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Day 291: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 22 Jan 2025 (same type asked 19 times) See all 19 of this type

    73
    Let AA be a square matrix of order 3 such that det(A)=−2det(A) = - 2 and det(3adj(−6adj(3A)))=2m+n⋅3mndet(3adj( - 6adj(3A))) =2^{m + n}\cdot3^{mn}, m>nm > n. Then 4 m+2n4\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

    73
    Let a→=i^+j^+k^,b→=3i^+2j^−k^,c→=λj^+μk^\overrightarrow{a} = \widehat{i} + \widehat{j} + \widehat{k},\overrightarrow{b} = 3\widehat{i} + 2\widehat{j} - \widehat{k},\overrightarrow{c} = \lambda\widehat{j} + \mu\widehat{k} and d^\widehat{d} be a unit vector such that a→×d^=b→×d^\overrightarrow{a} \times \widehat{d} = \overrightarrow{b} \times \widehat{d} and c→.d^=1\overrightarrow{c}.\widehat{d} = 1, If c→\overrightarrow{c} is perpendicular to a→\overrightarrow{a}, then ∣3λd^+μc→∣2|3\lambda\widehat{d} + \mu\overrightarrow{c}|^{2} is equal to

  3. Question 3

    Limits and Continuity. Asked once: 23 Jan 2026 S1 (same type asked 16 times) See all 16 of this type

    59
    Let f(x)={ax2+2ax+34x2+4x−3,x≠−32,12bx=−32,12f(x) =\left\{ \begin{matrix} \frac{ax^{2}+ 2ax + 3}{4x^{2}+ 4x - 3}, & x \neq -\frac{3}{2},\frac{1}{2} \\ b & x = -\frac{3}{2},\frac{1}{2} \end{matrix} \right. be continuous at x=−32x = -\frac{3}{2}. If fof(x)=75fof(x) =\frac{7}{5}, then xx is equal to :

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  4. Question 4

    Three Dimensional Geometry. Asked once: 1 Feb 2023 (same type asked 15 times) See all 15 of this type

    161
    Let the plane PP pass through the intersection of the planes 2x+3y−z=22x + 3y - z = 2 and x+2y+3z=6x + 2y + 3z = 6 and be perpendicular to the plane 2x+y−z=02x + y - z = 0. If dd is the distance of PP from the point (−7,1,1)(-7,1,1), then d2d^{2} is equal to:

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  5. Question 5

    Determinants. Asked once: 10 Apr 2023 (same type asked 14 times) See all 14 of this type

    172
    Let SS be the set of values of λ\lambda, for which the system of equations 6λx−3y+3z=4λ26\lambda x - 3y + 3z = 4\lambda^{2}, 2x+6λy+4z=12x + 6\lambda y + 4z = 1, 3x+2y+3λz=λ3x + 2y + 3\lambda z = \lambda has no solution. Then 12∑λ∈S∣λ∣12\sum_{\lambda \in S} |\lambda| is equal to