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 each of sides 5 cm are joined end to end .Find the surface area of the resulting solid. 250
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 each of sides 5 cm are joined end to end .Find the surface area of the resulting solid. 250
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