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Application of Derivatives — NDA Mathematics PYQs

66 previous year questions from Application of Derivatives with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

66 questionsMathematicsSolutions on every page
1

Passage: Let S and T be the sets where f(x)= x^3 3 - 5x^2 2 +6x+7 decreases and increases respectively. Question: What is T equal to ?

NDA 2026 Solution View → 2

What is the length of the longest interval in which the function f(x)=2 ^2 x-1 is decreasing ?

NDA 2026 Solution View → 3

Passage: Let S and T be the sets where f(x)= x^3 3 - 5x^2 2 +6x+7 decreases and increases respectively. Question: What is S equal to ?

NDA 2026 Solution View → 4

For the following three (03) items: Let y = f(x) = x ⁻¹ x 1 - x^2 + 1 - x^2 . What is the slope of the tangent to the curve y = f(x) at x = 0.5 ?

NDA 2025 Solution View → 5

Consider the following statements regarding the function f(x) = 1 x - 5 : Statement-I: f(x) is decreasing on the intervals x 5 . Statement-II: f'(x) > 0 for all x 5 . Which one of

NDA 2025 Solution View → 6

Consider the following for the two (02) items that follow: Let ABC be a triangle right-angled at B and AB + AC = 3 units. What is the maximum area of the triangle?

NDA 2025 Solution View → 7

Consider the following for the two (02) items that follow: Let ABC be a triangle right-angled at B and AB + AC = 3 units. What is A equal to if the area of the triangle is maximum?

NDA 2025 Solution View → 8

A wire of length 20 cm is to be bent into a rectangle. Which of the following statements is/are correct? I. The rectangle of the largest area is the square. II. It is possible to f

NDA 2025 Solution View → 9

Consider the following for the two (02) items that follow: Let the function f(x) = x^2 + 9 . Consider the following statements: I. f(x) is an increasing function. II. f(x) has loca

NDA 2025 Solution View → 10

For the following two (02) items: Consider the function f(x) = 1 - [3] (x-1)^2 . The function has

NDA 2025 Solution View → 11

Consider the following for the two (02) items that follow: The slope of the tangent to the curve y = f(x) at (x, f(x)) is 4 for every real number x and the curve passes through the

NDA 2025 Solution View → 12

For the following three (03) items: Consider the function f(x) = x|x| . Consider the following statements: I. The function is increasing in the interval (- , ) . II. The function i

NDA 2025 Solution View → 13

Consider the following statements: Statement-I: The function f(x) = x^3 + 128 x has a minimum value 48 at x = 4 . Statement-II: As x increases through 4, f'(x) changes sign from po

NDA 2025 Solution View → 14

Paragraph: Let f(x)= 2 x+x on [ - 2 , 2 ] Question: What is the greatest value of f(x) ?

NDA 2024 Solution View → 15

Let f(x)= x x ;(x 1) Consider the following statements: 1. f(x) is increasing in the interval (e, ) 2. f(x) is decreasing in the interval (1, e) 3. 9 7 7 9 Which of the statements

NDA 2024 Solution View → 16

Paragraph: Let f(x)= 2 x+x on [ - 2 , 2 ] Question: What is the least value of f(x) ?

NDA 2024 Solution View → 17

The non-negative values of b for which the function 16 x^3 3 -4 b x^2+x has neither maximum nor minimum in the range x 0 is:

NDA 2024 Solution View → 18

A differentiable function f(x) has a local maximum at x=0 . Let y=2 f(x)+a x-b . Which of the following is/are correct? 1. f^ (0)=0 2. f^ (0) 0 Select the correct answer using the

NDA 2024 Solution View → 19

A differentiable function f(x) has a local maximum at x=0 . Let y=2 f(x)+a x-b . The function y has a relative maxima at x=0 for

NDA 2024 Solution View → 20

Let f(x)= x x ;(x 1) Consider the following statements: 1. f^ (e)= 1 e 2. f ( x ) attains local minimum value at x=e 3. A local minimum value of f(x) is e Which of the statements g

NDA 2024 Solution View → 21

A function is defined by f(x)= | array ccc x+1 & 2 & 3 2 & x+4 & 6 3 & 6 & x+9 array | The function attains local minimum value at:

NDA 2023 Solution View → 22

Paragraph: Let x= ^2 A+ A+1 A where 0 A 2 Question: At what value of A does x attain the minimum value?

NDA 2023 Solution View → 23

Paragraph: Given that m( )= ^2 +n^2 ^2 +2 n , where n is a fixed positive real number. Question: Under what condition does m attain the least value?

NDA 2023 Solution View → 24

Consider the following statements: 1. f(x)= x is increasing in (0, ) 2. g(x)=e^x+e^ 1 x is decreasing in (0, ) Which of the statements given above is/are correct?

NDA 2023 Solution View → 25

Paragraph: Let x= ^2 A+ A+1 A where 0 A 2 Question: What is the minimum value of x ?

NDA 2023 Solution View → 26

Given that 4 x^2+y^2=9 What is the maximum value of xy?

NDA 2023 Solution View → 27

Let f(x)= 2-x + 2+x . What is the greatest value of the function?

NDA 2023 Solution View → 28

How many extreme values does 4 x+2 x , where 0 x 2 have?

NDA 2022 Solution View → 29

In which one of the following intervals is the function f(x)= x^3 3 - 7 x^2 2 +6 x+5 decreasing?

NDA 2022 Solution View → 30

If the derivative of the function f(x)= m x +2 n x+1 vanishes at x=2 , then what is the value of m+8 n ?

NDA 2022 Solution View → 31

Where does the function f(x)= _ j=1 ^7(x-j)^2 attain its minimum value ?

NDA 2022 Solution View → 32

Under which one of the following conditions does the function f(x)=(p x)^2+(q cosec x)^2 attain minimum value?

NDA 2022 Solution View → 33

Let f(x) be a function such that f^ (x)=g(x) and f^ (x)=-f(x) . Let h(x)= f(x) ^2+ g(x) ^2 . Then consider the following statements : 1. h^ (3)=0 2. h(1)=h(2) Which of the statemen

NDA 2022 Solution View → 34

For what value of , where 0 2 , does + attain maximum value?

NDA 2021 Solution View → 35

Consider the following statements in respect of the function f(x)=x+ 1 x : 1. The local maximum value of f(x) is less than its local minimum value. 2. The local maximum value of f(

NDA 2021 Solution View → 36

What is the maximum area of a rectangle that can be inscribed in a circle of radius 2 units?

NDA 2021 Solution View → 37

If the function f(x)=x^2-k x is monotonically increasing in the interval (1, ) , then which one of the following is correct?

NDA 2021 Solution View → 38

What is the condition that f(x)=x^3+x^2+k x has no local extremum?

NDA 2021 Solution View → 39

The tangent to the curve x^2=y at (1,1) makes an angle with the positive direction of x -axis. Which one of the following is correct?

NDA 2021 Solution View → 40

Where does the tangent to the curve y=e^x at the point (0,1) meet x -axis?

NDA 2021 Solution View → 41

Consider the following statements in respect of the function f(x)=x^2+1 in the interval (1,2) . 1. The maximum value of the function is 5 . 2. The minimum value of the function is

NDA 2021 Solution View → 42

The curve y=-x^3+3 x^2+2 x-27 has the maximum slope at

NDA 2021 Solution View → 43

A 24 cm long wire is bent to form a triangle with one of the angles as 60^ . What is the altitude of the triangle having the greatest possible area?

NDA 2021 Solution View → 44

Consider the following statements in respect of the function f(x)= x : 1. f(x) increases in the interval (0, ) . 2. f(x) decreases in the interval ( 5 2 , 3 ) . Which of the above

NDA 2021 Solution View → 45

Let l be the length and b be the breadth of a rectangle such that l+b=k . What is the maximum area of the rectangle?

NDA 2020 Solution View → 46

Consider the following statements : 1. The function f(x)= x increases in the interval (0, ) . 2. The function f(x)= x increases in the interval (- 2 , 2 ) . Which of the above stat

NDA 2020 Solution View → 47

Let y=3 x^2+2 . If x changes from 10 to 10.1 , then what is the total change in y ?

NDA 2020 Solution View → 48

The radius of a circle is increasing at the rate of 0.7 ~cm / sec . What is the rate of increase of its circumference?

NDA 2020 Solution View → 49

What is the minimum value of a^2 ^2 x + b^2 ^2 x where a 0 and b 0 ?

NDA 2019 Solution View → 50

Paragraph: A curve y = m e^ m x where m > 0 intersects y-axis at a point P. Question: What is the equation of tangent to the curve at P ?

NDA 2019 Solution View → 51

Paragraph: A curve y = m e^ m x where m > 0 intersects y-axis at a point P. Question: How much angle does the tangent at P make with y -axis?

NDA 2019 Solution View → 52

Paragraph: A curve y = m e^ m x where m > 0 intersects y-axis at a point P. Question: What is the slope of the curve at the point of intersection P ?

NDA 2019 Solution View → 53

What is the minimum value of a^2 x+b^2 y where x y=c^2 ?

NDA 2019 Solution View → 54

Paragraph: Consider the function f(x)=3 x^4-20 x^3-12 x^2+288 x+1 Question: In which one of the following intervals is the function increasing?

NDA 2019 Solution View → 55

Which one of the following is correct in respect of the function f(x)=x x+ x+ 1 2 ^2 x ?

NDA 2018 Solution View → 56

In which one of the following intervals is the function f(x)=x^2-5 x+6 decreasing?

NDA 2018 Solution View → 57

Paragraph: Three sides of a trapezium are each equal to 6 cm . Let (0, 2 ) be the angle between a pair of adjacent sides. Question: If the area of the trapezium is the maximum poss

NDA 2018 Solution View → 58

Paragraph: Three sides of a trapezium are each equal to 6 cm . Let (0, 2 ) be the angle between a pair of adjacent sides. Question: What is the maximum area of the trapezium?

NDA 2018 Solution View → 59

Paragraph: Three sides of a trapezium are each equal to 6 cm . Let (0, 2 ) be the angle between a pair of adjacent sides. Question: If the area of the trapezium is maximum, what is

NDA 2018 Solution View → 60

What is the maximum value of 16 -12 ^2 ?

NDA 2018 Solution View → 61

Which one of the following is correct in respect of the function f( x )= x ( x -1)( x +1) ?

NDA 2017 Solution View → 62

Consider the following statements : 1. dy dx at a point on the curve given slope of the tangent at that point. 2. If a(t) denotes acceleration of a particle, then a ( t ) dt + c gi

NDA 2017 Solution View → 63

The maximum value of In x x is

NDA 2017 Solution View → 64

A cylindrical jar without a lid has to be constructed using a given surface area of a metal sheet. If the capacity of the jar is to be maximum, then the diameter of the jar must be

NDA 2017 Solution View → 65

What is the length of the longest interval in which the function f( x )=3 x -4 ^3 x is increasing?

NDA 2017 Solution View → 66

What is the maximum area of a triangle that can be inscribed in a circle of radius a?

NDA 2017 Solution View →
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