Applications of Derivatives MCQ for ISC Class-12 Maths .These MCQ / Objective Type Questions is based on latest reduced syllabus according 2021-22 session on bifurcated pattern. Main motto of MCQ Type Question is cracking the next upcoming exam of council. Visit official website CISCE for detail information about ISC Board Class-12 Physics.

** ISC Class-12 Maths , Applications of Derivatives MCQ Type Questions**

Board | ISC |

Class | 12th (XII) |

Subject | Maths |

Ch-Name | Applications of Derivatives |

Syllabus | on bifurcated syllabus (after reduction) |

Bifurcated pattern |
Semester-1 |

Session | 2021-22 |

Topic | MCQ / Objective Type Question |

** Applications of Derivatives MCQ Type Questions for ISC ****Class-12 Maths**

**Question 1: If f and g are differentiable functions on [0, 1] satisfying f(0) = 2 = g(l), g(0) = 0 and f(1) = 6, then for some c ∈ ] 0, 1 :**

(a) 2f'(c) = 3g'(c)

(b) f'(c) = g'(c)

(c) f'(c) = 2g'(c)

(d) 2f'(c) = g'(c).

**Answer: (c) f'(c) = 2g'(c)
**

**Question 2: Twenty metres of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower bed is:**

(a) 25

(b) 30

(c) 12.5

(d) 10.

**Answer: (a) 25
**

**Question 3: 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 4: The total revenue in ₹ received from the sale of x units of an article is given by R(x) = 3x² + 36x + 5. The marginal revenue when x = 15 is (in ₹ )**

(a) 126

(b) 116

(c) 96

(d) 90

**Answer: (a) 126
**

**Question 5: The point(s) on the curve y = x², at which y-coordinate is changing six times as fast as x-coordinate is/are**

(a) (2, 4)

(b) (3, 9)

(c) (3, 9), (9, 3)

(d) (6, 2)

**Answer: (b) (3, 9)
**

**Question 6: The sides of an equilateral triangle are increasing at the rate of 2cm/sec. The rate at which the are increases, when side is 10 cm is**

(a) 10 cm²/s

(b) √3 cm²/s

(c) 10√3 cm²/s

(d) 10/3 cm²/s

**Answer: (c) 10√3 cm²/s
**

**Question 7: A ladder, 5 meter long, standing oh a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is**

(a) 1/10 radian/sec

(b) 1/20 radian/sec

(c) 20 radiah/sec

(d) 10 radiah/sec

**Answer: (b) 1/20 radian/sec
**

**Question 8: The curve y – x ^{1/5} at (0, 0) has**

(a) a vertical tangent (parallel to y-axis)

(b) a horizontal tangent (parallel to x-axis)

(c) an oblique tangent

(d) no tangent

**Answer: (b) a horizontal tangent (parallel to x-axis)
**

**Question 9: ****The equation of tangent to curve y = e ^{–|x|} at the points where the curve cuts the line x = 1 is**

(a) x+ y = e

(b) e (x + y) = 1

(c) y + ex = 1

(d) None of these

**Answer: (d) None of these**

**Question 10: ****The number of roots of x ^{3}– 3x + 1 = 0 in [1, 2] is**

(a) One

(b) Two

(c) Three

(d) None of these

**Answer: (a) One**

**Question 11: ****Let h(x) = f(x) – [f (x)] ^{2} + [f (x)]^{3} for every real number x. Then**

(a) h is increasing whenever f is increasing

(b) h is increasing whenever f is decreasing

(c)h is decreasing whenever f is increasing

(d) Nothing can be said in general

**Answer: (a) h is increasing whenever f is increasing**

**Question 12: ****Let y = |x| + |x – 2|, then dy/dx at x = 2**

(a) 2

(b) 0

(c) Does not exist

(d) None of these

**Answer: (c) Does not exist**

**Question 13: ****The number of solutions of equations 3x ^{2} + xsinx + cosx = 0**

(a) 3

(b) 2

(c) 1

(d) 0

**Answer: (d) 0**

** Question 14: **The maximum value of (1/x)

^{x}is

(a) (1/e)^{1/e}

(b) (e)^{2/e}

(c) (e)^{-1/e}

(d) (e)^{1/e}

**Answer: (d) (e) ^{1/e}**

** Question 15: **The global maximum and global minimum of f (x) = 2x

^{3}– 9x

^{2}+ 12x + 6 in [0, 2]

(a) (11, 6)

(b) ( 6,11)

(c) ( -6,11)

(d) ( -11, 6)

**Answer: (a) (11, 6)**

**Question 16: The real number k for which the equation 2x³ + 3x + k = 0 has two distinct real roots in [0,1]:**

(a) lies between 2 and 3

(b) lies between -1 and 0

(c) does not exist

(d) lies between 1 and 2.

**Answer: (c) does not exist
**

**Question 17: The point on the curve y² = x, where the tangent makes an angle of π/4 with x-axis is:**

(a) (1/2, 1/4)

(b) (1/4, 1/2)

(c) (4, 2)

(d) (1, 1).

**Answer: (b) (1/4, 1/2)
**

**Question 18: The equation of the normal to the curve y = sin x at (0, 0) is**

(a) x = 0

(b) y = 0

(c) x + y = 0

(d) x – y = 0.

**Answer: (c) x + y = 0
**

**Question 19: Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x ^{2}.**

(a) 25

(b) 43

(c) 62

(d) 49

Answer: (d) 49

**Question 20: If y = x ^{3} + x^{2} + 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 21: **Find both the maximum and minimum values respectively of 3x^{4} – 8x^{3} + 12x^{2} – 48x + 1 on the interval [1, 4].

(a) -63, 257

(b) 257, -40

(c) 257, -63

(d) 63, -257

**Answer: (c) 257, -63**

**Question 22: **It is given that at x = 1, the function x^{4} – 62x^{2} + 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 23: The equation of the normal to the curve y = sin x at (0, 0) is**

(a) x = 0

(b) y = 0

(c) x + y = 0

(d) x – y = 0

**Answer: (c) x + y = 0
**

**Question 24: The line y = x + 1 is a tangent to the curve y2 = 4x at the point**

(a) (-1, 2)

(b) (1, 2)

(c) (1, -2)

(d) (2, 1)

**Answer: (b) (1, 2)
**

**Question 25: The curves y = ae ^{-x} and y = be^{x} are orthogonal if**

(a) a = b

(b) a = -b

(c) ab = -1

(d) ab = 1

**Answer: (d) ab = 1**

**Question 26: If the curves ay + x2 = 7 and x3 = y cut orthogonally at (1,1), then the value of a is**

(a) 1

(b) 0

(c) -6

(d) 6

**Answer: (d) 6**

**Question 27: The equation of normal to the curve 3x² – y² = 8 which is parallel to the line ,x + 3y = 8 is**

(a) 3x – y = 8

(b) 3x + y + 8 = 0

(c) x + 3y ± 8 = 0

(d) x + 3y = 0

**Answer: (c) x + 3y ± 8 = 0
**

**Question 28: If y = x ^{4} – 10 and if x changes from 2 to 1.99 what is the change in y**

(a) 0.32

(b) 0.032

(c) 5.68

(d) 5.968

**Answer: (a) 0.32
**

**Question 29: The points at which the tangents to the curve y = x² – 12x +18 are parallel to x-axis are**

(a) (2, – 2), (- 2, -34)

(b) (2, 34), (- 2, 0)

(c) (0, 34), (-2, 0)

(d) (2, 2),(-2, 34).

**Answer: (d) (2, 2),(-2, 34).**

**Question 30: The function f(x) = x ^{5} – 5x^{4} + 5x^{3} – 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 31: **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 32: 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 33: The absolute maximum value of y = x ^{3} – 3x + 2 in 0 ≤ x ≤ 2 is**

(a) 4

(b) 6

(c) 2

(d) 0

**Answer: (a) 4
**

**Question 34: The tangent to the curve y = e ^{2x} at the point (0, 1) meets x-axis at**

(a) (0, 1)

(b) (-1/2, 0)

(c) (2, 0)

(d) (0, 2)

**Answer: (b) (-1/2, 0)
**

**Question 35: 2x ^{3} – 6x + 5 is an increasing function, if**

(a) 0 < x < 1

(b) -1 < x < 1

(c) x < -1 or x > 1

(d) -1 < x < −1/2

**Answer: (c) x < -1 or x > 1**

** Question 36: **The slope of the tangent to the curve x = a sin t, y = a{cot t + log(tan t/2)} at the point ‘t’ is

(a) tan t

(b) cot t

(c) tan t/2

(d) None of these

**Answer: (a) tan t**

**Question 37: 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 38: The interval on which the function f (x) = 2x³ + 9x² + 12x – 1 is decreasing is**

(a) [-1, ∞]

(b) [-2, -1]

(c) [-∞, -2]

(d) [-1, 1]

**Answer: (b) [-2, -1]
**

**Question 39: Let the f: R → R be defined by f (x) = 2x + cos x, then f**

(a) has a minimum at x = 3t

(b) has a maximum, at x = 0

(c) is a decreasing function

(d) is an increasing function

**Answer: (d) is an increasing function**

**Question 40: **The maximum and the minimum value of 3x^{4} – 8x^{3} + 12x^{2} – 48x + 1 on the interval [1,4]

(a) -40,257

(b) -48,258

(c) -49,258

(d) -58,257

**Answer: (a) -40,257**

**Question 41: **Find the maximum and minimum values of f (x) = 2x^{3} – 24x + 107 in the interval [1, 3].

(a) 89, 69

(b) 89, 75

(c) 59, 56

(d) 89, -9

**Answer: (b) 89, 75**

**Question 42: **The radius of air bubble is increasing at the rate of 0. 25 cm/s. At what rate the volume of the bubble is increasing when the radius is 1 cm.

(a) 4π cm^{3}/s

(b) 22π cm^{3}/s

(c) 2π cm^{3}/s

(d) π cm^{3}/s

**Answer: (d) π cm ^{3}/s**

**Question 43: **The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 5x^{2} + 22x + 35. Find the marginal revenue, when x = 7, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant

(a) Rs 7

(b) Rs 127

(c) Rs 92

(d) Rs 48

**Answer: (c) Rs 92**

**Question 44: **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 45: Tangents to the curve x ^{2} + y^{2} = 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 46: **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 47: 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: (b) a/2 %**

**Question 48: Which of the following functions is decreasing on(0, π/2)?**

(a) sin 2x

(b) tan x

(c) cos x

(d) cos 3x

**Answer: (c) cos x
**

**Question 49: The function f(x) = tan x – x**

(a) always increases

(b) always decreases

(c) sometimes increases and sometimes decreases

(d) never increases

**Answer: (a) always increases
**

**Question 50: The smallest value of the polynomial x³ – 18x² + 96x in [0, 9] is**

(a) 126

(b) 0

(c) 135

(d) 160

**Answer: (b) 0
**

– : End of **Applications of Derivatives MCQ** for ISC Class-12 Maths :-

-: also visit :-

- ISC Class-12 Text book Solutions, Notes , Syllabus, Paper
- MCQ Type Questions ISC Class-12 Semester-1 Session 2021-22

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