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Day 168: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 31 Jan 2024 (same type asked 4 times) See all 4 of this type

    78
    If f(x)=∣x32x2+11+3x3x2+22xx3+6x3−x4x2−2∣f(x) =\left| \begin{matrix} x^{3} & 2x^{2}+ 1 & 1 + 3x \\ 3x^{2}+ 2 & 2x & x^{3}+ 6 \\ x^{3}- x & 4 & x^{2}- 2 \end{matrix} \right| for all x∈Rx \in R, then 2f(0)+f′(0)2f(0) +f^{'}(0) is equal to

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  2. Question 2

    Definite Integration. Asked once: 28 Jan 2025 (same type asked 4 times) See all 4 of this type

    66
    Let for some function y=f(x),∫0xtf(t)dt=x2f(x)y = f(x),\int_{0}^{x} tf(t)dt =x^{2}f(x), x>0x > 0 and f(2)=3f(2) = 3. Then f(6)f(6) is equal to :

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  3. Question 3

    Matrices. Asked once: 29 Jan 2025 (same type asked 4 times) See all 4 of this type

    137
    Let A=[aij]A =\left\lbrack a_{ij} \right\rbrack be a matrix of order 3×33 \times 3, with aij=(2)i+ja_{ij}= (\sqrt{2})^{i + j}. If the sum of all the elements in the third row of A2A^{2} is α+β2,α,β∈Z\alpha + \beta\sqrt{2},\alpha,\beta \in Z, then α+β\alpha + \beta is equal to

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  4. Question 4

    Vector Algebra. Asked once: 10 Apr 2023 (same type asked 4 times) See all 4 of this type

    161
    Let a→=2i^+7j^−k^,b→=3i^+5k^\overrightarrow{a}= 2\widehat{i}+ 7\widehat{j}-\widehat{k},\overrightarrow{b}= 3\widehat{i}+ 5\widehat{k} and c→=i^−j^+2k^\overrightarrow{c}=\widehat{i}-\widehat{j}+ 2\widehat{k} . Let d→\overrightarrow{d} be a vector which is perpendicular to both a→\overrightarrow{a} and  b→,\ \overrightarrow{b}, and  c→⋅d→=12\ \overrightarrow{c}\cdot\overrightarrow{d}= 12. Then (−i^+j^−k^)⋅(c→×d→)( -\widehat{i}+\widehat{j}-\widehat{k}) \cdot (\overrightarrow{c}\times\overrightarrow{d}) is equal to

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  5. Question 5

    Definite Integration. Asked once: 10 Apr 2023 (same type asked 4 times) See all 4 of this type

    151
    Let ff be aa continuous function satisfying ∫0t2(f(x)+x2)dx=43t3,∀t>0\int_{0}^{t^{2}} \left( f(x) +x^{2} \right)dx =\frac{4}{3}t^{3},\forall t > 0. Then f(π24)f\left( \frac{\pi^{2}}{4} \right) is equal to:

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