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Day 121: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. This type asked 2 times: 25 Jun 2022, 25 Jan 2023. This one: 25 Jan 2023 See all 2 of this type

    64
    The vector a→=−ı^+2ȷ^+k^\overrightarrow{a}= -\widehat{\imath}+ 2\widehat{\jmath}+\widehat{k} is rotated through a right angle, passing through the y-axis in its way and the resulting vector is b→\overrightarrow{b}. Then the projection of 3a→+2b→3\overrightarrow{a}+\sqrt{2}\overrightarrow{b} on c→=5ı^+4ȷ^+3k^\overrightarrow{c}= 5\widehat{\imath}+ 4\widehat{\jmath}+ 3\widehat{k} is:

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  2. Question 2

    Limits and Continuity. This type asked 2 times: 27 Jun 2022, 24 Jan 2023. This one: 24 Jan 2023 See all 2 of this type

    167
    The set of all values of a for which lim⁡x→a([x−5]−[2x+2])=0\lim_{x \rightarrow a} (\lbrack x - 5\rbrack - \lbrack 2x + 2\rbrack) = 0, where [α]\lbrack\alpha\rbrack denotes the greatest integer less than or equal to α\alpha is equal to

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  3. Question 3

    Sequences and Series. This type asked 2 times: 2021 Paper 10, 29 Jul 2022. This one: 29 Jul 2022 See all 2 of this type

    157
    ∑r=120(r2+1)(r!)\sum_{r = 1}^{20} \left( r^{2}+ 1 \right)(r!) is equal to:

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  4. Question 4

    Differentiation. This type asked 2 times: 2021 Paper 15, 27 Jul 2022. This one: 27 Jul 2022 See all 2 of this type

    80
    Let a function f:R→Rf:R \rightarrow R be defined as:
    f(x)={∫0x(5−∣t−3∣)dt,x>4x2+bx ,x≤4f(x) =\left\{ \begin{matrix} \int_{0}^{x} (5 - |t - 3|)dt, & x > 4 \\ x^{2}+ bx\ , & x \leq 4 \end{matrix} \right.
    where b∈Rb \in R. If ff is continuous at x=4x = 4, then which of the following statements is NOT true?

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  5. Question 5

    Matrices. This type asked 2 times: 2021 Paper 25, 27 Jul 2022. This one: 27 Jul 2022 See all 2 of this type

    88
    Let SS be the set containing all 3×33 \times 3 matrices with entries from {−1,0,1}\mathbf{\{ - 1,0,1\}}. The total number of matrices A∈SA \in S such that the sum of all the diagonal elements of ATAA^{T}A is 6 is