Question 1 :
Let $A$ $=$ set of all cuboids and B $=$ set of all cubes. Which of the following is true?

Question 3 :
Which one of the following is an example of non-empty set?

Question 5 :
Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Find the values of m and n.

Question 6 :
M represents the children in a class who have no brothers and 8 represents the children who have no sisters. $+$ denotes union, $*$ denotes intersection, and $(^\prime)$ denotes complement. The set of children who have no siblings is

Question 8 :
Which set is the subset of the set containing all the whole numbers?

Question 10 :
If A and B are two sets such that $n(A)=17, n(B)=23, n(A \cup B)=38$, find $n(A \cap B)$.

Question 11 :
<b></b>In a class of 55 students, the number of students studying different subjects are 23 in Mathematics and 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects, The number of students who have taken exactly one subject is

Question 12 :
If n is a member of both set A$=\left\{\displaystyle\frac{4}{7}, 1, \frac{5}{2}, 4, \frac{1}{2}, 7\right\}$ and set B$=\left\{\displaystyle\frac{4}{7}, \frac{7}{4}, 4, 7\right\}$, which of the following must be true?<br>I. n is an integer.<br>II. $4n$ is an integer.<br>III. $n=4$

Question 13 :
Let $A = \{2,3,5,7,8,11\}$ then which among the following is true?

Question 14 :
If $X = \left \{1, 2, 3, ..., 10\right \}$ and $A = \left \{1, 2, 3, 4, 5\right \}$. Then, the number of subsets $B$ of $X$ such that $A - B = \left \{4\right \}$ is

Question 15 :
If A={a,b,c,d,e}, B={a,c,e,g} and C={b,d,e,g} then which of the following is true?

Question 16 :
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.<br>If $x A$ and $A B$, then $x B$<br>

Question 17 :
$A = \{x | x \in I, x^2$ is not positive$\}$<br/>Then $A$ is a&#160;<br/>

Question 18 :
State whether the following statement is True or False$A=\{x| x \epsilon R, x^2=-9 \}$ is Null Set

Question 19 :
Choose the correct answer from the given four options<br>If A = {x | x is a positive multiple of 3 less than 20} and B = {x | x is a prime number less than 20}, then n(A) + n(B) is

Question 21 :
If $X=\left\{ { 4 }^{ n }-3n-1;n\in R \right\} $ and $Y=\left\{ 9\left( n-1 \right) ;n\in N \right\} $, then $X\cap Y=$

Question 22 :
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 $\underset{i = 1}{\overset{30}{\cup}} A_i = \underset{j = 1}{\overset{n}{\cup}} B_j = S$ and each element of S belongs to exactly 10 of the $A_i's$ and exactly 9 of the $B_j'S$. then n is equal to

Question 23 :
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 $\displaystyle \bigcup _{ i=1 }^{ 30 }{ { A }_{ i } } =\bigcup _{ j=1 }^{ n }{ { B }_{ j } =S}$ and each element of $S$ belongs to exactly $10$ of the ${A}_{i}s$ and exactly $9$ of the ${B}_{j}s.$ Then $n$ is equal to

Question 24 :
Suman is given an aptitude test containing 80 problems, each carrying I mark to be tackled in 60 minutes. The problems are of 2 types; the easy ones and the difficult ones. Suman can solve the easy problems in half a minute each and the difficult ones in 2 minutes each. (The two type of problems alternate in the test). Before solving a problem, Suman must spend one-fourth of a minute for reading it. What is the maximum score that Suman can get if he solves all the problems that he attempts?

Question 25 :
Consider the non-empty set consisting of children in a family and a relation $R$ defined as a $Rb$ if $a$ is brother of $b$. Then $R$ is