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Day 328: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 2021 Paper 26 (same type asked 4 times) See all 4 of this type

    88
    Let the normals at all the points on a given curve pass through a fixed point (a,b)(a,b). If the curve passes through (3,−3)(3, - 3) and (4,−22)(4, - 2\sqrt{2}), and given that a−22 b=3a- 2\sqrt{2}\text{ }b = 3, then (a2+b2+ab)\left( a^{2}+b^{2}+ ab \right) is equal to

  2. Question 2

    Relations and Functions. Asked once: 2021 Paper 3 (same type asked 4 times) See all 4 of this type

    70
    Let f,g:N→Nf,g:N \rightarrow N such that f(n+1)=f(n)+f(1) ∀n∈Nf(n + 1) = f(n) + f(1)\ \forall n \in N and gg be any arbitrary function. Which of the following statements is NOT true?

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  3. Question 3

    Binomial Theorem. Asked once: 2021 Paper 23 (same type asked 4 times) See all 4 of this type

    81
    If the coefficient of a7b8a^{7}b^{8} in the expansion of (a+2b+4ab)10(a+ 2b+ 4ab)^{10} is K.216K.2^{16}, then KK is equal to

  4. Question 4

    Three Dimensional Geometry. Asked once: 2021 Paper 1 (same type asked 4 times) See all 4 of this type

    69
    The distance of the point (1,1,9)(1,1,9) from the point of intersection of the line x−31=y−42=z−52\frac{x- 3}{1}=\frac{y- 4}{2}=\frac{z- 5}{2} and the plane x+y+z=17x+y+z= 17 is:

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  5. Question 5

    Trigonometric Equations. Asked once: 2021 Paper 5 (same type asked 4 times) See all 4 of this type

    79
    The number of roots of the equation,
    (81)sin⁡2x+(81)cos⁡2x=30(81)^{\sin^{2}x}+ (81)^{\cos^{2}x}= 30
    in the interval [0,π]\lbrack 0,\pi\rbrack is equal to:

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