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Day 181: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 2021 Paper 19 (same type asked 3 times) See all 3 of this type

    71
    Two fair dice are thrown. The numbers on them are taken as λ\lambda and μ\mu, and a system of linear equations
    x+y+z=5x+2y+3z=μx+3y+λz=1\begin{matrix} & x+y+z= 5 \\ & x+ 2y+ 3z=\mu \\ & x+ 3y+\lambda z= 1 \end{matrix}
    is constructed. If pp is the probability that the system has a unique solution and qq is the probability that the system has no solution, then :

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  2. Question 2

    Relations and Functions. Asked once: 6 Apr 2023 (same type asked 3 times) See all 3 of this type

    88
    Let A={1,2,3,4,….10}\mathbf{A = \{ 1,2,3,4,\ldots.10\}} and B={0,1,2,3,4}\mathbf{B = \{ 0,1,2,3,4\}}. The number of elements in the relation R={(a,b)\mathbf{R = \{(a,b)}  ∈A×A:2(a−b)2+3(a−b)∈B}\left. \ \in A \times A:2(a - b)^{2}+ 3(a - b) \in B \right\} is

  3. Question 3

    Sequences and Series. Asked once: 24 Jan 2023 (same type asked 3 times) See all 3 of this type

    163
    Let f(x)f(x) be a function such that f(x+y)=f(x)⋅f(y)f(x + y) = f(x) \cdot f(y) for all x,y∈Nx,y \in N. If f(1)=3f(1) = 3 and ∑k=1nf(k)=3279\sum_{k = 1}^{n} f(k) = 3279, then the value of nn is

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  4. Question 4

    Straight Lines. Asked once: 9 Apr 2024 (same type asked 3 times) See all 3 of this type

    156
    Two vertices of a triangle ABCABC are A(3,−1)A(3, - 1) and B(−2,3)B( - 2,3), and its orthocentre is P(1,1)P(1,1). If the coordinates of the point CC are (α,β)(\alpha,\beta) and the centre of the circle circumscribing the triangle PABPAB is (h,k)(h,k), then the value of (α+β)+2( h+k)(\alpha + \beta) + 2(\text{ }h + k) equals :

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  5. Question 5

    Application of Integrals. Asked once: 14 Jun 2022 (same type asked 3 times) See all 3 of this type

    89
    Let SS be the region bounded by the curves y=x3y =x^{3} and y2=xy^{2}= x. The curve y=2∣x∣y = 2|x| divides SS into two regions of areas R1R_{1} and R2R_{2}. If max⁡{R1,R2}=R2\max\left\{ R_{1},R_{2} \right\}=R_{2}, then R2R1\frac{R_{2}}{R_{1}} is equal to