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Day 356: JEE Mains Maths

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

  1. Question 1

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

    90
    The line of shortest distance between the lines x−20=y−11=z1\frac{x - 2}{0}=\frac{y - 1}{1}=\frac{z}{1} and x−32=y−52=z−11\frac{x - 3}{2}=\frac{y - 5}{2}=\frac{z - 1}{1} makes an angle of cos⁡−1(227)\cos^{- 1}\left( \sqrt{\frac{2}{27}} \right) with the plane :ax−y−:ax - y - z=0,(a>0)z = 0,(a > 0). If the image of the point (1,1,−5)(1,1, - 5) in the plane PP is (α,β,γ)(\alpha,\beta,\gamma), then α+β−γ\alpha + \beta - \gamma is equal to

  2. Question 2

    Application of Derivatives. Asked once: 14 Jun 2022 (same type asked 5 times) See all 5 of this type

    72
    The sum of absolute maximum and absolute minimum values of the function f(x)=∣2x2+3x−2∣+sin⁡xcosxf(x) =\left| 2x^{2}+ 3x - 2 \right|+ \sin xcosx in the interval [0,1]\lbrack 0,1\rbrack is :

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  3. Question 3

    Three Dimensional Geometry. Asked once: 2021 Paper 9 (same type asked 5 times) See all 5 of this type

    82
    Let the plane ax+by+cz+d=0ax+by+cz+d=0 bisect the line joining the points (4,−3,1)(4,-3,1) and (2,3,−5)(2,3,-5) at right angles. If a,b,c,da,b,c,d are integers, then the minimum value of (a2+b2+c2+d2)\left(a^{2}+b^{2}+c^{2}+d^{2}\right) is

  4. Question 4

    Quadratic Equations. Asked once: 2021 Paper 19 (same type asked 5 times) See all 5 of this type

    87
    Let λ≠0\lambda \neq 0 be in RR. If α\alpha and β\beta are the roots of the equation x2−x+2λ=0x^{2}- x + 2\lambda = 0, and α\alpha and γ\gamma are the roots of equation 3x2−10x+27λ=03x^{2}- 10x + 27\lambda = 0, then βγλ\frac{\beta\gamma}{\lambda} is equal to

  5. Question 5

    Complex Numbers. Asked once: 29 Jun 2022 (same type asked 4 times) See all 4 of this type

    68
    Let α\alpha and β\beta be the roots of the equation x2+(2i−x^{2}+ (2i - 1)=01) = 0. Then, the value of ∣α8+β8∣\left| \alpha^{8}+\beta^{8} \right| is equal to:

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