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Saturday, 10 October

JEE Main Maths · Application of Derivatives

Maxima and Minima in JEE Main

Maxima and Minima (Maths, Application of Derivatives) came 30 times in 25 of the 42 JEE Main shifts Lumi analysed, across 17 distinct ideas. 20 of them came in 2024–26; it was last asked in 2026.

Questions
30
in 25 shifts
Ideas asked
17
7 asked more than once
Numerical answer
3
10% of its questions
Pattern
Asked most years
last asked 2026
Questions each year
05101’173’201’215’220’239’247’254’26

In the shifts Lumi analysed for each year.

Difficulty and format
Easy 0Medium 23Hard 7

Format

  • Single correct27 Q
  • Numerical value3 Q
Ideas inside the topic
17 ideas
Where it sits

Part of Application of Derivatives, which had 47 questions in all. Maxima and Minima accounts for 64% of them. In Lumi's JEE taxonomy it belongs to Calculus.

Some questions sit in other chapters too: Conic Sections, Continuity and Differentiability, Straight Lines, Trigonometric Functions.

Every question

All 30 Maxima and Minima questions

Newest first, each with its options and official answer.

  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
  4. 5 Apr 2026, Shift 1 · Q12The sum of all the integral values of pp such that the equation 3sin⁡2x+12cos⁡x−3=p3\sin^2 x + 12\cos x - 3 = p, x∈Rx \in \mathbb{R}, has at least one…MediumSingle correct
  5. 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
  6. 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
  7. 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
  8. 4 Apr 2025, Shift 2 · Q16Let ff be a differentiable function on R\mathbf{R} such that f(2)=1f(2)=1, f′(2)=4f'(2)=4. Let…HardSingle correct
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 9 Apr 2024, Shift 1 · Q7A variable line L passes through the point (3,5)(3,5) and intersects the positive coordinate axes at the points A and B. The minimum area of…MediumSingle correct
  16. 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
  17. 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
  18. 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
  19. 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
  20. 31 Jan 2024, Shift 2 · Q10Let a variable line passing through the centre of the circle x2+y2−16x−4y=0x^2+y^2-16x-4y=0, meet the positive co-ordinate axes at the points AA and…MediumSingle correct
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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