PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

The distance between the directrices of the hyperbola x = 8 sec θ, y = 8 tan θ, is

A point moves in a plane so that its distances PA and PB from two fixed points A and B in the plane satisfy the relation PA − PB = k (k ≠ 0), then the locus of P is

The length of the straight line x − 3y = 1 intercepted by the hyperbola x² − 4y² = 1 is 

If X = {a, b, c, d} and Y = {f, b, d, g}, find 

Y – X

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find A'

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find B'

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (A ∪ C)'

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (A ∪ B)'

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (A')'

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (B -C)'

If U = {a, b, c, d, e, f, g, h}, find the complements of the following set:

A = {a, b, c}

If U = {a, b, c, d, e, f, g, h}, find the complements of the following set:

B = {d, e, f, g}

If U = {a, b, c, d, e, f, g, h}, find the complements of the following set:

C = {a, c, e, g}

If U = {a, b, c, d, e, f, g, h}, find the complements of the following set:

D = {f, g, h, a}

Taking the set of natural numbers as the universal set, write down the complements of the following set:

{x : x is an even natural number}

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that (A ∪ B)' = A' ∩ B'

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that (A ∩ B)' = A' ∪ B'

Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A'?

Fill in the blank to make the following a true statement:

A ∪ A' = _____

Fill in the blank to make the following a true statement:

Φ′ ∩ A = _____