PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

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 \[\sqrt{\frac{2}{5}}\]

Find the equation of the ellipse in the case:

eccentricity e = \[\frac{1}{2}\] and foci (± 2, 0)

Find the equation of the ellipse in the case:

 eccentricity e = \[\frac{2}{3}\] and length of latus rectum = 5

Find the equation of the ellipse in the case: 

 eccentricity e = \[\frac{1}{2}\]  and semi-major axis = 4

Find the equation of the ellipse in the case:

eccentricity e = \[\frac{1}{2}\]  and major axis = 12

Find the equation of the ellipse in the case:

 The ellipse passes through (1, 4) and (−6, 1).

Find the equation of the ellipse in the case:

 Vertices (± 5, 0), foci (± 4, 0)

Find the equation of the ellipse in the case:

Vertices (0, ± 13), foci (0, ± 5)

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

A ∪ C

Find the intersection of pair of sets:

X = {1, 3, 5}, Y = {1, 2, 3}

Find the intersection of pair of sets:

A = {a, e, i, o, u}, B = {a, b, c}

Find the intersection of pair of sets:

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

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