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Day 251: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 10 Apr 2023 (same type asked 5 times) See all 5 of this type

    67
    Let the complex number z=x+z = x + iy be such that 2z−3i2z+i\frac{2z - 3i}{2z + i} is purely imaginary. If x+y2=0x +y^{2}= 0, then y4+y2−yy^{4}+y^{2}- y is equal to:

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  2. Question 2

    Conic Sections. Asked once: 28 Jun 2022 (same type asked 5 times) See all 5 of this type

    165
    If vertex of a parabola is (2,−1)(2, - 1) and the equation of its directrix is 4x−3y=214x - 3y = 21, then the length of its latus rectum is

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  3. Question 3

    Matrices. Asked once: 6 Apr 2023 (same type asked 5 times) See all 5 of this type

    160
    Let PP be a square matrix such that P2=I−PP^{2}= I - P. For α,β,γ,δ∈N\alpha,\beta,\gamma,\delta \in N, if Pα+Pβ=γI−29PP^{\alpha}+P^{\beta}= \gamma I - 29P and Pα−Pβ=P^{\alpha}-P^{\beta}= δI−13P\delta I - 13P, then α+β+γ−δ\alpha + \beta + \gamma - \delta is equal to

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  4. Question 4

    Sequences and Series. Asked once: 10 Apr 2023 (same type asked 5 times) See all 5 of this type

    162
    If Sn=4+11+21+34+50+S_{n}= 4 + 11 + 21 + 34 + 50 + to nn terms, then 160( S29−S9)\frac{1}{60}\left( {\text{ }S}_{29}-S_{9} \right) is equal to

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  5. Question 5

    Application of Integrals. Asked once: 10 Apr 2023 (same type asked 5 times) See all 5 of this type

    180
    If the area of the region {(x,y):∣x2−2∣≤y≤x}\left\{ (x,y):\left| x^{2}- 2 \right|\leq y \leq x \right\} is AA, then 6 A+1626\text{ }A + 16\sqrt{2} is equal to