Other Maths · JEE Main previous year questions

2022 53 questions

1. Q122022 · 24 Jun 2022 · Shift 2

   If the shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{\lambda }$ and $\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-5}{5}$ is $\frac{1}{\sqrt{3}}$, then the sum of all possible value of $\lambda$ is :

   1. A.16
   2. B.6
   3. C.12
   4. D.15
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   Answer: A

2. Q222022 · 24 Jun 2022 · Shift 2· Numerical answer

   Let $S=\left\{\left(\begin{array}{cc}-1& a\\ 0& b\end{array}\right);a,b\in \{1,2,3,\dots ,100\}\right\}$ and let $T_n=\{A\in S:A^{n(n+1)}=I\}$. Then the number of elements in ${\bigcap }_{n=1}^{100}{T}_n$ is ____.

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   Answer: 100

3. Q252022 · 24 Jun 2022 · Shift 2· Numerical answer

   The remainder on dividing $1+3+3^2+3^3+\cdots +3^{2021}$ by 50 is ____.

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   Answer: 4