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Day 354: JEE Mains Maths

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

  1. Question 1

    Differentiation. Asked once: 2021 Paper 24 (same type asked 5 times) See all 5 of this type

    89
    Let [t]\lbrack t\rbrack denote the greatest integer ≤t\leq t. The number of points where the function
    f(x)=[x]∣x2−1∣+sin⁡(π[x]+3)−[x+1],x∈(−2,2)f(x) = \lbrack x\rbrack\left| x^{2}- 1 \right|+ \sin\left( \frac{\pi}{\lbrack x\rbrack + 3} \right)- \lbrack x+ 1\rbrack,x\in ( - 2,2)
    is not continuous is

  2. Question 2

    Probability. Asked once: 2021 Paper 19 (same type asked 5 times) See all 5 of this type

    69
    A fair die is tossed until six is obtained on it. Let XX be the number of required tosses, then the conditional probability P(X≥5∣X>2)P(X \geq 5 \mid X > 2) is:

    Tap an option to check your answer.

  3. Question 3

    Relations and Functions. Asked once: 24 Jan 2023 (same type asked 5 times) See all 5 of this type

    178
    The minimum number of elements that must be added to the relation R={(a,b),(b,c),(b,d)}\mathbf{R = \{(a,b),(b,c),(b,d)\}} on the set {a,b,c,d}\mathbf{\{ a,b,c,d\}} so that it is an equivalence relation, is

  4. Question 4

    Application of Derivatives. Asked once: 2021 Paper 5 (same type asked 5 times) See all 5 of this type

    74
    The range of a∈Ra\in\mathbb{R} for which the function f(x)=(4a−3)(x+log⁡e5)+2(a−7)cot⁡(x2)sin⁡2(x2)f(x) = (4a- 3)\left( x+\log_{e}5 \right)+ 2(a- 7)\cot\left( \frac{x}{2} \right)\sin^{2}\left( \frac{x}{2} \right), x≠2nπ,n∈Nx\neq 2n\pi,n\in\mathbb{N}, has critical points, is:

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  5. Question 5

    Binomial Theorem. Asked once: 2021 Paper 8 (same type asked 5 times) See all 5 of this type

    86
    Let the coefficients of third, fourth and fifth terms in the expansion of (x+ax2)n,x≠0\left( x+\frac{a}{x^{2}} \right)^{n},x\neq 0, be in the ratio 12:8:312:8:3. Then the term independent of xx in the expansion, is equal to