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

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 = _____

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

A ∩ A' = _____

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

U' ∩ A = _____

Find the centre, eccentricity, foci and directrice of the hyperbola .

16x² − 9y² + 32x + 36y − 164 = 0

Find the centre, eccentricity, foci and directrice of the hyperbola.

 x² − y² + 4x = 0

Find the centre, eccentricity, foci and directrice of the hyperbola .

x² − 3y² − 2x = 8.

Find the eccentricity of the hyperbola, the length of whose conjugate axis is \[\frac{3}{4}\] of the length of transverse axis.

If the distance between the foci of a hyperbola is 16 and its ecentricity is \[\sqrt{2}\],then obtain its equation.

Write the coordinates of the foci of the hyperbola 9x² − 16y² = 144.

Write the equation of the hyperbola of eccentricity \[\sqrt{2}\],  if it is known that the distance between its foci is 16.

If the foci of the ellipse \[\frac{x^2}{16} + \frac{y^2}{b^2} = 1\] and the hyperbola \[\frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25}\] coincide, write the value of b².