HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∪ C) = (A × B) ∪ (A × C)

Express {(x, y) / x² + y² = 100, where x, y ∈ W} as a set of ordered pairs

Let A = {6, 8} and B = {1, 3, 5}
Show that R₁ = {(a, b)/a ∈ A, b ∈ B, a − b is an even number} is a null relation. R₂ = {(a, b)/a ∈ A, b ∈ B, a + b is odd number} is an universal relation

Write the relation in the Roster Form. State its domain and range

R₁ = {(a, a²)/a is prime number less than 15}

Write the relation in the Roster Form. State its domain and range

R₂ = `{("a", 1/"a") // 0 < "a" ≤ 5, "a" ∈ "N"}`

Write the relation in the Roster Form. State its domain and range

R₃ = {(x, y)/y = 3x, y∈ {3, 6, 9, 12}, x∈ {1, 2, 3}

Write the relation in the Roster Form. State its domain and range

R₄ = {(x, y)/y > x + 1, x = 1, 2 and y = 2, 4, 6}

Write the relation in the Roster Form. State its domain and range

R₅ = {(x, y)/x + y = 3, x, y∈ {0, 1, 2, 3}

Write the relation in the Roster Form. State its domain and range

R₆ = {(a, b)/a ∈ N, a < 6 and b = 4}

Write the relation in the Roster Form. State its domain and range

R₇ = {(a, b)/a, b ∈ N, a + b = 6}

Write the relation in the Roster Form. State its domain and range

R₈ = {(a, b)/b = a + 2, a ∈ z, 0 < a < 5}

Identify which of if the following relations are reflexive, symmetric, and transitive.

Select the correct answer from given alternative.

Let R be a relation on the set N be defined by {(x, y)/x, y ∈ N, 2x + y = 41} Then R is ______.

Select the correct answer from given alternative.

The relation ">" in the set of N (Natural number) is

Select the correct answer from given alternative.

A relation between A and B is

Select the correct answer from given alternative.

If (x, y) ∈ R × R, then xy = x² is a relation which is

Select the correct answer from given alternative

If A = {a, b, c} The total no. of distinct relations in A × A is

Answer the following:

If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R₁ = {(1, 4), (1, 5), (1, 6)}

Answer the following:

If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R₂ = {(1, 5), (2, 4), (3, 6)}

Answer the following:

If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R₃ = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}