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Day 577: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 25 Jul 2022

    172
    Let f(x)f(x) be a quadratic polynomial with leading coefficient 1 such that f(0)=p,p≠0f(0) = p,p \neq 0 and f(1)=13f(1) =\frac{1}{3}. If the equation f(x)=0f(x) = 0 and (f∘f∘f∘f)(x)=0(f\circ f\circ f\circ f)(x) = 0 have a common real root, then f(−3)f( - 3) is equal to

  2. Question 2

    Relations and Functions. Asked once: 28 Jun 2022

    179
    Let S={1,2,3,4}S\mathbf{= \{ 1,2,3,4\}}. Then the number of elements in the set {f:S×S→S:f\mathbf{\{}f:S\times S\rightarrow S:f is onto and f(a,b)=f(b,a)f(a,b) =f(b,a) ≥a∀(a,b)∈S×S}\geq a\forall(a,b) \in S \times S\} is

  3. Question 3

    Sequences and Series. Asked once: 30 Jan 2024

    156
    Let aa and bb be be two distinct positive real numbers. Let 11th 11^{\text{th~}} term of a GP, whose first term is aa and third term is bb, is equal to pth p^{\text{th~}} term of another GP, whose first term is a and fifth term is bb. Then pp is equal to

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  4. Question 4

    Straight Lines. Asked once: 24 Jan 2023

    165
    The equations of the sides ABAB and ACAC of a triangle ABCABC are (λ+1)x+λy=4(\lambda + 1)x + \lambda y = 4 and λx+(1−λ)y+λ=0\lambda x + (1 - \lambda)y + \lambda = 0 respectively. Its vertex AA is on the yy - axis and its orthocentre is (1,2)(1,2). The length of the tangent from the point CC to the part of the parabola y2=6xy^{2}= 6x in the first quadrant is:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 2021 Paper 8

    80
    If the equation of plane passing through the mirror image of a point (2,3,1)(2,3,1) with respect to line x+12=y−31=z+2−1\frac{x+ 1}{2}=\frac{y- 3}{1}=\frac{z+ 2}{- 1} and containing the line x−23=1−y2=z+11\frac{x- 2}{3}=\frac{1 -y}{2}=\frac{z+ 1}{1} is αx+βy+γz=24\alpha x+\beta y+\gamma z= 24, then α+β+γ\alpha+\beta+\gamma is equal to :

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