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Day 260: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 29 Jan 2025 (same type asked 4 times) See all 4 of this type

    69
    Let ∣z1−8−2i∣≤1\left| z_{1}- 8 - 2i \right|\leq 1 and ∣z2−2+6i∣≤2\left| z_{2}- 2 + 6i \right|\leq 2, z1,z2∈Cz_{1},z_{2}\in C. Then the minimum value of ∣z1−z2∣\left| z_{1}-z_{2} \right| is :

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  2. Question 2

    Relations and Functions. Asked once: 29 Jan 2025 (same type asked 4 times) See all 4 of this type

    129
    If the domain of the function log⁡5(18x−x2−77)\log_{5}\left( 18x -x^{2}- 77 \right) is (α,β)(\alpha,\beta) and the domain of the functionlog⁡(x−1)(2x2+3x−2x2−3x−4)\log_{(x - 1)}\left( \frac{2x^{2}+ 3x - 2}{x^{2}- 3x - 4} \right) is (γ,δ)(\gamma,\delta), then α2+β2+γ2\alpha^{2}+\beta^{2}+\gamma^{2} is equal to :

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  3. Question 3

    Inverse Trigonometric Functions. Asked once: 9 Apr 2024 (same type asked 4 times) See all 4 of this type

    179
    Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2sin⁡−1x+3cos⁡−1x=2π52\sin^{- 1}x+ 3\cos^{- 1}x=\frac{2\pi}{5}, is

  4. Question 4

    Relations and Functions. Asked once: 25 Jan 2023 (same type asked 4 times) See all 4 of this type

    82
    For some a,b,c∈Na,b,c \in N, let f(x)=ax−3f(x) = ax - 3 and g(x)=xb+c,x∈Rg(x) =x^{b}+ c,x \in R. If (f∘g)−1(x)=(x−72)1/3(f \circ g)^{- 1}(x) =\left( \frac{x - 7}{2} \right)^{1/3}, then (f∘g)(ac)+(g∘f)(b)(f \circ g)(ac) + (g \circ f)(b) is equal to

  5. Question 5

    Permutations and Combinations. Asked once: 2 Apr 2025 (same type asked 4 times) See all 4 of this type

    51
    The largest n∈Nn \in N such that 3n3^{n} divides 50 ! is:

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