jee-main 2025 Q90

jee-main · India · session2_03apr_shift1 Vectors: Cross Product & Distances
Q90. Let $\overrightarrow { \mathrm { a } } = \hat { i } - 3 \hat { j } + 7 \hat { k } , \overrightarrow { \mathrm {~b} } = 2 \hat { i } - \hat { j } + \hat { k }$ and $\overrightarrow { \mathrm { c } }$ be a vector such that $\overrightarrow { \mathrm { a } } + 2 \overrightarrow { \mathrm {~b} } ) \times \overrightarrow { \mathrm { c } } = 3 ( \overrightarrow { \mathrm { c } } \times \overrightarrow { \mathrm { a } } )$. If $\vec { a } \cdot \vec { c } = 130$, then $\vec { b } \cdot \vec { c }$ is equal to $\_\_\_\_$
ANSWER KEYS

1. (2)2. (3)
9. (2)10. (3)
17. (2)18. (4)
25. (4)26. (5)
33. (4)34. (3)
41. (1)42. (2)
49. (4)50. (2)
57. (5)58. (2)
65. (2)66. (3)
73. (1)74. (4)
81. (125)82. (910)
89. (72)90. (30)

  1. (4)
  2. (2)
  3. (2)
  4. (5)
  5. (3)
  6. (3)
  7. (80)
  8. (14)
  9. (1)
  10. (4)
  11. (54)
  12. (2)
  13. (2)
  14. (3)
  15. (50)
  16. (3)
  17. (2)
  18. (22)
  19. (6)
  20. (4)
  21. (1)
  22. (108)
  23. (4)
  24. (2)
  25. (19)
  26. (10)
  27. (2)
  28. (3)
  29. (8)
  30. (1)
  31. (3)
  32. (3)
  33. (24)
  34. (4)
  35. (1)
  36. (240)
  37. (727)
  38. (4)
  39. (2)
  40. (150)
  41. (2)
  42. (2)
  43. (4)
  44. (56)
  45. (4)
  46. (4)
  47. (600)
  48. (3)
  49. (2)
  50. (3)
  51. (25)
  52. (3)
  53. (1)
  54. (4)
  55. (3)
  56. (1)
  57. (2)
  58. (86)
  59. (2)
  60. (2)
  61. (1)
  62. (3)
  63. (2)
  64. (4)
  65. (2)
  66. (18) 
Q90. Let $\overrightarrow { \mathrm { a } } = \hat { i } - 3 \hat { j } + 7 \hat { k } , \overrightarrow { \mathrm {~b} } = 2 \hat { i } - \hat { j } + \hat { k }$ and $\overrightarrow { \mathrm { c } }$ be a vector such that $\overrightarrow { \mathrm { a } } + 2 \overrightarrow { \mathrm {~b} } ) \times \overrightarrow { \mathrm { c } } = 3 ( \overrightarrow { \mathrm { c } } \times \overrightarrow { \mathrm { a } } )$. If $\vec { a } \cdot \vec { c } = 130$, then $\vec { b } \cdot \vec { c }$ is equal to $\_\_\_\_$

\section*{ANSWER KEYS}
\begin{center}
\begin{tabular}{|l|l|}
\hline
1. (2) & 2. (3) \\
\hline
9. (2) & 10. (3) \\
\hline
17. (2) & 18. (4) \\
\hline
25. (4) & 26. (5) \\
\hline
33. (4) & 34. (3) \\
\hline
41. (1) & 42. (2) \\
\hline
49. (4) & 50. (2) \\
\hline
57. (5) & 58. (2) \\
\hline
65. (2) & 66. (3) \\
\hline
73. (1) & 74. (4) \\
\hline
81. (125) & 82. (910) \\
\hline
89. (72) & 90. (30) \\
\hline
\end{tabular}
\end{center}

\begin{enumerate}
  \setcounter{enumi}{2}
  \item (4)
  \item (2)
  \item (2)
  \item (5)
  \item (3)
  \item (3)
  \item (80)
  \item (14)
  \item (1)
  \item (4)
  \item (54)
  \item (2)
  \item (2)
  \item (3)
  \item (50)
  \item (3)
  \item (2)
  \item (22)
  \item (6)
  \item (4)
  \item (1)
  \item (108)
  \item (4)
  \item (2)
  \item (19)
  \item (10)
  \item (2)
  \item (3)
  \item (8)
  \item (1)
  \item (3)
  \item (3)
  \item (24)
  \item (4)
  \item (1)
  \item (240)
  \item (727)
  \item (4)
  \item (2)
  \item (150)
  \item (2)
  \item (2)
  \item (4)
  \item (56)
  \item (4)
  \item (4)
  \item (600)
  \item (3)
  \item (2)
  \item (3)
  \item (25)
  \item (3)
  \item (1)
  \item (4)
  \item (3)
  \item (1)
  \item (2)
  \item (86)
  \item (2)
  \item (2)
  \item (1)
  \item (3)
  \item (2)
  \item (4)
  \item (2)
  \item (18)
\end{enumerate}
Paper Questions
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