PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

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}

Find the intersection of pair 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 intersection of pair of sets:

A = {1, 2, 3}, B = Φ

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find

A ∩ B

If A = {x : x is a natural number}, B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number}, find:

A ∩ B

Let A, B and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. Show that B = C.

Show that the following four conditions are equivalent:

1. A ⊂ B
2. A – B = Φ
3. A ∪ B = B 
4. A ∩ B = A

Using properties of sets show that A ∪ (A ∩ B) = A

Show that A ∩ B = A ∩ C need not imply B = C.

Let A and B be sets. If A ∩ X = B ∩ X = Φ and A ∪ X = B ∪ X for some set X, show that A = B.

(Hints A = A ∩ (A ∪ X), B = B ∩ (B ∪ X) and use distributive law)