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Two ships A and B are sailing straight away from a fixed point O along routes such that ∠AOB is always 120°. At a certain instance, OA=8km,OB=6km and the ship A is sailing at the rate of 20km/hr while the ship B sailing at the rate of 30km/hr. Then the distance between A and B is changing at the rate (in km/hr ):

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Important Questions on Application of Derivatives

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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
The value of 24.99 is
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
Using differentiation, approximate value of fx=x2-2x+1 at x=2.99 is ….
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
The sides of an equilateral triangle are increasing at the rate of 4 cm/sec. The rate at which its area is increasing, when the side is 14 cm
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder in cm3/min, when the radius is 2 cm and the height is 3 cm is
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
If the error committed in measuring the radius of the circle is 0.05%, then the corresponding error in calculating the area is
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
The position of a moving car at time t is given by f(t)=at2+bt+c, t>0, where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval t1,t2 is attained at the point:
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
A spherical iron ball of 10cm radius is coated with a layer of ice of uniform thickness that melts at a rate of 50cm3/min . When the thickness of ice is 5cm , then the rate (in cm/min .) at which the thickness of ice decreases, is:
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
The radius of a circle is increasing at the rate 2 cm/sec. The rate at which its area is increasing, when the radius of the circle is 5 decimeters, is
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is tan-112. Water is poured into it at a constant rate of 5 cubic m/min. Then the rate (in m/min), at which the level of water is rising at the instant when the depth of water in the tank is 10 m; is:
MEDIUM
Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm3/min. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of the ice decreases, is :
MEDIUM
Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
An inverted conical flask is being filled with water at the rate of 3 cm3 sec-1. The height of the flask is 10 cm and the radius of the base is 5 cm. How fast is the water level rising when the level is 4 cm?
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
If the volume of spherical ball is increasing at the rate of 4π cm3/sec then the rate of change of its surface area when the volume is 288π cm3 is
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
If the side of a cube is increased by 5%, then the surface area of a cube is increased by
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
If the surface area of a cube is increasing at a rate of 3.6cm2/sec, retaining its shape; then the rate of change of its volume (in cm3/sec), when the length of a side of the cube is 10cm, is:
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
If the relative errors in the base radius and the height of a cone are same and equal to 0.02, then the percentage error in the volume of that cone is
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
A ladder of 5 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate 3 m/sec. The height of the upper end (in meters) while it is descending at the rate of 4 m/sec, is
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
The displacement of a particle at the time t is given by s=1+t, then its acceleration a is proportional to
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
A 2m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25cm/sec , then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is:
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
If the volume of a spherical ball is increasing at the rate of 4π cc/sec then the rate of increase of its radius in cm/sec, when the volume is 288π cc is 
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Mathematics>Differential Calculus>Application of Derivatives>Rate of Change of Quantities
A man 6 ′ tall moves away from a source of light 20 ′ above the ground level, his rate of walking being 4m/h. At what rate is the tip of his shadow moving?