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Day 91: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked 2 times: 2021 Paper 15*, 31 Jan 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    87
    Let a→\overrightarrow{a} and b→\overrightarrow{b} be two vectors such that ∣a→∣=14,∣b→∣=6|\overrightarrow{a}| =\sqrt{14},|\overrightarrow{b}| =\sqrt{6} and ∣a→×b→∣=48|\overrightarrow{a}\times\overrightarrow{b}| =\sqrt{48}. Then (a→⋅b→)2(\overrightarrow{a}\cdot\overrightarrow{b})^{2} is equal to

  2. Question 2

    Limits and Continuity. Asked 2 times: 2021 Paper 16*, 25 Jan 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    163
    If the function f(x)={(1+∣cos⁡x∣)λ∣cos⁡x∣,0<x<π2μ,x=π2ecot⁡6xcot⁡4xπ2<x<πf(x) =\left\{ \begin{matrix} (1 + |\cos x|)^{\frac{\lambda}{|\cos x|}} & ,0 < x <\frac{\pi}{2} \\ \mu & ,x =\frac{\pi}{2} \\ e^{\frac{\cot6x}{\cot4x}} & \frac{\pi}{2}< x < \pi \end{matrix} \right. is continuous at x=π2x =\frac{\pi}{2}, then 9λ+6log⁡eμ+μ6−e6λ9\lambda + 6\log_{e}\mu +\mu^{6}-e^{6\lambda} is equal to

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  3. Question 3

    Matrices. Asked 2 times: 2021 Paper 18*, 25 Jan 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    158
    Let A=[110310−310110]A =\begin{bmatrix} \frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{- 3}{\sqrt{10}} & \frac{1}{\sqrt{10}} \end{bmatrix} and B=[1−i01]B =\begin{bmatrix} 1 & - i \\ 0 & 1 \end{bmatrix}, where i=−1i =\sqrt{- 1}. If M=ATBAM =A^{T}BA, then the inverse of the matrix A2023ATA^{2023}A^{T} is

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  4. Question 4

    Permutations and Combinations. Asked 2 times: 2021 Paper 21*, 25 Jan 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    83
    Let S={1,2,3,5,7,10,11}\mathbf{S = \{ 1,2,3,5,7,10,11\}}. The number of non-empty subsets of SS that have the sum of all elements a multiple of 3, is

  5. Question 5

    Permutations and Combinations. Asked 2 times: 24 Jan 2023*, 25 Jan 2023 (* = numbers or wording changed that year) See all 2 times it was asked

    168
    The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is

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