# Maths MCQs for Class 12 with Answers Chapter 6 Application of Derivatives

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 6 Application of Derivatives. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Application of Derivatives MCQs Pdf with Answers to know their preparation level.

## Application of Derivatives Class 12 Maths MCQs Pdf

Question 1.
Find all the points of local maxima and local minima of the function f(x) = (x – 1)3 (x + 1)2
(a) 1, -1, -1/5
(b) 1, -1
(c) 1, -1/5
(d) -1, -1/5
Answer:
(a) 1, -1, -1/5

Question 2.
Find the local minimum value of the function f(x) = sin4x + cos4x, 0 < x < $$\frac{\pi}{2}$$
(a) $$\frac { 1 }{ \surd 2 }$$
(b) $$\frac { 1 }{ 2 }$$
(c) $$\frac { \surd 3 }{ 2 }$$
(d) 0
Answer:
(b) $$\frac { 1 }{ 2 }$$

Question 3.
Find the points of local maxima and local minima respectively for the function f(x) = sin 2x – x , where
$$-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}$$
(a) $$\frac { -\pi }{ 6 }$$, $$\frac { \pi }{ 6 }$$
(b) $$\frac { \pi }{ 3 }$$, $$\frac { -\pi }{ 3 }$$
(c) $$\frac { -\pi }{ 3 }$$, $$\frac { \pi }{ 3 }$$
(d) $$\frac { \pi }{ 6 }$$, $$\frac { -\pi }{ 6 }$$
Answer:
(d) $$\frac { \pi }{ 6 }$$, $$\frac { -\pi }{ 6 }$$

Question 4.
If $$y=\frac{a x-b}{(x-1)(x-4)}$$ has a turning point P(2, -1), then find the value of a and b respectively.
(a) 1, 2
(b) 2, 1
(c) 0, 1
(d) 1, 0
Answer:
(d) 1, 0

Question 5.
sinp θ cosq θ attains a maximum, when θ =
(a) $$\tan ^{-1} \sqrt{\frac{p}{q}}$$
(b) $$\tan ^{-1}\left(\frac{p}{q}\right)$$
(c) $$\tan ^{-1} q$$
(d) $$\tan ^{-1}\left(\frac{q}{p}\right)$$
Answer:
(a) $$\tan ^{-1} \sqrt{\frac{p}{q}}$$

Question 6.
Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x2.
(a) 25
(b) 43
(c) 62
(d) 49
Answer:
(d) 49

Question 7.
If y = x3 + x2 + x + 1, then y
(a) has a local minimum
(b) has a local maximum
(c) neither has a local minimum nor local maximum
(d) None of these
Answer:
(c) neither has a local minimum nor local maximum

Question 8.
Find both the maximum and minimum values respectively of 3x4 – 8x3 + 12x2 – 48x + 1 on the interval [1, 4].
(a) -63, 257
(b) 257, -40
(c) 257, -63
(d) 63, -257
Answer:
(c) 257, -63

Question 9.
It is given that at x = 1, the function x4 – 62x2 + ax + 9 attains its maximum value on the interval [0, 2]. Find the value of a.
(a) 100
(b) 120
(c) 140
(d) 160
Answer:
(b) 120

Question 10.
The function f(x) = x5 – 5x4 + 5x3 – 1 has
(a) one minima and two maxima
(b) two minima and one maxima
(c) two minima and two maxima
(d) one minima and one maxima
Answer:
(d) one minima and one maxima

Question 11.
Find the height of the cylinder of maximum volume that can be is cribed in a sphere of radius a.
(a) $$\frac { 2a }{ 3 }$$
(b) $$\frac{2 a}{\sqrt{3}}$$
(c) $$\frac { a }{ 3 }$$
(d) $$\frac { a }{ 3 }$$
Answer:
(b) $$\frac{2 a}{\sqrt{3}}$$

Question 12.
Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cm.
(a) $$\frac{\pi r^{3}}{3 \sqrt{3}}$$
(b) $$\frac{4 \pi r^{2} h}{3 \sqrt{3}}$$
(c) 4πr3
(d) $$\frac{4 \pi r^{3}}{3 \sqrt{3}}$$
Answer:
(d) $$\frac{4 \pi r^{3}}{3 \sqrt{3}}$$

Question 13.
The area of a right-angled triangle of the given hypotenuse is maximum when the triangle is
(a) scalene
(b) equilateral
(c) isosceles
(d) None of these
Answer:
(c) isosceles

Question 14.
Find the area of the largest isosceles triangle having perimeter 18 metres.
(a) 9√3
(b) 8√3
(c) 4√3
(d) 7√3
Answer:
(a) 9√3

Question 15.
2x3 – 6x + 5 is an increasing function, if
(a) 0 < x < 1
(b) -1 < x < 1
(c) x < -1 or x > 1
(d) -1 < x < $$-\frac{1}{2}$$
Answer:
(c) x < -1 or x > 1

Question 16.
If f(x) = sin x – cos x, then interval in which function is decreasing in 0 ≤ x ≤ 2π, is
(a) $$\left[\frac{5 \pi}{6}, \frac{3 \pi}{4}\right]$$
(b) $$\left[\frac{\pi}{4}, \frac{\pi}{2}\right]$$
(c) $$\left[\frac{3 \pi}{2}, \frac{5 \pi}{2}\right]$$
(d) None of these
Answer:
(d) None of these

Question 17.
The function which is neither decreasing nor increasing in $$\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right)$$ is
(a) cosec x
(b) tan x
(c) x2
(d) |x – 1|
Answer:
(a) cosec x

Question 18.
The function f(x) = tan-1 (sin x + cos x) is an increasing function in
(a) $$\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$$
(b) $$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$
(c) $$\left(0, \frac{\pi}{2}\right)$$
(d) None of these
Answer:
(d) None of these

Question 19.
The function f(x) = x3 + 6x2 + (9 + 2k)x + 1 is strictly increasing for all x, if
(a) $$k>\frac{3}{2}$$
(b) $$k<\frac{3}{2}$$
(c) $$k \geq \frac{3}{2}$$
(d) $$k \leq \frac{3}{2}$$
Answer:
(a) $$k>\frac{3}{2}$$

Question 20.
The point on the curves y = (x – 3)2 where the tangent is parallel to the chord joining (3, 0) and (4, 1) is
(a) $$\left(-\frac{7}{2}, \frac{1}{4}\right)$$
(b) $$\left(\frac{5}{2}, \frac{1}{4}\right)$$
(c) $$\left(-\frac{5}{2}, \frac{1}{4}\right)$$
(d) $$\left(\frac{7}{2}, \frac{1}{4}\right)$$
Answer:
(d) $$\left(\frac{7}{2}, \frac{1}{4}\right)$$

Question 21.
The slope of the tangent to the curve x = a sin t, y = a{cot t + log(tan $$\frac{t}{2}$$)} at the point ‘t’ is
(a) tan t
(b) cot t
(c) tan $$\frac{t}{2}$$
(d) None of these
Answer:
(a) tan t

Question 22.
The equation of the normal to the curves y = sin x at (0, 0) is
(a) x = 0
(b) x + y = 0
(c) y = 0
(d) x – y = 0
Answer:
(b) x + y = 0

Question 23.
The tangent to the parabola x2 = 2y at the point (1, $$\frac{1}{2}$$) makes with the x-axis an angle of
(a) 0°
(b) 45°
(c) 30°
(d) 60°
Answer:
(b) 45°

Question 24.
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 $$\frac { \pi }{ 4 }$$
(d) cut at an angle $$\frac { \pi }{ 3 }$$
Answer:
(a) cut at right angles

Question 25.
The distance between the point (1, 1) and the tangent to the curve y = e2x + x2 drawn at the point x = 0
(a) $$\frac{1}{\sqrt{5}}$$
(b) $$\frac{-1}{\sqrt{5}}$$
(c) $$\frac{2}{\sqrt{5}}$$
(d) $$\frac{-2}{\sqrt{5}}$$
Answer:
(c) $$\frac{2}{\sqrt{5}}$$

Question 26.
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:
(d) (1, 2)

Question 27.
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:
(b) (-3, 0)

Question 28.
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:
(a) (3, 1)

Question 29.
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:
(b) perpendicular

Question 30.
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:
(a) 1%

Question 31.
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) $$\frac{a}{2}$$ %
(c) 3a%
(d) None of these
Answer:
(b) $$\frac{a}{2}$$ %

Question 32.
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:
(c) 9.72π cm3

Question 33.
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:
(a) 45.46

Question 34.
f(x) = 3x2 + 6x + 8, x ∈ R
(a) 2
(b) 5
(c) -8
(d) does not exist
Answer:
(d) does not exist

Question 35.
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:
(a) 80π cu m/s

Question 36.
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) $$\frac{10}{\sqrt{3}}$$ cm2/s
Answer:
(c) 10√3 cm2/s

Question 37.
A particle is moving along the curve x = at2 + bt + c. If ac = b2, then particle would be moving with uniform
(a) rotation
(b) velocity
(c) acceleration
(d) retardation
Answer:
(c) acceleration

Question 38.
The distance ‘s’ metres covered by a body in t seconds, is given by s = 3t2 – 8t + 5. The body will stop after
(a) 1 s
(b) $$\frac{3}{4}$$ s
(c) $$\frac{4}{3}$$ s
(d) 4 s
Answer:
(c) $$\frac{4}{3}$$ s

Question 39.
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
(b) b + c
(c) 2b – 2c
(d) $$2 \sqrt{b^{2}+c^{2}}$$
Answer:
(d) $$2 \sqrt{b^{2}+c^{2}}$$

Question 40.
The function f(x) = log (1 + x) – $$\frac{2 x}{2+x}$$ is increasing on
(a) (-1, ∞)
(b) (-∞, 0)
(c) (-∞, ∞)
(d) None of these
Answer:
(a) (-1, ∞)

Question 41.
$$f(x)=\left(\frac{e^{2 x}-1}{e^{2 x}+1}\right)$$ is
(a) an increasing function
(b) a decreasing function
(c) an even function
(d) None of these
Answer:
(a) an increasing function

Question 42.
The function f(x) = cot-1 x + x increases in the interval
(a) (1, ∞)
(b) (-1, ∞)
(c) (0, ∞)
(d) (-∞, ∞)
Answer:
(d) (-∞, ∞)

Question 43.
The function f(x) = $$\frac{x}{\log x}$$ increases on the interval
(a) (0, ∞)
(b) (0, e)
(c) (e, ∞)
(d) none of these
Answer:
(c) (e, ∞)

Question 44.
The length of the longest interval, in which the function 3 sin x – 4sin3x is increasing, is
(a) $$\frac{\pi}{3}$$
(b) $$\frac{\pi}{2}$$
(c) $$\frac{3 \pi}{2}$$
(d) π
Answer:
(a) $$\frac{\pi}{3}$$

Question 45.
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:
(a) (2, -4)

Question 46.
The distance of that point on y = x4 + 3x2 + 2x which is nearest to the line y = 2x – 1 is
(a) $$\frac{3}{\sqrt{5}}$$
(b) $$\frac{4}{\sqrt{5}}$$
(c) $$\frac{2}{\sqrt{5}}$$
(d) $$\frac{1}{\sqrt{5}}$$
Answer:
(d) $$\frac{1}{\sqrt{5}}$$

Question 47.
The function f(x) = x + $$\frac{4}{x}$$ 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:
(b) local minima at x = 2, and local maxima at x = -2

Question 48.
The combined resistance R of two resistors R1 and R2 (R1, R2 > 0) is given by $$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$$. 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:
(c) R1 = R2

Question 49.
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) $$\frac { r }{ 2 }$$
(d) $$\frac { 3\pi r }{ 2 }$$
Answer:
(a) r

We hope the given Maths MCQs for Class 12 with Answers Chapter 6 Application of Derivatives will help you. If you have any query regarding CBSE Class 12 Maths Application of Derivatives MCQs Pdf, drop a comment below and we will get back to you at the earliest.