PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

Describe the following sets in set-builder form: 

{1, 4, 9, 16, ..., 100} 

Describe the following sets in set-builder form: 

{2, 4, 6, 8 .....}

Describe the following sets in set-builder form: 

{5, 25, 125 625} 

List all the elements of the following sets: 

\[A = \left\{ x: x^2 \leq 10, x \in Z \right\}\] 

List all the elements of the following set: 

\[B = \left\{ x: x = \frac{1}{2n - 1}, 1 \leq n \leq 5 \right\}\]

List all the elements of the following set: 

\[C = \left\{ x: x \text{ is an integer }, - \frac{1}{2} < x < \frac{9}{2} \right\}\]

List all the elements of the following set: 

D = {x : x is a vowel in the word "EQUATION"}

List all the elements of the following set:

F = {x : x is a letter of the word "MISSISSIPPI"}

If A = [1, 2, 3], B = [4, 5, 6], which of the following are relations from A to B? Give reasons in support of your answer.

(i) [(1, 6), (3, 4), (5, 2)]
(ii) [(1, 5), (2, 6), (3, 4), (3, 6)]
(iii) [(4, 2), (4, 3), (5, 1)]
(iv) A × B.

Match each of the sets on the left in the roster form with the same set on the right described in the set-builder form: 

Find the inverse relation R⁻¹ in each of the cases:

(i) R = {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}

Find the inverse relation R⁻¹ in each of the cases:

(ii) R = {(x, y), : x, y ∈ N, x + 2y = 8}

Find the inverse relation R⁻¹ in each of the cases:

Write the set of all vowels in the English alphabet which precede q.

Write the set of all positive integers whose cube is odd.

Write the set \[\left\{ \frac{1}{2}, \frac{2}{5}, \frac{3}{10}, \frac{4}{17}, \frac{5}{26}, \frac{6}{37}, \frac{7}{50} \right\}\]  in the set-builder form.

Let A = (3, 5) and B = (7, 11). Let R = {(a, b) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.

Determine the domain and range of the relation R defined by

(i) R = [(x, x + 5): x ∈ (0, 1, 2, 3, 4, 5)]

Determine the domain and range of the relation R defined by