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Day 153: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 27 Jul 2022 (same type asked 5 times) See all 5 of this type

    163
    If the length of the latus rectum of a parabola, whose focus is (a,a)(a,a) and the tangent at its vertex is x+y=ax + y = a, is 16, then ∣a∣|a| is equal to :

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  2. Question 2

    Matrices. Asked once: 2 Apr 2025 (same type asked 5 times) See all 5 of this type

    145
    Let AA be a 3×33 \times 3 real matrix such that A2(A−2I)−A^{2}(A- 2I) - 4( A−I)=O4(\text{ }A - I) = O, where I and O are the identity and null matrices, respectively. If A5=αA2+βA+γIA^{5}=\alpha A^{2}+\beta A+\gamma I, where α,β\alpha,\beta and γ\gamma are real constants, then α+β+γ\alpha+\beta+\gamma is equal to:

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  3. Question 3

    Sequences and Series. Asked once: 30 Jan 2024 (same type asked 5 times) See all 5 of this type

    90
    Let α=12+42+82+132+192+262+……\alpha =1^{2}+4^{2}+8^{2}+13^{2}+19^{2}+26^{2}+ \ldots\ldots upto 10 terms and β=∑n=110n4\beta =\sum_{n = 1}^{10} n^{4}. If 4α−β=55k+404\alpha - \beta = 55k + 40, then kk is equal to

  4. Question 4

    Application of Integrals. Asked once: 13 Apr 2023 (same type asked 5 times) See all 5 of this type

    167
    The area of the region {(x,y):x2≤y≤∣x2−4∣,y≥1}\left\{ (x,y):x^{2}\leq y \leq\left| x^{2}- 4 \right|,y \geq 1 \right\} is

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  5. Question 5

    Determinants. Asked once: 23 Jan 2025 (same type asked 5 times) See all 5 of this type

    69
    If the system of equations
    (λ−1)x+(λ−4)y+λz=5λx+(λ−1)y+(λ−4)z=7 (λ+1)x+(λ+2)y−(λ+2)z=9\begin{matrix} & (\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 \\ & \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 \\ & \ (\lambda + 1)x + (\lambda + 2)y - (\lambda + 2)z = 9 \end{matrix}
    has infinitely many solutions, then λ2+λ\lambda^{2}+ \lambda is equal to

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