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Day 113: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. This type asked 2 times: 31 Jan 2024, 4 Apr 2024. This one: 4 Apr 2024 See all 2 of this type

    72
    Let the first three terms 2,p2,p and qq, with q≠2q\neq 2, of a G.P. be respectively the 7th ,8th 7^{\text{th~}},8^{\text{th~}} and 13th 13^{\text{th~}} terms of an A.P. If the 5th 5^{\text{th~}} term of the G.P. is the nth n^{\text{th~}} term of the A.P., then nn is equal to

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  2. Question 2

    Vector Algebra. This type asked 2 times: 29 Jan 2024, 4 Apr 2024. This one: 4 Apr 2024 See all 2 of this type

    71
    Let a unit vector which makes an angle of 60∘60^{\circ} with 2i^+2j^−k^2\widehat{i}+ 2\widehat{j}-\widehat{k} and an angle of 45∘45^{\circ} with i^−k^\widehat{i}-\widehat{k} be C→\overrightarrow{C}. Then C→+(−12i^+132j^−23k^)\overrightarrow{C}+\left( -\frac{1}{2}\widehat{i}+\frac{1}{3\sqrt{2}}\widehat{j}-\frac{\sqrt{2}}{3}\widehat{k} \right) is:

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  3. Question 3

    Conic Sections. This type asked 2 times: 24 Jan 2023, 1 Feb 2024. This one: 1 Feb 2024 See all 2 of this type

    170
    Let the locus of the mid points of the chords of circle x2+(y−1)2=1x^{2}+ (y - 1)^{2}= 1 drawn from the origin intersect the line x+y=1x + y = 1 at PP and QQ. Then, the length of PQPQ is:

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  4. Question 4

    Conic Sections. This type asked 2 times: 31 Jan 2024, 1 Feb 2024. This one: 1 Feb 2024 See all 2 of this type

    76
    Let x2a2+y2 b2=1,a>b\frac{x^{2}}{a^{2}}+\frac{y^{2}}{{\text{ }b}^{2}}= 1,a > b be an ellipse, whose eccentricity is 12\frac{1}{\sqrt{2}} and the length of the latus rectum is 14\sqrt{14}. Then the square of the eccentricity of x2a2−y2b2=1\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1 is :

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  5. Question 5

    Relations and Functions. This type asked 2 times: 28 Jun 2022, 1 Feb 2024. This one: 1 Feb 2024 See all 2 of this type

    90
    Let A={1,2,3,…20}\mathbf{A = \{ 1,2,3,\ldots 20\}}. Let R1R_{1} and R2R_{2} two relation on A such that R1={(a,b):bR_{1}\mathbf{= \{(a,b):b} is divisible by a}a\} R2={(a,b)R_{2}\mathbf{= \{(a,b)} : aa is an integral multiple of b}b\}. Then, number of elements in R1−R2R_{1}-R_{2} is equal to