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Day 127: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 5 Apr 2026 S2 (same type asked 19 times) See all 19 of this type

    65
    If the distance of the point (a,2,5)(a,2,5) from the image of the point (1,2,7)(1,2,7) in the line x1=y−11=z−22\frac{x}{1}=\frac{y- 1}{1}=\frac{z- 2}{2} is 4, then the sum of all possible values of a is equal to :

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  2. Question 2

    Differential Equations. Asked once: 23 Jan 2025 (same type asked 19 times) See all 19 of this type

    136
    Let x=x(y)x = x(y) be the solution of the differential equation
    y=(x−ydxdy)sin⁡(xy),y>0 and x(1)=π2y =\left( x - y\frac{dx}{dy} \right)\sin\left( \frac{x}{y} \right),y > 0\text{~and~}x(1) =\frac{\pi}{2}
    Then cos⁡(x(2))\cos(x(2)) is equal to :

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  3. Question 3

    Determinants. Asked once: 3 Apr 2025 (same type asked 19 times) See all 19 of this type

    51
    Let AA be a matrix of order 3×33\times 3 and ∣A∣=5|A|=5. If ∣2 adj(3A adj(2A))∣=2α⋅3β⋅5γ, α,β,γ∈N|2\,\mathrm{adj}(3A\,\mathrm{adj}(2A))|=2^{\alpha}\cdot3^{\beta}\cdot5^{\gamma},\ \alpha,\beta,\gamma\in N, then α+β+γ\alpha+\beta+\gamma is equal to

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  4. Question 4

    Vector Algebra. Asked once: 5 Apr 2026 S1 (same type asked 18 times) See all 18 of this type

    64
    Let a→=7i^+j^−k^\overrightarrow{a}=\sqrt{7}\widehat{i}+\widehat{j}-\widehat{k} and b→=j^+2k^\overrightarrow{b}=\widehat{j}+ 2\widehat{k}. If r→\overrightarrow{r} is a vector such that r→×a→+a→×b→=0→\overrightarrow{r}\times\overrightarrow{a}+\overrightarrow{a}\times\overrightarrow{b}=\overrightarrow{0} and r→⋅a→=0\overrightarrow{r}\cdot\overrightarrow{a}= 0, then ∣3r→∣2|3\overrightarrow{r}|^{2} is equal to :

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  5. Question 5

    Limits and Continuity. Asked once: 24 Jan 2026 S2 (same type asked 16 times) See all 16 of this type

    70
    Let [t]\lbrack t\rbrack denote the greatest integer less than or equal to tt. If the function f(x)={b2sin⁡(π2[π2(cos⁡x+sin⁡x)cos⁡x]) ,x<0sin⁡x−12sin⁡2xx3 ,x>0a ,x=0f\left( x \right)=\left\{ \begin{matrix} b^{2}\sin\left( \frac{\pi}{2}\left\lbrack \frac{\pi}{2}\left( \cos x + \sin x \right)\cos x \right\rbrack \right) & \ ,x < 0 \\ \frac{\sin x -\frac{1}{2}\sin2x}{x^{3}} & \ ,x > 0 \\ a & \ ,x = 0 \end{matrix} \right. is continuous at x=0x = 0, then a2+b2a^{2}+b^{2} is equal to

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