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Day 13: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. This type asked 7 times: 27 Jun 2022, 28 Jun 2022, 27 Jul 2022, 13 Apr 2023, 30 Jan 2024, 4 Apr 2024, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 7 of this type

    54
    Let S={z∈C:4z2+z‾=0}S =\left\{ z\in C:4z^{2}+\overline{z}= 0 \right\}. Then ∑z∈S∣z∣2\sum_{z \in S} |z|^{2} is equal to :

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  2. Question 2

    Vector Algebra. This type asked 7 times: 2021 Paper 4, 2021 Paper 20, 28 Jun 2022, 13 Apr 2023, 4 Apr 2024, 9 Apr 2024, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 7 of this type

    58
    Let a→=2i^−j^+k^\overrightarrow{a}= 2\widehat{i}-\widehat{j}+\widehat{k} and b→=λj^+2k^,λ∈Z\overrightarrow{b}= \lambda\widehat{j}+ 2\widehat{k},\lambda \in Z be two vectors, Let c→=a→×b→\overrightarrow{c}=\overrightarrow{a}\times\overrightarrow{b} and d→\overrightarrow{d} be a vector of magnitude 2 in yz-plane. If ∣c→∣=53|\overrightarrow{c}| =\sqrt{53}, then the maximum possible value of (c→⋅d→)2(\overrightarrow{c}\cdot\overrightarrow{d})^{2} is equal to :

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  3. Question 3

    Conic Sections. This type asked 7 times: 2021 Paper 7, 2021 Paper 9, 15 Apr 2023, 30 Jan 2024, 1 Feb 2024, 22 Jan 2025, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 7 of this type

    62
    Let the set of all values of r , for which the circles (x+1)2+(y+4)2=r2(x + 1)^{2}+ (y + 4)^{2}=r^{2} and x2+y2−4x−2y−4=0x^{2}+y^{2}- 4x - 2y - 4 = 0 intersect at two distinct points be the interval ( α\alpha, β\beta ). Then αβ\alpha\beta is equal to

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  4. Question 4

    Binomial Theorem. This type asked 7 times: 2021 Paper 11, 28 Jun 2022, 27 Jan 2024, 31 Jan 2024, 1 Feb 2024, 5 Apr 2024, 21 Jan 2026 S1. This one: 21 Jan 2026 S1 See all 7 of this type

    66
    If the coefficient of xx in the expansion of (ax2+bx+c)(1−2x)26\left( ax^{2}+ bx + c \right)(1 - 2x)^{26} is -56 and the coefficients of x2x^{2} and x3x^{3} are both zero, then a+b+ca + b + c is equal to

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  5. Question 5

    Definite Integration. This type asked 7 times: 26 Jun 2022, 31 Jan 2024, 1 Feb 2024, 5 Apr 2024, 23 Jan 2025, 3 Apr 2025, 7 Apr 2025. This one: 7 Apr 2025 See all 7 of this type

    60
    The integral ∫0π(x+3)sin⁡x1+3cos⁡2xdx\int_{0}^{\pi} \frac{(x+ 3)\sin x}{1 + 3\cos^{2}x}dx is equal to :

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