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Day 8: JEE Mains Maths

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

  1. Question 1

    Determinants. This type asked 8 times: 2021 Paper 10, 2021 Paper 23, 27 Jun 2022, 8 Apr 2023, 4 Apr 2024, 6 Apr 2024, 5 Apr 2026 S1, 6 Apr 2026 S2. This one: 6 Apr 2026 S2 See all 8 of this type

    54
    The sum of all possible values of θ∈[0,2π]\theta\in \lbrack 0,2\pi\rbrack, for which the system of equations :
    xcos3θ−8y−12z=0xcos3\theta- 8y- 12z= 0
    xcos2θ+3y+3z=0xcos2\theta+ 3y+ 3z= 0
    x+y+3z=0x+y+ 3z= 0
    has a non-trivial solution, is equal to:

    Tap an option to check your answer.

  2. Question 2

    Differential Equations. This type asked 8 times: 2021 Paper 26, 31 Jan 2023, 3 Apr 2025, 4 Apr 2025, 22 Jan 2026 S1, 23 Jan 2026 S1, 5 Apr 2026 S2, 6 Apr 2026 S2. This one: 6 Apr 2026 S2 See all 8 of this type

    68
    Let f:R→Rf:R\rightarrow R be such that f(xy)=f(x)f(y)f(xy) =f(x)f(y), for all x,y∈Rx,y\in R and f(0)≠0f(0) \neq 0. Let g:[1,∞)→Rg:\lbrack 1,\infty) \rightarrow R be a differentiable function such that x2g(x)=∫1x(t2f(t)−tg(t))dtx^{2}g(x) =\int_{1}^{x} \left( t^{2}f(t) - tg(t) \right)dtThen g(2)g(2) is equal to :

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  3. Question 3

    Sequences and Series. This type asked 8 times: 27 Jun 2022, 26 Jul 2022, 1 Feb 2023, 31 Jan 2024, 2 Apr 2025, 4 Apr 2025, 28 Jan 2026 S2, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 8 of this type

    55
    If the sum of the first 10 terms of the series 11+14×4+21+24×4+31+34×4+41+44×4+…\frac{1}{1 +1^{4}\times 4}+\frac{2}{1 +2^{4}\times 4}+\frac{3}{1 +3^{4}\times 4}+\frac{4}{1 +4^{4}\times 4}+ \ldots is mn,gcd(m,n)=1\frac{m}{n},gcd(m,n) = 1, then m+nm + n is equal to :

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  4. Question 4

    Vector Algebra. This type asked 8 times: 2021 Paper 10, 27 Jun 2022, 29 Jul 2022, 30 Jan 2023, 30 Jan 2024, 31 Jan 2024, 7 Apr 2025, 4 Apr 2026 S2. This one: 4 Apr 2026 S2 See all 8 of this type

    65
    Let u^\widehat{u} and v^\widehat{v} be unit vectors inclined at an acute angle such that ∣u^×v^∣=32|\widehat{u}\times\widehat{v}| =\frac{\sqrt{3}}{2}. If A→=λu^+v^+(u^×v^)\overrightarrow{A}=\lambda\widehat{u}+\widehat{v}+ (\widehat{u}\times\widehat{v}). Then λ\lambda is equal to :

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  5. Question 5

    Vector Algebra. This type asked 8 times: 2021 Paper 1, 2021 Paper 8, 2021 Paper 24, 26 Jun 2022, 28 Jun 2022, 24 Jan 2025, 24 Jan 2026 S2, 2 Apr 2026 S2. This one: 2 Apr 2026 S2 See all 8 of this type

    64
    Let the vectors a→=−i^+j^+3k^\overrightarrow{a}= -\widehat{i}+\widehat{j}+ 3\widehat{k} and b→=i^+3j^+k^\overrightarrow{b}=\widehat{i}+ 3\widehat{j}+\widehat{k}. For some λ,μ∈R\lambda,\mu\in R, let c→=λa→+μb→\overrightarrow{c}=\lambda\overrightarrow{a}+\mu\overrightarrow{b}. If c→⋅(3i^−6j^+2k^)=10\overrightarrow{c}\cdot (3\widehat{i}- 6\widehat{j}+ 2\widehat{k}) = 10 and c→⋅(i^+j^+k^)=−2\overrightarrow{c}\cdot (\widehat{i}+\widehat{j}+\widehat{k}) = - 2, then ∣c→∣2|\overrightarrow{c}|^{2} is equal to :

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