HSC Arts (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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.

Find the value of ¹⁵C₄ 

Find the value of ⁸⁰C₂

Find the value of ¹⁵C₄ + ¹⁵C₅ 

Find the value of ²⁰C₁₆ – ¹⁹C₁₆ 

Answer the following:

A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?