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Day 15: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. This type asked 7 times: 2021 Paper 6, 2021 Paper 20, 29 Jul 2022, 24 Jan 2023, 11 Apr 2023, 13 Apr 2023, 15 Apr 2023. This one: 15 Apr 2023 See all 7 of this type

    83
    Let the plane PP contain the line 2x+y−z−3=0=5x−3y+4z+92x + y - z - 3 = 0 = 5x - 3y + 4z + 9 and be parallel to the line x+22=3−y−4=z−75\frac{x + 2}{2}=\frac{3 - y}{- 4}=\frac{z - 7}{5}. Then the distance of the point A(8,−1,−19)A(8, - 1, - 19) from the plane P measured parallel to the line x−3=y−54=2−z−12\frac{x}{- 3}=\frac{y - 5}{4}=\frac{2 - z}{- 12} is equal to

  2. Question 2

    Probability. This type asked 7 times: 2021 Paper 1, 2021 Paper 10, 2021 Paper 25, 14 Jun 2022, 26 Jun 2022, 27 Jun 2022, 10 Apr 2023. This one: 10 Apr 2023 See all 7 of this type

    158
    Let a die be rolled nn times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is k215\frac{k}{2^{15}}, then kk is equal to:

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  3. Question 3

    Binomial Theorem. This type asked 6 times: 12 Apr 2023, 29 Jan 2024, 22 Jan 2025, 22 Jan 2026 S2, 23 Jan 2026 S1, 8 Apr 2026 S2. This one: 8 Apr 2026 S2 See all 6 of this type

    58
    If 26(233( 13C2)+255( 12C4)+277( 12C6)+...+21313( 12C12))=313−α26\left( \frac{2^{3}}{3}\left( \ ^{13}C_{2} \right)+\frac{2^{5}}{5}\left( \ ^{12}C_{4} \right)+\frac{2^{7}}{7}\left( \ ^{12}C_{6} \right)+ ... +\frac{2^{13}}{13}\left( \ ^{12}C_{12} \right) \right)=3^{13}-\alpha, then α\alpha is equal to :

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  4. Question 4

    Statistics. This type asked 6 times: 2021 Paper 26, 29 Jul 2022, 1 Feb 2024, 29 Jan 2025, 4 Apr 2026 S2, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 6 of this type

    59
    A data consists of 20 observations x1,x2,…..,x20x_{1},x_{2},\ldots..,x_{20}. If ∑i=120(xi+5)2=2500\sum_{i= 1}^{20} \left( x_{i}+ 5 \right)^{2}= 2500 and ∑i=120(xi−5)2=100\sum_{i= 1}^{20} \left( x_{i}- 5 \right)^{2}= 100, then the ratio of mean to standard deviation of this data is :

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  5. Question 5

    Matrices. This type asked 6 times: 27 Jan 2024, 23 Jan 2025, 24 Jan 2025, 22 Jan 2026 S1, 5 Apr 2026 S1, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 6 of this type

    54
    Let M be a 3×33 \times 3 matrix such that M(100)=(123),M(010)=(012)M\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}=\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix},M\begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}=\begin{pmatrix} 0 \\ 1 \\ 2 \end{pmatrix} and M(001)=(−111)M\begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}=\begin{pmatrix} - 1 \\ 1 \\ 1 \end{pmatrix}. If M(xyz)=(1711)M\begin{pmatrix} x \\ y \\ z \end{pmatrix}=\begin{pmatrix} 1 \\ 7 \\ 11 \end{pmatrix}, then x+y+zx + y + z equals :

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