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Day 93: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked 2 times: 25 Jun 2022*, 27 Jul 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    175
    A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semivertical angle is tan⁡−134\tan^{- 1}\frac{3}{4}. Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is

  2. Question 2

    Limits and Continuity. Asked 2 times: 2021 Paper 4*, 26 Jul 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    157
    Let β=lim⁡x→0αx−(e3x−1)αx(e3x−1)\beta =\lim_{x \rightarrow 0} \frac{\alpha x -\left( e^{3x}- 1 \right)}{\alpha x\left( e^{3x}- 1 \right)} for some α∈R\alpha \in R. Then the value of α+β\alpha + \beta is:

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  3. Question 3

    Three Dimensional Geometry. Asked 2 times: 28 Jun 2022*, 26 Jul 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    90
    Let QQ and RR be two points on the line x+12=y+23=z−12\frac{x + 1}{2}=\frac{y + 2}{3}=\frac{z - 1}{2} at a distance 26\sqrt{26} from the point P(4,2,7)P(4,2,7). Then the square of the area of the triangle PQRPQR is

  4. Question 4

    Binomial Theorem. Asked 2 times: 2021 Paper 25*, 25 Jul 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    83
    If the maximum value of the term independent of tt in the expansion of (t2x15+(1−x)110t)15,x≥0\left( t^{2}x^{\frac{1}{5}}+\frac{(1 - x)^{\frac{1}{10}}}{t} \right)^{15},x \geq 0, is KK, then 8 K8\text{ }K is equal to

  5. Question 5

    Limits and Continuity. Asked 2 times: 2021 Paper 21*, 25 Jul 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    65
    If lim⁡n→∞(n2−n−1+nα+β)=0\lim_{n \rightarrow \infty} \left( \sqrt{n^{2}- n - 1}+ n\alpha + \beta \right)= 0 then 8(α+β)8(\alpha + \beta) is equal to:

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