PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?

\[\left\{ a, b, c \right\} \subset A\]

Let A = {a, b, {c, d}, e}. Which of the following statement are false and why? 

\[\phi \in A\]

Let A = {a, b, {c, d}, e}. Which of the following statement are false and why? 

\[\phi \in A\]

Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false: 

\[1 \in A\] 

Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false: 

\[\left\{ 1, 2, 3 \right\} \subset A\] 

Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false: 

\[\left\{ 6, 7, 8 \right\} \in A\] 

Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false: 

\[\left\{ \left\{ 4, 5 \right\} \right\} \subset A\] 

Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false: 

\[\phi \in A\] 

Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false: 

\[\phi \in A\] 

Evaluate the following:

i⁴⁵⁷

Let\[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true? 

Evaluate the following:

(ii) i⁵²⁸

Let\[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? 

Evaluate the following:

 \[\frac{1}{i^{58}}\]

Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[\left\{ 1 \right\} \in A\]

Evaluate the following:

\[i^{37} + \frac{1}{i^{67}}\].

Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true? \[\left\{ 1 \right\} \in A\]

Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[2 \subset A\]

Evaluate the following:

\[\left( i^{41} + \frac{1}{i^{257}} \right)^9\]

Evaluate the following:

\[( i^{77} + i^{70} + i^{87} + i^{414} )^3\]