5 votes
2 answers
121
Let $S$ be the set $\{1,2,3, \dots ,8\}$. Let $n$ be the number of sets of two non-empty disjoint subsets of $S$. The value of $n$ is _______.
5 votes
1 answer
122
Total number of ways we can fill a $4 \times 4$ matrix by $0$ and $1$’s such that every row and column contains odd no of $0$'s and $1$'s is ________.
2 votes
1 answer
123
What is the solution of the following recurrence relation? $a_n = 6.a_{n-1} - 9.a_{n-2}$ Base cases : $a_0 = 1$ and $a_1 = 6$.$3n$$2.3n$$3n + n.3n$$3n - n.3n$
2 votes
2 answers
124
3 votes
1 answer
125
$O(G) = 12$ and $G$ is cyclic. The total number of generators possible in $G$ are __________.
8 votes
3 answers
126
See the above table of a,b,c,d. The total number of subgroups possible from the above diagram are _______.
2 votes
1 answer
127
5 votes
3 answers
128
$U = \{1,2,3,4,5 \}$ and $A$ and $B$ are two subsets. If $n(A \cap B) = 2$ and $A \neq B$ then, total number of ordered pairs $(A,B)$ possible are _________ (where $n(A...
1 votes
2 answers
129
Which one of the following is a Partial Order Relation ?Refer the Partial Order Diagram above.b and ca and ba and cc only
2 votes
3 answers
131
An equivalent relation $R$ has three equivalent classes of sizes $5,6,7$. The cardinality of $R$, therefore, is ______.
2 votes
2 answers
133
The total number of pairs of positive integers possible for $p, \:q$ to satisfy $( 1/p + 4/q = 1/12)$ is _________ (where $q$ is any odd integer less than $60$).
1 votes
1 answer
134
$\forall \: x \: \exists \: y \: [ x + y = 2 \wedge 2x - y = 1 ]$. Truth value of this statement is :TFBoth T and FNeither T nor F
2 votes
1 answer
135
The diameter of a pipe is assumed to be a continuous random variable with density function $f(x) = 6x(1+x)/5$, where $x$ is between $0$ and $1$. The mean of the pipe is _...
2 votes
2 answers
137
1 votes
2 answers
139
The total number of functions from the set $\{1,2,3,4, \dots ,10\}$ to the set $\{0,1\}$ that assign $1$ to exactly one of the positive integers less than $10$ are ______...
5 votes
2 answers
140
$3x + y + z + w = 14$The number of non negative integral solutions possible is _______.