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Day 232: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 6 Apr 2024 (same type asked 8 times) See all 8 of this type

    81
    Let αβγ=45;α,β,γ∈R\alpha\beta\gamma = 45;\alpha,\beta,\gamma \in R. If x(α,1,2)+y(1,β,2)x(\alpha,1,2) + y(1,\beta,2) +z(2,3,γ)=(0,0,0)+ z(2,3,\gamma) = (0,0,0) for some x,y,z∈R,xyz≠x,y,z \in R,xyz \neq 0 , then 6α+4β+γ6\alpha + 4\beta + \gamma is equal to

  2. Question 2

    Differential Equations. Asked once: 23 Jan 2026 S1 (same type asked 8 times) See all 8 of this type

    73
    Let f be a twice differentiable non-negative function such that (f(x))2=25+∫0x((f(t))2+(f′(t))2)dt(f(x))^{2} = 25 + \int_{0}^{x} \left( (f(t))^{2} + \left( f'(t) \right)^{2} \right)dt. Then the mean of f(log⁡e(1)),f(log⁡e(2)),…..,f(log⁡e(625))f\left( \log_{e}(1) \right),f\left( \log_{e}(2) \right),\ldots..,f\left( \log_{e}(625) \right) is equal to ____\_\_\_\_.

  3. Question 3

    Sequences and Series. Asked once: 31 Jan 2024 (same type asked 8 times) See all 8 of this type

    73
    The sum of the series 11−3⋅12+14+\frac{1}{1 - 3 \cdot1^{2}+1^{4}}+ 21−3⋅22+24+31−3⋅32+34+….\frac{2}{1 - 3 \cdot2^{2}+2^{4}}+\frac{3}{1 - 3 \cdot3^{2}+3^{4}}+ \ldots.. up to 10 terms is

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  4. Question 4

    Vector Algebra. Asked once: 30 Jan 2024 (same type asked 8 times) See all 8 of this type

    158
    Let a→\overrightarrow{a} and b→\overrightarrow{b} be two vectors such that ∣b→∣=1|\overrightarrow{b}| = 1 and ∣b→×a→∣=2|\overrightarrow{b}\times\overrightarrow{a}| = 2. Then ∣(b→×a→)−b→∣2|(\overrightarrow{b}\times\overrightarrow{a}) -\overrightarrow{b}|^{2} is equal to

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  5. Question 5

    Vector Algebra. Asked once: 26 Jun 2022 (same type asked 8 times) See all 8 of this type

    166
    Let a→=i^+j^+2k^,b→=2i^−3j^+k^\overrightarrow{a}=\widehat{i}+\widehat{j}+ 2\widehat{k},\overrightarrow{b}= 2\widehat{i}- 3\widehat{j}+\widehat{k} and c→=i^−j^+k^\overrightarrow{c}=\widehat{i}-\widehat{j}+\widehat{k} be three given vectors. Let v→\overrightarrow{v} be a vector in the plane of a→\overrightarrow{a} and b→\overrightarrow{b} whose projection on c→\overrightarrow{c} is 23\frac{2}{\sqrt{3}}. If v→⋅j^=7\overrightarrow{v}\cdot\widehat{j}= 7, then v→⋅(i^+k^)\overrightarrow{v}\cdot (\widehat{i}+\widehat{k}) is equal to:

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