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Day 226: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 2 Apr 2025 (same type asked 19 times) See all 19 of this type

    69
    Let a∈Ra \in R and A be a matrix of order 3×33 \times 3 such that det(A)=−4det(A) = - 4 and A+I=[1a1210a12]A+I=\begin{bmatrix} 1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2 \end{bmatrix}, where II is the identity matrix of order 3×33 \times 3.If det((a+1)adj((a−1)A))det((a+ 1)adj((a- 1)A)) is 2m3n,m,n∈2^{m}3^{n},m,n\in {0,1,2,….20}\mathbf{\{ 0,1,2,\ldots.20\}}, then m+nm + n is equal to :

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  2. Question 2

    Vector Algebra. Asked once: 24 Jan 2026 S2 (same type asked 18 times) See all 18 of this type

    69
    Let a→=2i^−5j^+5k^\overrightarrow{a}= 2\widehat{i}- 5\widehat{j}+ 5\widehat{k} and b→=i^−j^+3k^\overrightarrow{b}=\widehat{i}-\widehat{j}+ 3\widehat{k}. If c→\overrightarrow{c} is a vector such that 2(a→×c→)+3(b→×c→)=0→2(\overrightarrow{a}\times\overrightarrow{c}) + 3(\overrightarrow{b}\times\overrightarrow{c}) =\overrightarrow{0} and (a→−b→)⋅c→=−97(\overrightarrow{a}-\overrightarrow{b}) \cdot\overrightarrow{c}= - 97, then ∣c→×k^∣2|\overrightarrow{c}\times\widehat{k}|^{2} is equal to

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  3. Question 3

    Limits and Continuity. Asked once: 23 Jan 2026 S2 (same type asked 16 times) See all 16 of this type

    51
    If f(x)={a∣x∣+x2−2(sin⁡∣x∣)(cos⁡∣x∣)x,x≠0b,x=0f(x) =\left\{ \begin{matrix} \frac{a|x| +x^{2}- 2(\sin|x|)(\cos|x|)}{x} & ,x \neq 0 \\ b & ,x = 0 \end{matrix} \right. is continuous at x=0x = 0, then a+ba + b is equal to :

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  4. Question 4

    Three Dimensional Geometry. Asked once: 6 Apr 2023 (same type asked 15 times) See all 15 of this type

    163
    A plane PP contains the line of intersection of the plane r→⋅(i^+j^+k^)=6\overrightarrow{r}\cdot (\widehat{i}+\widehat{j}+\widehat{k}) = 6 and r→⋅(2i^+3j^+4k^)=−5\overrightarrow{r}\cdot (2\widehat{i}+ 3\widehat{j}+ 4\widehat{k}) = - 5. If PP passes through the point (0,2,−2)(0,2, - 2), then the square of distance of the point (12,12,18)(12,12,18) from the plane PP is

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  5. Question 5

    Determinants. Asked once: 23 Jan 2025 (same type asked 14 times) See all 14 of this type

    128
    The system of equations
    x+y+z=6x+2y+5z=9x+5y+λz=μ\begin{matrix} & x + y + z = 6 \\ & x + 2y + 5z = 9 \\ & x + 5y + \lambda z = \mu \end{matrix}
    has no solution if

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