Loading...
Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h. The relation between fuel consumption F (l/100 km) and speed V (km/h) under some constraints is given as F = V²/500 – V/4 + 14. On the basis of the above information, answer the following questions :
Given a curve y = 7x − x³ and x increases at the rate of 2 units per second. The rate at which the slope of the curve is changing, when x = 5 is :
The surface area of a cube increases at the rate of 72 cm²/sec. Find the rate of change of its volume, when the edge of the cube measures 3 cm.
If the distance travelled by a particle in t seconds is given by S = 72t + 3t² − t³, then time taken by the particle to come to rest is :
At a birthday party, children are being served orange juice in conical cups, as shown in the figure. Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm³/s. On the basis of the above information, answer the following questions :
A spherical balloon loses its volume due to escape of air from it in such a way that decrease of volume at any instant is proportional to its surface area. Show that the radius is decreasing at a constant rate.
© 2026 PadhAiPro. This question is provided for educational purposes.
