question_answer53) Find the equation of a curve passing through the point (0, –2), given that at any point (x, y) on the curve, the product of the slope of its tangent any y-coordinate of the point is equal to the x-coordinate of the point.View Answer play_arrow
question_answer54) At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (–4, –3). Find the equation of the curve, given that it passes through (–2, 1)View Answer play_arrow
question_answer55) The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units, find the radius of balloon after t second.View Answer play_arrow
question_answer58) In a culture the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. It how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present.View Answer play_arrow
question_answer77) Which of the following is a homogeneous differential equation ? (a) (4x + 6y + 5) dy – (3y + 2x + 4) dx = 0 (b) xy dx – (x3 + y3) dy = 0 (c) (x3 + 2y2) dx + 2xy dy = 0 (d) y2 dx + (x2 – xy – y2) dy = 0View Answer play_arrow
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