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Day 574: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 29 Jun 2022

    71
    Let aa set A=A1∪A2∪…∪AkA =A_{1}\cup A_{2}\cup \ldots \cup A_{k} where Ai∩Aj=ϕA_{i}\cap A_{j}= \phi for i≠j, 1≤i,j≤ki \neq j,\ 1 \leq i,j \leq k. Define the relation RR from AA to AA by R={(x,y):y∈AiR =\left\{ (x,y):y \in A_{i} \right. if and only if  x∈Ai,1≤i≤k}\left. \ x \in A_{i},1 \leq i \leq k \right\}. Then, RR is:

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  2. Question 2

    Sequences and Series. Asked once: 30 Jan 2024

    175
    Let SnS_{n} be the sum to nn-terms of an arithmetic progression 3,7,11,……3,7,11,\ldots\ldots. If 40<(6n(n+1)∑k=1nSk)<4240 <\left( \frac{6}{n(n + 1)}\sum_{k = 1}^{n} S_{k} \right)< 42, then nn equals

  3. Question 3

    Straight Lines. Asked once: 24 Jan 2023

    69
    Let PQRPQR be a triangle. The points A,BA,B and CC are on the sides QR,RPQR,RP and PQPQ respectively such that QAAR=RBBP=PCCQ=12\frac{QA}{AR}=\frac{RB}{BP}=\frac{PC}{CQ}=\frac{1}{2}. Then  Area (△PQR) Area (△ABC)\frac{\text{~Area~}( \bigtriangleup PQR)}{\text{~Area~}( \bigtriangleup ABC)} is equal to

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  4. Question 4

    Three Dimensional Geometry. Asked once: 2021 Paper 8

    90
    Let PP be an arbitrary point having sum of the squares of the distance from the planes x+y+z=0,lx−nz=0x + y + z = 0,lx - nz = 0 and x−2y+z=0x - 2y + z = 0, equal to 9. If the locus of the point PP is x2+y2+z2=9x^{2}+y^{2}+z^{2}= 9, then the value of l−nl- n is equal to

  5. Question 5

    Vector Algebra. Asked once: 26 Jun 2022

    76
    If a→⋅b→=1,b→⋅c→=2\overrightarrow{a}\cdot\overrightarrow{b}= 1,\overrightarrow{b}\cdot\overrightarrow{c}= 2 and c→⋅a→=3\overrightarrow{c}\cdot\overrightarrow{a}= 3, then the value of [a→×(b→×c→),b→×(c→×a→),c→×(b→×a→)]\lbrack\overrightarrow{a}\times (\overrightarrow{b}\times\overrightarrow{c}),\overrightarrow{b}\times (\overrightarrow{c}\times\overrightarrow{a}),\overrightarrow{c}\times (\overrightarrow{b}\times\overrightarrow{a})\rbrack is :

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