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NDA Application of Derivatives PYQs with Solutions

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

66 questionsMathematics2017–2026Answers + solutions

About Application of Derivatives PYQs

Application of Derivatives has 66 previous year questions in the Quantrex Academy NDA Mathematics bank. The 66 questions in this list come from NDA (66), spanning 2017 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Application of Derivatives PYQs with Solutions

About Application of Derivatives PYQs

Questions by year (this list)

Application of Derivatives questions with solutions

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 ?

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

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 ?

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 ?

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

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?

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

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

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

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

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

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

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

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

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

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

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:

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

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

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

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:

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

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

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?

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

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

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

How many extreme values does 4 x+2 x , where 0 < x < (π)/(2) have?

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

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 ?

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

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

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

For what value of θ , where 0 < θ < (π)/(2) , does θ+ θ θ attain maximum value?

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

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

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

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

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

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

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

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

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?

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

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?

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 (-(π)/(2), (π)/(2)) . Which of the

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

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

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

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 ?

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?

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 ?

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

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?

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

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

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

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

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

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

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

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

The maximum value of In x x is

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

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

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

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