WBJEE · Mathematics

Matrices, calculus and coordinate geometry

38 practice questions, each with the answer and an explanation.

Practise Matrices, calculus and coordinate geometry now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 38 questions

  1. Find the determinant of the 3×3 matrix with rows (-2, 0, 3); (-1, 5, -1); (2, 1, -1).
  2. If A has rows (3, -3) and (3, -1) and B has rows (-3, 4) and (3, 2), find the entry in row 2, column 1 of AB.
  3. Find the coordinates of the focus of the parabola y² = 12x.
  4. Find a × b for a = 3i + 4j − 1k and b = 2i − 2j + 3k.
  5. Solve dy/dx = 2x with y(0) = -1. What is y(3)?
  6. How many permutations of 10 objects taken 3 at a time are there?
  7. What are the eigenvalues of the matrix with rows (6, -4) and (0, 5)?
  8. If and are the roots of , find .
  9. Find the coefficient of in the expansion of .
  10. A geometric progression has first term and common ratio . Find its sum to infinity.
  11. Evaluate .
  12. If , find at .
  13. Find the determinant of the matrix with rows (9, 5) and (9, 3).
  14. Find the determinant of the 3×3 matrix with rows (-1, 1, -1); (2, 0, 1); (0, -1, -2).
  15. If A has rows (-2, 1) and (3, 3) and B has rows (2, -3) and (2, 0), find the entry in row 2, column 1 of AB.
  16. Find the coordinates of the focus of the parabola y² = 4x.
  17. Find the eccentricity of the ellipse x²/25 + y²/9 = 1.
  18. Find a × b for a = 0i + 1j − 2k and b = -3i + 3j + 4k.
  19. How many permutations of 5 objects taken 4 at a time are there?
  20. What are the eigenvalues of the matrix with rows (4, -2) and (0, 5)?
  21. If and are the roots of , find .
  22. Find the remainder when is divided by .
  23. Find the coefficient of in the expansion of .
  24. Evaluate .
  25. The first term of an arithmetic progression is and the common difference is . Find the sum of the first terms.
  26. Evaluate .
  27. Find the coordinates of the centre of the circle .
  28. Find the determinant of the matrix with rows (7, 9) and (-6, 4).
  29. Find the determinant of the 3×3 matrix with rows (1, 3, 0); (-1, 1, -2); (3, -2, -3).
  30. If A has rows (3, 1) and (-2, 0) and B has rows (-2, -1) and (4, -1), find the entry in row 2, column 1 of AB.
  31. How many permutations of 5 objects taken 3 at a time are there?
  32. What are the eigenvalues of the matrix with rows (2, -3) and (0, 6)?
  33. If and are the roots of , find .
  34. Evaluate .
  35. A geometric progression has first term and common ratio . Find its sum to infinity.
  36. Solve .
  37. If , find .
  38. Evaluate .

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