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Day 461: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 7 Apr 2025

    53
    Let x=−1x= - 1 and x=2x= 2 be the critical points of the function f(x)=x3+ax2+f\left( x \right)=x^{3}+ax^{2}+ b log⁡e∣x∣+1,x≠0b\ \log_{e}|x| + 1,x \neq 0. Let mm and M respectively be the absolute minimum and the absolute maximum values of ff in the interval [−2,−12]\left\lbrack - 2, -\frac{1}{2} \right\rbrack. Then ∣M+m∣|M +m| is equal to (Take log⁡e2=0.7\log_{e}2 = 0.7 ):

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  2. Question 2

    Application of Integrals. Asked once: 24 Jan 2026 S2

    62
    Let f(α)f(\alpha) denote the area of the region in the first quadrant bounded by x=0,x=1,y2=xx = 0,x = 1,y^{2}= x and y=∣αx−5∣−∣1−αx∣+αx2y = |\alpha x - 5| - |1 - \alpha x| + \alpha x^{2}. Then (f(0)+f(1))(f(0) + f(1)) is equal to

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  3. Question 3

    Binomial Theorem. Asked once: 2 Apr 2025

    140
    If ∑r=010(10r+1−110r)⋅ 11Cr+1=α11−11111010\sum_{r = 0}^{10} \left( \frac{10^{r + 1}- 1}{10^{r}} \right)\cdot\ ^{11}C_{r + 1}=\frac{\alpha^{11}-11^{11}}{10^{10}}, then α\alpha is equal to :

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  4. Question 4

    Complex Numbers. Asked once: 24 Jan 2026 S2

    73
    Let z=(1+i)(1+2i)(1+3i)…(1+ni)z = (1 + i)(1 + 2i)(1 + 3i)\ldots(1 + ni), where i=−1i = \sqrt{- 1}. If ∣z∣2=44200|z|^{2} = 44200, then nn is equal to -

  5. Question 5

    Conic Sections. Asked once: 6 Apr 2026 S1

    53
    Let e1e_{1} and e2e_{2} be two distinct roots of the equation x2−ax+2=0x^{2}-ax+2=0. Let the set of all a∈Ra\in R for which e1e_{1} and e2e_{2} are the eccentricities of two hyperbolas be (α,β)(\alpha,\beta), and the set of all a∈Ra\in R for which e1e_{1} and e2e_{2} are the eccentricities of an ellipse and a hyperbola, respectively, be (γ,∞)(\gamma,\infty). Then α2+β2+γ2\alpha^{2}+\beta^{2}+\gamma^{2} is equal to:

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