HSC Science (General) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Jay and Ram are two friends in a class. Jay wanted to buy 4 pens and 8 notebooks, Ram wanted to buy 5 pens and 12 notebooks. Both of them went to a shop. The price of a pen and a notebook which they have selected was Rs.6 and Rs.10. Using Matrix multiplication, find the amount required from each one of them

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

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

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

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

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

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

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

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

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

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

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

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

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

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If A = `[(2, -1),(3, -2)]`, find A³  

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

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

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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)]`

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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)]`

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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