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Day 51: JEE Mains Maths

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

  1. Question 1

    Conic Sections. This type asked 4 times: 2021 Paper 10, 2021 Paper 19, 25 Jun 2022, 26 Jun 2022. This one: 26 Jun 2022 See all 4 of this type

    163
    The normal to the hyperbola x2a2−y29=1\frac{x^{2}}{a^{2}}-\frac{y^{2}}{9}= 1 at the point (8,33)(8,3\sqrt{3}) on it passes through the point :

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  2. Question 2

    Probability. This type asked 4 times: 2021 Paper 4, 2021 Paper 6, 2021 Paper 26, 26 Jun 2022. This one: 26 Jun 2022 See all 4 of this type

    179
    If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96p96p is equal to

  3. Question 3

    Application of Integrals. Asked 3 times: 1 Feb 2023*, 28 Jan 2026 S1*, 5 Apr 2026 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    66
    The area of the region R={(x,y):xy≤27,1≤y≤x2}R =\left\{ (x,y):xy \leq 27,1 \leq y \leq x^{2} \right\} is equal to :

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  4. Question 4

    Three Dimensional Geometry. Asked 3 times: 2021 Paper 2*, 22 Jan 2026 S1*, 4 Apr 2026 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    64
    If (2α+1,α2−3α,α−12)\left( 2\alpha+ 1,\alpha^{2}- 3\alpha,\frac{\alpha- 1}{2} \right) is the image of (α,2α,1)(\alpha,2\alpha,1) in the line x−23=y−12=z1\frac{x - 2}{3}=\frac{y - 1}{2}=\frac{z}{1}, then the possible value(s) of α\alpha is(are) :

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  5. Question 5

    Sequences and Series. Asked 3 times: 26 Jul 2022*, 1 Feb 2023*, 28 Jan 2026 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    71
    If ∑r=125(rr4+r2+1)=pq\sum_{r = 1}^{25} \left( \frac{r}{r^{4} + r^{2} + 1} \right) = \frac{p}{q}, where p and q are positive integers such that gcd⁡(p,q)=1\gcd(p,q) = 1, then p+qp + q is equal to ............ .