Hardayal Public School Holiday Assignment of ... - Educomp Online

55. A stone is dropped in a quite lake waves move in a circle at a speed of 3.5cm/s.How fast is the enclosed area increasing when the radius of wave is 7.5cm?Ans : 165cm 2 /s56. The radius of a cylinder is increasing at 2cm/s and its height is decreasing at3cm/s. Find the rate of change of volume when radius = 3cm and height = 5cm.Ans : 33 π57. A conical vessel 10m high is filled with water at a uniform rate of 1.5cm 3 /s. If theradius of base is 5m.58. Water is running into a conical vessel 12cm deep and 4cm is radius at the rate of0.2 cm 3 /s. When the water is 6cm deep. Find at what rate water level is rising (ii)S.A. of water increasing:Ans:1 1,20 π 1559. At what points on the ellipse 16x 2 + 9y 2 = 400 does the ordinate change at thesame rate at which the abscissa increase.Ans:⎛ 16 ⎞ ⎛ − 16 ⎞⎜ 3 , ⎟;⎜ − 3, ⎟⎝ 3 ⎠ ⎝ 3 ⎠60. A man of height 180cm is moving away from a lamp post at the rate of 1.2m/s. Ifthe height of lamp post is 4.5 find the rate at which his shadow lengthening?(Ans : 0.8m/s)61.4A particle moves along a curve y = x2 + 5 . Find the points on the curve at3which y-cordinate change twice as fast as abscissa.Ans:⎛ 5 ⎞ ⎛ 1 ⎞⎜1, ⎟;⎜ − 1, ⎟⎝ 3 ⎠ ⎝ 3 ⎠62. Using differentiate find the approximate value of the following:(i) 49 . 5 (ii) 401 (iii) 0 . 037 (iv) p 4 – 620 = 0find p(v)30 . 007 (vi) 0 . 48 (vii) 26 (viii) 37 (ix)0 .082Ans : (i) 7.04 (ii) 20.025 (iii) 0.1925 (iv) 4.99 (v)0.192(vi) 0.693 (vii) 5.1 (viii) 6.083 (ix) 0.28763. Find the equation of tangent and normal to the curve x = Cos t, y = Sin t at t =π4Ans : x + y – 2 = 0, x – y= 064. Find the equation of tangent to the curve x + y2 2= a ⎛ a a⎟ ⎞⎜ ,⎝ 4 4 ⎠Ans : 2x + 2y= a 2