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Day 261: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 1 Feb 2023 (same type asked 4 times) See all 4 of this type

    155
    Let f:R−{0,1}→Rf:R - \{0,1\} \rightarrow R be a function such that f(x)+f(11−x)=1+xf(x) + f\left( \frac{1}{1 - x} \right)= 1 + x. Then f(2)f(2) is equal to

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  2. Question 2

    Differentiation. Asked once: 8 Apr 2023 (same type asked 4 times) See all 4 of this type

    172
    Let kk and mm be positive real numbers such that the function  f(x)={3x2+kx+1,0<x<1mx2+k2,x≥1\ f(x) =\left\{ \begin{matrix} 3x^{2}+ k\sqrt{x + 1}, & 0 < x < 1 \\ mx^{2}+k^{2}, & x \geq 1 \end{matrix} \right. is differentiable for all x>0x > 0. Then 8f′(8)f′(18)\frac{8f^{'}(8)}{f^{'}\left( \frac{1}{8} \right)} is equal to

  3. Question 3

    Permutations and Combinations. Asked once: 8 Apr 2024 (same type asked 4 times) See all 4 of this type

    155
    The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to:

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  4. Question 4

    Three Dimensional Geometry. Asked once: 2021 Paper 21 (same type asked 4 times) See all 4 of this type

    61
    The angle between the straight lines, whose direction cosines are given by the equations 2l+2m−n=02l+ 2m-n= 0 and mn+nl+lm=0mn+nl+lm= 0, is :

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  5. Question 5

    Conic Sections. Asked once: 2 Apr 2025 (same type asked 4 times) See all 4 of this type

    66
    If SS and S′S^{'} are the foci of the ellipse x218+y29=1\frac{x^{2}}{18}+\frac{y^{2}}{9}= 1 and P be a point on the ellipse, then min⁡(SP.S′P)+\min\left( SP.S^{'}P \right)+ max⁡(SP.S′P)\max\left( SP.S^{'}P \right) is equal to :

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