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Day 599: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 2021 Paper 13

    53
    Let A={0,1,2,3,…,9}A=\{0,1,2,3,\ldots,9\}. The number of bijective functions f:A→Af:A\rightarrow A satisfying f(1)+f(2)+f(3)=3f(1)+f(2)+f(3)=3 is

  2. Question 2

    Sequences and Series. Asked once: 10 Apr 2023

    83
    The sum of all those terms, of the arithmetic progression 3,8,13,…….3733,8,13,\ldots\ldots.373, which are not divisible by 3 , is equal to

  3. Question 3

    Straight Lines. Asked once: 27 Jun 2022

    72
    In an isosceles triangle ABCABC, the vertex AA is (6,1)(6,1) and the equation of the base BCBC is 2x+y=42x + y = 4. Let the point BB lie on the line x+3y=7x + 3y = 7. If (α,β)(\alpha,\beta) is the centroid △ABC\bigtriangleup ABC, then 15(α+β)15(\alpha + \beta) is equal to:

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  4. Question 4

    Application of Derivatives. Asked once: 25 Jun 2022

    72
    Let g:(0,∞)→Rg:(0,\infty) \rightarrow R be a differentiable function such that ∫(x(cos⁡x−sin⁡x)ex+1+g(x)(ex+1−xex)(ex+1)2)dx=xg(x)ex+1+c\int\left( \frac{x(\cos x - \sin x)}{e^{x}+ 1}+\frac{g(x)\left( e^{x}+ 1 - xe^{x} \right)}{\left( e^{x}+ 1 \right)^{2}} \right)dx =\frac{xg(x)}{e^{x}+ 1}+ c, for all x>0x > 0, where cc is an arbitrary constant. Then.

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  5. Question 5

    Complex Numbers. Asked once: 2021 Paper 24

    83
    If for the complex numbers zz satisfying ∣z−2−2i∣≤1|z - 2 - 2i| \leq 1, the maximum value of ∣3iz+6∣|3iz + 6| is attained at a+iba + ib, then a+ba + b is equal to