JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 5 April 2026, Shift 1, Maths Q12

Question 12 of 75 in this shift, Maths question 12 of 25, Section A.

The sum of all the integral values of

p

such that the equation

3\sin^2 x + 12\cos x - 3 = p

x \in \mathbb{R}

, has at least one solution, is:

(1)-54
(2)-60
(3)-75Official answer
(4)-84

Official answer

Option 3

NTA final key.

Chapter: Trigonometric Functions
Topic: Maxima and Minima
Idea tested: Extrema of Trigonometric Compositions

Same topic in other shifts

All Maxima and Minima questions

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2 Apr 2026, Shift 2 · Q18Let $f(x)$ be a polynomial of degree 5, and have extrema at $x = 1$ and $x = -1$ . If $\lim_{x \to 0}\left(\frac{f(x)}{x^3}\right) = -5$ ,…MediumSingle correct
4 Apr 2026, Shift 2 · Q12 $\max_{0\le x\le\pi}\left(16\sin\left(\frac x2\right)\cos^3\left(\frac x2\right)\right)$ is equal to:MediumSingle correct
2 Apr 2025, Shift 1 · Q8If the function $f(x)=2x^3-9ax^2+12a^2x+1$ , where $a>0$ , attains its local maximum and local minimum values at p and q, respectively, such…MediumSingle correct
3 Apr 2025, Shift 2 · Q16Let $f: \mathrm{R} \to \mathrm{R}$ be a function defined by $f(x) = \left||x+2| - 2|x|\right|$ . If $m$ is the number of points of local…MediumSingle correct
3 Apr 2025, Shift 2 · Q17The shortest distance between the curves $y^2 = 8x$ and $x^2 + y^2 + 12y + 35 = 0$ is:MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.