PYQ Vault

Day 393: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 25 Jan 2023 (same type asked 9 times) See all 9 of this type

    67
    Let S1S_{1} and S2S_{2} be respectively the sets of all a∈R−{0}\mathbf{a \in R - \{ 0\}} for which the system of linear equations
    ax+2ay−3az=1 (2a+1)x+(2a+3)y+(a+1)z=2 (3a+5)x+(a+5)y+(a+2)z=3\begin{matrix} & ax + 2ay - 3az = 1 \\ & \ (2a + 1)x + (2a + 3)y + (a + 1)z = 2 \\ & \ (3a + 5)x + (a + 5)y + (a + 2)z = 3 \end{matrix}
    has unique solution and infinitely many solutions respectively. Then

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  2. Question 2

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

    82
    Consider the statistics of two sets of observations as follows:
    SetSizeMeanVariance
    Observation I1022
    Observation IInn31
    If the variance of the combined set of these two observations is 179\frac{17}{9}, then the value of nn is equal to
  3. Question 3

    Determinants. Asked once: 2021 Paper 10 (same type asked 8 times) See all 8 of this type

    63
    Let the system of linear equations
    4x+λy+2z=04x +\lambda y + 2z = 0
    2x−y+z=02x - y + z = 0
    μx+2y+3z=0,λ,μ∈R\mu x + 2y + 3z = 0,\lambda,\mu\in R. has a non-trivial solution. Then which of the following is true?

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  4. Question 4

    Statistics. Asked once: 2021 Paper 17 (same type asked 8 times) See all 8 of this type

    68
    Let the mean and variance of the frequency distribution
    xxx1=2x_{1}= 2x2=6x_{2}= 6x3=8x_{3}= 8x4=9x_{4}= 9
    ff44α\alphaβ\beta
    be 6 and 6.8 respectively. If x3x_{3} is changed from 8 to 7, then the mean for the new data will be:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 2021 Paper 12 (same type asked 8 times) See all 8 of this type

    43
    The lines x=ay−1=z−2x = ay - 1 = z - 2 and x=3y−2=bz−2,(ab≠0)x= 3y- 2 =bz- 2,(ab\neq 0) are coplanar, if :

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