CBSE Board Students Helpline

1. Given H.C.F (306, 657) = 9, find L.C.M (306, 657) (22335) 2. Prove that 3 + 2 √5 is irrational. 3. For which value of ‘P’ does the pair of equations have unique solutions.(p≠4) 4x + Py + 8 = 0 2x + 2y + 2 = 0 4. Find the length of the arc of a circle with radius 6cm if the angle of sector is 600.(44/7 cm) 5. Find the co-ordinates of the centre of a circle whose end points of the diameter are ( 3, -10 ) and ( 1, 4). (2,3) 6. If tan 2A = cot (A – 180), where 2A is an acute angle, find the value of A.(36◦) 6. Use Euclid’s algorithm to find the H.C.F of 135 and 225.(45) 7. Show that any positive integer is of the form 6q + 1, or 6q + 3, 0r 6q + 5, where q Is some integer? 8. Draw the graphs of the equation x – y + 1 = 0 and 3x + 2y – 2 = 0. 9. Determine the coordinates of the vertices of the triangle formed by these lines and the x – axis, and shade the triangular region. 10. A train travels 360 km at a uniform speed. If the speed had been km/hr more, it...

11. A motorboat whose speed is 18km/hr in still water takes 1 hour more to go 24km upstream than to return downstream to the same spot. Find the speed of the stream. (6km/h) 12. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are ( 0, -1 ), ( 2, 1 ) and ( 0, 3 ). (4 sq unit) 13. In fig. 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 = 7cm, find the area of the Shaded region.In a triangle, if the square of one side is equal to the sum of squares of the remaining two sides, prove that the angle opposite to the first side is a right angle. Using the above, do the following: ABC is an isosceles triangle with AB = BC. If AB2 = 2AC2, prove that ABC is a right Triangle. 14. As observed from the top of a 75m high lighthouse from the sea-level, the angles of Depression of two ships is 300 and 450. If one ship is exactly behind th...

21. If A and B are (1,4) and (5,2) respectively, find the coordinate of P when AP/PB=3/4.(19/7 , 22/7 ) 22. Find the area of the shaded region in figure, ABCD is a square of side 4 cm.(24/7 cm3) 23. If the surface area of a sphere is 616cm2, find its volume.(205.3 cm3) 24. Find the angle of elevation of the sun (Sun’s altitude) when the length of shadow of a vertical pole is equal to its height. (45) 25. What is the probability that an ordinary year has 53 Sundays?(1/7) 26. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides. Using this theorem, find the area of ABC if AB = 10 cm and area of  PQR= 12 cm2, PQ = 11cm. (10 cm2) 27. A solid cone, with height and base radius of 28 cm each, is cut along a plane parallel to its base so that the bottom and top radii of the remaining part are in the ratio 1 : 4. Find its volume. Also find the cost of painting its outer surface @ Re 0.70 per sq.cm. 28. A wooden toy i...

41. A solid cylinder of radius ‘r’ cm and height ‘h’ cm is melted and changed into a right circular cone of radius ‘4r; cm. Find the height of the cone. (h=3/16) 42. Find the value of ‘k’ for which the quadratic equation (k+1) x2 + (k+4) x + 1 = 0 has equal Roots.(2,-6) 43. Find the value of p for which the points (-1, 3), (2, p) and (5, -1) are collinear.(-3) 44. If the point P(x, y) is equidistant from the points A (5,1) and B(-1, 5), prove that 3x = 2y. 45. How many terms of the AP will give the sum zero.(-5,5) 46) Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre. 47. If the sum of first n terms of an A.P. is given by Sn = 4n2 – 3n, find the nth term of the A.P.  48. Obtain all the zeroes of the polynomial 3x4 + 6x3 - 2x3 – 10x + 5, if two of its zeroes are √5 / √3 and -√5 / √3. 49. One letter is selected at random from the word ‘UNNECESSARY’. Find the probability of selecting an E. (2/11) 50. Three cubes e...

31. The following table gives weekly wages in rupees of workers in a certain commercial organization. The frequency of class 49-52 is missing. It is known that the mean frequency distribution is 47.2. Find the missing frequency.(44) Weekly Wages (Rs.) 40-43 43-46 46-49 49-52 52-55 Number of workers 31 58 60 ? 27 32. The area of an equilateral triangle is 17300 cm2. With each vertex of the triangle as centre, a circle is drawn with a radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles.( π = 3.14 and √3 =1.73 )(1600cm2) 33. A solid composed of a cylinder with hemi spherical ends . The whole height of the solid is 19cm and the radius of the cylinder is 3.5cm. Find the weight of the solid if 1cm3 of the metal weighs 4.5g. (2111.8g or 2.1kg) 34. Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level will rise ...

61. If a line is drawn parallel to one side of a triangle, prove that the other two sides are divided in the same ratio. Using the above result, find AB when in ∆ABC , DE ║ BC so that AD = 2.4 cm , AE = 3.2 cm and EC = 4.8 cm.(6 cm) 62. In a triangle, if square of one side is equal to the sum of the squares of other two sides, then angle opposite the first side is a right angle.using the converse of above theorem determines the length of an altitude of an equilateral triangle of side 2a.(√3a) 63. The ratio of areas of similar triangles is equal to the ratio of the squares on the corresponding sides. Prove.Using the above theorem, prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangle described on the diagonal.  64. If the radii of the ends of a bucket 45cm high are 28cm and 7cm.Find its capacity and surface area.(48510 cm3 , 5461.5 cm2) 65. A bucket is in the form of a frustum of a cone and holes 28.490 litres of ...

51. The lengths of two cylinders are in the ratio 3:1 and their diameters are in the ratio 1:2 .Calculate the ratio of their volumes.(3:4) 52. Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number which is a number of 3 or 7?(2/5) 53. Find the least number of coins of diameter 2.5 cm and height 3 mm which are to be melted to form a solid cylinder of radius 3 cm and height 5 cm.(96) 54. The radii of two cylinders are in the ratio 2:3 and their heights are in 5:3. Calculate the ratio of their volume.(20/81) 55. The volume of two spheres are in the ratio 64 : 27. Find their radii if the sum of their radii is 21cm.the height of a cylinder is 15 cm. the curved surface area is 660 cm². find the radius .(7 cm) 56. The circumference of the edge f a hemispherical bowl is 132 cm. find the capacity of the bowl.(19404 cm3) 57. An electric pole is 10 m high. If its shadow is 10√3 m in length. Find the elevation...

71. A solid iron pole consists of cylinder of height 220cm and base diameter 24cm, which is surmounted by another cylinder of height 60cm and radius 8cm. find the mass of the pole, given that 1cm3 of iron has approximately 8g mass. (Use =3.14).(892.26) 72. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be of the volume of the given cone, at what height above the base, the section has been made? (20) 73. If the nth terms of an A.P is (2n + 1), find the sum of first n terms of the A.P. 74. Find the sum of first 10 terms of an A.P., in which 3rd term is 7 and 7th term is two more than thrice of its 3rd term. 75. If the sum of n terms of an A.P.is same as the sum of its n terms, show that the sum of its (m + n) terms is zero. 76. Find the sum of first n odd natural numbers. 77. If the 8th terms of an A.P.is 31 and the 15th terms is 16 more than the 11th terms find the sum of first 20 terms. 78. How many terms of A.P.: 24,...

90. A is a point on the y-axis who’s ordinate is 5 and B is the point (3, 1). Calculate the length of AB. 91. The mid point of the line segment joining (2a, 4) and (2, 3b) is (1, 2a +1). Find the values of a and Prove that the points (3, 0), (6, 4) and (-1, 3) are vertices of a right-angled triangle. Also, prove that these are the vertices of an isosceles triangle. 92. In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by they-axis? Also, find the coordinates of the point of division. 93. Show that the points A (1, 2), B(S, 4), C(3, 8) and D(— 1,6) are the vertices of a square. 94. Find the co-ordinates of the point equidistant from three given points A (5, 1), B (- 3, -7) and C (7, -1). 95. Find the value of p for which the point (-1, 3), (2, p) and (5, -1) are collinear. 96. If (-2, -1); (a, 0); (4, b) and (1, 2) are the vertices of a parallelogram, find the values of a and b. 97. Prove that the points (-4, -1); (-2, -4); (4, 0) and (2, 3) are vertices ...

Sample Paper – 2009 Class – X Subject – Mathematics Section-A 1. Without actually performing the long division, state whether the following no. will have a terminating decimal expansion. 2. If tan A = cot B prove A + B =900. 4. Find the circumference of circle whose area is 6.16 cm2. 5. Write the frequency distributor from following data : Marks (more than) 0 10 20 30 40 50 60 70 upto 80 No. of students 100 97 87 73 50 25 6 2 6. If Cos and tan , find value of sin ( ), where are acute angles. 7. The sides of traingle are given below, Determine the given triangle is right angle or not a = 9 cm, b = 12 cm, and c = 15 cm. 8. If Sin A = , Calculate tan A. 9. PErimeter of a sector = _________________________ 10. Empirical relation between the three measures of tendency. Section - B 11. For what value of k the following system of eq. will be inconsistent. kx + 2y - 5 = 0 8x + ky - 10 = 0 12. Show that (-1, -1), (5, 7) & (8, 11) are collinear. 15. Five cards : tan, Jack, queen a...

Sample Paper – 2009 Class – X Subject – Mathematics Section-A 1. Without actually performing the long division, state whether the following no. will have a terminating decimal expansion. 2. If tan A = cot B prove A + B =900. 4. Find the circumference of circle whose area is 6.16 cm2. 5. Write the frequency distributor from following data : Marks (more than) 0 10 20 30 40 50 60 70 upto 80 No. of students 100 97 87 73 50 25 6 2 6. If Cos and tan , find value of sin ( ), where are acute angles. 7. The sides of traingle are given below, Determine the given triangle is right angle or not a = 9 cm, b = 12 cm, and c = 15 cm. 8. If Sin A = , Calculate tan A. 9. PErimeter of a sector = _________________________ 10. Empirical relation between the three measures of tendency. Section - B 11. For what value of k the following system of eq. will be inconsistent. kx + 2y - 5 = 0 8x + ky - 10 = 0 12. Show that (-1, -1), (5, 7) & (8, 11) are collinear. 15. Five cards : tan, Jack, queen a...

Sample Paper – 2009-2010 Class – X Subject – Mathematics 1 A die is thrown. Find the probability of getting a number greater than 4. 1/3 2 In a simultaneous throw of a pair of dice, find the probability of getting 8 as sum. 5/36 3 Three coins are tossed together. Find the probability of getting exactly two heads. 3/8 4 A bag contains 5 white and 7 red balls. One ball is drawn at random. What is the probability that the ball drawn is white? 5/12 5 There are 30 cards, of same size, in a bag on which numbers 1 to 30 are written. One card is taken out of the bag at random. Find the probability that the number on the selected card is not divisible by 3 2/3 6 A bag contains 5 red, 8 white and 7 black balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is (i) red or white (ii) not black (iii) neither white nor black. 13/20, 13/20 1/4 7 A bag contains 8 red, 6 white and 4 black balls. A ball is drawn a random from the bag. Find the probability that the dra...

Sample Paper – 2009 Class – X Subject - Mathematics Time : 3 Hours. M. Marks: 80. Note : Q. No. 1 to 10 each 1 mark, 11 to 15 each 2 marks, 16 to 25 each 3 marks, 26 to 30 each 6 marks. 1. Find the HCF of 6 and 20 by prime factorization. 2. Out of three equations which two of them have infinite many solutions : 3x – 2y = 4, 6x + 2y = 4, 9x – 6y = 12. 3. Find the nature of the roots of quadratic equation: 2x2 – 4x + 3 = 0. 4. Is 310 is a term of the A.P. 3, 8, 13, 18………..? 5. The areas of two similar triangles ABC and DEF are 64 cm2 and 121 cm2 respectively. If EF = 13.2 cm, then find BC. 6. Show that the tangent lines at the end points of a diameter of a circle are parallel. 7. If sin 3A = cos ( A – 60 ) where 3A and ( A – 6 ) are acute angles, then find the value of A. 8. A chord of a circle of radius 7 cm subtends a right angle...

Max. Marks: 50 Find the ratio in which the point (-3,p) divides the line segment joining the points (-5, -4) and (-2,3). Also find the value of p.(3) Determine the ration in which the line 3x + y – 9 = 0 divides the segment joining the pt (1,3) and (2,7).(3) Find the value of x if the distance between the points (x, 1) and (3,2) is 5. (3) If the mid points of sides of the triangle are (2,6), (6.4) and (4,2) find its vertices.(5) The coordinates of the mid-point of the line joining the points (3p, 4) and (-2, 2q) are (5, p). Find the values of p and q. Find the ratio in which the line-segment joining the points (6, 4) and (1, -7) is divided by x-axis. Find the value of m for which the points with coordinates (3, 5), (m, 6) and are collinear. Find the value of k for which the points with coordinates (3, 2), (4, k) and (5, 3) are collinear. If the point P(x, y) is equidistant from the points A (5, 1) and B (-1, 5), prove that 3x - 2y = 0(5) The line joining the points (2, 1) and (5, -8) i...

Subject: Mathematics Find the ratio in which the point (-3,p) divides the line segment joining the points (-5, -4) and (-2,3). Also find the value of p.(3) Determine the ration in which the line 3x + y – 9 = 0 divides the segment joining the pt (1,3) and (2,7).(3) Find the value of x if the distance between the points (x, 1) and (3,2) is 5. (3) If the mid points of sides of the triangle are (2,6), (6.4) and (4,2) find its vertices.(5) The coordinates of the mid-point of the line joining the points (3p, 4) and (-2, 2q) are (5, p). Find the values of p and q. Find the ratio in which the line-segment joining the points (6, 4) and (1, -7) is divided by x-axis. Find the value of m for which the points with coordinates (3, 5), (m, 6) and are collinear. Find the value of k for which the points with coordinates (3, 2), (4, k) and (5, 3) are collinear. If the point P(x, y) is equidistant from the points A (5, 1) and B (-1, 5), prove that 3x - 2y = 0(5) The line joining the poi...