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Day 63: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. This type asked 3 times: 8 Apr 2024, 2 Apr 2025, 4 Apr 2025. This one: 4 Apr 2025 See all 3 of this type

    126
    Let a>0a > 0. If the function f(x)=6x3−45ax2+108a2x+1f(x) = 6x^{3}- 45ax^{2}+ 108a^{2}x + 1 attains its local maximum and minimum values at the points x1x_{1} and x2x_{2} respectively such that x1x2=x_{1}x_{2}= 54 , then a+x1+x2a +x_{1}+x_{2} is equal to :-

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  2. Question 2

    Application of Integrals. This type asked 3 times: 24 Jan 2025, 3 Apr 2025, 4 Apr 2025. This one: 4 Apr 2025 See all 3 of this type

    71
    If the area of the region {(x,y):∣x−5∣≤y≤4x}\{(x,y):|x - 5| \leq y \leq 4\sqrt{x}\} is A , then 3 A is equal to.

  3. Question 3

    Binomial Theorem. This type asked 3 times: 2021 Paper 24, 27 Jan 2024, 4 Apr 2025. This one: 4 Apr 2025 See all 3 of this type

    54
    For an integer n≥2n \geq 2, if the arithmetic mean of all coefficients in the binomial expansion of (x+y)2n−3(x+y)^{2n- 3} is 16 , then the distance of the point P(2n−1,n2−4n)P\left( 2n - 1,n^{2}- 4n \right) from the line x+y=8x+y= 8 is:

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  4. Question 4

    Straight Lines. This type asked 3 times: 8 Apr 2023, 13 Apr 2023, 4 Apr 2025. This one: 4 Apr 2025 See all 3 of this type

    65
    Let the three sides of a triangle are on the lines 4x−7y+10=0,x+y=54x- 7y+ 10 = 0,x+y=5 and 7x+4y=157x+ 4y= 15. Then the distance of its orthocenter from the orthocenter of the triangle formed by the lines x=0,y=0x= 0,y= 0 and x+y=1x+y= 1 is.

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  5. Question 5

    Vector Algebra. This type asked 3 times: 24 Jan 2023, 28 Jan 2025, 4 Apr 2025. This one: 4 Apr 2025 See all 3 of this type

    64
    Consider two vectors u→=3i^−j^\overrightarrow{u}= 3\widehat{i}-\widehat{j} and v→=2i^+j^−λk^,λ>0\overrightarrow{v}= 2\widehat{i}+\widehat{j}-\lambda\widehat{k},\lambda> 0. The angle between them is given by cos⁡−1(527)\cos^{- 1}\left( \frac{\sqrt{5}}{2\sqrt{7}} \right). Let v→=v→1+v→2\overrightarrow{v}={\overrightarrow{v}}_{1}+{\overrightarrow{v}}_{2}, where v→1{\overrightarrow{v}}_{1} is parallel to u→\overrightarrow{u} and v→2{\overrightarrow{v}}_{2} is perpendicular to u→\overrightarrow{u}. Then the value ∣v→1∣2+∣v→2∣2\left| {\overrightarrow{v}}_{1} \right|^{2}+\left| {\overrightarrow{v}}_{2} \right|^{2} is equal to.

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