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Day 544: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 1 Feb 2023

    156
    Let P(S)P(S) denote the power set of S={1,2,3,…,10}S=\{1,2,3,\ldots,10\}. Define the relations R1R_{1} and R2R_{2} on P(S)P(S) as AR1BAR_{1}B if (A∩BC)∪(B∩AC)=∅\left( A \cap B^{C} \right)\cup\left( B \cap A^{C} \right)= \varnothing and AR2BAR_{2}B if A∪BC=B∪AC,∀A,B∈P(S)A \cup B^{C}= B \cup A^{C},\forall A,B \in P(S). Then:

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  2. Question 2

    Sequences and Series. Asked once: 8 Apr 2024

    86
    If the range of f(θ)=sin⁡4θ+3cos⁡2θsin⁡4θ+cos⁡2θ,θ∈Rf(\theta) =\frac{\sin^{4}\theta + 3\cos^{2}\theta}{\sin^{4}\theta +\cos^{2}\theta},\theta \in R is [α,β]\lbrack\alpha,\beta\rbrack, then the sum of the infinite G.P., whose first term is 64 and the common ratio is αβ\frac{\alpha}{\beta}, is equal to

  3. Question 3

    Straight Lines. Asked once: 30 Jan 2024

    61
    A line passing through the point A(9,0)A(9,0) makes an angle of 30∘30^{\circ} with the positive direction of xx-axis. If this line is rotated about A through an angle of 15∘15^{\circ} in the clockwise direction, then its equation in the new position is

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  4. Question 4

    Three Dimensional Geometry. Asked once: 25 Jul 2022

    74
    Let PP be the plane containing the straight line x−39=y+4−1=z−7−5\frac{x - 3}{9}=\frac{y + 4}{- 1}=\frac{z - 7}{- 5} and perpendicular to the plane containing the straight lines x2=y3=z5\frac{x}{2}=\frac{y}{3}=\frac{z}{5} and x3=y7=z8\frac{x}{3}=\frac{y}{7}=\frac{z}{8}. If dd is the distance of PP from the point (2,−5,11)(2, - 5,11), then d2d^{2} is equal to:

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  5. Question 5

    Vector Algebra. Asked once: 1 Feb 2023

    81
    Let v→=αı^+2ȷ^−3k^,w→=2αı^+ȷ^−k^\overrightarrow{v}= \alpha\widehat{\imath}+ 2\widehat{\jmath}- 3\widehat{k},\overrightarrow{w}= 2\alpha\widehat{\imath}+\widehat{\jmath}-\widehat{k} and u→\overrightarrow{u} be a vector such that ∣u→∣=α>0|\overrightarrow{u}| = \alpha > 0. If the minimum value of the scalar triple product [u→v→w→]\lbrack\overrightarrow{u}\overrightarrow{v}\overrightarrow{w}\rbrack is −α3401- \alpha\sqrt{3401}, and ∣u→⋅ı^∣2=mn|\overrightarrow{u}\cdot\widehat{\imath}|^{2}=\frac{m}{n} where mm and nn are coprime natural numbers, then m+nm + n is equal to