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Day 317: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 28 Jun 2022 (same type asked 5 times) See all 5 of this type

    166
    Let the plane ax+by+cz=dax + by + cz = d pass through (2,3,−5)(2,3, - 5) and is perpendicular to the planes 2x+y−5z=102x + y - 5z = 10 and 3x+5y−7z=123x + 5y - 7z = 12. If a,b,c,da,b,c,d are integers d>0d > 0 and gcd⁡(∣a∣,∣b∣,∣c∣,d)=1\gcd(|a|,|b|,|c|,d)= 1, then the value of a+7b+c+20da + 7b + c + 20d is equal to

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  2. Question 2

    Three Dimensional Geometry. Asked once: 27 Jul 2022 (same type asked 5 times) See all 5 of this type

    165
    If the line of intersection of the planes ax+by=3ax + by = 3 and ax+by+cz=0,a>0ax + by + cz = 0,a > 0 makes an angle 30∘30^{\circ} with the plane y−z+2=0y - z + 2 = 0, then the direction cosines of the line are :

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  3. Question 3

    Conic Sections. Asked once: 2021 Paper 8 (same type asked 5 times) See all 5 of this type

    74
    Two tangents are drawn from a point PP to the circle x2+y2−2x−4y+4=0x^{2}+y^{2}- 2x- 4y+ 4 = 0, such that the angle between these tangents is tan⁡−1(125)\tan^{- 1}\left( \frac{12}{5} \right), where tan⁡−1(125)∈(0,π)\tan^{- 1}\left( \frac{12}{5} \right)\in (0,\pi). If the centre of the circle is denoted by CC and these tangents touch the circle at points AA and BB, then the ratio of the areas of △PAB\bigtriangleup PAB and △CAB\bigtriangleup CAB is:

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  4. Question 4

    Application of Derivatives. Asked once: 26 Jun 2022 (same type asked 5 times) See all 5 of this type

    68
    The sum of the absolute minimum and the absolute maximum values of the function f(x)=∣3x−x2+2∣−xf(x) =\left| 3x-x^{2}+ 2 \right|-x in the interval [−1,2]\lbrack - 1,2\rbrack is :

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  5. Question 5

    Three Dimensional Geometry. Asked once: 2021 Paper 25 (same type asked 5 times) See all 5 of this type

    87
    Let (λ,2,1)(\lambda,2,1) be a point on the plane which passes through the point (4,−2,2)(4, - 2,2). If the plane is perpendicular to the line joining the point (−2,−21,29)( - 2, - 21,29) and (−1,−16,23)( - 1, - 16,23), then (λ11)2−4λ11−4\left( \frac{\lambda}{11} \right)^{2}-\frac{4\lambda}{11}- 4 is equal to