# 12 - Maths Unit 5 - Differential Calculus Applications - I

44 Questions | Total Attempts: 579  Settings  Prepard by, R VISVANATHAN, PG ASST IN MATHS, GHSS, PERIYATHACHUR, TINDIVANAM TK-605651   ; &nbs p; & www. Padasalai. Net

Related Topics
• 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)

• 26.
If a normal makes an angle  with positive axis then the slope of the curve at the point where the normal is drawn is  (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 27.
is = (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 28.
If , the velocity when the acceleration is zero is  (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 29.
If the velocity of a particle moving along a straight line is directly proportional to the square of its distance from  a fixed point on the line. Then its acceleration is proportional to (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 30.
If then the value of  is (1)  5  (2)  - 5  (3)  3  (4)  -3
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 31.
The  of Lagranges Mean Value Theorem for the function is (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 32.
The value of  in Rolle's Theorem for the function on  is  (1)   (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 33.
(1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 34.
The function   is increasing in (1)    (2)    (3)    (4)  everywhere
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 35.
Which of the following function is increasing in (1)    (2)    (3)     (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 36.
The function is decreasing in (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 37.
The function is (1)  an increasing function in   (2)  a decreasing function in   (3)  increasing in and decreasing in   (4)  decreasing in and increasing in
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 38.
In a given semi circle of diameter 4 cm a rectangle is to be inscribed. The maximum area of the rectangle is (1)  2  (2)  4  (3)  8  (4)  16
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 39.
The least possible perimeter of a rectangle of area is (1)  10  (2)  20  (3)  40  (4)  60
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 40.
If on then the absolute maximum value is (1)  2  (2)  3  (3)  4  (4)  5
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 41.
The curve is  (1)  concave upward for   (2)  concave downward for     (3)  everywhere concave upward  (4)  everywhere concave downward
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 42.
Which of the following curves is concave down? (1)    (2)    (3)    (4)
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 43.
The point of inflexion of the curve is at (1)  x=0  (2)  x=3  (3)  x=12  (4)  nowhere
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)

• 44.
The curve has a point of inflexion at x = 1 then (1)  a + b = 0  (2)  a + 3b = 0  (3)  3a + b = 0  (4)  3a + b = 1
• A.

(1)

• B.

(2)

• C.

(3)

• D.

(4)