HSC Arts (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Without expanding, find the value of (x + 1)⁴ − 4(x + 1)³ (x − 1) + 6 (x + 1)² (x − 1)² − 4(x + 1) (x − 1)³ + (x − 1)⁴

Without expanding, find the value of (2x − 1)⁴ + 4(2x − 1)³ (3 − 2x) + 6(2x − 1)² (3 − 2x)² + 4(2x − 1)¹ (3 − 2x)³ + (3 − 2x)⁴ 

Find the value of (1.02)⁶, correct upto four places of decimal

Find the value of (1.01)⁵, correct up to three places of decimals.

Find the value of (0.9)⁶, correct upto four places of decimal

If A, B, C are the sets for the letters in the words 'college', 'marriage' and 'luggage' respective, then verify that [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 ∪ 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')