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Day 437: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 5 Apr 2026 S1

    69
    Let f:R→Rf:R \rightarrow R be a differentiable function such that f(x+y3)=f(x)+f(y)3f\left( \frac{x+y}{3} \right)=\frac{f(x) +f(y)}{3} for all x,y∈Rx,y\in R and f′(0)=3f^{'}(0) = 3. Then the minimum value of the function g(x)=3+exf(x)g(x) = 3 +e^{x}f(x), is

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  2. Question 2

    Application of Integrals. Asked once: 8 Apr 2026 S2

    68
    Let f:(1,∞)→Rf:(1,\infty) \rightarrow R be function defined as f(x)=x−1x+1f(x) =\frac{x - 1}{x + 1}. Let fi+1(x)=f(fi(x))f^{i + 1}(x) = f\left( f^{i}(x) \right), i=1,2,…,25i = 1,2,\ldots,25, where f1(x)=f(x)f^{1}(x) = f(x). If g(x)+f26(x)=0g(x) +f^{26}(x) = 0, x∈(1,∞)x\in (1,\infty), then the area of the region bounded by the curves y=g(x),2y=2x−3,y=0y = g(x),2y = 2x - 3,y = 0 and x=4x = 4 is:

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  3. Question 3

    Binomial Theorem. Asked once: 6 Apr 2026 S2

    72
    If (1−x3)10=∑r=010arxr(1−x)30−2r\left( 1 - x^{3} \right)^{10} = \sum_{r = 0}^{10} a_{r}x^{r}(1 - x)^{30 - 2r}, then 9a9a10\frac{9a_{9}}{a_{10}} is equal to ____\_\_\_\_

  4. Question 4

    Complex Numbers. Asked once: 5 Apr 2026 S1

    51
    Let a,b∈Ca,b \in C. Let α,β\alpha,\beta be the roots of the equation x2+ax+b=0x^{2}+ ax + b = 0. If β−α=11\beta-\alpha=\sqrt{11} and β2−α2=3i11\beta^{2}-\alpha^{2}= 3i\sqrt{11}, then (β3−α3)2\left( \beta^{3}-\alpha^{3} \right)^{2} is equal to:

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  5. Question 5

    Conic Sections. Asked once: 8 Apr 2026 S2

    74
    Consider the circle C : x2+y2−6x−8y−11=0x^{2} + y^{2} - 6x - 8y - 11 = 0. Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord AB is the circle x2+y2−αx−βy−γ=0x^{2} + y^{2} - \alpha x - \beta y - \gamma = 0, then α+β+2γ\alpha + \beta + 2\gamma is equal to ____\_\_\_\_ .