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Day 255: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 24 Jan 2023 (same type asked 5 times) See all 5 of this type

    157
    The number of real solutions of the equation 3(x2+1x2)−2(x+1x)+5=03\left( x^{2}+\frac{1}{x^{2}} \right)- 2\left( x +\frac{1}{x} \right)+ 5 = 0, is

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  2. Question 2

    Three Dimensional Geometry. Asked once: 25 Jul 2022 (same type asked 5 times) See all 5 of this type

    165
    A plane EE is perpendicular to the two planes 2x−2y+z=02x - 2y + z = 0 and x−y+2z=4x - y + 2z = 4, and passes through the point P(1,−1,1)P(1, - 1,1). If the distance of the plane EE from the point Q(a,a,2)Q(a,a,2) is 323\sqrt{2}, then (PQ)2(PQ)^{2} is equal to

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  3. Question 3

    Three Dimensional Geometry. Asked once: 31 Jan 2023 (same type asked 5 times) See all 5 of this type

    85
    Let θ\theta be the angle between the planes P1:r→⋅(ı^+ȷ^+2k^)=9P_{1}:\overrightarrow{r}\cdot (\widehat{\imath}+\widehat{\jmath}+ 2\widehat{k}) = 9 and P2:r→⋅(2ı^−ȷ^+k^)=15P_{2}:\overrightarrow{r}\cdot (2\widehat{\imath}-\widehat{\jmath}+\widehat{k}) = 15. Let LL be the line that meets P2P_{2} at the point (4,−2,5)(4, - 2,5) and makes an angle θ\theta with the normal of P2P_{2}. If α\alpha is the angle between LL and P2P_{2}, then (tan⁡2θ)(cot⁡2α)\left( \tan^{2}\theta \right)\left( \cot^{2}\alpha \right) is equal to

  4. Question 4

    Conic Sections. Asked once: 2021 Paper 1 (same type asked 5 times) See all 5 of this type

    61
    The locus of the mid-point of the line segment joining the focus of the parabola y2=4axy^{2}= 4ax to aa moving point of the parabola, is another parabola whose directrix is: .

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  5. Question 5

    Conic Sections. Asked once: 2021 Paper 23 (same type asked 5 times) See all 5 of this type

    89
    Let BB be the centre of the circle x2+y2−2x+4y+1=0x^{2}+y^{2}- 2x+ 4y+ 1 = 0. Let the tangents at two points PP and QQ on the circle intersect at the point A(3,1)A(3,1). Then 8. (area△APQarea△BPQ)\left( \frac{area \bigtriangleup APQ}{area \bigtriangleup BPQ} \right) is equal to