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Physics Exam  >  Physics Test  >  Topic wise Tests for IIT JAM   >  Differential Calculus NAT Level - 2 - Physics MCQ

Differential Calculus NAT Level - 2 - Free MCQ Test with solutions


MCQ Practice Test & Solutions: Differential Calculus NAT Level - 2 (10 Questions)

You can prepare effectively for Physics Topic wise Tests for IIT JAM Physics with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Differential Calculus NAT Level - 2". These 10 questions have been designed by the experts with the latest curriculum of Physics 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 45 minutes
  • - Number of Questions: 10

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*Answer can only contain numeric values
Differential Calculus NAT Level - 2 - Question 1
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Maximum area of a rectangle which can be inscribed in a circle of given radius R is given by αR2. Find the value of α.


Detailed Solution: Question 1

Let rectangle has width b and height h.
Area = h·b
Also,  b2 + h2 = (2R)2 = 4R2

Area is maximum when A2 is maxima
A2 = h2(4R2 – h2)]
f(h) = h2(4R2 – h2)
For maxima,  
⇒   = h2(–2h) + (4R2 – h2)2h = 0

–h2 + 4R2 – h2 = 0
h2 = 2R2
h = √2

From physical nature of problem, it is clear that this should be maximum area since minimum area will tend towards zero.

Hence, value of α = 2
The correct answer is: 2

*Answer can only contain numeric values
Differential Calculus NAT Level - 2 - Question 2
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The radius of a right circular cylinder increases at a constant rate. Its altitude is a linear function of the radius and increases three times as fast as radius. When the radius is 1 cm the altitude is 6 cm. When the radius is 6 cm, the volume is increasing at the rate of 1 cm/s. When the radius is 36 cm, the volume is increasing at a rate of n cm3/s. The value of 'n' is equal to :


Detailed Solution: Question 2


h = αr + c
α = 3
h = 3r + c
h = 6, r = 1
c = 3


= 33 cm3/second
The correct answer is: 33

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Differential Calculus NAT Level - 2 - Question 3
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The maximum value of  is given as (λ/e). The value of  λ is


Detailed Solution: Question 3


⇒ 
For maxima or minima of y.

⇒ 
and 

Hence, y attains maximum value at 
The value of λ = 1.

The correct answer is: 1

*Answer can only contain numeric values
Differential Calculus NAT Level - 2 - Question 4
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Consider the function  If α is the length of interval of decrease and β be the length of interval of increase, then β/α is


Detailed Solution: Question 4

f(x) is decreasing in  and increasing in 

The correct answer is: 7

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Differential Calculus NAT Level - 2 - Question 5
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The ratio of absolute maxima and minima of  is


Detailed Solution: Question 5

Absolute Maxima = 3
and The Absolute Minima = 1/3

The correct answer is: 9

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Differential Calculus NAT Level - 2 - Question 6
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If the interval of monotonicity of the function  Find the value of  α?


Detailed Solution: Question 6


⇒ 
⇒ 
⇒ 
Hence,    value of α = 1
The correct answer is: 1

*Answer can only contain numeric values
Differential Calculus NAT Level - 2 - Question 7
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The least area of a circle circumscribing any right triangle of area S is given as απS. Find the value of α.


Detailed Solution: Question 7


Area of 
S = r2sin θ
⇒ 
Area of circle = 
Least area = πS

So,               Value of α = 1

The correct answer is: 1

*Answer can only contain numeric values
Differential Calculus NAT Level - 2 - Question 8
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Let  f(x) = 2x3 + ax2 + bx - 3cos2 x is an increasing function for all  x∈R  such that  ma2 + nb + 18 < 0 then the value of m + n + 7 is


Detailed Solution: Question 8

Given   


D < 0

m = 1, n = – 6
m + n + 7 = 1 – 6 + 7
= 8 – 6 = 2

The correct answer is: 2

*Answer can only contain numeric values
Differential Calculus NAT Level - 2 - Question 9
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If the maximum value of the function f(x) = (sin-1 x)3 + (cos-1 x)3, -1 < x  < 1 is α and minimum value is β and α - β is of the form n · π3. Find the value of n.


Detailed Solution: Question 9

Let  

π/4  is point of minima

The correct answer is: 0.844

*Answer can only contain numeric values
Differential Calculus NAT Level - 2 - Question 10
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If a, b, c, d are real numbers such that then the equation ax3 + bx2 + cx + d = 0  has at least one root in (0, α). Find the value of α.


Detailed Solution: Question 10

⇒  6a + 4b + 3c + 3d = 0
Let  

f(0) = e

Since f(x) is continuous and differentiable in (0,2) and f(0) = f(2) = e

Hence, according to Rolle's Theorem, the equation

 has at least one root in (0,2). Thus, value of α = 2.

The correct answer is: 2

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About this Physics Practice Test

This test contains 10 MCQs on Differential Calculus NAT Level - 2 with detailed solutions for each question. It is part of the Topic wise Tests for IIT JAM Physics course on EduRev, designed to align with the current Physics syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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