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Day 223: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 2021 Paper 3 (same type asked 2 times) See all 2 of this type

    65
    If 0<θ,ϕ<π2,x=∑n=0∞cos⁡2nθ,y=∑n=0∞sin⁡2nϕ0 <\theta,\phi<\frac{\pi}{2},x=\sum_{n= 0}^{\infty} \cos^{2n}\theta,y=\sum_{n= 0}^{\infty} \sin^{2n}\phi and z=∑n=0∞cos⁡2nθ⋅sin⁡2nϕz =\sum_{n = 0}^{\infty} \cos^{2n}\theta\cdot\sin^{2n}\phi then:

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  2. Question 2

    Straight Lines. Asked once: 2021 Paper 21 (same type asked 2 times) See all 2 of this type

    69
    Let A(a,0),B(b,2 b+1)A(a,0),B(b,2\text{ }b + 1) and C(0, b),b≠0,∣ b∣≠1C(0,\text{ }b),b \neq 0,|\text{ }b| \neq 1, be points such that the area of triangle ABCABC is 1 sq. unit, then the sum of all possible values of aa is :

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  3. Question 3

    Conic Sections. Asked once: 2021 Paper 11 (same type asked 2 times) See all 2 of this type

    61
    Let the tangent to the parabola S:y2=2xS:y^{2}= 2x at the point P(2,2)P(2,2) meet the xx-axis at QQ and normal at it meet the parabola SS at the point RR. Then the area (in sq. units) of the triangle PQRPQR is equal to:

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  4. Question 4

    Conic Sections. Asked once: 2021 Paper 2 (same type asked 2 times) See all 2 of this type

    73
    For which of the following curves, the line x+3y=23x+\sqrt{3}y= 2\sqrt{3} is the tangent at the point (332,12)\left( \frac{3\sqrt{3}}{2},\frac{1}{2} \right) ?

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  5. Question 5

    Limits and Continuity. Asked once: 2021 Paper 8 (same type asked 2 times) See all 2 of this type

    77
    The value of the limit lim⁡θ→0tan⁡(πcos⁡2θ)sin⁡(2πsin⁡2θ)\lim_{\theta\rightarrow 0} \frac{\tan\left( \pi\cos^{2}\theta \right)}{\sin\left( 2\pi\sin^{2}\theta \right)} is equal to :

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