HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Show with the usual notation that for any matrix A = `["a"_"ij"]_(3xx3)  "is"   "a"_11"A"_11 + "a"_12"A"_12 + "a"_13"A"_13 = |"A"|` 

If A = `[(1,0,1),(0,2,3),(1,2,1)]` and B = `[(1,2,3),(1,1,5),(2,4,7)]`, then find a matrix X such that XA = B.

Find the inverse of the following matrix (if they exist).

`[(1,3,-2),(-3,0,-5),(2,5,0)]`

Choose the correct answer from the given alternatives in the following question:

If A = `[(1,2),(3,4)]` , adj A = `[(4,"a"),(-3,"b")]`, then the values of a and b are

Choose the correct answer from the given alternatives in the following question:

The inverse of `[(0,1),(1,0)]` is

Choose the correct answer from the given alternatives in the following question:

If A = `[(1,2),(2,1)]` and A(adj A) = k I, then the value of k is

The differential equation `y dy/dx + x = 0` represents family of ______.

Choose the correct option from the given alternatives:

The solution of `1/"x" * "dy"/"dx" = tan^-1 "x"` is

The element of second row and third column in the inverse of `[(1, 2, 1),(2, 1, 0),(-1, 0, 1)]` is ______.

If A = `[(2, -1, 1),(-2, 3, -2),(-4, 4, -3)]` the find A² 

If A = `[(-2, 4),(-1, 2)]` then find A² 

Find the matrix X such that AX = I where A = `[(6, 17),(1, 3)]`

Find A⁻¹ using column transformations:

A = `[(5, 3),(3, -2)]`

Find A⁻¹ using column transformations:

A = `[(2, -3),(-1, 2)]`

If A = `[(1, 2, -1),(3, -2, 5)]`, apply R₁ ↔ R₂ and then C₁ → C₁ + 2C₃ on A

Find the matrix X such that `[(1, 2, 3),(2, 3, 2),(1, 2, 2)]` X = `[(2, 2, -5),(-2, -1, 4),(1, 0, -1)]`

Find the inverse of A = `[(2, -3, 3),(2, 2, 3),(3, -2, 2)]` by using elementary row transformations.

If A = `[(2, 3),(1, 2)]`, B = `[(1, 0),(3, 1)]`, find AB and (AB)⁻¹ 

Select and write the correct alternative from the given option for the question

Bacterial increases at the rate proportional to the number present. If original number M doubles in 3 hours, then number of bacteria will be 4M in

Select and write the correct alternative from the given option for the question

The differential equation of y = Ae^5x + Be^–5x is