PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions

State whether the following statements are true or false: 

\[a \subset {b, c, a}\] 

State whether the following statements are true or false: 

\[\left\{ a \right\} \in \left\{ a, b, c \right\}\]

State whether the following statements are true or false: 

\[\left\{ a, b \right\} = \left\{ a, a, b, b, a \right\}\] 

State whether the following statements are true or false:

The set {x ; x + 8 = 8} is the null set. 

Decide among the following sets, which are subsets of which:

\[A = {x : x \text{ satisfies } x^2 - 8x + 12 = 0},\]

\[B = \left\{ 2, 4, 6 \right\}, C = \left\{ 2, 4, 6, 8, . . . \right\}, D = \left\{ 6 \right\} .\]

Write which of the following statements are true? Justify your answer. 

The set of all integers is contained in the set of all set of all rational numbers. 

Write which of the following statement are true? Justify your answer. 

The set of all crows is contained in the set of all birds. 

Write which of the following statement are true? Justify your answer. 

 The set of all rectangle is contained in the set of all squares.

Write which of the following statement are true? Justify your answer.

 The set of all real numbers is contained in the set of all complex numbers.

Write which of the following statement are true? Justify your answer.

The sets P = {a} and B = {{a}} are equal.

Write which of the following statement are true? Justify your answer. 

The sets A = {x : x is a letter of the word "LITTLE"} and,B = {x : x is a letter of the word "TITLE"} are equal. 

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

\[a \subset A\]

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

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

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?\[\left\{ 2 \left\{ 1 \right\} \right\} \not\subset A\] 

Write down all possible subsets of each of the following set:

\[\left\{ \phi \right\}\]

Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then, the values of m and n are: 

In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone? 

Suppose \[A_1 , A_2 , . . . , A_{30}\] are thirty sets each having 5 elements and \[B_1 , B_2 , . . . , B_n\] are n sets each with 3 elements. Let \[\cup^{30}_{i = 1} A_i = \cup^n_{j = 1} B_j = S\] and each element of S belong to exactly 10 of the \[A_i 's\]and exactly 9 of the\[B_j 's\] then n is equal to 

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of m and n are respectively