Refer to BITSAT Mathematics Application Of Derivatives MCQs provided below. BITSAT Full Syllabus Mathematics MCQ questions with answers are available for download in Pdf. The MCQ Questions for Full Syllabus Mathematics with answers are aligned as per the latest syllabus and exam pattern suggested in Full Syllabus by BITSAT, NCERT and KVS. Multiple Choice Questions for Application Of Derivatives are an important part of exams for Full Syllabus Mathematics and if practiced properly can help you to improve your understanding of Application Of Derivatives and get higher marks. Refer to more Chapter-wise MCQs for BITSAT Full Syllabus Mathematics and also download more latest study material for all subjects

## MCQ for Full Syllabus Mathematics Application Of Derivatives

Full Syllabus Mathematics students should refer to the following multiple-choice questions with answers for Application Of Derivatives in Full Syllabus.

### Application Of Derivatives MCQ Questions Full Syllabus Mathematics with Answers

#### Question: If f (x) = x^{x}, then f (x) is increasing in interval :

- a) [0, e]
- b)
- c) [0, 1]
- d) None of these

**Answer:**

#### Question: A cylindircal gas container is closed at the top and open at the bottom. if the iron plate of the top is time as thick as the plate forming the cylindrical sides. The ratio of the radius to the height of the cylinder using minimum material for the same capacity i

- a)
- b)
- c)
- d)

**Answer:**

#### Question: The set of all values of a for which the function f(x) = (a^{2} – 3a + 2) (cos^{2}x/4 –sin^{2}x/4) + (a –1) x + sin 1does not possess critical points is

- a) [1, ∞)
- b)
- c) (–2, 4)
- d)

**Answer:**

#### Question: Match List I with List II and select the correct answer using the code given below the lists:

- a) (A) (B) (C) (D)
1 4 5 3

- b) (A) (B) (C) (D)
1 3 5 4

- c) (A) (B) (C) (D)
5 4 2 3

- d) (A) (B) (C) (D)
5 3 2 4

**Answer: ****(A) (B) (C) (D)**

** 5 4 2 3**

#### Question: What is the x-coordinate of the point on the curve where the tangent is parallel to x-axis?

- a)
- b)
- c)
- d)

**Answer:**

#### Question: A wire 34 cm long is to be bent in the form of a quadrilateral of which each angle is 90°. What is the maximum area which can be enclosed inside the quadrilateral?

- a) 68 cm
^{2} - b) 70 cm
^{2} - c) 71.25 cm
^{2} - d) 72. 25 cm
^{2}

**Answer: ****72. 25 cm ^{2}**

#### Question: Consider the following statements in respect of the function

f (x) = x^{3} – 1, xÎ[-1,1]

I. f (x) is increasing in [– 1, 1]

II. f (x) has no root in (– 1, 1).

Which of the statements given above is/are correct?

- a) Only I
- b) Only II
- c) Both I and II
- d) Neither I nor II

**Answer: Only I**

#### Question: At an extreme point of a function f (x), the tangent to the curve is

- a) Parallel to the x-axis
- b) Perpendicular to the x-axis
- c) Inclined at an angle 45° to the x-axis
- d) Inclined at an angle 60° to the x-axis

**Answer: Parallel to the x-axis**

#### Question: The curve y = xe^{x} has minimum value equal to

- a)
- b)
- c)
– e

- d) e

**Answer:**

#### Question: The line which is parallel to X-axis and crosses the curve y = √x at an angle of 45°, is

- a)
- b)
- c)
- d) y = 1

**Answer:**

#### Question: Tangents are drawn from the origin to the curve y = cos x. Their points of contact lie on

- a) x
^{2}y^{2}= y^{2}– x^{2} - b) x
^{2}y^{2}= x^{2}+ y^{2} - c) x
^{2}y^{2}= x^{2}– y^{2} - d) None of these

**Answer: ****x ^{2}y^{2} = x^{2} – y^{2}**

#### Question: The slope of the tangent to the curve y = e^{x} cos x is minimum at x = α,, then the value of a is

- a) 0
- b) π
- c) 2π
- d) 3π/2

**Answer: ****π**

#### Question: The function has a local minimum at

- a) x = 2
- b) x = –2
- c) x = 0
- d) x = 1

**Answer: x = 1**

#### Question: If a and b are non-zero roots of x^{2} + ax + b = 0 then the least value of x^{2} + ax + b is

- a)
- b)
- c)
- d) 1

**Answer:**

#### Question: If , then

- a) tan x < x < sin x
- b) x < sin x < tan x
- c) sin x < tan x < x
- d) None of these

**Answer: ****None of these**

#### Question: The interval in which the function 2x^{3} + 15 increases less rapidly than the function 9x^{2} – 12x, is –

- a) (–∞, 1)
- b) (1, 2)
- c) (2, ∞)
- d) None of these

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

#### Question: The fuel charges for running a train are proportional to the square of the speed generated in miles per hour and costs 48 per hour at 16 miles per hour. The most economical speed if the fixed charges i.e. salaries etc. amount to `300 per hour is

- a) 10
- b) 20
- c) 30
- d) 40

**Answer: ****40**

#### Question: The equation of all lines having slope 2 which are tangent to the curve x≠3 is

- a) y = 2
- b) y = 2x
- c) y = 2x + 3
- d) None of these

**Answer: None of these**

#### Question: The function f (x) = (x(x–2))^{2} is increasing in the set

- a)
- b) (– ∞, 1)
- c)
- d) (1, 2)

**Answer:**

#### Question: If a^{2} x^{4} + b^{2} y^{4} = c^{4}, then the maximum value of xy is

- a)
- b)
- c)
- d)

**Answer:**

#### Question: If is a decreasing function of x in R then the set of possible values of a (independent of x) is

- a) (1, ∞)
- b) (-∞, -1)
- c) [-1, 1]
- d) None of these

**Answer: ****[-1, 1]**

#### Question: The diagonal of a square is changing at the rate of 0.5 cm/sec. Then the rate of change of area, when the area is 400 cm^{2}, is equal to

- a)
- b) 10 √2 cm
^{2}/ sec - c)
- d)

**Answer: ****10 √2 cm ^{2} / sec**

#### Question: If the normal to the curve y = f (x) at the point (3,4) makes an angle 3p/4 with the positive x-axis, then f ' (3) =

- a) –1
- b) – 3/4
- c) 4/3
- d) 1

**Answer: 1**

#### Question: The function f(x) = sin x – kx – c, where k and c are constants, decreases always when

- a) k > 1
- b)
- c) k < 1
- d)

**Answer:**

#### Question: The minimum value of f (x) = sin^{4} x + cos^{4} x in the interval is

- a)
- b) 2
- c) √2
- d) 1

**Answer:**

#### Question: The curve y –e^{xy}+ x = 0 has a vertical tangent at

- a) (1, 1)
- b) (0, 1)
- c) (1, 0)
- d) No point

**Answer: (1, 0)**

** **

#### Question: The function f(x) = 2x^{3} – 3x^{2} – 12x + 4, has

- a) Two points of local maximum
- b) Two points of local minimum
- c) One maxima and one minima
- d) No maxima or minima

**Answer: One maxima and one minima**

#### Question: If a circular plate is heated uniformly, its area expands 3c times as fast as its radius, then the value of c when the radius is 6 units, is

- a) 4 π
- b) 2 π
- c) 6 π
- d) 3 π

**Answer: ****4 π**

#### Question: The function f(x) = tan x – 4x is strictly decreasing on

- a)
- b)
- c)
- d)

**Answer:**

#### Question: The slope of the tangent to the hyperbola 2x^{2} – 3y^{2} = 6 at (3, 2) is

- a) –1
- b) 1
- c) 0
- d) 2

**Answer: 1**

#### Question: The minimum value of the function y = x^{4} – 2x^{2} + 1 in the interval is

- a) 0
- b) 2
- c) 8
- d) 9

**Answer: ****0**

#### Question: The value of a in order that f (x) = sin x – cos x – ax + b decreases for all real values is given by

- a)
- b) a < √2
- c)
- d) a < 1

**Answer:**

#### Question: The equation of tangent to the curve y = sin x at the point (π, 0) is

- a) x + y = 0
- b) x + y = π
- c) x – y =π
- d) x – y = 0

**Answer: ****x + y = π**

#### Question: If f(x) = cos x, then

- a) f(x) is strictly decreasing in (0, π)
- b) f(x) is strictly increasing in (0, 2π)
- c) f(x) is neither increasing nor decreasing in (π, 2π)
- d) All the above are correct

**Answer: ****f(x) is strictly decreasing in (0, π)**

#### Question: The greatest value of f (x) = cos (xe^{[x]} + 7x^{2} – 3x),x £ [–1, ∞) is –

- a) –1
- b) 1
- c) 0
- d) None of these

**Answer: 1**

#### Question: The function f (x) = cot^{–1} x + x increases in the interval

- a) (1,∞)
- b) (–1,∞)
- c) (–∞, ∞)
- d) (0, ∞)

**Answer: ****(–∞, ∞)**

#### Question: The total revenue in rupees received from the sale of x units of a product is given by R(x) = 13x^{2} + 26x + 15. Then the marginal revenue in rupees, when x = 15 is

- a) 116
- b) 126
- c) 136
- d) 416

**Answer: 416**

#### Question: If at any point S of the curve by^{2} = (x + a)^{3}, the relation between subnormal SN and subtangent ST be p (SN) = q (ST)^{2} then p/q is equal to

- a) 8b/27
- b) 8a/27
- c) b/a
- d) None of these

**Answer: 8b/27**

#### Question: The equation of one of the tangents to the curve y = cos(x +y), that is parallel to the line x + 2y = 0, is

- a) x + 2y = 1
- b) x + 2y = π/2
- c) x + 2y = π/4
- d) None of these

**Answer: ****x + 2y = π/2**

#### Question: For all values of x, function f (x) = 2x^{3} + 6x^{2} + 7x – 19 is

- a) Monotonic increasing
- b) Monotonic decreasing
- c) Not monotonic
- d) None of these

**Answer: Monotonic increasing**

#### Question:

is

- a) increasing in [0,∞)
- b) Decreasing in [0, ∞)
- c)
- d)

**Answer: ****Decreasing in [0, ∞)**

#### Question: The largest value of y = 2x^{3} – 3x^{2} – 12x + 5 for occurs at x is equal to :

- a) -2
- b) -1
- c) 2
- d) 4

**Answer: ****-1**

#### Question: Function f(x) = cos x – 2λx is monotonic decreasing when

- a) λ > 1/2
- b) λ < 1/2
- c) λ < 2
- d) λ > 2

**Answer: ****λ > 1/2**

#### Question: The curve y –e^{xy}+ x = 0 has a vertical tangent at

- a) (1, 1)
- b) (0, 1)
- c) (1, 0)
- d) No point

**Answer: (1, 0)**

#### Question: The slope of the tangent to the hyperbola 2x^{2} – 3y^{2} = 6 at (3, 2) is

- a) -1
- b) 1
- c) 0
- d) 2

**Answer: ****1**

## More Study Material

### BITSAT Full Syllabus Mathematics Application Of Derivatives MCQs

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