HSC Commerce: Marketing and Salesmanship 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the following relation as sets of ordered pairs:
{(x, y) / y = 3x, x ∈ {1, 2, 3}, y ∈ {3, 6, 9, 12}}

Find the following relation as sets of ordered pairs:
{(x, y) / y > x + 1, x ∈ {1, 2} and y ∈ {2, 4, 6}}

Find the following relation as sets of ordered pairs:
{(x, y) / x + y = 3, x, y ∈ {0, 1, 2, 3}}

If A = {1, 2, 3} and B = {2, 4}, state the elements of A × A, A × B, B × A, B × B, (A × B) ∩ (B × A).

If A = {– 1, 1}, find A × A × A.

Determine the Domain and Range of the following relations : R = {(a, b) / a ∈ N, a < 5, b = 4}

If A = {1, 2, 3}, B = {4, 5, 6} which of following are relation from A to B : R₁ = {(1, 4), (1, 5), (1, 6)}

If A = {1, 2, 3}, B = {4, 5, 6} which of following are relation from A to B : R₂ = {(1, 5), (2, 4), (3, 6)}

If A = {1, 2, 3}, B = {4, 5, 6} which of following are relation from A to B : R₃ = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}

If A = {1, 2, 3}, B = {4, 5, 6} which of following are relation from A to B : R₄ = {(4, 2), (2, 6), (5, 1), (2, 4)}

Express the following recurring decimal as a rational number:

`0.bar32`

Express the following recurring decimal as a rational number:

`3.dot5`

Express the following recurring decimals as a rational number:

`4.bar18`

Express the following recurring decimals as a rational number:

`0.3bar45`

Express the following recurring decimals as a rational number:

`3.4bar56`

If the first term of a G.P. is 16 and sum of its terms to infinity is `176/5`, find the common ratio.

Find the area of the triangle whose vertices are: (4, 5), (0, 7), (–1, 1)

Find the area of the triangle whose vertices are: (3, 2), (–1, 5), (–2, –3)

Find the area of the triangle whose vertices are: (0, 5), (0, – 5), (5, 0)

Find the value of k, if the area of the triangle with vertices at A(k, 3), B(–5, 7), C(–1, 4) is 4 square units.