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Day 512: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 2 Apr 2025

    58
    Let a1,a2,a3…a_{1},a_{2},a_{3}\ldots be in an A.P. such that ∑k=112a2k−1=−725a1,a1≠0\sum_{k= 1}^{12} a_{2k- 1}= -\frac{72}{5}a_{1},a_{1}\neq 0. If ∑k=1nak=0\sum_{k= 1}^{n} a_{k}= 0, then nn is:

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  2. Question 2

    Straight Lines. Asked once: 23 Jan 2025

    130
    A rod of length eight units moves such that its ends AA and BB always lie on the lines x−y+2=0x - y + 2 = 0 and y+2=0y + 2 = 0, respectively. If the locus of the point PP, that divides the rod ABAB internally in the ratio 2:12:1 is 9(x2+αy2+βxy+γx+28y)−76=09\left( x^{2}+ \alpha y^{2}+ \beta xy + \gamma x + 28y \right)- 76 = 0, then α−β−γ\alpha - \beta - \gamma is equal to :

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  3. Question 3

    Three Dimensional Geometry. Asked once: 30 Jan 2023

    76
    Let a unit vector OP^\widehat{OP} make angles α,β,γ\alpha,\beta,\gamma with the positive directions of the co-ordinate axes OX,OY,OZOX,OY,OZ respectively, where β∈(0,π2)\beta \in\left( 0,\frac{\pi}{2} \right). If OP^\widehat{OP} is perpendicular to the plane through points (1,2,3),(2,3,4)(1,2,3),(2,3,4) and (1,5,7)(1,5,7), then which one of the following is true?

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  4. Question 4

    Trigonometric Equations. Asked once: 2021 Paper 13

    44
    The number of solutions of sin⁡7x+cos⁡7x=1,x∈[0,4π]\sin^{7}x+\cos^{7}x= 1,x\in \lbrack 0,4\pi\rbrack, is

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  5. Question 5

    Trigonometric Identities. Asked once: 30 Jan 2023

    70
    If tan⁡15∘+1tan⁡75∘+1tan⁡105∘+tan⁡195∘=2a\tan15^{\circ}+\frac{1}{\tan75^{\circ}}+\frac{1}{\tan105^{\circ}}+ \tan195^{\circ}= 2a, then the value of (a+1a)\left( a +\frac{1}{a} \right) is :

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