is any point on the side BC of ?ABC such that ?ADC= ?BAC. Prove that CA2= BC.CD 15. Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is? neither 9 or 11.
SECTION C ( Qns 16 – 25 carry 3 marks each )
16. Prove that 5 + 2 is irrational. 17 The sum of two numbers is 15. If the sum of their reciprocals is 3/10, find the two numbers. 18.Prove quadratic formula. 19 Solve 4x + 6y = 3xy, 8x + 9y = 5xy given (x ¹ y, x ¹ 0 20.Prove that: CosA + SinA = CosA + SinA 1tanA 1 Cot A Or sin ? + cos ? = p and sec ? + cosec ? = q, then prove that q.( p2 –1 ) = 2.p 21. If the point (x,y) is equidistant from the points (a+b, ba) and (ab,a+b,))prove that bx=ay. Or Determine the ratio in which the point (6,a) divides the join of A(3,1) and B(8,9). Also find the value of a.
22.Find the area of the triangle ABC formed by joining the midpoints of the sides of the triangle whose vertices are A( 4, 6 ), B( 3, 2 ) and C ( 5, 2 ).
Or Determine the ratio in which the point (6,a) divides the join of A(3,1) and B(8,9). Also find the value of a.
23. Construct a triangle similar to a given triangle ABC with its sides 3/5 th of the corresponding side of triangle ABC . It is given that AB= 5cm, angle B =600, and angle C = 550Write the steps of contraction also. 24. If triangle ABC is isosceles with AB= AC and C(o,r) is the incircle of triangle ABC touching BC at F, Prove that the point F bisects BC.
25A well with 10m inside diameter is dug 14m deep Earth taken out of it is spread all around to a width of 5m to form an embarkment. Find the height of embarkment. .
SECTION D ( Qns 26 – 30 carry 6marks each)
26. The mean of the following frequency distribution is 57.6 and the sum of the observations is 50. Find the missing frequencies f1 and f2. Class 020 2040 4060 6080 80100 100120 Frequency 7 f1 12 f2 8 5
27.Prove that the ratio of the area of two similar triangles is equal to the ratio of squares of their corresponding sides. Use the above in the following: Similar triangle ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of ? ABE and ? ACD. 28. A vertical tower is surmounted by a flagstaff of height h meters. At a point on the ground, the angles of elevation of the bottom and top of the flagstaff are ? and ? respectively. Prove that height of the tower is h tan? tan ?  tan? Or From a window (60 meters high above the ground) of a house in a street, the angles of elevation and depression of the top and the foot of another house on opposite side of street are 600 and 450 respectively. Show that the height of the opposite house is 60(1+?3) meters. 29.A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm., and its base of radius 3.5 cm, find the total surface area and volume of the article. Or The diameters of the ends of a bucket 45 cm high are 56 cm and 14 cm. Find its volume, the curved surface area and the total surface area. ( use ? = 22/7) 30. . Solve graphically: 2x +3 y = 4 and x y+3=0 Find the area of the triangle formed by these lines and the xaxis.
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