Rate of Change
Application of Derivatives

85123 If \(x\) and \(y\) are the sides of two squares such that \(y=x-x^{2}\), then what is the rate of change of the area of second square with respect to the area of first square?

1 \(\left(1-x^{2}\right) x\)
2 \(2\left(1-x^{2}\right) x\)
3 \(2 x^{2}-3 x+1\)
4 \(2\left(2 x^{2}-3 x+1\right)\)
Application of Derivatives

85124 A balloon is coming down at the rate of 4 \(\mathrm{m} / \mathrm{min}\) and its angle of elevation is \(45^{\circ}\) from a point on the ground which has been reduced to \(3^{\circ}\), after \(10 \mathrm{~min}\). Balloon will be on the ground at a distance of how many metres from the observer?

1 \(20 \sqrt{3} \mathrm{~m}\)
2 \(20(3+\sqrt{3}) \mathrm{m}\)
3 \(10(3+\sqrt{3}) \mathrm{m}\)
4 None of these
Application of Derivatives

85125 The radius of a cylinder is increasing at the rate of \(2 \mathrm{~m} / \mathrm{s}\) and its height is decreasing at the rate of \(3 \mathrm{~m} / \mathrm{s}\). When the radius is \(3 \mathrm{~m}\) and height is \(5 \mathrm{~m}\), then the volume of the cylinder would change at the rate of

1 \(87 \pi \mathrm{m}^{3} / \mathrm{s}\)
2 \(33 \pi \mathrm{m}^{3} / \mathrm{s}\)
3 \(27 \pi \mathrm{m}^{3} / \mathrm{s}\)
4 \(15 \pi \mathrm{m}^{3} / \mathrm{s}\)
Application of Derivatives

85126 A cylindrical tank of radius \(2 \mathrm{~m}\) is being filled with rice at the rate of 314 cubic \(\mathrm{m} / \mathrm{h}\). The depth of the rice is increasing at the rate of

1 \(25 \mathrm{~m} / \mathrm{h}\)
2 \(0.25 \mathrm{~m} / \mathrm{h}\)
3 \(1 \mathrm{~m} / \mathrm{h}\)
4 \(\frac{3}{4} \mathrm{~m} / \mathrm{h}\)
Application of Derivatives

85127 The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :

1 9
2 10
3 11
4 12
Application of Derivatives

85123 If \(x\) and \(y\) are the sides of two squares such that \(y=x-x^{2}\), then what is the rate of change of the area of second square with respect to the area of first square?

1 \(\left(1-x^{2}\right) x\)
2 \(2\left(1-x^{2}\right) x\)
3 \(2 x^{2}-3 x+1\)
4 \(2\left(2 x^{2}-3 x+1\right)\)
Application of Derivatives

85124 A balloon is coming down at the rate of 4 \(\mathrm{m} / \mathrm{min}\) and its angle of elevation is \(45^{\circ}\) from a point on the ground which has been reduced to \(3^{\circ}\), after \(10 \mathrm{~min}\). Balloon will be on the ground at a distance of how many metres from the observer?

1 \(20 \sqrt{3} \mathrm{~m}\)
2 \(20(3+\sqrt{3}) \mathrm{m}\)
3 \(10(3+\sqrt{3}) \mathrm{m}\)
4 None of these
Application of Derivatives

85125 The radius of a cylinder is increasing at the rate of \(2 \mathrm{~m} / \mathrm{s}\) and its height is decreasing at the rate of \(3 \mathrm{~m} / \mathrm{s}\). When the radius is \(3 \mathrm{~m}\) and height is \(5 \mathrm{~m}\), then the volume of the cylinder would change at the rate of

1 \(87 \pi \mathrm{m}^{3} / \mathrm{s}\)
2 \(33 \pi \mathrm{m}^{3} / \mathrm{s}\)
3 \(27 \pi \mathrm{m}^{3} / \mathrm{s}\)
4 \(15 \pi \mathrm{m}^{3} / \mathrm{s}\)
Application of Derivatives

85126 A cylindrical tank of radius \(2 \mathrm{~m}\) is being filled with rice at the rate of 314 cubic \(\mathrm{m} / \mathrm{h}\). The depth of the rice is increasing at the rate of

1 \(25 \mathrm{~m} / \mathrm{h}\)
2 \(0.25 \mathrm{~m} / \mathrm{h}\)
3 \(1 \mathrm{~m} / \mathrm{h}\)
4 \(\frac{3}{4} \mathrm{~m} / \mathrm{h}\)
Application of Derivatives

85127 The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :

1 9
2 10
3 11
4 12
Application of Derivatives

85123 If \(x\) and \(y\) are the sides of two squares such that \(y=x-x^{2}\), then what is the rate of change of the area of second square with respect to the area of first square?

1 \(\left(1-x^{2}\right) x\)
2 \(2\left(1-x^{2}\right) x\)
3 \(2 x^{2}-3 x+1\)
4 \(2\left(2 x^{2}-3 x+1\right)\)
Application of Derivatives

85124 A balloon is coming down at the rate of 4 \(\mathrm{m} / \mathrm{min}\) and its angle of elevation is \(45^{\circ}\) from a point on the ground which has been reduced to \(3^{\circ}\), after \(10 \mathrm{~min}\). Balloon will be on the ground at a distance of how many metres from the observer?

1 \(20 \sqrt{3} \mathrm{~m}\)
2 \(20(3+\sqrt{3}) \mathrm{m}\)
3 \(10(3+\sqrt{3}) \mathrm{m}\)
4 None of these
Application of Derivatives

85125 The radius of a cylinder is increasing at the rate of \(2 \mathrm{~m} / \mathrm{s}\) and its height is decreasing at the rate of \(3 \mathrm{~m} / \mathrm{s}\). When the radius is \(3 \mathrm{~m}\) and height is \(5 \mathrm{~m}\), then the volume of the cylinder would change at the rate of

1 \(87 \pi \mathrm{m}^{3} / \mathrm{s}\)
2 \(33 \pi \mathrm{m}^{3} / \mathrm{s}\)
3 \(27 \pi \mathrm{m}^{3} / \mathrm{s}\)
4 \(15 \pi \mathrm{m}^{3} / \mathrm{s}\)
Application of Derivatives

85126 A cylindrical tank of radius \(2 \mathrm{~m}\) is being filled with rice at the rate of 314 cubic \(\mathrm{m} / \mathrm{h}\). The depth of the rice is increasing at the rate of

1 \(25 \mathrm{~m} / \mathrm{h}\)
2 \(0.25 \mathrm{~m} / \mathrm{h}\)
3 \(1 \mathrm{~m} / \mathrm{h}\)
4 \(\frac{3}{4} \mathrm{~m} / \mathrm{h}\)
Application of Derivatives

85127 The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :

1 9
2 10
3 11
4 12
Application of Derivatives

85123 If \(x\) and \(y\) are the sides of two squares such that \(y=x-x^{2}\), then what is the rate of change of the area of second square with respect to the area of first square?

1 \(\left(1-x^{2}\right) x\)
2 \(2\left(1-x^{2}\right) x\)
3 \(2 x^{2}-3 x+1\)
4 \(2\left(2 x^{2}-3 x+1\right)\)
Application of Derivatives

85124 A balloon is coming down at the rate of 4 \(\mathrm{m} / \mathrm{min}\) and its angle of elevation is \(45^{\circ}\) from a point on the ground which has been reduced to \(3^{\circ}\), after \(10 \mathrm{~min}\). Balloon will be on the ground at a distance of how many metres from the observer?

1 \(20 \sqrt{3} \mathrm{~m}\)
2 \(20(3+\sqrt{3}) \mathrm{m}\)
3 \(10(3+\sqrt{3}) \mathrm{m}\)
4 None of these
Application of Derivatives

85125 The radius of a cylinder is increasing at the rate of \(2 \mathrm{~m} / \mathrm{s}\) and its height is decreasing at the rate of \(3 \mathrm{~m} / \mathrm{s}\). When the radius is \(3 \mathrm{~m}\) and height is \(5 \mathrm{~m}\), then the volume of the cylinder would change at the rate of

1 \(87 \pi \mathrm{m}^{3} / \mathrm{s}\)
2 \(33 \pi \mathrm{m}^{3} / \mathrm{s}\)
3 \(27 \pi \mathrm{m}^{3} / \mathrm{s}\)
4 \(15 \pi \mathrm{m}^{3} / \mathrm{s}\)
Application of Derivatives

85126 A cylindrical tank of radius \(2 \mathrm{~m}\) is being filled with rice at the rate of 314 cubic \(\mathrm{m} / \mathrm{h}\). The depth of the rice is increasing at the rate of

1 \(25 \mathrm{~m} / \mathrm{h}\)
2 \(0.25 \mathrm{~m} / \mathrm{h}\)
3 \(1 \mathrm{~m} / \mathrm{h}\)
4 \(\frac{3}{4} \mathrm{~m} / \mathrm{h}\)
Application of Derivatives

85127 The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :

1 9
2 10
3 11
4 12
Application of Derivatives

85123 If \(x\) and \(y\) are the sides of two squares such that \(y=x-x^{2}\), then what is the rate of change of the area of second square with respect to the area of first square?

1 \(\left(1-x^{2}\right) x\)
2 \(2\left(1-x^{2}\right) x\)
3 \(2 x^{2}-3 x+1\)
4 \(2\left(2 x^{2}-3 x+1\right)\)
Application of Derivatives

85124 A balloon is coming down at the rate of 4 \(\mathrm{m} / \mathrm{min}\) and its angle of elevation is \(45^{\circ}\) from a point on the ground which has been reduced to \(3^{\circ}\), after \(10 \mathrm{~min}\). Balloon will be on the ground at a distance of how many metres from the observer?

1 \(20 \sqrt{3} \mathrm{~m}\)
2 \(20(3+\sqrt{3}) \mathrm{m}\)
3 \(10(3+\sqrt{3}) \mathrm{m}\)
4 None of these
Application of Derivatives

85125 The radius of a cylinder is increasing at the rate of \(2 \mathrm{~m} / \mathrm{s}\) and its height is decreasing at the rate of \(3 \mathrm{~m} / \mathrm{s}\). When the radius is \(3 \mathrm{~m}\) and height is \(5 \mathrm{~m}\), then the volume of the cylinder would change at the rate of

1 \(87 \pi \mathrm{m}^{3} / \mathrm{s}\)
2 \(33 \pi \mathrm{m}^{3} / \mathrm{s}\)
3 \(27 \pi \mathrm{m}^{3} / \mathrm{s}\)
4 \(15 \pi \mathrm{m}^{3} / \mathrm{s}\)
Application of Derivatives

85126 A cylindrical tank of radius \(2 \mathrm{~m}\) is being filled with rice at the rate of 314 cubic \(\mathrm{m} / \mathrm{h}\). The depth of the rice is increasing at the rate of

1 \(25 \mathrm{~m} / \mathrm{h}\)
2 \(0.25 \mathrm{~m} / \mathrm{h}\)
3 \(1 \mathrm{~m} / \mathrm{h}\)
4 \(\frac{3}{4} \mathrm{~m} / \mathrm{h}\)
Application of Derivatives

85127 The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :

1 9
2 10
3 11
4 12