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Day 134: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 7 Apr 2025 (same type asked 8 times) See all 8 of this type

    69
    Let the angle θ,0<θ<π2\theta,0 <\theta<\frac{\pi}{2} between two unit vectors a^\widehat{a} and b^\widehat{b} be sin⁡−1(659)\sin^{- 1}\left( \frac{\sqrt{65}}{9} \right). If the vector c→=3a^+6b^+9(a^×b^)\overrightarrow{c}= 3\widehat{a}+ 6\widehat{b}+ 9(\widehat{a}\times\widehat{b}), then the value of 9(c→⋅a^)−3(c→⋅b^)9(\overrightarrow{c}\cdot\widehat{a}) - 3(\overrightarrow{c}\cdot\widehat{b}) is.

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  2. Question 2

    Vector Algebra. Asked once: 24 Jan 2026 S2 (same type asked 8 times) See all 8 of this type

    54
    Let  a→=2i^−j^−k^,b→=i^+3j^−k^\ \overrightarrow{a}= 2\widehat{i}-\widehat{j}-\widehat{k},\overrightarrow{b}=\widehat{i}+ 3\widehat{j}-\widehat{k} and c→=2i^+j^+3k^\overrightarrow{c}= 2\widehat{i}+\widehat{j}+ 3\widehat{k}. Let v→\overrightarrow{v} be the vector in the plane of the vectors a→\overrightarrow{a} and b→\overrightarrow{b}, such that the length of its projection on the vector c→\overrightarrow{c} is 114\frac{1}{\sqrt{14}}. Then ∣v→∣|\overrightarrow{v}| is equal to

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  3. Question 3

    Statistics. Asked once: 23 Jan 2026 S2 (same type asked 8 times) See all 8 of this type

    68
    If the mean and the variance of the data
    Class4-88-1212-1616-20
    Frequency3λ\lambda47
    are μ\mu and 19 respectively, then the value of λ+μ\lambda + \mu is

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  4. Question 4

    Three Dimensional Geometry. Asked once: 13 Apr 2023 (same type asked 8 times) See all 8 of this type

    169
    The line, that is coplanar to the line x+3−3=y−11=z−55\frac{x + 3}{- 3}=\frac{y - 1}{1}=\frac{z - 5}{5}, is

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  5. Question 5

    Permutations and Combinations. Asked once: 29 Jan 2024 (same type asked 8 times) See all 8 of this type

    82
    All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" IS