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Day 311: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 31 Jan 2024 (same type asked 5 times) See all 5 of this type

    63
    If the foci of a hyperbola are same as that of the ellipse x29+y225=1\frac{x^{2}}{9}+\frac{y^{2}}{25}= 1 and the eccentricity of the hyperbola is 158\frac{15}{8} times the eccentricity of the ellipse, then the smaller focal distance of the point (2,14325)\left( \sqrt{2},\frac{14}{3}\sqrt{\frac{2}{5}} \right) on the hyperbola, is equal to

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  2. Question 2

    Definite Integration. Asked once: 2021 Paper 12 (same type asked 5 times) See all 5 of this type

    44
    If [x]\lbrack x\rbrack denotes the greatest integer less than or equal to xx, then the value of the integral ∫−π/2π/2[[x]−sin⁡x]dx\int_{-\pi/2}^{\pi/2} \lbrack\lbrack x\rbrack - \sin x\rbrack dx is equal to:

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  3. Question 3

    Probability. Asked once: 4 Apr 2024 (same type asked 5 times) See all 5 of this type

    165
    If the mean of the following probability distribution of a random variable XX;
    XX02468
    P(X)P(X)aa2a2aa+ba+b2b2b3b3b
    is 469\frac{46}{9}, then the variance of the distribution is

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  4. Question 4

    Statistics. Asked once: 11 Apr 2023 (same type asked 5 times) See all 5 of this type

    165
    Let the mean of 6 observation 1, 2, 4, 5, xx and yy be 5 and their variance be 10 . Then their mean deviation about the mean is equal to

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  5. Question 5

    Vector Algebra. Asked once: 4 Apr 2024 (same type asked 5 times) See all 5 of this type

    152
    If λ>0\lambda > 0, let θ\theta be the angle between the vectors a→=i^+λj^−3k^\overrightarrow{a}=\widehat{i}+ \lambda\widehat{j}- 3\widehat{k} and b→=3i^−j^+2k^\overrightarrow{b}= 3\widehat{i}-\widehat{j}+ 2\widehat{k}. If the vectors a→+b→\overrightarrow{a}+\overrightarrow{b} and a→−b→\overrightarrow{a}-\overrightarrow{b} are mutually perpendicular, then the value of (14cos⁡θ)2(14\cos\theta)^{2} is equal to

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