C B A P 4 cm 3 cm WiZiQ.com presents En-depth analysis MATHEMATICS Question Paper CBSE X 2008 Section A 1. Write the prime factors of 84. 2. Write the polynomial whose zeros are -5 and 4. 3. Is x = 2, y = 3 a solution of the linear equation 2x+3y-13 = 0 ? 4. Write the next term of the AP 2 , 8 , 18…… 5. If cosA = 3/5, find 9 cot2A – 1. 6. If the probability of winning a game is 5/11, what is the probability of losing it? 7. In figure angle ABC = 900 and P is the mid-point of AC. Find the length of AP. 9. The radii of two circles are 3 cm and 4 cm. Find the radius of a circle whose area is equal to the sum of the areas of the two circles. 10. The point of intersection of the ogives (more than and less than type) is given by (20.5, 30.4). What is the median? SECTION-B 11. Find the zeros of the quadratic polynomial 2x2 – 9 – 3x and verify the relationship between the zeros and the coefficients. 12. If 3 cotq = 4, find the value of q qq q 5sin 3cos 5sin 3cos +− Or Without using trigonometric tables, find the value of the following: 0 0 0 2 00 2 0 0 2 tan15 tan 45 tan 75 sec70 cot 20 cos 70 tan 20 + + ec 13. If the vertices of a triangle are (1, k), (4, -3), (-9, 7) and is area is 15square units, find the value of k. 15. A box contains cards bearing numbers from 6 to 70. If one card is drawn at random from the box, find the probability that it bears (i) a one digit number, (ii) a number divisible by 5. SECTION – C 16. Using prime factorization method, find the HCF and LCM of 72, 126 and 168. Also show that HCF X LCM ¹ Product of the three numbers. 17. Represent the following system of linear equations graphically. From the graph, find the points where the lines intersect x-axis: 2x – y = 2, 4x – y = 8 18. Solve the following system of equations for x and y: (a-b)x + (a+b)y = a2 – 2ab – b2 (a+b)(x+y) = a2 + b2 Or, For what value of ‘m’ will the equation 2mx2 – 2(1+2m)x + (3+2m) = 0 have real but distinct roots? When will the roots be equal? 19. Prove that: q q q qq q cos cot cos sin 1cos sin 1 = + + −− + ec Or, Prove that: (cosecq -sin q )(secq -cosq ) = 1 /(tanq + cotq ) 20. Find the sum of all two digit natural numbers which when divided by 3 yeild 1 as remainder. 21. The line joining the points (2, -1) and (5, -6) is bisected at P. If lies on the line 2x + 4y + k = 0, find the value of k. 22. In triangle ABC, if AD is the median, show that AB2 + AC2 = 2(AD2+BD2) Or, In triangle ABC, angle A is acute. BD and CE are perpendicular on AC and AB respectively. Prove that AB X AE = AC X AD 23. Show that the points (5, 6), (1, 5), (2, 1) and (6, 2) are the vertices of a square. 24. Draw a circle of radius 4 cm. From a point P, 7cm from the centre of the circle, draw a pair of tangents to the circle. Measure the length of each tangent segment. 25. In figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 14cm, find the area of the shaded region. SECTION – D 26. Rs 6500 is divided equally among a certain number of persons. Had there been 15 more persons, each would have got Rs 30 less. Find the original number of person. Or, A train travels 360 km at a uniform speed. If the speed of the train had been 5 km/hr more, it would have taken one hour less for the same journey. Find the original speed of the train. 27. The angle of elevation of a cloud from a point 60 m above a lake is 300 and the angle of depression of the reflection of the cloud in the lake in 600. Find the height of the cloud. 28. Prove that the lengths of the tangents drawn from an external point to a circle are equal. Using the above do the following: Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre. Or, Prove that the ratio of the areas of two similar triangles is equal ot the ratio of the squares on their corresponding sides. Using the above, prove the following: If the areas of twp similar triangles are equal, prove that they are congruent. 29. A bucket is in the form of a frustum of a cone whose radii of bottom and top are 7cm and 28cm respectively. If the capacity of the bucket is 21560 cm3, find the whole surface area of the bucket.