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Day 361: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 1 Feb 2023 (same type asked 12 times) See all 12 of this type

    177
    The total number of six digit numbers, formed using the digits 4, 5,9 only and divisible by 6, is

  2. Question 2

    Definite Integration. Asked once: 29 Jan 2024 (same type asked 11 times) See all 11 of this type

    78
    If the value of the integral ∫−π2π2(x2cos⁡x1+πx+1+sin⁡2x1+esin⁡x2023)dx=π4(π+a)−2\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( \frac{x^{2}\cos x}{1 +\pi^{x}}+\frac{1 +\sin^{2}x}{1 +e^{\sin x^{2023}}} \right)dx =\frac{\pi}{4}(\pi + a) - 2, then the value of aa is

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  3. Question 3

    Limits and Continuity. Asked once: 31 Jan 2024 (same type asked 11 times) See all 11 of this type

    177
    If lim⁡x→0ax2ex−blog⁡e(1+x)+cxe−xx2sin⁡x=1\lim_{x\rightarrow 0} \frac{ax^{2}e^{x}-b\log_{e}(1 +x) +cxe^{-x}}{x^{2}\sin x}= 1, then 16(a2+b2+c2)16\left( a^{2}+b^{2}+c^{2} \right) is equal to

  4. Question 4

    Binomial Theorem. Asked once: 26 Jun 2022 (same type asked 11 times) See all 11 of this type

    65
    The remainder when (2021)2023(2021)^{2023} is divided by 7 is:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 1 Feb 2023 (same type asked 11 times) See all 11 of this type

    74
    Let the image of the point P(2,−1,3)P(2, - 1,3) in the plane x+2y−z=0x + 2y - z = 0 be QQ. Then the distance of the plane 3x+2y+z+29=03x + 2y + z + 29 = 0 from the point QQ is

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