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Day 373: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 2021 Paper 1 (same type asked 6 times) See all 6 of this type

    70
    lim⁡x→0∫0x2(sin⁡t)dtx3\lim_{x\rightarrow 0} \frac{\int_{0}^{x^{2}} (\sin\sqrt{t})dt}{x^{3}} is equal to:

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  2. Question 2

    Application of Derivatives. Asked once: 2021 Paper 1 (same type asked 6 times) See all 6 of this type

    68
    The function f(x)=4x3−3x26−2sin⁡x+(2x−1)cos⁡xf(x) =\frac{4x^{3}- 3x^{2}}{6}- 2\sin x+ (2x- 1)\cos x :

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  3. Question 3

    Vector Algebra. Asked once: 2021 Paper 8 (same type asked 6 times) See all 6 of this type

    73
    Let OO be the origin. Let OP→=xi^+yj^−k^\overrightarrow{OP}=x\widehat{i}+y\widehat{j}-\widehat{k} and OQ→=−i^+2j^+3xk^,x,y∈R,x>0\overrightarrow{OQ}= -\widehat{i}+ 2\widehat{j}+ 3x\widehat{k},x,y \in R,x > 0, be such that ∣PQ→∣=20|\overrightarrow{PQ}| =\sqrt{20} and the vector OP→\overrightarrow{OP} is perpendicular to OQ→\overrightarrow{OQ}. If OR→=3i^+zj^−7k^,z∈R\overrightarrow{OR}= 3\widehat{i}+z\widehat{j}- 7\widehat{k},z \in R, is coplanar with OP→\overrightarrow{OP} and OQ→\overrightarrow{OQ}, then the value of x2+y2+z2x^{2}+y^{2}+z^{2} is equal to

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  4. Question 4

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

    168
    Let XX be a binomially distributed random variable with mean 4 and variance 43\frac{4}{3}. Then 54P(X≤2)54P(X \leq 2) is equal to

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  5. Question 5

    Binomial Theorem. Asked once: 25 Jul 2022 (same type asked 6 times) See all 6 of this type

    154
    The remainder when (11)1011+(1011)11(11)^{1011}+ (1011)^{11} is divided by 9 is

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