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Day 480: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 24 Jan 2025

    139
    Let a→=3i^−j^+2k^,b→=a→×(i^−2k^)\overrightarrow{a}= 3\widehat{i}-\widehat{j}+ 2\widehat{k},\overrightarrow{b}=\overrightarrow{a}\times (\widehat{i}- 2\widehat{k}) and c→=b→×k^\overrightarrow{c}=\overrightarrow{b}\times\widehat{k}. Then the projection of c→−2j^\overrightarrow{c}- 2\widehat{j} on a→\overrightarrow{a} is:

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  2. Question 2

    Application of Derivatives. Asked once: 9 Apr 2024

    83
    Let the set of all positive values of λ\lambda, for which the point of local minimum of the function (1+x(λ2−x2))\left( 1 + x\left( \lambda^{2}-x^{2} \right) \right) satisfies x2+x+2x2+5x+6<0\frac{x^{2}+ x + 2}{x^{2}+ 5x + 6}< 0, be (α,β)(\alpha,\beta). Then α2+β2\alpha^{2}+\beta^{2} is equal to

  3. Question 3

    Application of Integrals. Asked once: 21 Jan 2026 S1

    52
    The area of the region, inside the ellipse x2+4y2=4x^{2}+ 4y^{2}= 4 and outside the region bounded by the curves y=∣x∣−1y = |x| - 1 and y=1−∣x∣y = 1 - |x|, is :

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  4. Question 4

    Binomial Theorem. Asked once: 22 Jan 2025

    126
    Let α,β,γ\alpha,\beta,\gamma and δ\delta be the coefficients of x7,x5,x3x^{7},x^{5},x^{3} and xx respectively in the expansion of (x+x3−1)5+(x−x3−1)5,x>1\left( x +\sqrt{x^{3}- 1} \right)^{5}+\left( x -\sqrt{x^{3}- 1} \right)^{5},x > 1. If uu and vv satisfy the equations
    αu+βv=18,γu+δv=20,\begin{matrix} & \alpha u + \beta v = 18, \\ & \gamma u + \delta v = 20, \end{matrix}
    then u+vu + v equals :

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  5. Question 5

    Complex Numbers. Asked once: 2 Apr 2025

    60
    Let zz be a complex number such that ∣z∣=1|z| = 1. If 2+k2zk+z‾=kz,k∈R\frac{2 +k^{2}z}{k +\overline{z}}= kz,k \in R, then the maximum distance of k+ik2k+ik^{2} from the circle ∣z−(1+2i)∣=1|z- (1 + 2i)| = 1 is:

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