JEE Mathematics MCQs - Area of Triangles and Matrix Inverses

31. If A = [[2, 3], [1, 4]], what is the determinant of A?

    • a) 7
    • b) 8
    • c) 5
    • d) 10

    Answer: a) 7

32. What is the value of the determinant [[1, 2], [3, 4]]?

    • a) -2
    • b) 2
    • c) -1
    • d) 1

    Answer: a) -2

33. If A = [[0, 1], [-1, 0]], then det(A) is:

    • a) 1
    • b) -1
    • c) 0
    • d) 2

    Answer: b) -1

34. The determinant of a 3x3 identity matrix is:

    • a) 0
    • b) 1
    • c) 2
    • d) 3

    Answer: b) 1

35. For the matrix [[2, 3], [4, 6]], the determinant is:

    • a) 0
    • b) 5
    • c) 10
    • d) -10

    Answer: a) 0

36. What is the value of the determinant [[1, 2, 3], [0, 4, 5], [1, 0, 6]]?

    • a) 10
    • b) -10
    • c) 5
    • d) -5

    Answer: b) -10

37. If A = [[1, 2], [3, 4]], find det(2A):

    • a) 40
    • b) 80
    • c) 20
    • d) 60

    Answer: b) 80

38. The determinant of a triangular matrix is:

    • a) The sum of diagonal elements
    • b) The product of diagonal elements
    • c) Zero
    • d) None of the above

    Answer: b) The product of diagonal elements

39. If det(A) = 5, then det(A-1) is:

    • a) 1
    • b) -5
    • c) 1/5
    • d) 5

    Answer: c) 1/5

40. If A is a square matrix of order n, then det(kA) is:

    • a) k * det(A)
    • b) kn * det(A)
    • c) kn-1 * det(A)
    • d) None of the above

    Answer: b) kn * det(A)

41. If A = [[1, 1], [1, 1]], what is det(A)?

    • a) 2
    • b) 0
    • c) 1
    • d) -1

    Answer: b) 0

42. If A and B are 2x2 matrices, which of the following is true about det(AB)?

    • a) det(AB) = det(A) + det(B)
    • b) det(AB) = det(A) * det(B)
    • c) det(AB) = det(A - B)
    • d) det(AB) = det(A) - det(B)

    Answer: b) det(AB) = det(A) * det(B)

43. The determinant of the matrix [[a, b], [b, a]] is:

    • a) a2 + b2
    • b) a2 - b2
    • c) a2 + 2b2
    • d) a2 - 2b2

    Answer: b) a2 - b2

44. If A = [[2, 3], [4, 5]], what is the determinant of A + I, where I is the identity matrix?

    • a) 11
    • b) 14
    • c) 13
    • d) 12

    Answer: c) 13

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