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Day 379: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 29 Jan 2025 (same type asked 10 times) See all 10 of this type

    67
    Let L1:x−11=y−2−1=z−12L_{1}:\frac{x - 1}{1}=\frac{y - 2}{- 1}=\frac{z - 1}{2} and L2:x+1−1=y−22=z1L_{2}:\frac{x + 1}{- 1}=\frac{y - 2}{2}=\frac{z}{1} be two lines. Let L3L_{3} be a line passing through the point (α,β,γ)(\alpha,\beta,\gamma) and be perpendicular to both L1L_{1} and L2L_{2}. If L3L_{3} intersects L1L_{1}, then ∣5α−11β−8γ∣|5\alpha - 11\beta - 8\gamma| equals :

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  2. Question 2

    Quadratic Equations. Asked once: 5 Apr 2024 (same type asked 10 times) See all 10 of this type

    180
    The number of real solutions of the equation x∣x+5∣+2∣x+7∣−2=0x|x+ 5| + 2|x+ 7| - 2 = 0 is

  3. Question 3

    Vector Algebra. Asked once: 2021 Paper 25 (same type asked 10 times) See all 10 of this type

    65
    If a→&b→\overrightarrow{a}\&\overrightarrow{b} are perpendicular vectors, then a→×(a→×(a→×(a→×b→)))\overrightarrow{a}\times (\overrightarrow{a}\times (\overrightarrow{a}\times (\overrightarrow{a}\times\overrightarrow{b}))) is equal to

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  4. Question 4

    Sequences and Series. Asked once: 29 Jan 2023 (same type asked 10 times) See all 10 of this type

    85
    Let a1,a2,a3,…a_{1},a_{2},a_{3},\ldots be a GP of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24 , then a1a9+a2a4a9+a5+a7a_{1}a_{9}+a_{2}a_{4}a_{9}+a_{5}+a_{7} is equal to

  5. Question 5

    Matrices. Asked once: 25 Jul 2022 (same type asked 9 times) See all 9 of this type

    173
    Let A=[1aa01b001],a,b∈RA =\begin{bmatrix} 1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1 \end{bmatrix},a,b \in R. If for some n∈Nn \in N, An=[14821600196001]A^{n}=\begin{bmatrix} 1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1 \end{bmatrix} then n+a+bn + a + b is equal to