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Day 516: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 31 Jan 2024

    61
    For 0<c<b<a0 < c < b < a, let (a+b−2c)x2+(b+c−2a)x(a + b - 2c)x^{2}+ (b + c - 2a)x +(c+a−2b)=0+ (c + a - 2b) = 0 and α≠1\alpha \neq 1 be one of its roots. Then, among the two statements (I) If α∈(−1,0)\alpha \in ( - 1,0), then bb cannot be the geometric mean of a and c (II) If α∈(0,1)\alpha \in (0,1), then bb may be the geometric mean of a and c

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  2. Question 2

    Relations and Functions. Asked once: 1 Feb 2024

    163
    If the domain of the function f(x)=x2−25(4−x2)f(x) =\frac{\sqrt{x^{2}- 25}}{\left( 4 -x^{2} \right)} +log⁡10(x2+2x−15)+\log_{10}\left( x^{2}+ 2x - 15 \right) is (−∞,α)U[β,∞)( - \infty,\alpha)U\lbrack\beta,\infty), then α2+β3\alpha^{2}+\beta^{3} is equal to :

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  3. Question 3

    Sequences and Series. Asked once: 29 Jan 2025

    148
    Let a1,a2,…,a2024a_{1},a_{2},\ldots,a_{2024} be an Arithmetic Progression such that a1+(a5+a10+a15+…+a2020)+a2024=a_{1}+\left( a_{5}+a_{10}+a_{15}+ \ldots +a_{2020} \right)+a_{2024}= 2233. Then a1+a2+a3+…+a2024a_{1}+a_{2}+a_{3}+ \ldots +a_{2024} is equal to

  4. Question 4

    Straight Lines. Asked once: 8 Apr 2024

    73
    The equations of two sides ABAB and ACAC of a triangle ABCABC are 4x+y=144x + y = 14 and 3x−2y=53x - 2y = 5, respectively. The point (2,−43)\left( 2, -\frac{4}{3} \right) divides the third side BCBC internally in the ratio 2:12:1. The equation of the side BCBC is:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 30 Jan 2023

    151
    A vector v→\overrightarrow{v} in the first octant is inclined to the xx-axis at 60∘60^{\circ}, to the yy-axis at 45∘45^{\circ} and to the zz-axis at an acute angle. If a plane passing through the points (2,−1,1)(\sqrt{2}, - 1,1) and (a,b,c)(a,b,c), is normal to v→\overrightarrow{v}, then

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