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Day 97: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked 2 times: 2021 Paper 10*, 2021 Paper 12 (* = numbers or wording changed that year) See all 2 times it was asked

    58
    In a triangle ABCABC, if ∣BC→∣=3,∣CA→∣=5|\overrightarrow{BC}| = 3,|\overrightarrow{CA}| = 5 and ∣BA→∣=7|\overrightarrow{BA}| = 7, then the projection of the vector BA→\overrightarrow{BA} on BC→\overrightarrow{BC} is equal to

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  2. Question 2

    Quadratic Equations. Asked 2 times: 2021 Paper 7*, 2021 Paper 9 (* = numbers or wording changed that year) See all 2 times it was asked

    80
    The value of 3+14+13+14+13+…∞3 +\frac{1}{4 +\frac{1}{3 +\frac{1}{4 +\frac{1}{3 + \ldots\infty}}}} is equal to

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  3. Question 3

    Probability. Asked 2 times: 2021 Paper 1, 2021 Paper 7 See all 2 times it was asked

    84
    Let there be three independent events E1,E2E_{1},E_{2} and E3E_{3}. The probability that only E1E_{1} occurs is α\alpha, only E2E_{2} occurs is β\beta and only E3E_{3} occurs is γ\gamma. Let ' pp ' denote the probability of none of events occurs that satisfies the equations (α−2β)p=αβ(\alpha - 2\beta)p = \alpha\beta and (β−3γ)p=2βγ(\beta - 3\gamma)p = 2\beta\gamma. All the given probabilities are assumed to lie in the interval (0,1)(0,1). Then,  Probability of occurrence of E1 Probability of occurrence of E3\frac{\text{~Probability of occurrence of~}E_{1}}{\text{~Probability of occurrence of~}E_{3}} is equal to

  4. Question 4

    Conic Sections. This type asked 2 times: 22 Jan 2026 S1, 8 Apr 2026 S2. This one: 8 Apr 2026 S2 See all 2 of this type

    61
    Let O be the vertex of the parabola y2=4xy^{2}= 4x and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C , then the length of its latus rectum is :

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  5. Question 5

    Relations and Functions. This type asked 2 times: 28 Jan 2025, 8 Apr 2026 S2. This one: 8 Apr 2026 S2 See all 2 of this type

    75
    Let f be a polynomial function such that log⁡2(f(x))=(log⁡2(2+23+29+...∞))\log_{2}(f(x)) = \left( \log_{2}\left( 2 + \frac{2}{3} + \frac{2}{9} + ...\infty \right) \right). log⁡3(1+f(x)f(1/x)),x>0\log_{3}\left( 1 + \frac{f(x)}{f(1/x)} \right),x > 0 and f(6)=37f(6) = 37. Then ∑n=110f(n)\sum_{n = 1}^{10} f(n) is equal to ____\_\_\_\_ .