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Day 270: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 14 Jun 2022 (same type asked 4 times) See all 4 of this type

    174
    The sum of all the elements of the set {α∈{1,2,…,100}:HCF(α,24)=1}\mathbf{\{}\alpha\mathbf{\in \{ 1,2,\ldots,100\}:HCF(}\alpha,24) = 1\} is

  2. Question 2

    Conic Sections. Asked once: 2021 Paper 13 (same type asked 4 times) See all 4 of this type

    54
    If P:y2=αx;L:2x+y=k LP:y^{2}=\alpha x;L:2x+y=k\ L is a tangent to x2−y2=3x^{2}-y^{2}= 3 and PP. Find ' α\alpha '

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  3. Question 3

    Complex Numbers. Asked once: 2021 Paper 22 (same type asked 4 times) See all 4 of this type

    82
    A point zz moves in the complex plane such that arg(z−2z+2)=π4arg\left( \frac{z - 2}{z + 2} \right)=\frac{\pi}{4}, then the minimum value of ∣z−92−2i∣2|z- 9\sqrt{2}- 2i|^{2} is equal to

  4. Question 4

    Conic Sections. Asked once: 2021 Paper 19 (same type asked 4 times) See all 4 of this type

    65
    The point P(−26,3)P( - 2\sqrt{6},\sqrt{3}) lies on the hyperbola x2a2−y2b2=1\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1 having eccentricity 52\frac{\sqrt{5}}{2}. If the tangent and normal at PP to the hyperbola intersect its conjugate axis at the point QQ and RR respectively, then QRQR is equal to:

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  5. Question 5

    Probability. Asked once: 2021 Paper 6 (same type asked 4 times) See all 4 of this type

    62
    Let A denote the event that a 6 -digit integer formed by 0,1,2,3,4,50,1,2,3,4,5, 6 without repetitions, be divisible by 3 . Then probability of event AA is equal to:

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