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Day 38: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Complex Numbers. This type asked 4 times: 1 Feb 2024, 29 Jan 2025, 23 Jan 2026 S1, 2 Apr 2026 S2. This one: 2 Apr 2026 S2 See all 4 of this type

    52
    Let the circle C1:∣z∣=rC_{1}:|z| = r and C2:∣z−3−4i∣=5,z∈CC_{2}:|z - 3 - 4i| = 5,z \in\mathbb{C}, be such that C2C_{2} lies within C1C_{1}. If z1z_{1} moves on C1,z2C_{1},z_{2} moves on C2C_{2} and min⁡∣z1−z2∣=2\min\left| z_{1}-z_{2} \right|= 2, then max ∣z1−z2∣\left| z_{1}-z_{2} \right| is equal to :-

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  2. Question 2

    Relations and Functions. This type asked 4 times: 29 Jan 2023, 29 Jan 2025, 24 Jan 2026 S1, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 4 of this type

    71
    If the domain of the function f(x)=log⁡(0.6)(∣2x−5x2−4∣)f(x) = \sqrt{\log_{(0.6)}\left( \left| \frac{2x - 5}{x^{2} - 4} \right| \right)} is (−∞,a]∪{b}∪[c,d)∪(e,∞)( - \infty,a\rbrack \cup \{ b\} \cup \lbrack c,d) \cup (e,\infty), then the value of a+b+c+d+ea + b + c + d + e is ____\_\_\_\_ .

  3. Question 3

    Application of Derivatives. This type asked 4 times: 27 Jun 2022, 31 Jan 2024, 22 Jan 2025, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 4 of this type

    73
    Let ff be a differentiable function satisfying
    f(x)=1−2x+∫0xe(x−t)f(t)dt,x∈R and let f(x) = 1 - 2x + \int_{0}^{x} e^{(x - t)}f(t)dt,x \in R\text{~and let~}
    g(x)=∫0x(f(t)+2)15(t−4)6(t+12)17dt,x∈Rg(x) = \int_{0}^{x} (f(t) + 2)^{15}(t - 4)^{6}(t + 12)^{17}dt,x \in R
    If pp and qq are respectively the points of local minima and local maxima of g , then the value of ∣p+q∣|p + q| is equal to ............ .

  4. Question 4

    Inverse Trigonometric Functions. This type asked 4 times: 28 Jul 2022, 9 Apr 2024, 29 Jan 2025, 28 Jan 2026 S1. This one: 28 Jan 2026 S1 See all 4 of this type

    73
    If k=tan⁡(π4+12cos⁡−1(23))+tan⁡(12sin⁡−1(23))k = \tan\left( \frac{\pi}{4} + \frac{1}{2}\cos^{- 1}\left( \frac{2}{3} \right) \right) + \tan\left( \frac{1}{2}\sin^{- 1}\left( \frac{2}{3} \right) \right) then the number of solutions of the equation sin⁡−1(kx−1)=sin⁡−1x−cos⁡−1x\sin^{- 1}(kx - 1) = \sin^{- 1}x - \cos^{- 1}x is......... .

  5. Question 5

    Relations and Functions. This type asked 4 times: 29 Jun 2022, 25 Jan 2023, 13 Apr 2023, 28 Jan 2026 S1. This one: 28 Jan 2026 S1 See all 4 of this type

    51
    If g(x)=3x2+2x−3,f(0)=−3g(x) = 3x^{2}+ 2x- 3,f(0) = - 3 and 4g(f(x))=3x2−32x+724g(f(x)) = 3x^{2}- 32x + 72, then f( g(2))f(\text{ }g(2)) is equal to:

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