PYQ Vault

Day 364: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 25 Jun 2022 (same type asked 9 times) See all 9 of this type

    158
    The sum 1+2⋅3+3⋅32+…..+10⋅391 + 2 \cdot 3 + 3 \cdot3^{2}+ \ldots.. + 10 \cdot3^{9} is equal to

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  2. Question 2

    Determinants. Asked once: 31 Jan 2023 (same type asked 9 times) See all 9 of this type

    72
    For the system of linear equations
    x+y+z=6x + y + z = 6
    αx+βy+7z=3\alpha x + \beta y + 7z = 3
    x+2y+3z=14x + 2y + 3z = 14
    which of the following is NOT true?

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  3. Question 3

    Statistics. Asked once: 2021 Paper 21 (same type asked 8 times) See all 8 of this type

    89
    An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2 . The variance of marks obtained by 30 girls is also 2 . The average marks of all 50 candidates is 15. If μ\mu is the average marks of girls and σ2\sigma^{2} is the variance of marks of 50 candidates, then μ+σ2\mu+\sigma^{2} is equal to
  4. Question 4

    Determinants. Asked once: 27 Jun 2022 (same type asked 8 times) See all 8 of this type

    153
    Let for some real numbers α\alpha and β,a=α−iβ\beta,a = \alpha - i\beta. If the system of equations 4ix+(1+i)y=04ix + (1 + i)y = 0 and 8(cos⁡2π3+isin⁡2π3)x+aˉy=08\left( \cos\frac{2\pi}{3}+ i\sin\frac{2\pi}{3} \right)x +\bar{a}y = 0 has more than one solution then αβ\frac{\alpha}{\beta} is equal to:

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  5. Question 5

    Differential Equations. Asked once: 31 Jan 2023 (same type asked 8 times) See all 8 of this type

    62
    Let a differentiable function ff satisfy f(x)+∫3xf(t)tdt=x+1,x≥3f(x) +\int_{3}^{x} \frac{f(t)}{t}dt =\sqrt{x + 1},x \geq 3. Then 12f(8)12f(8) is equal to:

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