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

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following: 

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:

(A ∪ B)' = (A' ∩ B)'

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:

(A ∩ B)' = A' ∪ B'

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:

A = (A ∩ B) ∪ (A ∩ B')

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:

B = (A ∩ B) ∪ (A' ∩ B)

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:

(A ∪ B) = (A − B) ∪ (A ∩ B) ∪ (B − A)

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:

A ∩ (B ∆ C) = (A ∩ B) ∆ (A ∩ C)

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:

n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:

n(B) = (A' ∩ B) + n(A ∩ B)

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A'∩ B') = 5, find n(A ∪ B)

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A'∩ B') = 5, find n(A ∩ B)

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A'∩ B') = 5, find n(A'∩ B)

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A'∩ B') = 5, find n(A ∩ B')

Write down the power set of A = {1,2,3}

Solve the following inequality and write the solution set using interval notation

− 9 < 2x + 7 ≤ 19

Solve the following inequality and write the solution set using interval notation

x² − x > 20

Solve the following inequality and write the solution set using interval notation

`(2x)/(x - 4) ≤ 5`

Solve the following inequality and write the solution set using interval notation

6x² + 1 ≤ 5x

If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A ∪ B