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Friday, 9 October

JEE Main Maths · Class 12

Application of Derivatives: JEE Main previous year questions

Application of Derivatives had 47 questions in the 42 JEE Main shifts Lumi analysed, about 1.2 a shift, asked in 30 of 42 shifts. It ranks 13 of 22 Maths chapters by questions; 21% of its questions were hard.

Questions
47
in 30 of 42 shifts
A shift, on average
1.2
of 25 Maths questions
Since 2024
-0.6
1.4 a shift in 2017–23, 0.8 in 2024–26
Numerical answer
6
13% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
06122’177’205’2110’221’2312’247’253’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20172
  • 20207
  • 20215
  • 202210
  • 20231
  • 202412
  • 20257
  • 20263
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

9 topics and 29 distinct ideas; 9 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

1 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
9 repeat

Study it on Lumi

Application of Derivatives: the interactive lesson

Every question

All 47 Application of Derivatives questions

Newest first. Each opens with its options and the official answer.

2026 3 questions

  1. 2 Apr 2026, Shift 1 · Q18The number of critical points of the function f(x)={∣sin⁡xx∣,x≠01,x=0f(x)=\begin{cases}\left|\frac{\sin x}{x}\right|, & x\neq0\\ 1, & x=0\end{cases} in the…HardSingle correct
  2. 2 Apr 2026, Shift 2 · Q18Let f(x)f(x) be a polynomial of degree 5, and have extrema at x=1x = 1 and x=−1x = -1. If lim⁡x→0(f(x)x3)=−5\lim_{x \to 0}\left(\frac{f(x)}{x^3}\right) = -5,…MediumSingle correct
  3. 4 Apr 2026, Shift 2 · Q12max⁡0≤x≤π(16sin⁡(x2)cos⁡3(x2))\max_{0\le x\le\pi}\left(16\sin\left(\frac x2\right)\cos^3\left(\frac x2\right)\right) is equal to:MediumSingle correct

2025 7 questions

  1. 2 Apr 2025, Shift 1 · Q8If the function f(x)=2x3−9ax2+12a2x+1f(x)=2x^3-9ax^2+12a^2x+1, where a>0a>0, attains its local maximum and local minimum values at p and q, respectively, such…MediumSingle correct
  2. 3 Apr 2025, Shift 2 · Q16Let f:R→Rf: \mathrm{R} \to \mathrm{R} be a function defined by f(x)=∣∣x+2∣−2∣x∣∣f(x) = \left||x+2| - 2|x|\right|. If mm is the number of points of local…MediumSingle correct
  3. 3 Apr 2025, Shift 2 · Q17The shortest distance between the curves y2=8xy^2 = 8x and x2+y2+12y+35=0x^2 + y^2 + 12y + 35 = 0 is:MediumSingle correct
  4. 4 Apr 2025, Shift 2 · Q17Let a>0a>0. If the function f(x)=6x3−45ax2+108a2x+1f(x)=6x^3-45ax^2+108a^2x+1 attains its local maximum and minimum values at the points x1x_1 and x2x_2…MediumSingle correct
  5. 7 Apr 2025, Shift 1 · Q17Let x=−1x = -1 and x=2x = 2 be the critical points of the function f(x)=x3+ax2+blog⁡e∣x∣+1f(x) = x^3 + ax^2 + b\log_e|x| + 1, x≠0x \neq 0. Let mm and MM…MediumSingle correct
  6. 7 Apr 2025, Shift 2 · Q18Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a polynomial function of degree four having extreme values at x=4x=4 and x=5x=5. If…MediumSingle correct
  7. 8 Apr 2025, Shift 2 · Q17Let the function f(x)=x3+3x+3f(x) = \frac{x}{3} + \frac{3}{x} + 3, x≠0x \neq 0 be strictly increasing in…EasySingle correct

2024 12 questions

  1. 6 Apr 2024, Shift 2 · Q8If the function f(x)=(1x)2xf(x)=\left(\frac{1}{x}\right)^{2x} ; x>0x>0 attains the maximum value at x=1ex=\frac{1}{e} then :HardSingle correct
  2. 8 Apr 2024, Shift 1 · Q7For the function f(x)=(cos⁡x)−x+1f(x)=(\cos x)-x+1, x∈Rx\in\mathbb{R}, between the following two statements (S1) f(x)=0f(x)=0 for only one value of xx in…MediumTwo statements
  3. 8 Apr 2024, Shift 1 · Q8The number of critical points of the function f(x)=(x−2)2/3(2x+1)f(x)=(x-2)^{2/3}(2x+1) isMediumSingle correct
  4. 8 Apr 2024, Shift 1 · Q9Let f(x)=4cos⁡3x+33cos⁡2x−10f(x)=4\cos^3x+3\sqrt{3}\cos^2x-10. The number of points of local maxima of ff in interval (0,2π)(0,2\pi) isHardSingle correct
  5. 9 Apr 2024, Shift 1 · Q6Let f(x)=ax3+bx2+cx+41f(x)=ax^3+bx^2+cx+41 be such that f(1)=40f(1)=40, f′(1)=2f'(1)=2 and f′′(1)=4f''(1)=4. Then a2+b2+c2a^2+b^2+c^2 is equal to :EasySingle correct
  6. 9 Apr 2024, Shift 1 · Q27Let the set of all positive values of λ\lambda, for which the point of local minimum of the function (1+x(λ2−x2))(1+x(\lambda^2-x^2)) satisfies…MediumNumerical value
  7. 9 Apr 2024, Shift 2 · Q25Let the set of all values of pp, for which f(x)=(p2−6p+8)(sin⁡22x−cos⁡22x)+2(2−p)x+7f(x)=(p^2-6p+8)\left(\sin^2 2x-\cos^2 2x\right)+2(2-p)x+7 does not have any critical point,…MediumNumerical value
  8. 29 Jan 2024, Shift 1 · Q10Consider the function f:[12,1]→Rf:\left[\frac{1}{2},1\right]\to\mathbb{R} defined by f(x)=42x3−32x−1f(x)=4\sqrt{2}x^3-3\sqrt{2}x-1. Consider the statements (I)…MediumTwo statements
  9. 29 Jan 2024, Shift 1 · Q24Let f(x)=2x−x2f(x)=2^x-x^2, x∈Rx\in\mathbb{R}. If mm and nn are respectively the number of points at which the curves y=f(x)y=f(x) and y=f′(x)y=f'(x)…MediumNumerical value
  10. 30 Jan 2024, Shift 2 · Q9Let f(x)=(x+3)2(x−2)3f(x) = (x+3)^2 (x-2)^3, x∈[−4,4]x \in [-4, 4]. If MM and mm are the maximum and minimum values of ff, respectively in [−4,4][-4, 4], then…MediumSingle correct
  11. 31 Jan 2024, Shift 1 · Q25Let S=(−1,∞)S=(-1,\infty) and f:S→Rf:S\to\mathbb{R} be defined as f(x)=∫−1x(et−1)11(2t−1)5(t−2)7(t−3)12(2t−10)61 dtf(x)=\int_{-1}^{x}(e^t-1)^{11}(2t-1)^5(t-2)^7(t-3)^{12}(2t-10)^{61}\,dt, Let p…HardNumerical value
  12. 31 Jan 2024, Shift 2 · Q1If the function f:(−∞,−1]→(a,b]f:(-\infty,-1]\to(a,b] defined by f(x)=ex3−3x+1f(x)=e^{x^3-3x+1} is one - one and onto, then the distance of the point…MediumSingle correct

2023 1 questions

  1. 11 Apr 2023, Shift 1 · Q10Let f:[2,4]→Rf : [2, 4] \to \mathbb{R} be a differentiable function such that (xlog⁡ex)f′(x)+(log⁡ex)f(x)+f(x)≥1, x∈[2,4](x \log_e x) f'(x) + (\log_e x) f(x) + f(x) \ge 1,\ x \in [2, 4]…HardTwo statements

2022 10 questions

  1. 25 Jul 2022, Shift 1 · Q6If the absolute maximum value of the function f(x)=(x2−2x+7) e(4x3−12x2−180x+31)f(x)=(x^2-2x+7)\,\mathrm{e}^{(4x^3-12x^2-180x+31)} in the interval [−3,0][-3,0] is…MediumSingle correct
  2. 25 Jul 2022, Shift 1 · Q7The curve y(x)=ax3+bx2+cx+5y(x)=ax^3+bx^2+cx+5 touches the xx-axis at the point P(−2,0)\mathrm{P}(-2,0) and cuts the yy-axis at the point Q\mathrm{Q},…MediumSingle correct
  3. 28 Jul 2022, Shift 1 · Q17If the minimum value of f(x)=5x22+αx5, x>0f(x)=\frac{5x^2}{2}+\frac{\alpha}{x^5},\ x>0, is 14, then the value of α\alpha is equal to :MediumSingle correct
  4. 28 Jul 2022, Shift 1 · Q20The minimum value of the twice differentiable function f(x)=∫0xex−tf′(t) dt−(x2−x+1)ex, x∈Rf(x)=\int_0^x e^{x-t}f'(t)\,dt-(x^2-x+1)e^x,\ x\in\mathbf{R}, is :HardSingle correct
  5. 28 Jul 2022, Shift 1 · Q23Let f:[0,1]→Rf:[0,1]\to\mathbf{R} be a twice differentiable function in (0,1)(0,1) such that f(0)=3f(0)=3 and f(1)=5f(1)=5. If the line y=2x+3y=2x+3 intersects…MediumNumerical value
  6. 24 Jun 2022, Shift 1 · Q3The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3…MediumSingle correct
  7. 24 Jun 2022, Shift 1 · Q10For the function f(x)=4log⁡e(x−1)−2x2+4x+5, x>1f(x)=4\log_e(x-1)-2x^2+4x+5,\ x>1, which one of the following is NOT correct ?HardSingle correct
  8. 24 Jun 2022, Shift 1 · Q11If the tangent at the point (x1,y1)(x_1, y_1) on the curve y=x3+3x2+5y=x^3+3x^2+5 passes through the origin, then (x1,y1)(x_1, y_1) does NOT lie on the…MediumSingle correct
  9. 24 Jun 2022, Shift 1 · Q12The sum of absolute maximum and absolute minimum values of the function f(x)=∣2x2+3x−2∣+sin⁡xcos⁡xf(x)=|2x^2+3x-2|+\sin x\cos x in the interval [0,1][0, 1] is :HardSingle correct
  10. 29 Jun 2022, Shift 1 · Q14A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral…MediumSingle correct

2021 5 questions

  1. 3 Aug 2021, Shift 2 · Q70Let f:R→Rf : \mathbb{R} \to \mathbb{R} be a differentiable function such that f(0)=2f(0) = 2. If ∣dfdx∣≤3\left|\frac{df}{dx}\right| \le 3, for all…MediumSingle correct
  2. 3 Aug 2021, Shift 2 · Q71If the function f:R→Rf : \mathbb{R} \to \mathbb{R} defined by f(x)=x33−(2a+3b)x2+24abx+5f(x) = \frac{x^3}{3} - (2a+3b)x^2 + 24abx + 5 has a local maxima at −4-4 and…MediumSingle correct
  3. 25 Jul 2021, Shift 1 · Q67Let f(x)=3sin⁡4x+10sin⁡3x+6sin⁡2x−3f(x)=3\sin^4x+10\sin^3x+6\sin^2x-3, x∈[−π6,π2]x\in\left[-\frac{\pi}{6},\frac{\pi}{2}\right]. Then, ff is :MediumSingle correct
  4. 16 Mar 2021, Shift 2 · Q64Let ff be a real valued function, defined on R−{−1,1}\mathbf R-\{-1,1\} and given by f(x)=3log⁡e∣x−1x+1∣−2x−1f(x)=3\log_e\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1}.…MediumSingle correct
  5. 16 Mar 2021, Shift 2 · Q79Let f:S→Sf:S\to S where S=(0,∞)S=(0,\infty) be a twice differentiable function such that f(x+1)=xf(x)f(x+1)=xf(x). If g:S→Rg:S\to\mathbf R be defined as…HardSingle correct

2020 7 questions

  1. 8 Jan 2020, Shift 1 · Q74Let the normal at a point P on the curve y2−3x2+y+10=0y^2-3x^2+y+10=0 intersect the yy-axis at (0,32)\left(0,\frac{3}{2}\right). If m is the slope of…MediumNumerical value
  2. 9 Jan 2020, Shift 2 · Q61Let a function f:[0,5]→Rf:[0,5]\to\mathbf{R} be continuous, f(1)=3f(1)=3 and FF be defined as : F(x)=∫1xt2g(t) dtF(x)=\int_1^x t^2g(t)\,dt, where…MediumSingle correct
  3. 2 Sep 2020, Shift 1 · Q60If the tangent to the curve y=x+sin⁡yy=x+\sin y at a point (a,b)(a, b) is parallel to the line joining (0,32)\left(0, \frac{3}{2}\right) and…MediumSingle correct
  4. 2 Sep 2020, Shift 1 · Q61If p(x)p(x) be a polynomial of degree three that has a local maximum value 8 at x=1x=1 and a local minimum value 4 at x=2x=2; then p(0)p(0) is…MediumSingle correct
  5. 2 Sep 2020, Shift 1 · Q64Let P(h, k) be a point on the curve y=x2+7x+2y=x^{2}+7x+2, nearest to the line, y=3x−3y=3x-3. Then the equation of the normal to the curve at P is :MediumSingle correct
  6. 6 Sep 2020, Shift 2 · Q59If the tangent to the curve, y=f(x)=xlog⁡exy=f(x)=x\log_e x, (x>0)(x>0) at a point (c,f(c))(c, f(c)) is parallel to the line - segment joining the points…MediumSingle correct
  7. 6 Sep 2020, Shift 2 · Q60The set of all real values of λ\lambda for which the function f(x)=(1−cos⁡2x)⋅(λ+sin⁡x)f(x)=(1-\cos^2 x)\cdot(\lambda+\sin x),…HardSingle correct

2017 2 questions

  1. 2 Apr 2017 (offline) · Q72The normal to the curve y(x−2)(x−3)=x+6y(x-2)(x-3)=x+6 at the point where the curve intersects the yy-axis passes through the point :MediumSingle correct
  2. 2 Apr 2017 (offline) · Q73Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the…MediumSingle correct

Pattern: Asked most years.