1
GATE CSE 2022
Numerical
+1
-0.33

The number of arrangements of six identical balls in three identical bins is ___________.

Your input ____
2
GATE CSE 2022
Numerical
+1
-0.33

The value of the following limit is _____________.

$$\mathop {\lim }\limits_{x \to {0^ + }} {{\sqrt x } \over {1 - {e^{2\sqrt x }}}}$$

Your input ____
3
GATE CSE 2022
MCQ (Single Correct Answer)
+1
-0.33

Which one of the following is the closed form for the generating function of the sequence (an}n $$\ge$$ 0 defined below?

$${a_n} = \left\{ {\matrix{ {n + 1,} & {n\,is\,odd} \cr {1,} & {otherwise} \cr } } \right.$$

A
$${{x(1 + {x^2})} \over {{{(1 - {x^2})}^2}}} + {1 \over {1 - x}}$$
B
$${{x(3 - {x^2})} \over {{{(1 - {x^2})}^2}}} + {1 \over {1 - x}}$$
C
$${{2x} \over {{{(1 - {x^2})}^2}}} + {1 \over {1 - x}}$$
D
$${x \over {{{(1 - {x^2})}^2}}} + {1 \over {1 - x}}$$
4
GATE CSE 2022
MCQ (Single Correct Answer)
+1
-0.33

Consider a simple undirected unweighted graph with at least three vertices. If A is the adjacency matrix of the graph, then the number of 3-cycles in the graph is given by the trace of

A
A3
B
A3 divided by 2
C
A3 divided by 3
D
A3 divided by 6
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