HSC Science (Electronics) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Select the correct option from the given alternatives:

If `[(5, 7),(x, 1),(2, 6)] - [(1, 2),(-3, 5),(2, y)] = [(4, 5),(4, -4),(0, 4)]` then __________

Select the correct option from the given alternatives:

If A + B = `[(7, 4),(8, 9)]` and A − B = `[(1, 2),(0, 3)]` then the value of A is _______

Select the correct option from the given alternatives:

If `[("x", 3"x" - "y"),("zx" + "z", 3"y" - "w")] = [(3, 2),(4, 7)]` then ______

Select the correct option from the given alternatives:

If A = `[(-2, 1),(0, 3)]` and f(x) = 2x² – 3x, then f(A) = ………

Answer the following question:

If f(α) = A = `[(cosalpha, -sinalpha, 0),(sinalpha, cosalpha, 0),(0, 0, 1)]`, Find f(– α)

Answer the following question:

If f (α) = A = `[(cosalpha, -sinalpha, 0),(sinalpha, cosalpha, 0),(0, 0, 1)]`, Find f(–α) + f(α)

Answer the following question:

If A_α = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, show that A_α . A_β = A_α+β 

Answer the following question:

If A = `[(2, -2, -4),(-1, 3, 4),(1, -2, -3)]` show that A² = A

Answer the following question:

If A = `[(4, -1, -4),(3, 0, -4),(3, -1, -3)]`, show that A² = I

Answer the following question:

If A = `[(3, -5),(-4, 2)]`, show that A² – 5A – 14I = 0

Answer the following question:

If A = `[(2, -1),(-1, 2)]`, show that A² – 4A + 3I = 0

Answer the following question:

if A = `[(-3, 2),(2, -4)]`, B = `[(1, x),(y, 0)]`, and (A + B)(A – B) = A² – B² , find x and y

Answer the following question:

If A = `[(0, 1),(1, 0)]` and B = `[(0, -1),(1, 0)]` show that (A + B)(A – B) ≠ A² – B² 

Answer the following question:

If A = `[(2, -1),(3, -2)]`, find A³  

Answer the following question:

Find x, y if, `[(0, -1, 4)]{2[(4, 5),(3, 6),(2, -1)] + 3[(4, 3),(1, 4),(0, -1)]} = [(x, y)]`

Answer the following question:

Find x, y if, `{-1 [(1, 2, 1),(2, 0, 3)] + 3[(2, -3, 7),(1, -1, 3)]} [(5),(0),(-1)] = [(x),(y)]`

Answer the following question:

Find x, y, z if `{5[(0, 1),(1, 0),(1, 1)] -3[(2, 1),(3, -2),(1, 3)]} [(2),(1)] = [(x - 1),(y + 1),(2z)]`

Answer the following question:

Find x, y, z if `{[(1, 3, 2),(2, 0, 1),(3, 1, 2)] + 2[(3, 0, 2),(1, 4, 5),(2, 1, 0)]} [(1),(2),(3)] = [(x),(y),(z)]`

Answer the following question:

Two farmers Shantaram and Kantaram cultivate three crops rice,wheat and groundnut. The sale (In Rupees) of these crops by both the farmers for the month of April and may 2008 is given below,

Find The total sale in rupees for two months of each farmer for each crop

Answer the following question:

Two farmers Shantaram and Kantaram cultivate three crops rice,wheat and groundnut. The sale (In Rupees) of these crops by both the farmers for the month of April and may 2008 is given below,

Find the increase in sales from April to May for every crop of each farmer.