Integral Calculus and DEs NDA PYQ Topic Wise (2016–2026)

Explore: All NDA topics · NDA Mathematics PYQs · NDA hub · Syllabus & pattern · NDA 2026

Answer first

Integral Calculus and Differential Equations PYQs (previous year questions) for NDA: Integral Calculus and Differential Equations (Mathematics) had 232 questions across the 42 official NDA papers we tagged (2016–2026), and appeared in 21 of them. Asked in 11 of 11 years. The concepts asked in the most papers: Definite Integrals, Area Under Curves, Indefinite Integrals.

Year-wise question count

Asked in 11 of 11 years.

Most-asked concepts

Sorted by the number of papers a concept appeared in.

How to practise Integral Calculus and Differential Equations PYQs

1. Start with the concepts at the top of the table. They have come back the most.
2. Solve one year’s Integral Calculus and Differential Equations questions from the official PDF against the clock, then check the answer listed below.
3. Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
4. Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.

Questions by year

Each line gives the question number and paper, type, concept, our one-line summary and the official answer, with a link to the official PDF.

NDA2026

• Q.79 (NDA (I) Mathematics) · MCQ · Differential Equations: Solve cos(dy/dx) = p with an initial condition PDF
• Q.83 (NDA (I) Mathematics) · MCQ · Definite Integrals: Value of k for a definite trigonometric integral PDF
• Q.84 (NDA (I) Mathematics) · MCQ · Definite Integrals: Related integral of (a cos x + b sin x)/(sin x + cos x) PDF
• Q.87 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area under y = sin x on an interval in terms of k PDF
• Q.88 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area under y = cos x on an interval in terms of k PDF
• Q.89 (NDA (I) Mathematics) · MCQ · Area Under Curves: Number of intersection points of y = x² and y = 2|x| PDF
• Q.90 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area bounded by y = x², y = 2|x| and lines x = 0, x = 1 PDF
• Q.91 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Coefficient A in a log-form integral of a trig rational function PDF
• Q.92 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Coefficient B in the same integral PDF
• Q.93 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of f/g over [0,4] using f(4-x) property PDF
• Q.94 (NDA (I) Mathematics) · MCQ · Definite Integrals: Companion integral with g(4-x) in the denominator PDF
• Q.97 (NDA (I) Mathematics) · MCQ · Differential Equations: Second derivative of x with respect to y from an exponential DE PDF
• Q.98 (NDA (I) Mathematics) · MCQ · Differential Equations: Particular solution of the DE with y(0) = 0 PDF
• Q.71 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of a √x expression over √(1 - x³) PDF
• Q.72 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of a rational expression in a, b, c PDF
• Q.73 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of 10ˣeˣ PDF
• Q.74 (NDA (II) Mathematics) · MCQ · Definite Integrals: Definite integral of a power of x times (1 + ln x) PDF
• Q.75 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of an additive function over symmetric limits PDF
• Q.76 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area under y = e^|x| between |x| = 1 and y = 0 PDF
• Q.77 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area under a curve with slope 2x through the origin PDF
• Q.78 (NDA (II) Mathematics) · MCQ · Differential Equations: Solve y dx - x dy - y² cos x dx = 0 PDF
• Q.79 (NDA (II) Mathematics) · MCQ · Differential Equations: DE of a family of straight lines through a point PDF
• Q.80 (NDA (II) Mathematics) · MCQ · Differential Equations: Degree of the DE of a family of curves PDF
• Q.98 (NDA (II) Mathematics) · MCQ · Differential Equations: Solve dy/dx = 1 + x cot(y - x) PDF

NDA2025

• Q.77 (NDA (I) Mathematics) · MCQ · Differential Equations: Nature of a curve through the origin from its tangent slope condition PDF
• Q.78 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area bounded by the curve, x-axis and x=4 PDF
• Q.82 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Integral of 1/(1-cos x) PDF
• Q.86 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area between y=|x-3| and y=3 PDF
• Q.90 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area bounded by x^2-1 and the x-axis PDF
• Q.99 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of [x^2] from √2 to √3 PDF
• Q.100 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of [x^2] from √2 to 2 PDF
• Q.74 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area bounded by y=x|x|, the x-axis, x=-2 and x=1 PDF
• Q.85 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: u+v for integrals of e^x cos x and e^x sin x PDF
• Q.86 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Statements relating derivatives of u and v PDF
• Q.91 (NDA (II) Mathematics) · MCQ · Order and Degree: Degree of a differential equation with fractional powers PDF
• Q.92 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of x-[x] from n to n+1 PDF
• Q.93 (NDA (II) Mathematics) · MCQ · Differential Equations: Verify given functions as solutions of two differential equations PDF
• Q.94 (NDA (II) Mathematics) · MCQ · Differential Equations: General solution of (x+y)^2 dy/dx = k^2 PDF
• Q.95 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of 1/(10^x+10^-x) PDF
• Q.97 (NDA (II) Mathematics) · MCQ · Definite Integrals: Relation between two definite integrals by substitution PDF
• Q.98 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area of region |x|≤2k and |y|≤k PDF

NDA2024

• Q.71 (NDA (I) Mathematics) · MCQ · Differential Equations: Intersection of two solution curves of dy/dx=x PDF
• Q.72 (NDA (I) Mathematics) · MCQ · Formation of DE: Differential equation of y=e^x(a cos x + b sin x) PDF
• Q.74 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of an odd function over [-1,1] PDF
• Q.75 (NDA (I) Mathematics) · MCQ · Order and Degree: Order and degree of a differential equation with fractional power PDF
• Q.76 (NDA (I) Mathematics) · MCQ · Differential Equations: Value of an expression from solving dy/dx=2e^x y^3 PDF
• Q.77 (NDA (I) Mathematics) · MCQ · Definite Integrals: Relation between integrals of e^-x and |e^-x| PDF
• Q.78 (NDA (I) Mathematics) · MCQ · Definite Integrals: Definite integral of a trig rational function on [0,π/2] PDF
• Q.81 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Constant α in an integral of (3cosx+4sinx)/(2cosx+5sinx) PDF
• Q.82 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Constant β in the same trig rational integral PDF
• Q.89 (NDA (I) Mathematics) · MCQ · Definite Integrals: Value of integral of |sin x| over a 100π interval PDF
• Q.90 (NDA (I) Mathematics) · MCQ · Definite Integrals: Derivative of φ(a), an integral with variable limits PDF
• Q.93 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral over [-1,0] of |x-1|·[x] PDF
• Q.94 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral over [0,2] of |x-1|·[x] PDF
• Q.95 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Constant α in integral of 1/(√(x+1)-√(x-1)) PDF
• Q.96 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Constant β in integral of 1/(√(x+1)-√(x-1)) PDF
• Q.97 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area of the major segment of a circle cut by y=x PDF
• Q.98 (NDA (I) Mathematics) · MCQ · Area Under Curves: Value of a ratio of the two segment areas of a circle PDF
• Q.100 (NDA (I) Mathematics) · MCQ · Definite Integrals: Value of 8 times the integral of f over [1,2] PDF
• Q.87 (NDA (II) Mathematics) · MCQ · Area Under Curves: k for area between y^2=kx and x=k equal to 4/3 PDF
• Q.88 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area of the parabola bounded by its latus rectum PDF
• Q.89 (NDA (II) Mathematics) · MCQ · Order and Degree: Order and degree of y dx + (x - y^3) dy = 0 PDF
• Q.90 (NDA (II) Mathematics) · MCQ · Differential Equations: Solution of y dx + (x - y^3) dy = 0 PDF
• Q.91 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of |x^2-x-2| over [0,2] PDF
• Q.92 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of |x^2-x-2| over [0,3] PDF
• Q.94 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of the odd function g over [-π,π] PDF
• Q.97 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of 1/(sinx+cosx+1) over [0,π/2] PDF
• Q.98 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of sinx/(sinx+cosx+1) over [0,π/2] PDF
• Q.99 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: |U^2-V^2| from the result of integrating (x^2-1)/√(x^2+1) PDF
• Q.100 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Identify U(x)V(x) in the same integral PDF

NDA2023

• Q.59 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area of the minor segment cut from a circle by y = x (official answer: A) PDF
• Q.60 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area of the major segment cut from the circle by y = x (official answer: B) PDF
• Q.71 (NDA (I) Mathematics) · MCQ · Definite Integrals: Find Q in a sum of exponentials from value, derivative and integral data (official answer: B) PDF
• Q.72 (NDA (I) Mathematics) · MCQ · Definite Integrals: Find R in the same exponential function (official answer: C) PDF
• Q.74 (NDA (I) Mathematics) · MCQ · Differential Equations: Order of the differential equation of a family of curves (official answer: A) PDF
• Q.75 (NDA (I) Mathematics) · MCQ · Differential Equations: Degree of the differential equation of the family (official answer: B) PDF
• Q.81 (NDA (I) Mathematics) · MCQ · Definite Integrals: Ratio (I1 + I2)/(I1 - I2) for two definite integrals (official answer: dropped in the final key) PDF
• Q.82 (NDA (I) Mathematics) · MCQ · Definite Integrals: Value of 8 I1^2 (official answer: D) PDF
• Q.83 (NDA (I) Mathematics) · MCQ · Definite Integrals: Value of the second integral I2 (official answer: A) PDF
• Q.84 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of |x|/x from a to b when a < 0 < b (official answer: A) PDF
• Q.85 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of |x|/x from a to b when both are negative (official answer: B) PDF
• Q.93 (NDA (I) Mathematics) · MCQ · Area Under Curves: Negative m for which lines y = x, y = mx, x = 2 bound area 3 (official answer: A) PDF
• Q.95 (NDA (I) Mathematics) · MCQ · Differential Equations: Which function solves a given differential equation (official answer: D) PDF
• Q.51 (NDA (II) Mathematics) · MCQ · Differential Equations: Directrix of the parabola solving a given differential equation (official answer: A) PDF
• Q.61 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of sin^4 x + cos^4 x over a given interval (official answer: B) PDF
• Q.62 (NDA (II) Mathematics) · MCQ · Definite Integrals: Value of a definite integral with a 1 + 3^x denominator (official answer: C) PDF
• Q.67 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of |sin x| over a multiple of π (official answer: D) PDF
• Q.68 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area between y = x|x| and the x-axis on [-1, 1] (official answer: A) PDF
• Q.69 (NDA (II) Mathematics) · MCQ · Differential Equations: Order and degree of a given differential equation (official answer: D) PDF
• Q.70 (NDA (II) Mathematics) · MCQ · Differential Equations: Differential equation of parabolas y^2 = 4a(x - b) (official answer: D) PDF

NDA2022

• Q.57 (NDA (I) Mathematics) · MCQ · Order and Degree: Degree of a given differential equation (official answer: D) PDF
• Q.58 (NDA (I) Mathematics) · MCQ · Formation of Differential Equations: Decay constant of a radioactive substance with half-life 100 years (official answer: A) PDF
• Q.60 (NDA (I) Mathematics) · MCQ · Area Under Curves: Value of k from area bounded by a parabola and its latus rectum (official answer: C) PDF
• Q.61 (NDA (I) Mathematics) · MCQ · Definite Integrals: Definite integral of 1/(sin x + cos x)^2 from 0 to pi/4 (official answer: B) PDF
• Q.62 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Integral of (sin x)^(-1/2) (cos x)^(-3/2) (official answer: B) PDF
• Q.63 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Sum of two exponential indefinite integrals (official answer: B) PDF
• Q.64 (NDA (I) Mathematics) · MCQ · Definite Integrals: Definite integral of x/|x| from -2 to -1 (official answer: B) PDF
• Q.72 (NDA (I) Mathematics) · MCQ · Solving Differential Equations: Value of y(1) for a first-order differential equation (official answer: D) PDF
• Q.78 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area in the first quadrant between y = x and a curve (official answer: B) PDF
• Q.80 (NDA (I) Mathematics) · MCQ · Formation of Differential Equations: Family of curves represented by a differential equation (official answer: C) PDF
• Q.74 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of a power of x times (1 + ln x) (official answer: B) PDF
• Q.75 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of e^x times a logarithmic expression (official answer: A) PDF
• Q.76 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of a trigonometric quotient (official answer: C) PDF
• Q.80 (NDA (II) Mathematics) · MCQ · Area Under Curves: First-quadrant area bounded by a circle arc, y = x and y = 0 (official answer: C) PDF
• Q.81 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area bounded by x = |y| and x = 2 (official answer: C) PDF
• Q.94 (NDA (II) Mathematics) · MCQ · Definite Integrals: Evaluate a definite integral (official answer: B) PDF
• Q.95 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of sin^4 + cos^4 over a longer interval in terms of k (official answer: D) PDF
• Q.96 (NDA (II) Mathematics) · MCQ · Definite Integrals: Definite integral of exponential times sin and cos (official answer: A) PDF
• Q.97 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area enclosed by a circle, y = sin x and x = 0 (official answer: B) PDF
• Q.98 (NDA (II) Mathematics) · MCQ · Order and Degree: Statements on order and degree of two differential equations (official answer: B) PDF
• Q.99 (NDA (II) Mathematics) · MCQ · Formation of Differential Equations: Differential equation of parabolas with vertex at origin (official answer: B) PDF
• Q.100 (NDA (II) Mathematics) · MCQ · Solving Differential Equations: Solution of a first-order differential equation with cos x (official answer: C) PDF

NDA2021

• Q.77 (NDA (I) Mathematics) · MCQ · Variable Separable: Time for a particle with dx/dt = x+1 to cover 24 m (official answer: C) PDF
• Q.78 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of f(a-x)/(f(x)+f(a-x)) from 0 to a (official answer: D) PDF
• Q.80 (NDA (I) Mathematics) · MCQ · Definite Integrals: Identify g(x) from an integral of f(x)+f(-x) (official answer: A) PDF
• Q.81 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area under upper semicircle y = sqrt(16-x^2) (official answer: B) PDF
• Q.85 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Integrate 1/(sec x + tan x) (official answer: D) PDF
• Q.86 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Integrate 1/sec^2(tan^-1 x) (official answer: B) PDF
• Q.96 (NDA (I) Mathematics) · MCQ · Order and Degree: Order of the DE from a one-parameter family (official answer: A) PDF
• Q.97 (NDA (I) Mathematics) · MCQ · Order and Degree: Degree of a DE with a square root of second derivative (official answer: A) PDF
• Q.98 (NDA (I) Mathematics) · MCQ · Formation of DE: DE whose general solution is ae^x + be^-x (official answer: B) PDF
• Q.99 (NDA (I) Mathematics) · MCQ · Variable Separable: Solve ln(dy/dx) + y = x (official answer: C) PDF
• Q.100 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Integrate e^(2 ln x + ln x^2) (official answer: D) PDF
• Q.81 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of a polynomial with respect to x^2 (official answer: D) PDF
• Q.83 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of f' over [1, 4] when f(1) = f(4) (official answer: B) PDF
• Q.84 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of e^(ln cos x) over [0, pi/2] (official answer: C) PDF
• Q.85 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integrate sqrt(1 - sin 2x) in a given range (official answer: B) PDF
• Q.86 (NDA (II) Mathematics) · MCQ · Order and Degree: Order of the DE of axis-aligned ellipses (official answer: B) PDF
• Q.87 (NDA (II) Mathematics) · MCQ · Order and Degree: Degree of the DE of circles touching both axes (official answer: B) PDF
• Q.88 (NDA (II) Mathematics) · MCQ · Formation of DE: DE satisfied by y = A - B/x (official answer: B) PDF
• Q.89 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of ln tan(x/2) over [0, pi] (official answer: A) PDF
• Q.93 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integrate 1/(x(x^2+1)) (official answer: A) PDF
• Q.96 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of f'/f for f = 2^x over [2, 10] (official answer: D) PDF
• Q.97 (NDA (II) Mathematics) · MCQ · Definite Integrals: Compare integral of |f| with integral of f (official answer: D) PDF
• Q.99 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area under greatest integer function between two lines (official answer: C) PDF

NDA2020

• Q.74 (NDA (I & II) Mathematics) · MCQ · Differential Equations: Order and degree of an integro-differential equation (official answer: B) PDF
• Q.77 (NDA (I & II) Mathematics) · MCQ · Differential Equations: Express φ dθ from e^(θφ) = c + 4θφ (official answer: B) PDF
• Q.78 (NDA (I & II) Mathematics) · MCQ · Indefinite Integrals: Integral of (4e)^(2x) (official answer: B) PDF
• Q.79 (NDA (I & II) Mathematics) · MCQ · Definite Integrals: Integral of tan³x + tan x over 0 to π/4 (official answer: B) PDF
• Q.82 (NDA (I & II) Mathematics) · MCQ · Differential Equations: Solution of dy = (1 + y²) dx (official answer: B) PDF
• Q.83 (NDA (I & II) Mathematics) · MCQ · Indefinite Integrals: Integral of (e^(log x) + sin x) cos x (official answer: C) PDF
• Q.85 (NDA (I & II) Mathematics) · MCQ · Area Under Curves: Area between y² = 2x and y = x (official answer: C) PDF
• Q.88 (NDA (I & II) Mathematics) · MCQ · Indefinite Integrals: Integral of 1/(x(xⁿ + 1)) (official answer: A) PDF
• Q.90 (NDA (I & II) Mathematics) · MCQ · Indefinite Integrals: k making an integral a rational function (official answer: C) PDF
• Q.95 (NDA (I & II) Mathematics) · MCQ · Differential Equations: Solution of x(dx - dy) + y(dy - dx) = 0 (official answer: B) PDF
• Q.99 (NDA (I & II) Mathematics) · MCQ · Differential Equations: Solution of ln(dy/dx) = x (official answer: A) PDF

NDA2019

• Q.81 (NDA (I) Mathematics) · MCQ · Differential Equations: Solve dy/dx = cos(y - x) + 1 (official answer: A) PDF
• Q.82 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of |sin x - cos x| over 0 to π/2 (official answer: B) PDF
• Q.83 (NDA (I) Mathematics) · MCQ · Differential Equations: Differential equation satisfied by y = a cos 2x + b sin 2x (official answer: D) PDF
• Q.85 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of e^(sin x) cos x over 0 to π/2 (official answer: B) PDF
• Q.87 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Integral of ln(x²) (official answer: A) PDF
• Q.89 (NDA (I) Mathematics) · MCQ · Differential Equations: DE of circles touching the y-axis at the origin (official answer: C) PDF
• Q.90 (NDA (I) Mathematics) · MCQ · Differential Equations: Order and degree of a given differential equation (official answer: C) PDF
• Q.91 (NDA (I) Mathematics) · MCQ · Differential Equations: General solution of dy/dx + x/y = 0 (official answer: A) PDF
• Q.94 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Integral of e^(x ln a) (official answer: A) PDF
• Q.95 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area of one loop of y = c sin x and the x-axis (official answer: B) PDF
• Q.71 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area bounded by |x| < 5, y = 0 and y = 8 (official answer: B) PDF
• Q.74 (NDA (II) Mathematics) · MCQ · Differential Equations: Degree of a given differential equation (official answer: A) PDF
• Q.81 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of 1/(2x² - 2x + 1) (official answer: D) PDF
• Q.82 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of 1/(x(1 + ln x)^n) (official answer: D) PDF
• Q.83 (NDA (II) Mathematics) · MCQ · Differential Equations: DE of the family y = 1/(2x² - c) (official answer: D) PDF
• Q.94 (NDA (II) Mathematics) · MCQ · Definite Integrals: Value of integral of x/(1 + sin x) from 0 to π (official answer: C) PDF
• Q.95 (NDA (II) Mathematics) · MCQ · Definite Integrals: Sum of two related definite integrals (official answer: A) PDF
• Q.96 (NDA (II) Mathematics) · MCQ · Differential Equations: DE of the family tan y = c(1 - e^x) (official answer: B) PDF
• Q.99 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area between y² = 2x and y = x (official answer: A) PDF

NDA2018

• Q.75 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area between two parabolas (official answer: C) PDF
• Q.79 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral involving sin x (official answer: A) PDF
• Q.81 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Integral of a product with x (official answer: B) PDF
• Q.82 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of greatest integer of x² (official answer: A) PDF
• Q.86 (NDA (I) Mathematics) · MCQ · Differential Equations: Solution of x dy − y dx = 0 (official answer: B) PDF
• Q.88 (NDA (I) Mathematics) · MCQ · Differential Equations: DE with periodic solution (official answer: A) PDF
• Q.90 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Integral of 1/(2ˣ−1) (official answer: B) PDF
• Q.91 (NDA (I) Mathematics) · MCQ · Order and Degree: Order and degree of DE of y²=4a(x−a) (official answer: dropped in the final key) PDF
• Q.92 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of sinx−tanx over a symmetric interval (official answer: C) PDF
• Q.93 (NDA (I) Mathematics) · MCQ · Definite Integrals: Limits a, b from two definite integrals (official answer: A) PDF
• Q.94 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of a polynomial x(1−x)ⁿ (official answer: A) PDF
• Q.99 (NDA (I) Mathematics) · MCQ · Differential Equations: Solution of (1+2x)dy−(1−2y)dx=0 (official answer: A) PDF
• Q.100 (NDA (I) Mathematics) · MCQ · Order and Degree: Order and degree of a given DE (official answer: C) PDF
• Q.81 (NDA (II) Mathematics) · MCQ · Definite Integrals: Sum of integrals of [x] and [−x] (official answer: B) PDF
• Q.82 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of |x−5| from 2 to 8 (official answer: D) PDF
• Q.83 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of sin³x cos x (official answer: D) PDF
• Q.84 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of e^(ln tan x) (official answer: B) PDF
• Q.85 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of derivative of tan⁻¹(1/x) over [−1,1] (official answer: C) PDF
• Q.87 (NDA (II) Mathematics) · MCQ · Formation of Differential Equations: DE of y = p cos ax + q sin ax (official answer: D) PDF
• Q.88 (NDA (II) Mathematics) · MCQ · Differential Equations: Curve through (−1,−2) satisfying a given DE (official answer: B) PDF
• Q.89 (NDA (II) Mathematics) · MCQ · Order and Degree: Order of DE with four arbitrary constants (official answer: D) PDF
• Q.90 (NDA (II) Mathematics) · MCQ · Differential Equations: Solution of ln(dy/dx)=ax+by (official answer: D) PDF
• Q.97 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of 1/(a²sin²x+b²cos²x) (official answer: A) PDF
• Q.99 (NDA (II) Mathematics) · MCQ · Differential Equations: Solution of dx/dy=(x+y+1)/(x+y−1) (official answer: C) PDF

NDA2017

• Q.72 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Evaluate a given indefinite integral (official answer: B) PDF
• Q.73 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Integral of 1/(x(x⁷+1)) (official answer: D) PDF
• Q.76 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Integral of (x^(e−1)+e^(x−1))/(x^e+e^x) (official answer: D) PDF
• Q.83 (NDA (I) Mathematics) · MCQ · Differential Equations: Value y(−3) from x dy = y dx + y² dy (official answer: A) PDF
• Q.85 (NDA (I) Mathematics) · MCQ · Indefinite Integrals: Periodicity of an integral of sin²x (official answer: D) PDF
• Q.86 (NDA (I) Mathematics) · MCQ · Order and Degree: Degree and order of a given differential equation (official answer: D) PDF
• Q.87 (NDA (I) Mathematics) · MCQ · Formation of Differential Equations: DE from y²−2ay+x²=a² by eliminating a (official answer: A) PDF
• Q.88 (NDA (I) Mathematics) · MCQ · Differential Equations: General solution of a first-order DE (official answer: C) PDF
• Q.90 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of f·g using symmetry properties (official answer: B) PDF
• Q.91 (NDA (I) Mathematics) · MCQ · Differential Equations: Solution of a DE with a logarithm of dy/dx (official answer: A) PDF
• Q.100 (NDA (I) Mathematics) · MCQ · Definite Integrals: Integral of |ln x / x| from 1/e to e² (official answer: B) PDF
• Q.67 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral involving tan and sec x+tan x (official answer: A) PDF
• Q.74 (NDA (II) Mathematics) · MCQ · Differential Equations: Condition for solution of dy/dx=(ax+h)/(by+k) to be a circle (official answer: B) PDF
• Q.76 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral involving sin⁻¹ of an expression (official answer: A) PDF
• Q.77 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area bounded by |x|+|y|=1 (official answer: C) PDF
• Q.81 (NDA (II) Mathematics) · MCQ · Order and Degree: Order and degree of a given differential equation (official answer: B) PDF
• Q.88 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of (ln x)² type expressions (official answer: A) PDF
• Q.90 (NDA (II) Mathematics) · MCQ · Definite Integrals: Sum of two inverse-trigonometric definite integrals (official answer: D) PDF
• Q.92 (NDA (II) Mathematics) · MCQ · Formation of Differential Equations: DE by eliminating A and C (official answer: D) PDF
• Q.94 (NDA (II) Mathematics) · MCQ · Differential Equations: Solution of a separable differential equation (official answer: D) PDF

NDA2016

• Q.13 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area bounded by the two given curves (official answer: B) PDF
• Q.16 (NDA (I) Mathematics) · MCQ · Definite Integrals: Definite integral of a greatest-integer-based function g(x) (official answer: B) PDF
• Q.17 (NDA (I) Mathematics) · MCQ · Definite Integrals: Definite integral of f(x)=x·g(x) with greatest integer function (official answer: A) PDF
• Q.21 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area under y=|x−1|+x² between two ordinates (official answer: A) PDF
• Q.22 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area under y=|x−1|+x² between another pair of ordinates (official answer: D) PDF
• Q.23 (NDA (I) Mathematics) · MCQ · Definite Integrals: AP nature of a sequence defined by a trigonometric integral (official answer: C) PDF
• Q.24 (NDA (I) Mathematics) · MCQ · Definite Integrals: Difference of consecutive terms of an integral-defined sequence (official answer: B) PDF
• Q.33 (NDA (I) Mathematics) · MCQ · Area Under Curves: Area bounded by y=|x−1|, |x|=2 and the x-axis (official answer: C) PDF
• Q.78 (NDA (I) Mathematics) · MCQ · Order and Degree: Order and degree of DE whose solution has a parameter c (official answer: D) PDF
• Q.79 (NDA (I) Mathematics) · MCQ · Definite Integrals: Definite integral of a greatest integer function (official answer: C) PDF
• Q.80 (NDA (I) Mathematics) · MCQ · Definite Integrals: Combining definite integrals over adjacent intervals (official answer: B) PDF
• Q.86 (NDA (I) Mathematics) · MCQ · Definite Integrals: Definite integral of |cos x| over an interval (official answer: D) PDF
• Q.75 (NDA (II) Mathematics) · MCQ · Area Under Curves: Area bounded by |y|=1−x² (official answer: B) PDF
• Q.91 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of f over [−1,1] given a derivative relation (official answer: C) PDF
• Q.92 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of (x⁴−1)/(x²√(x⁴+x²+1)) (official answer: C) PDF
• Q.93 (NDA (II) Mathematics) · MCQ · Order and Degree: Degree and order of DE from a given solution family (official answer: A) PDF
• Q.94 (NDA (II) Mathematics) · MCQ · Differential Equations: Curve through (1,1) with slope 2y/x (official answer: B) PDF
• Q.95 (NDA (II) Mathematics) · MCQ · Differential Equations: Value y(−3) from x dy = y dx + y² dy (official answer: A) PDF
• Q.96 (NDA (II) Mathematics) · MCQ · Order and Degree: Order of an equation with derivative and integral (official answer: B) PDF
• Q.97 (NDA (II) Mathematics) · MCQ · Formation of Differential Equations: DE of lines at unit distance from origin (official answer: C) PDF
• Q.98 (NDA (II) Mathematics) · MCQ · Indefinite Integrals: Integral of e^(sin x) times a trigonometric expression (official answer: B) PDF
• Q.99 (NDA (II) Mathematics) · MCQ · Definite Integrals: Find k for ∫dx/(3cosx+5) over [0,π/2] (official answer: B) PDF
• Q.100 (NDA (II) Mathematics) · MCQ · Definite Integrals: Integral of |1−x⁴| from 1 to 3 (official answer: D) PDF

Other Mathematics topics

• Algebra PYQs
• Matrices and Determinants PYQs
• Trigonometry PYQs
• Analytical Geometry (2D and 3D) PYQs
• Differential Calculus PYQs
• Vector Algebra PYQs
• Statistics and Probability PYQs

FAQ

How many Integral Calculus and Differential Equations questions come in NDA?

In the official papers we tagged: 24 in 2026 (2 papers), 17 in 2025 (2 papers), 29 in 2024 (2 papers), 20 in 2023 (2 papers), 22 in 2022 (2 papers), 23 in 2021 (2 papers), 11 in 2020 (1 paper), 19 in 2019 (2 papers), 24 in 2018 (2 papers), 20 in 2017 (2 papers) and 23 in 2016 (2 papers). That is 232 questions in all, about 9% of Mathematics.

Which Integral Calculus and Differential Equations topics repeat in NDA?

Asked in the most papers: Definite Integrals, Area Under Curves, Indefinite Integrals. The concept table lists every one with its count.

Are these official NDA questions?

Yes. Every question is from an official NDA paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.