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Day 618: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2021 Paper 2

    70
    If the curve y=ax2+bx+c,x∈Ry=ax^{2}+bx+c,x\in R, passes through the point (1,2)(1,2) and the tangent line to this curve at origin is y=xy=x, then the possible values of a, b, c are :

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  2. Question 2

    Complex Numbers. Asked once: 2021 Paper 4

    63
    If α,β∈R\alpha,\beta\in R are such that 1−2i1 - 2i (here i2=−1i^{2}= -1) is a root of z2+αz+β=0z^{2}+\alpha z+\beta= 0, then (α−β)(\alpha-\beta) is equal to:

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  3. Question 3

    Conic Sections. Asked once: 5 Apr 2024

    72
    Let a circle CC of radius 1 and closer to the origin be such that the lines passing through the point (3,2)(3,2) and parallel to the coordinate axes touch it. Then the shortest distance of the circle CC from the point (5,5)(5,5) is:

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  4. Question 4

    Definite Integration. Asked once: 24 Jan 2023

    180
    Let ff be a differentiable function defined on [0,π2]\left\lbrack 0,\frac{\pi}{2} \right\rbrack such that f(x)>0f(x) > 0 and f(x)+∫0xf(t)1−(log⁡ef(t))2dt=e,∀x∈[0,π2]f(x) +\int_{0}^{x} f(t)\sqrt{1 -\left( \log_{e}f(t) \right)^{2}}dt = e,\forall x \in\left\lbrack 0,\frac{\pi}{2} \right\rbrack. Then (6log⁡ef(π6))2\left( 6\log_{e}f\left( \frac{\pi}{6} \right) \right)^{2} is equal to

  5. Question 5

    Sequences and Series. Asked once: 27 Jul 2022

    87
    Let f(x)=2x2−x−1f\left( x \right)= 2x^{2}- x - 1and S={n∈Z:∣f(n)∣≤800}\mathbf{S = \{ n \in Z:|f(n)| \leq 800\}}. Then, the value of ∑n∈Sf(n)\sum_{n \in S} f(n) is equal to