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Day 33: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. This type asked 5 times: 14 Jun 2022, 26 Jun 2022, 25 Jul 2022, 31 Jan 2023, 1 Feb 2023. This one: 1 Feb 2023 See all 5 of this type

    160
    The sum of the absolute maximum and minimum values of the function f(x)=∣x2−5x+6∣−3x+2f(x) =\left| x^{2}- 5x + 6 \right|- 3x + 2 in the interval [−1,3]\lbrack - 1,3\rbrack is equal to:

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  2. Question 2

    Three Dimensional Geometry. This type asked 5 times: 2021 Paper 9, 2021 Paper 25, 14 Jun 2022, 31 Jan 2023, 1 Feb 2023. This one: 1 Feb 2023 See all 5 of this type

    171
    Let αx+βy+γz=1\alpha x + \beta y + \gamma z = 1 be the equation of a plane through the point (3,−2,5)(3, - 2,5) and perpendicular to the line joining the points (1,2,3)(1,2,3) and (−2,3,5)( - 2,3,5). Then the value of αβγ\alpha\beta\gamma is equal to

  3. Question 3

    Quadratic Equations. This type asked 5 times: 2021 Paper 19, 25 Jun 2022, 27 Jun 2022, 29 Jan 2023, 30 Jan 2023. This one: 30 Jan 2023 See all 5 of this type

    178
    If the value of real number a>0a > 0 for which x2−5ax+1=0x^{2}- 5ax + 1 = 0 and x2−ax−5=0x^{2}- ax - 5 = 0 have a common real root is 32β\frac{3}{\sqrt{2\beta}} then β\beta is equal to

  4. Question 4

    Binomial Theorem. Asked 4 times: 2021 Paper 12*, 26 Jul 2022*, 10 Apr 2023*, 23 Jan 2025 (* = numbers or wording changed that year) See all 4 times it was asked

    126
    If in the expansion of (1+x)p(1−x)q(1 + x)^{p}(1 - x)^{q}, the coefficients of xx and x2x^{2} are 1 and -2 , respectively, then p2+q2p^{2}+q^{2} is equal to :

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  5. Question 5

    Inverse Trigonometric Functions. Asked 4 times: 2021 Paper 1*, 27 Jun 2022*, 28 Jun 2022*, 30 Jan 2023 (* = numbers or wording changed that year) See all 4 times it was asked

    153
    Let a1=1,a2,a3,a4,….a_{1}= 1,a_{2},a_{3},a_{4},\ldots.. be consecutive natural numbers. Then tan⁡−1(11+a1a2)+tan⁡−1(11+a2a3)+⋯⋅+tan⁡−1(11+a2021a2022)\tan^{- 1}\left( \frac{1}{1 +a_{1}a_{2}} \right)+\tan^{- 1}\left( \frac{1}{1 +a_{2}a_{3}} \right)+ \cdots \cdot +\tan^{- 1}\left( \frac{1}{1 +a_{2021}a_{2022}} \right) is equal to

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