NDA Application of Derivatives questions with solutions
Maxima, minima, monotonicity, tangents and rate of change. 34 questions from our 2016–2025 NDA pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.
NDA 2025
- The local maximum value of f(x)=2x^3-9x^2+12x+5 is
- The least value of the square of the distance of a point on the curve y=x^2 from the point (0,2) is
- The slope of the normal to the curve y=x^2 at the point (1,1) is
- F(x)=e^x is increasing for all real x. 2. f(x)=x^3 is increasing for all real x.
- F(x)=sin x is increasing in the interval (0,(π)/(2)). 2. f(x)=cos x is increasing in the interval (0,(π)/(2)).
NDA 2024
NDA 2023
- The function f(x)=x^2e^-x has a local maximum at x equal to
- The sum of two positive numbers is 20. The minimum value of the sum of their squares is
- A ladder 5 m long leans against a vertical wall. Its foot is pulled away at 2 m/s. When the foot is 3 m from the wall, the top of the ladder slides…
- The function f(x)=x^2 is increasing on the whole real line. 2. The function f(x)=x^3 is increasing on the whole real line.
NDA 2022
NDA 2021
NDA 2020
NDA 2019
- The slope of the normal to the curve x^2+xy+y^2=7 at the point (1,2) is
- The tangent to the curve y=x^3-3x+1 is parallel to the line y=9x+4 at the point with positive abscissa. The point is
- The function f(x)=x^3 is strictly increasing on mathbb R even though f'(0)=0. 2. The function f(x)=1/x is decreasing on its entire domain mathbb…
- For the function f(x)=x^3 on the interval [0,3], the value of c in Lagrange's mean value theorem is
- The function f(x)=2x^3-15x^2+36x+7 is strictly decreasing in the interval
- The local minimum value of f(x)=xln x for x>0 is
- Non-negative numbers x and y satisfy x+y=9. The maximum value of x^2y is
- The difference between the greatest and the least values of f(x)=x^3-3x^2+2 on [0,3] is
NDA 2017
NDA 2016
Other Mathematics topics
Three Dimensional Geometry 48Vector Algebra 60Complex Numbers and Quadratic Equations 35Binomial Theorem 16Sequences and Series 36Quadratic Equations 27Permutations and Combinations 25Statistics 35Probability 27Matrices 37Determinants 13Sets, Relations and Functions 39Binary Number System 11Logarithms 11Inverse Trigonometric Functions 22Trigonometric Functions and Identities 49Trigonometric Equations 16Properties of Triangles 18Heights and Distances 12Straight Lines 43Circles 21Conic Sections 28Limits 23Continuity and Differentiability 16Derivatives 33Integrals 16Definite Integrals 23Application of Integrals 12Differential Equations 30