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Day 580: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 28 Jun 2022

    152
    Let f(x)f(x) be a quadratic polynomial such that f(−2)+f(3)=0f( - 2) + f(3) = 0. If one of the roots of f(x)=0f(x) = 0 is -1 , then the sum of the roots of f(x)=0f(x) = 0 is equal to:

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  2. Question 2

    Relations and Functions. Asked once: 27 Jun 2022

    171
    Let S={1,2,3,4,5,6,7,8,9,10}S\mathbf{= \{ 1,2,3,4,5,6,7,8,9,10\}}. Define f:S→Sf:S\rightarrow S as f(n)={2n, if n=1,2,3,4,52n−11 if n=6,7,8,9,10f(n) =\left\{ \begin{matrix} 2n, & \text{~if~}n= 1,2,3,4,5 \\ 2n- 11 & \text{~if~}n= 6,7,8,9,10 \end{matrix} \right.. Let g:S→Sg:S \rightarrow S be a function such that fog(n)={n+1, if n is odd n−1, if n is even fog(n) =\left\{ \begin{matrix} n+ 1 & \text{, if~}n\text{~is odd~} \\ n- 1 & \text{, if~}n\text{~is even~} \end{matrix} \right., then g(10)((g(1)+g(2)+g(3)+g(4)+g(5))g(10)((g(1) + g(2) + g(3) + g(4) + g(5)) is equal to:

  3. Question 3

    Sequences and Series. Asked once: 29 Jan 2024

    163
    If each term of a geometric progression a1,a2,a3,…a_{1},a_{2},a_{3},\ldots with a1=18a_{1}=\frac{1}{8} and a2≠a1a_{2}\neq a_{1}, is the arithmetic mean of the next two terms and Sn=a1+a2+…+anS_{n}=a_{1}+a_{2}+ \ldots +a_{n}, then S20−S18S_{20}-S_{18} is equal to

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  4. Question 4

    Straight Lines. Asked once: 29 Jul 2022

    163
    Let A(α,−2),B(α,6)A(\alpha, - 2),B(\alpha,6) and C(α4,−2)C\left( \frac{\alpha}{4}, - 2 \right) be vertices of a △ABC\bigtriangleup ABC. If (5,α4)\left( 5,\frac{\alpha}{4} \right) is the circumcentre of △ABC\bigtriangleup ABC, then which of the following is NOT correct about △ABC\bigtriangleup ABC:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 2021 Paper 7

    66
    The equation of the plane which contains the yy-axis and passes through the point (1,2,3)(1,2,3) is :

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