PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

Find the union of the following pairs of sets:

A = {x : x is a natural number and multiple of 3}

B = {x : x is a natural number less than 6}

Find the union of the following pairs of sets:

A = {x : x is a natural number and 1 < x ≤ 6}

B = {x : x is a natural number and 6 < x < 10}

Find the union of the following pairs of sets:

A = {1, 2, 3}, B = Φ

Let A = {a, b}, B = {a, b, c}. Is A ⊂ B? What is A ∪ B?

If A and B are two sets such that A ⊂ B, then what is A ∪ B?

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

A ∪ B

Show that for any sets A and B, A = (A ∩ B) ∪ (A – B) and A ∪ (B – A) = (A ∪ B)

We have to find the smallest set A such that\[A \cup \left\{ 1, 2 \right\} = \left\{ 1, 2, 3, 5, 9 \right\}\] 

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identities: 

\[A \cup \left( B \cap C \right) = \left( A \cup B \right) \cap \left( A \cup C \right)\]

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identitie:

\[A \cap \left( B \cup C \right) = \left( A \cap B \right) \cup \left( A \cap C \right)\]

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identitie:

\[A \cap \left( B - C \right) = \left( A \cap B \right) - \left( A \cap C \right)\]

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identitie: 

\[A - \left( B \cup C \right) = A\left( A - B \right) \cap \left( A - C \right)\] 

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identitie: 

\[A - \left( B \cap C \right) = \left( A - B \right) \cup \left( A - C \right)\] 

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identitie:

\[A \cap \left( B ∆ C \right) = \left( A \cap B \right) ∆ \left( A \cap C \right)\]

Find the equation of the ellipse in the case: 

 focus is (0, 1), directrix is x + y = 0 and e = \[\frac{1}{2}\] .

Find the equation of the ellipse in the case: 

 focus is (−1, 1), directrix is x − y + 3 = 0 and e = \[\frac{1}{2}\]

Find the equation of the ellipse in the case: 

focus is (−2, 3), directrix is 2x + 3y + 4 = 0 and e = \[\frac{4}{5}\]

Find the equation of the ellipse in the case: 

 focus is (1, 2), directrix is 3x + 4y − 5 = 0 and e = \[\frac{1}{2}\]

Find the equation to the ellipse (referred to its axes as the axes of x and y respectively) which passes through the point (−3, 1) and has eccentricity \[\sqrt{\frac{2}{5}}\]