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Day 412: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 8 Apr 2023 (same type asked 19 times) See all 19 of this type

    74
    Let A=[21012−10−12]A =\begin{bmatrix} 2 & 1 & 0 \\ 1 & 2 & - 1 \\ 0 & - 1 & 2 \end{bmatrix}. If ∣adj(adj(adj2A))∣=(16)n|adj(adj(adj2A))| = (16)^{n}, then nn is equal to

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  2. Question 2

    Vector Algebra. Asked once: 31 Jan 2024 (same type asked 18 times) See all 18 of this type

    72
    Let  a→=3i^+j^−2k^, b→=4i^+j^+7k^\ \overrightarrow{a}= 3\widehat{i}+\widehat{j}- 2\widehat{k},\ \overrightarrow{b}= 4\widehat{i}+\widehat{j}+ 7\widehat{k} and c→=i^−3j^+4k^\overrightarrow{c}=\widehat{i}- 3\widehat{j}+ 4\widehat{k} be three vectors. If a vectors p→\overrightarrow{p} satisfies p→×b→=c→×b→\overrightarrow{p}\times\overrightarrow{b}=\overrightarrow{c}\times\overrightarrow{b} and p→⋅a→=0\overrightarrow{p}\cdot\overrightarrow{a}= 0, then p→⋅(i^−j^−k^)\overrightarrow{p}\cdot (\widehat{i}-\widehat{j}-\widehat{k}) is equal to

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  3. Question 3

    Limits and Continuity. Asked once: 2021 Paper 26 (same type asked 16 times) See all 16 of this type

    74
    Let f:R→Rf:\mathbb{R} \rightarrow \mathbb{R} be defined as f(x)={2sin⁡(−πx2),if x<−1∣ax2+x+b∣,if −1≤x≤1sin⁡(πx),if x>1f(x) =\left\{ \begin{matrix} 2\sin\left( -\frac{\pi x}{2} \right), & \text{if } x < -1 \\ \left| ax^{2}+ x + b \right|, & \text{if } -1 \leq x \leq 1 \\ \sin(\pi x), & \text{if } x > 1 \end{matrix} \right. If f(x)f(x) is continuous on R\mathbb{R}, then a+ba + b equals:

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  4. Question 4

    Three Dimensional Geometry. Asked once: 2021 Paper 20 (same type asked 15 times) See all 15 of this type

    69
    Equation of a plane at a distance 221\sqrt{\frac{2}{21}} from the origin, which contains the line of intersection of the planes x−y−z−1=0x - y - z - 1 = 0 and 2x+y−3z+4=02x + y - 3z + 4 = 0, is:

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  5. Question 5

    Determinants. Asked once: 2021 Paper 24 (same type asked 14 times) See all 14 of this type

    63
    Consider the system of linear equations
    −x+y+2z=0- x + y + 2z = 0
    3x−ay+5z=13x - ay + 5z = 1
    2x−2y−az=72x - 2y - az = 7
    Let S1S_{1} be the set of all a∈Ra\in R for which the system is inconsistent and S2S_{2} be the set of all a∈Ra\in R for which the system has infinitely many solutions. If n( S1)n\left( {\text{ }S}_{1} \right) and n(S2)n\left( S_{2} \right) denote the number of elements in S1S_{1} and S2S_{2} respectively, then

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