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Day 381: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 2021 Paper 25 (same type asked 9 times) See all 9 of this type

    68
    The sum of the infinite series 1+23+732+1233+1734+2235+…1 +\frac{2}{3}+\frac{7}{3^{2}}+\frac{12}{3^{3}}+\frac{17}{3^{4}}+\frac{22}{3^{5}}+ \ldots is equal to

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  2. Question 2

    Determinants. Asked once: 29 Jan 2023 (same type asked 9 times) See all 9 of this type

    64
    Consider the following system of equations
    αx+2y+z=1\alpha x + 2y + z = 1
    2αx+3y+z=12\alpha x + 3y + z = 1
    3x+αy+2z=β3x + \alpha y + 2z = \beta
    for some α,β∈R\alpha,\beta \in R. Then which of the following is NOT correct.

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  3. Question 3

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

    85
    Consider a set of 3n3n numbers having variance 4 In this set, the mean of first 2n2n numbers is 6 and the mean of the remaining numbers is 3. A new set is constructed by adding 1 into each of first 2 n numbers, and subtracting 1 from each of the remaining nn numbers. If the variance of the new set is kk, then 9k9k is equal to

  4. Question 4

    Determinants. Asked once: 2021 Paper 23 (same type asked 8 times) See all 8 of this type

    61
    If α+β+γ=2π\alpha + \beta + \gamma = 2\pi, then the system of equations
    x+(cos⁡γ)y+(cos⁡β)z=0x + (\cos\gamma)y + (\cos\beta)z = 0
    (cos⁡γ)x+y+(cos⁡α)z=0(\cos\gamma)x + y + (\cos\alpha)z = 0
    (cos⁡β)x+(cos⁡α)y+z=0(\cos\beta)x + (\cos\alpha)y + z = 0
    has:

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  5. Question 5

    Differential Equations. Asked once: 2021 Paper 26 (same type asked 8 times) See all 8 of this type

    79
    Let f(x)=∫0xetf(t)dt+exf(x) =\int_{0}^{x} e^{t}f(t)dt +e^{x} be a differentiable function for all x∈Rx \in R. Then f(x)f(x) equals.

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