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Day 348: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2021 Paper 2 (same type asked 6 times) See all 6 of this type

    69
    Let f:R→Rf:R \rightarrow R be defined as
    f(x)={−55x,if x<−52x3−3x2−120x,if −5≤x≤42x3−3x2−36x−336,if x>4f(x) = \begin{cases} -55x, & \text{if } x < -5 \\ 2x^3 - 3x^2 - 120x, & \text{if } -5 \leq x \leq 4 \\ 2x^3 - 3x^2 - 36x - 336, & \text{if } x > 4 \end{cases}
    Let A={x∈R:f is increasing}A = \{x \in R : f \text{ is increasing}\}. Then AA is equal to:

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  2. Question 2

    Vector Algebra. Asked once: 28 Jul 2022 (same type asked 6 times) See all 6 of this type

    63
    Let the vectors a→=(1+t)i^+(1−t)j^+k^\overrightarrow{a}= (1 + t)\widehat{i}+ (1 - t)\widehat{j}+\widehat{k}, b→=(1−t)i^+(1+t)j^+2k^\overrightarrow{b}= (1 - t)\widehat{i}+ (1 + t)\widehat{j}+ 2\widehat{k} and c→=ti^−tj^+k^,t∈R\overrightarrow{c}= t\widehat{i}- t\widehat{j}+\widehat{k},t \in R be such that for α,β,γ∈R,αa→+βb→+γc→=0→\alpha,\beta,\gamma \in R,\alpha\overrightarrow{a}+ \beta\overrightarrow{b}+ \gamma\overrightarrow{c}=\overrightarrow{0} ⇒α=β=γ=0\Rightarrow \alpha = \beta = \gamma = 0. Then, the set of all values of tt is:

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  3. Question 3

    Probability. Asked once: 26 Jul 2022 (same type asked 6 times) See all 6 of this type

    76
    The mean and variance of a binomial distribution are α\alpha and α3\frac{\alpha}{3} respectively. If P(X=1)=4243P(X = 1) =\frac{4}{243}, then P(X=4P(X = 4 or 5)) is equal to:

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  4. Question 4

    Binomial Theorem. Asked once: 27 Jul 2022 (same type asked 6 times) See all 6 of this type

    65
    The remainder when (2021)2022+(2022)2021(2021)^{2022}+ (2022)^{2021} is divided by 7 is

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  5. Question 5

    Limits and Continuity. Asked once: 2021 Paper 12 (same type asked 6 times) See all 6 of this type

    47
    If f:R→Rf:R \rightarrow R is given by f(x)=x+1f(x) = x + 1, then the value of lim⁡n→∞1n[f(0)+f(5n)+f(10n)+…..+f(5(n−1)n)]\lim_{n \rightarrow \infty} \frac{1}{n}\left\lbrack f(0) +f\left( \frac{5}{n} \right)+f\left( \frac{10}{n} \right)+ \ldots.. +f\left( \frac{5(n - 1)}{n} \right) \right\rbrack,is:

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