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Day 540: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 24 Jan 2023

    74
    Let Ω\Omega be the sample space and A⊆ΩA \subseteq \Omega be an event. Given below are two statements: (S1): If P(A)=0P(A) = 0, then A=∅A = \varnothing (S2): If P(A)=1P(A) = 1, then A=ΩA = \Omega Then

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  2. Question 2

    Quadratic Equations. Asked once: 8 Apr 2023

    175
    Let mm and nn be the numbers of real roots of the quadratic equations x2−12x+[x]+31=0x^{2}- 12x + \lbrack x\rbrack + 31 = 0 and x2−5∣x+2∣−4=0x^{2}- 5|x + 2| - 4 = 0 respectively, where [x] denotes the greatest integer ≤x\leq x. Then m2+mn+n2m^{2}+ mn +n^{2} is equal to

  3. Question 3

    Relations and Functions. Asked once: 6 Apr 2023

    80
    Let A={x∈R:[x+3]+[x+4]≤3}\mathbf{A = \{ x \in R:\lbrack x + 3\rbrack + \lbrack x + 4\rbrack \leq 3\}}, B={x∈R:3x(∑r=1∞310r)x−3<3−3x}B =\left\{ x \in R:3^{x}\left( \sum_{r = 1}^{\infty} \frac{3}{10^{r}} \right)^{x - 3}<3^{- 3x} \right\}, where [t]\lbrack t\rbrack denotes greatest integer function. Then,

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  4. Question 4

    Sequences and Series. Asked once: 9 Apr 2024

    178
    If (1α+1+1α+2+….+1α+1012)\left( \frac{1}{\alpha+ 1}+\frac{1}{\alpha+ 2}+ \ldots. +\frac{1}{\alpha+ 1012} \right)
    −(12⋅1+14⋅3+16⋅5+…+12024⋅2023)-\left( \frac{1}{2 \cdot 1}+\frac{1}{4 \cdot 3}+\frac{1}{6 \cdot 5}+ \ldots +\frac{1}{2024 \cdot 2023} \right)
    =12024=\frac{1}{2024}, then α\alpha is equal to-

  5. Question 5

    Straight Lines. Asked once: 31 Jan 2024

    70
    Let α,β,γ,δ∈Z\alpha,\beta,\gamma,\delta \in Z and let A(α,β),B(1,0),C(γ,δ)A(\alpha,\beta),B(1,0),C(\gamma,\delta) and D(1,2)D(1,2) be the vertices of a parallelogram ABCDABCD. If AB=10AB =\sqrt{10} and the points AA and CC lie on the line 3y=2x+13y = 2x + 1, then 2(α+β+γ+δ)2(\alpha + \beta + \gamma + \delta) is equal to

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