BITSAT Mathematics Application Of Derivatives MCQs

Refer to BITSAT Mathematics Application Of Derivatives MCQs provided below. BITSAT Full Syllabus Mathematics MCQs with answers available in Pdf for free download. The MCQ Questions for Full Syllabus Mathematics with answers have been prepared as per the latest syllabus, BITSAT books and examination 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 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. These MCQ questions with answers for Full Syllabus Mathematics will come in exams and help you to score good marks

Application Of Derivatives MCQ Questions Full Syllabus Mathematics with Answers

 

Question: If f (x) = xx, then f (x) is increasing in interval :

  • a) [0, e]
  • b)

    BITSAT Mathematics Application 1

  • c) [0, 1]
  • d) None of these

Answer:

 BITSAT Mathematics Application 1

Question: A cylindircal gas container is closed at the top and open at the bottom. if the iron plate of the top is BITSAT Mathematics Application 2time 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)

    BITSAT Mathematics Application 3

  • b)

    BITSAT Mathematics Application 4

  • c)

    BITSAT Mathematics Application 5

  • d)

    BITSAT Mathematics Application 6

Answer:

BITSAT Mathematics Application 5

 

Question: The set of all values of a for which the function f(x) = (a2 – 3a + 2) (cos2x/4 –sin2x/4) + (a –1) x + sin 1does not possess critical points is

  • a) [1, ∞)
  • b)

    BITSAT Mathematics Application 7

  • c)  (–2, 4) 
  • d)

    BITSAT Mathematics Application 8

Answer:

BITSAT Mathematics Application 7

 

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

BITSAT Mathematics Application 9

  • 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 BITSAT Mathematics Application 10where the tangent is parallel to x-axis?

  • a)

    BITSAT Mathematics Application 11

  • b)

    BITSAT Mathematics Application 12

  • c)

    BITSAT Mathematics Application 13

  • d)

    BITSAT Mathematics Application 14

Answer:

BITSAT Mathematics Application 12

 

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 cm2 
  • b) 70 cm2
  • c) 71.25 cm2
  • d) 72. 25 cm2

Answer: 72. 25 cm2

 

Question: Consider the following statements in respect of the function

f (x) = x3 – 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 = xex has minimum value equal to

  • a)

    BITSAT Mathematics Application 15

  • b)

    BITSAT Mathematics Application 16

  • c)

    – e

  • d) e

Answer:

BITSAT Mathematics Application 15

 

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

  • a)

    BITSAT Mathematics Application 17

  • b)

    BITSAT Mathematics Application 18

  • c)

    BITSAT Mathematics Application 19

  • d) y = 1

Answer:

BITSAT Mathematics Application 19

 

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

  • a) x2y2 = y2 – x2
  • b) x2y2 = x2 + y2
  • c) x2y2 = x2 – y2
  • d) None of these

Answer: x2y2 = x2 – y2

 

Question: The slope of the tangent to the curve y = ex cos x is minimum at x = α,BITSAT Mathematics Application 20, then the value of a is

  • a) 0
  • b) π
  • c) 2π
  • d) 3π/2

Answer: π

 

Question: The function BITSAT Mathematics Application 21has 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 x2 + ax + b = 0 then the least value of x2 + ax + b is

  • a)

    BITSAT Mathematics Application 22

  • b)

    BITSAT Mathematics Application 23

  • c)

    BITSAT Mathematics Application 24

  • d) 1

Answer:

 BITSAT Mathematics Application 23

Question: If BITSAT Mathematics Application 25 , 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 2x3 + 15 increases less rapidly than the function 9x2 – 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  BITSAT Mathematics Application 2648 per hour at 16 miles per hour. The most economical speed if the fixed charges i.e. salaries etc. amount to `BITSAT Mathematics Application 26300 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 BITSAT Mathematics Application 27 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)

    BITSAT Mathematics Application 28

  • b) (– ∞, 1)
  • c)

    BITSAT Mathematics Application 29

  • d) (1, 2)

Answer:

BITSAT Mathematics Application 29

 

Question: If a2 x4 + b2 y4 = c4, then the maximum value of xy is

  • a)

    BITSAT Mathematics Application 30

  • b)

    BITSAT Mathematics Application 31

  • c)

    BITSAT Mathematics Application 32

  • d)

    BITSAT Mathematics Application 33

Answer:

BITSAT Mathematics Application 33

Question: If BITSAT Mathematics Application 34is 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 cm2, is equal to

  • a)

    BITSAT Mathematics Application 35

  • b) 10 √2 cm2 / sec
  • c)

    BITSAT Mathematics Application 36

  • d)

    BITSAT Mathematics Application 37

Answer: 10 √2 cm2 / 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)

    BITSAT Mathematics Application 38

  • c) k < 1
  • d)

    BITSAT Mathematics Application 39

Answer:

BITSAT Mathematics Application 38

  

Question: The minimum value of f (x) = sin4 x + cos4 x in the interval BITSAT Mathematics Application 40 is

  • a)

    BITSAT Mathematics Application 41

  • b) 2
  • c) √2
  • d) 1

Answer:

BITSAT Mathematics Application 41

 

Question: The curve y –exy+ 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) = 2x3 – 3x2 – 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)

    BITSAT Mathematics Application 42

  • b)

    BITSAT Mathematics Application 43

  • c)

    BITSAT Mathematics Application 44

  • d)

    BITSAT Mathematics Application 45

Answer:

BITSAT Mathematics Application 42

 

Question: The slope of the tangent to the hyperbola 2x2 – 3y2 = 6 at (3, 2) is

  • a) –1
  • b) 1
  • c) 0
  • d) 2

Answer: 1


Question: The minimum value of the function y = x4 – 2x2 + 1 in the interval BITSAT Mathematics Application 46is

  • 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)

    BITSAT Mathematics Application 47

  • b) a < √2
  • c)

    BITSAT Mathematics Application 48

  • d) a < 1

Answer:

BITSAT Mathematics Application 47

 

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] + 7x2 – 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) = 13x2 + 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 by2 = (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), BITSAT Mathematics Application 49 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) = 2x3 + 6x2 + 7x – 19 is

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

Answer: Monotonic increasing


Question:

BITSAT Mathematics Application 50 is

  • a) increasing in [0,∞)
  • b) Decreasing in [0, ∞)
  • c) 

    BITSAT Mathematics Application 51

  • d)

    BITSAT Mathematics Application 52

Answer: Decreasing in [0, ∞)

 

Question: The largest value of y = 2x3 – 3x2 – 12x + 5 for BITSAT Mathematics Application 53 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 –exy+ 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 2x2 – 3y2 = 6 at (3, 2) is

  • a) -1
  • b) 1
  • c) 0
  • d) 2

Answer: 1

 

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BITSAT Full Syllabus Mathematics Application Of Derivatives MCQs

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