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Day 534: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 8 Apr 2023

    85
    If aαa_{\alpha} is the greatest term in the sequence an=n3n4+147,n=1,2,3…….a_{n}=\frac{n^{3}}{n^{4}+ 147},n = 1,2,3\ldots\ldots., then α\alpha is equal to

  2. Question 2

    Application of Integrals. Asked once: 1 Feb 2024

    178
    The sum of squares of all possible values of kk, for which area of the region bounded by the parabolas 2y2=kx2y^{2}= kx and ky2=2(y−x)ky^{2}= 2(y - x) is maximum, is equal to:

  3. Question 3

    Binomial Theorem. Asked once: 25 Jan 2023

    79
    If ara_{r} is the coefficient of x10−rx^{10 - r} in the Binomial expansion of (1+x)10(1 + x)^{10}, then ∑r=110r3(arar−1)2\sum_{r = 1}^{10} r^{3}\left( \frac{a_{r}}{a_{r - 1}} \right)^{2} is equal to

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  4. Question 4

    Complex Numbers. Asked once: 15 Apr 2023

    71
    If the set {Re(z−zˉ+zzˉ2−3z+5zˉ):z∈C,Re(z)=3}\left\{ Re\left( \frac{z -\bar{z}+ z\bar{z}}{2 - 3z + 5\bar{z}} \right):z\in C,Re(z) = 3 \right\} is equal to the interval (α,β](\alpha,\beta\rbrack, then 24(β−α)24(\beta - \alpha) is equal to

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  5. Question 5

    Conic Sections. Asked once: 21 Jan 2026 S1

    57
    Let c→\overrightarrow{c} and d→\overrightarrow{d} be vectors such that ∣c→+d→∣=29|\overrightarrow{c}+\overrightarrow{d}| =\sqrt{29} and c→×(2i^+3j^+4k^)=(2i^+3j^+4k^)×d→\overrightarrow{c}\times (2\widehat{i}+ 3\widehat{j}+ 4\widehat{k}) = (2\widehat{i}+ 3\widehat{j}+ 4\widehat{k}) \times\overrightarrow{d}. If λ1,λ2(λ1>λ2)\lambda_{1},\lambda_{2}\left( \lambda_{1}>\lambda_{2} \right) are the possible values of (c→+d→)⋅(−7i^+2j^+3k^)(\overrightarrow{c}+\overrightarrow{d}) \cdot ( - 7\widehat{i}+ 2\widehat{j}+ 3\widehat{k}), then the equation K2x2+(K2−5 K+λ1)xy+(3 K+λ22)y2−8x+12y+λ2=0K^{2}x^{2}+\left( K^{2}- 5\text{ }K +\lambda_{1} \right)xy +\left( 3\text{ }K +\frac{\lambda_{2}}{2} \right)y^{2}- 8x + 12y +\lambda_{2}= 0 represents a circle, for k equal to :

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