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Day 332: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 9 Apr 2024 (same type asked 19 times) See all 19 of this type

    87
    Let A be a non-singular matrix of order 3. If det(3adj(2adj((detA)A)))=3−13⋅2−10det(3adj(2adj((detA)A))) =3^{- 13}\cdot2^{- 10} and det⁡\det (3adj(2 A))=2m⋅3n(3adj(2\text{ }A)) =2^{m}\cdot3^{n}, then ∣3 m+2n∣|3\text{ }m + 2n| is equal to

  2. Question 2

    Vector Algebra. Asked once: 3 Apr 2025 (same type asked 18 times) See all 18 of this type

    149
    Let a→=i^+2j^+k^,b→=3i^−3j^+3k^\overrightarrow{a} = \widehat{i} + 2\widehat{j} + \widehat{k},\overrightarrow{b} = 3\widehat{i} - 3\widehat{j} + 3\widehat{k}, c→=2i^−j^+2k^\overrightarrow{c} = 2\widehat{i} - \widehat{j} + 2\widehat{k} and d→\overrightarrow{d} be a vector such that b→×d→=c→×d→\overrightarrow{b} \times \overrightarrow{d} = \overrightarrow{c} \times \overrightarrow{d} and a→⋅d→=4\overrightarrow{a} \cdot \overrightarrow{d} = 4. Then ∣(a→×d→)∣2|(\overrightarrow{a} \times \overrightarrow{d})|^{2} is equal to.

  3. Question 3

    Limits and Continuity. Asked once: 3 Apr 2025 (same type asked 16 times) See all 16 of this type

    69
    Let f(x)={(1+ax)1/x,x<01+b,x=0(x+4)1/2−2(x+c)1/3−2,x>0f(x) =\left\{ \begin{matrix} (1 + ax)^{1/x} & , & x < 0 \\ 1 + b & , & x = 0 \\ \frac{(x + 4)^{1/2}- 2}{(x + c)^{1/3}- 2} & , & x > 0 \end{matrix} \right. be continuous at x=0x = 0. Then eabce^{a}bc is equal to.

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  4. Question 4

    Three Dimensional Geometry. Asked once: 25 Jan 2023 (same type asked 15 times) See all 15 of this type

    84
    Let the equation of the plane passing through the line x−2y−z−5=0=x+y+3z−5x - 2y - z - 5 = 0 = x + y + 3z - 5 and parallel to the line x+y+2z−7=0=2x+3y+z−2x + y + 2z - 7 = 0 = 2x + 3y + z - 2 be ax+by+cz=65ax + by + cz = 65. Then the distance of the point (a,b,c)(a,b,c) from the plane 2x+2y−z+16=02x + 2y - z + 16 = 0 is

  5. Question 5

    Determinants. Asked once: 25 Jul 2022 (same type asked 14 times) See all 14 of this type

    64
    The number of θ∈(0,4π)\theta \in (0,4\pi) for which the system of linear equations
    3(sin⁡3θ)x−y+z=23(\sin3\theta)x - y + z = 2
    3(cos⁡2θ)x+4y+3z=33(\cos2\theta)x + 4y + 3z = 3
    6x+7y+7z=96x + 7y + 7z = 9
    has no solution is:

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