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Day 456: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 2 Apr 2026 S1

    64
    If a→\overrightarrow{a} and b→\overrightarrow{b} are two vectors such that ∣a→∣=2|\overrightarrow{a}| = 2 and ∣b→∣=3|\overrightarrow{b}| = 3, then the maximum value of 3∣(3a→+2b→)∣+4∣(3a→−2b→)∣3|(3\overrightarrow{a}+ 2\overrightarrow{b})| + 4|(3\overrightarrow{a}- 2\overrightarrow{b})| is :

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  2. Question 2

    Application of Derivatives. Asked once: 21 Jan 2026 S1

    71
    Let f:R→Rf:R \rightarrow R be a twice differentiable function such that the quadratic equation f(x)m2−2f′(x)m+f′(x)=0f(x)m^{2} - 2f'(x)m + f'(x) = 0 in m , has two equal roots for every x∈Rx \in R. If f(0)=1f(0) = 1, f′(0)=2f'(0) = 2 and (α,β)(\alpha,\beta) is the largest interval in which the function f(log⁡ex−x)f\left( \log_{e}x - x \right) is increasing, then α+β\alpha + \beta is equal to

  3. Question 3

    Application of Integrals. Asked once: 2 Apr 2026 S2

    74
    If the area of the region bounded by 16x2−9y2=16x^{2} - 9y^{2} = 144 and 8x−3y=248x - 3y = 24 is A , then 3( A+6log⁡e(3))3\left( \text{ }A + 6\log_{e}(3) \right) is equal to ____\_\_\_\_ .

  4. Question 4

    Binomial Theorem. Asked once: 21 Jan 2026 S2

    74
    If (1 15C0+1 15C1)(1 15C1+1 15C2)…(1 15C12+1 15C13)=α13 14C0 14C1… 14C12\left( \frac{1}{\ ^{15}C_{0}} + \frac{1}{\ ^{15}C_{1}} \right)\left( \frac{1}{\ ^{15}C_{1}} + \frac{1}{\ ^{15}C_{2}} \right)\ldots\left( \frac{1}{\ ^{15}C_{12}} + \frac{1}{\ ^{15}C_{13}} \right) = \frac{\alpha^{13}}{\ ^{14}C_{0}\ ^{14}C_{1}\ldots\ ^{14}C_{12}}, then 30α30\alpha is equal to ____\_\_\_\_ .

  5. Question 5

    Complex Numbers. Asked once: 28 Jan 2026 S2

    68
    Let A={z∈C:∣z−2∣≤4}A\mathbf{= \{}z\in\mathbb{C}:|z- 2| \leq 4\} and B={z∈C:∣z−2∣+∣z+2∣=5}B\mathbf{= \{}z\in\mathbb{C}:|z- 2| + |z+ 2| = 5\}. Then the max {∣z1−z2∣:z1∈A\left\{ \left| z_{1}-z_{2} \right|:z_{1}\in A \right. and  z2∈B}\left. \ z_{2}\in B \right\} is

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