12 - Maths Unit 5 - Differential Calculus Applications - I
44 Questions
| Attempts: 1019
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Prepard by, R VISVANATHAN, PG ASST IN MATHS, GHSS, PERIYATHACHUR, TINDIVANAM TK-605651 ; &nbs p; & www. Padasalai. Net
Questions and Answers
- 1.
The gradient of the curve at is (1) - 20 (2) 27 (3) - 16 (4) - 21- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 2.
The rate of change of area of a circle of radius is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 3.
The velocity of a particle moving along a straight line when at a distance from the origin is given by where and are constants. Then the accelaration is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 4.
The spherical snowball is melting in such a way that its volume is decreasing at a rate of . The rate at which the diameter is decreasing when the diameter is cms is (1) cm/min (2) cm/min (3) cm/min (4) cm/min
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 5.
The slope of the tangent to the curve at is (1) 3 (2) 2 (3) 1 (4) - 1
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 6.
The slope of the normal to the curve at the point whose coordinate is 2 is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 7.
The point on the curve at which the tangent is parallel to the - axis is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 8.
The equation of the tangent to the curve at the point is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 9.
The equation of the normal to the curve at the point is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 10.
The angle between the curves and is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 11.
The angle between the curve and for is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 12.
If the length of the diagonal of a square is increasing at the rate of What is the rate of increase of its area when the side is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 13.
If the normal to the curve makes an angle with the axis then the slope of the normal is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 14.
The parametric equations of the curve are (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 15.
The radius of a cylinder is increasing at the rate of and its altitude is decreasing at the rate of . The rate of change of volume when the radius is and the altitude is is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 16.
For what value of is the rate of increase of is twice the rate of increase of (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 17.
What is the surface area of a sphere when the volume is increasing at the same rate as its radius? (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 18.
If and increase at the rate of units per second, the rate of change of slope when is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 19.
The gradient of the tangent to the curve at the point where the curve cuts the axis is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 20.
If the volume of an expanding cube is increasing at the rate of then the rate of surface area when the volume of the cube is cubic cm is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 21.
The angle between the parabolas and at the origin is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 22.
For the curve ; the tangent line is parallel to the axis when is equal to (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 23.
The value of so that the curves and intersect orthogonally is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 24.
The Rolle's constant for the function on is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
- 25.
The value of of Lagranges Mean Value Theorem for when and is (1) (2) (3) (4)
- A.
(1)
- B.
(2)
- C.
(3)
- D.
(4)
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