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Day 414: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 2021 Paper 3 (same type asked 12 times) See all 12 of this type

    90
    The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1,2,3,4,51,2,3,4,5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5 is

  2. Question 2

    Differential Equations. Asked once: 24 Jan 2025 (same type asked 41 times) See all 41 of this type

    129
    Let f:(0,∞)→Rf:(0,\infty) \rightarrow R be a function which is differentiable at all points of its domain and satisfies the condition x2f′(x)=2xf(x)+3x^{2}f^{'}(x) = 2xf(x) + 3, with f(1)=4f(1) = 4. Then 2f(2)2f(2) is equal to:

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  3. Question 3

    Three Dimensional Geometry. Asked once: 6 Apr 2024 (same type asked 33 times) See all 33 of this type

    177
    If the shortest distance between the lines x−λ3=y−2−1=z−11\frac{x-\lambda}{3}=\frac{y- 2}{- 1}=\frac{z- 1}{1} and x+2−3=y+52=z−44\frac{x+ 2}{- 3}=\frac{y+ 5}{2}=\frac{z- 4}{4} is 4430\frac{44}{\sqrt{30}}, then the largest possible value of ∣λ∣|\lambda| is equal to

  4. Question 4

    Determinants. Asked once: 8 Apr 2024 (same type asked 26 times) See all 26 of this type

    157
    If the system of equations x+4y−z=λx+ 4y-z=\lambda, 7x+9y+μz=−3,5x+y+2z=−17x+ 9y+\mu z= - 3,5x+y+ 2z= - 1 has infinitely many solutions, then (2μ+3λ)(2\mu + 3\lambda) is equal to :

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  5. Question 5

    Three Dimensional Geometry. Asked once: 27 Jan 2024 (same type asked 19 times) See all 19 of this type

    153
    Let the image of the point (1,0,7)(1,0,7) in the line x1=y−12=z−23\frac{x}{1}=\frac{y - 1}{2}=\frac{z - 2}{3} be the point (α,β,γ)(\alpha,\beta,\gamma). Then which one of the following points lies on the line passing through (α,β,γ)(\alpha,\beta,\gamma) and making angles 2π3\frac{2\pi}{3} and 3π4\frac{3\pi}{4} with y-axis and z-axis respectively and an acute angle with xx-axis?

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