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Day 126: JEE Mains Maths

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

  1. Question 1

    Trigonometric Identities. This type asked 2 times: 2021 Paper 5, 2021 Paper 16. This one: 2021 Paper 16 See all 2 of this type

    47
    If sin⁡θ+cos⁡θ=12\sin\theta+ \cos\theta=\frac{1}{2}, then 16[sin⁡2θ+cos⁡4θ+sin⁡6θ]16\lbrack \sin2\theta+ \cos4\theta+ \sin6\theta\rbrack is equal to

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  2. Question 2

    Sequences and Series. This type asked 2 times: 2021 Paper 6, 2021 Paper 12. This one: 2021 Paper 12 See all 2 of this type

    57
    If sum of the first 21 terms of the series log⁡91/2X+log⁡91/3X+log⁡91/4X+…\log_{9^{1/2}}X +\log_{9^{1/3}}X +\log_{9^{1/4}}X + \ldots. , where x>0x > 0 is 504 , then xx is equal to

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  3. Question 3

    Differential Equations. Asked once: 6 Apr 2026 S1 (same type asked 41 times) See all 41 of this type

    75
    Let y=y(x)y = y(x) be the solution of the differential equation (x2−xx2−1)dy+(y(x−x2−1)−x)dx=0\left( x^{2} - x\sqrt{x^{2} - 1} \right)dy + \left( y\left( x - \sqrt{x^{2} - 1} \right) - x \right)dx = 0, x≥1x \geq 1. If y(1)=1y(1) = 1, then the greatest integer less than y(5)y(\sqrt{5}) is ____\_\_\_\_ .

  4. Question 4

    Three Dimensional Geometry. Asked once: 4 Apr 2026 S2 (same type asked 33 times) See all 33 of this type

    63
    The shortest distance between the lines r→=(13i^+2j^+83k^)+λ(2i^−5j^+6k^)\overrightarrow{r}=\left( \frac{1}{3}\widehat{i}+ 2\widehat{j}+\frac{8}{3}\widehat{k} \right)+\lambda(2\widehat{i}- 5\widehat{j}+ 6\widehat{k}) and r→=(−23i^−13k^)+μ(j^−k^),λ,μ∈R\overrightarrow{r}=\left( -\frac{2}{3}\widehat{i}-\frac{1}{3}\widehat{k} \right)+\mu(\widehat{j}-\widehat{k}),\lambda,\mu\in\mathbb{R}, is :

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  5. Question 5

    Determinants. Asked once: 4 Apr 2026 S2 (same type asked 26 times) See all 26 of this type

    53
    If the system of equations : x+y+z=5x+y+z= 5, x+2y+3z=9x+ 2y+ 3z= 9, x+3y+λz=μx+ 3y+\lambda z=\mu has infinitely many solutions, then the value of λ+μ\lambda+\mu is :

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