BITSAT SERIES Mathematics
Application Of Derivatives
27 previous year questions.
Volume: 27 Ques
Yield: High
High-Yield Trend
14
2024 1
2021 2
2020 2
2019 1
2018 1
2017 1
2016 3
2015 1
2012 1
2010 Chapter Questions 27 MCQs
01
PYQ 2010
medium
mathematics ID: bitsat-2
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
1
4π
2
2π
3
6π
4
3π
02
PYQ 2012
medium
mathematics ID: bitsat-2
For the function
, where is equal to:
1
50
2
0
3
100
4
200
03
PYQ 2015
medium
mathematics ID: bitsat-2
The line which is parallel to X-axis and crosses the curve at an angle of , is
1
2
3
4
y = 1
04
PYQ 2015
medium
mathematics ID: bitsat-2
If is the inverse of function and , then is equal to
1
2
3
4
None of these
05
PYQ 2015
medium
mathematics ID: bitsat-2
The number of real roots of the equation
is
1
2
3
4
06
PYQ 2016
medium
mathematics ID: bitsat-2
At an extreme point of a function f(x), the tangent to the curve is
1
parallel to the x-axis
2
perpendicular to the x-axis
3
inclined at an angle 45^∘ to the x-axis
4
inclined at an angle 60^∘ to the x-axis
07
PYQ 2017
medium
mathematics ID: bitsat-2
If
then the value of is equal to
then the value of is equal to
1
1
2
3
4
(2)/(e²)
08
PYQ 2018
medium
mathematics ID: bitsat-2
A ball is dropped from a platform 19.6 m high. Its position function is:
1
2
3
4
x=-4.9t²-19.6(0≤ t\le2)
09
PYQ 2019
medium
mathematics ID: bitsat-2
If y=x+√(1+x²), then (1+x²)dfracd²ydx²+x(dy)/(dx) is
1
2
3
4
0
10
PYQ 2019
medium
mathematics ID: bitsat-2
If g is the inverse of function f and f'(x)=sin x, then g'(x) is equal to
1
2
3
4
None of these
11
PYQ 2020
medium
mathematics ID: bitsat-2
Match List I with List II and select the correct answer using the code given below the lists. List I • [(A)] f(x)=cos x • [(B)] f(x)=ln x • [(C)] f(x)=x²-5x+4.3 • [(D)] f(x)=eˣ List II • [1.] The graph cuts y-axis in infinite number of points • [2.] The graph cuts x-axis in two points • [3.] The graph cuts y-axis in only one point • [4.] The graph cuts x-axis in only one point • [5.] The graph cuts x-axis in infinite number of points
1
1 4 5 3
2
1 3 5 4
3
5 4 2 3
4
5 3 2 4
12
PYQ 2020
medium
mathematics ID: bitsat-2
For any differentiable function y of x,
(d²x)/(dy²)((dy)/(dx))³+(d²y)/(dx²)=
1
2
3
4
x
13
PYQ 2021
medium
mathematics ID: bitsat-2
If
f(x)=cos⁻1[(1-(log x)²)/(1+(log x)²)],
then the value of f'(e) is equal to
1
1
2
(1)/(e)
3
(2)/(e)
4
(2)/(e²)
14
PYQ 2024
medium
mathematics ID: bitsat-2
If the function , defined below, is continuous on the interval , then:
1
a = 3, b = −2
2
a = −3, b = 2
3
a = −3, b = −2
4
a = 3, b = 2
15
PYQ 2024
medium
mathematics ID: bitsat-2
If the angle made by the tangent at the point on the curve , , with , with the positive x-axis is , then is equal to:
1
2
3
27
4
48
16
PYQ 2024
medium
mathematics ID: bitsat-2
The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of radius 12 units is:
1
2
3
4
17
PYQ 2024
medium
mathematics ID: bitsat-2
At ,
1
2
3
4
18
PYQ 2024
medium
mathematics ID: bitsat-2
If , then is equal to:
1
0
2
3
-1
4
19
PYQ 2024
medium
mathematics ID: bitsat-2
If , then find .
1
2
3
4
20
PYQ 2024
easy
mathematics ID: bitsat-2
If , then is:
1
2
3
4
21
PYQ 2024
medium
mathematics ID: bitsat-2
The solution of the differential equation is:
1
2
3
4
22
PYQ 2024
medium
mathematics ID: bitsat-2
If the area bounded by the curves and (where ) is 3 sq. units, then the value of is:
1
2
3
1
4
4
23
PYQ 2024
medium
mathematics ID: bitsat-2
The area of the region bounded by the curves and is:
1
2
9
3
4
24
PYQ 2024
medium
mathematics ID: bitsat-2
The line bisects the area enclosed by lines , , and and the curve . Then, the value of is:
1
2
3
4
25
PYQ 2024
medium
mathematics ID: bitsat-2
The population at time of a certain mouse species satisfies the differential equation:
If , then the time at which the population becomes zero is:
If , then the time at which the population becomes zero is:
1
2
3
4
26
PYQ 2024
medium
mathematics ID: bitsat-2
The point of inflexion for the curve , where is odd integer and , is:
1
2
3
4
None of these
27
PYQ 2024
medium
mathematics ID: bitsat-2
The altitude of a cone is 20 cm and its semi-vertical angle is . If the semi-vertical angle is increasing at the rate of per second, then the radius of the base is increasing at the rate of:
1
30 cm/sec
2
cm/sec
3
10 cm/sec
4
160 cm/sec
About Application Of Derivatives - BITSAT
Application Of Derivatives is a vital chapter for BITSAT aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.
By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.
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