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Day 533: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 23 Jan 2025

    150
    The roots of the quadratic equation 3x2−px+q=03x^{2}-px+q=0 are the 10th10^{\text{th}} and 11th11^{\text{th}} terms of an arithmetic progression with common difference 32\frac{3}{2}. If the sum of the first 11 terms of this arithmetic progression is 88, then q−2pq-2p is equal to

  2. Question 2

    Straight Lines. Asked once: 1 Feb 2024

    180
    Let ABCABC be an isosceles triangle in which AA is at (−1,0),∠A=2π3,AB=AC( - 1,0),\angle A =\frac{2\pi}{3},AB = AC and BB is on the positive xx-axis. If BC=43BC= 4\sqrt{3} and the line BCBC intersects the line y=x+3y=x+ 3 at (α,β)(\alpha,\beta), then β4α2\frac{\beta^{4}}{\alpha^{2}} is:

  3. Question 3

    Three Dimensional Geometry. Asked once: 28 Jul 2022

    82
    Let P(−2,−1,1)P( - 2, - 1,1) and Q(5617,4317,11117)Q\left( \frac{56}{17},\frac{43}{17},\frac{111}{17} \right) be the vertices of the rhombus PRQS. If the direction ratios of the diagonal RS are α,−1,β\alpha, - 1,\beta, where both α\alpha and β\beta are integers of minimum absolute values, then α2+β2\alpha^{2}+\beta^{2} is equal to

  4. Question 4

    Trigonometric Identities. Asked once: 2021 Paper 4

    80
    If 0<x,y<π0 <x,y<\pi and cos⁡x+cos⁡y−cos⁡(x+y)=32\cos x+ \cos y- \cos(x+y) =\frac{3}{2}, then sin⁡x+cos⁡y\sin x+ \cos y is equal to:

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  5. Question 5

    Vector Algebra. Asked once: 11 Apr 2023

    67
    For any vector a=a1i^+a2j^+a3k^a =a_{1}\widehat{i}+a_{2}\widehat{j}+a_{3}\widehat{k}, with 10∣ai∣<1,i=1,2,310\left| a_{i} \right|< 1,i = 1,2,3, consider the following statements: (A): max {∣a1∣,∣a2∣,∣a3∣}≤∣a→∣\left\{ \left| a_{1} \right|,\left| a_{2} \right|,\left| a_{3} \right| \right\}\leq |\overrightarrow{a}| (B) : ∣a→∣≤3max{∣a1∣,∣a2∣,∣a3∣}|\overrightarrow{a}| \leq 3max\left\{ \left| a_{1} \right|,\left| a_{2} \right|,\left| a_{3} \right| \right\}

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