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Day 81: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked 2 times: 30 Jan 2024*, 2 Apr 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    130
    If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :

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  2. Question 2

    Straight Lines. Asked 2 times: 30 Jan 2023*, 2 Apr 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    144
    Let the area of the triangle formed by a straight Line L:x+by+c=0L:x+by+c= 0 with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line LL makes an angle of 45∘45^{\circ} with the positive xx-axis, then the value of b2+c2b^{2}+c^{2} is:

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  3. Question 3

    Binomial Theorem. Asked 2 times: 13 Apr 2023*, 29 Jan 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    142
    The remainder, when 71037^{103} is divided by 23 , is equal to:

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  4. Question 4

    Differential Equations. Asked 2 times: 8 Apr 2023*, 29 Jan 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    60
    Let y=y(x)y = y(x) be the solution of the differential equation cos⁡x(log⁡e(cos⁡x))2dy+(sin⁡x−3ysinxlog⁡e(cos⁡x))dx=0\cos x\left( \log_{e}(\cos x) \right)^{2}dy +\left( \sin x - 3ysinx\log_{e}(\cos x) \right)dx = 0, x∈(0,π2)x \in\left( 0,\frac{\pi}{2} \right). If y(π4)=−1log⁡e2y\left( \frac{\pi}{4} \right)=\frac{- 1}{\log_{e}2}, then y(π6)y\left( \frac{\pi}{6} \right) is :

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  5. Question 5

    Relations and Functions. Asked 2 times: 29 Jun 2022*, 28 Jan 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    55
    Let f:R→Rf:R \rightarrow R be a function defined by f(x)=(2+3a)x2+(a+2a−1)x+b,a≠1f(x) = (2 + 3a)x^{2}+\left( \frac{a + 2}{a - 1} \right)x + b,a \neq 1. If f(x+y)=f(x)+f(y)+1−27xyf(x + y) = f(x) + f(y) + 1 -\frac{2}{7}xy, then the value of 28∑i=15∣f(i)∣28\sum_{i = 1}^{5} |f(i)| is:

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