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Free download in PDF Class 12 Maths Chapter 6 Application of Derivatives Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>
(1)
The combined resistance R of two resistors R1 and R2 (R1, R2 > 0) is given by 1/R=1/R1+1/R2. If R1 + R2 = C (a constant), then maximum resistance R is obtained if
[A]
R1 > R2
[B]
R1 < R2
[C]
R1 = R2
[D]
None of these
(2)
Find the height of a cylinder, which is open at the top, having a given surface area, greatest volume and of radius r.
[A]
r
[B]
2r
[C]
r/2
[D]
3πr/2
(3)
The function f(x) = x + 4/x has
[A]
a local maxima at x = 2 and local minima at x = -2
[B]
local minima at x = 2, and local maxima at x = -2
[C]
absolute maxima at x = 2 and absolute minima at x = -2
[D]
absolute minima at x = 2 and absolute maxima at x = -2
Answer: local minima at x = 2, and local maxima at x = -2
(4)
The coordinates of the point on the parabola y2 = 8x which is at minimum distance from the circle x2 + (y + 6)2 = 1 are
[A]
(2, -4)
[B]
(18, -12)
[C]
(2, 4)
[D]
none of these
(5)
The function f(x) = cot-1 x + x increases in the interval
[A]
(1, ∞)
[B]
(-1, ∞)
[C]
(0, ∞)
[D]
(-∞, ∞)
[A]
an increasing function
[B]
a decreasing function
[C]
an even function
[D]
None of these
Answer: an increasing function
(7)
The position of a point in time ‘t’ is given by x = a + bt – ct2, y = at + bt2. Its acceleration at time ‘t’ is
(a)
(b)
(c)
[A]
b – c
[B]
b + c
[C]
2b – 2c
(8)
The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases, when the side is 10 cm, is
[A]
√3 cm2/s
[B]
10 cm2/s
[C]
10√3 cm2/s
[D]
10/3√ cm2/s
(9)
The radius of a cylinder is increasing at the rate of 3 m/s and its height is decreasing at the rate of 4 m/s. The rate of change of volume when the radius is 4 m and height is 6 m, is
[A]
80π cu m/s
[B]
144π cu m/s
[C]
80 cu m/s
[D]
64 cu m/s
(10)
f(x) = 3x2 + 6x + 8, x ∈ R
[A]
2
[B]
5
[C]
-8
[D]
does not exist
(11)
Find the approximate value of f(3.02), where f(x) = 3x2 + 5x + 3
[A]
45.46
[B]
45.76
[C]
44.76
[D]
44.46
(12)
If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximating error in calculating its volume.
[A]
2.46π cm3
[B]
8.62π cm3
[C]
9.72π cm3
[D]
7.46π cm3
(13)
If there is an error of a% in measuring the edge of a cube, then percentage error in its surface area is
[A]
2a%
[B]
a/2 %
[C]
3a%
[D]
None of these
(14)
If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is
[A]
1%
[B]
2%
[C]
3%
[D]
4%
(15)
Tangents to the curve x2 + y2 = 2 at the points (1, 1) and (-1, 1) are
[A]
parallel
[B]
perpendicular
[C]
intersecting but not at right angles
[D]
none of these
(16)
Find a point on the curve y = (x – 2)2. at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).
[A]
(3, 1)
[B]
(4, 1)
[C]
(6,1)
[D]
(5, 1)
(17)
The tangent to the curve y = x2 + 3x will pass through the point (0, -9) if it is drawn at the point
[A]
(0, 1)
[B]
(-3, 0)
[C]
(-4, 4)
[D]
(1, 4)
(18)
The tangent to the curve y = 2x2 -x + 1 is parallel to the line y = 3x + 9 at the point
[A]
(2, 3)
[B]
(2, -1)
[C]
(2, 1)
[D]
(1, 2)
(19)
The two curves x3 – 3xy2 + 5 = 0 and 3x2y – y3 – 7 = 0
[A]
cut at right angles
[B]
touch each other
[C]
cut at an angle π/4
[D]
cut at an angle π/3
Answer: cut at right angles
(20)
The tangent to the parabola x2 = 2y at the point (1, 1/2) makes with the x-axis an angle of
[A]
0°
[B]
45°
[C]
30°
[D]
60°
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