NCERT Solutions for class 12 Maths | Chapter 6 - Application of Derivatives

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Questions
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

Answer:R1 = R2
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

Answer:r
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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

Answer:(2, -4)
5 The function f(x) = cot-1 x + x increases in the interval
A (1, ∞)
B (-1, ∞)
C (0, ∞)
D (-∞, ∞)

Answer:(-∞, ∞)
6 Class 12 Maths Application of Derivatives
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
D

Answer:
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

Answer: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

Answer:80π cu m/s
10 f(x) = 3x2 + 6x + 8, x ∈ R
A 2
B 5
C -8
D does not exist

Answer: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

Answer:45.46
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

Answer:9.72π 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

Answer:a/2 %
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%

Answer:1%
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

Answer:perpendicular
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)

Answer:(3, 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)

Answer:(-3, 0)
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)

Answer:(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°

Answer:45°

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