1
GATE CSE 2000
MCQ (Single Correct Answer)
+1
-0.3
The determinant of the matrix $$$\left[ {\matrix{ 2 & 0 & 0 & 0 \cr 8 & 1 & 7 & 2 \cr 2 & 0 & 2 & 0 \cr 9 & 0 & 6 & 1 \cr } } \right]\,\,is$$$
A
4
B
0
C
15
D
20
2
GATE CSE 2000
MCQ (Single Correct Answer)
+1
-0.3
An $$n\,\, \times \,\,n$$ array v is defined as follows v[i, j] = i - j for all i, j, $$1\,\, \le \,\,i\,\, \le \,\,n,\,1\,\, \le \,\,j\,\, \le \,\,n$$ The sum of elements of the array v is
A
0
B
n - 1
C
$${n^2}\, - \,3n\, + \,2$$
D
$${n^2}\,(n\, + \,1)/2$$
3
GATE CSE 2000
Subjective
+5
-0
A multiset is an unordered collection of elements where elements may repeat ay number of times. The size of a multiset is the number of elements in it counting repetitions.

(a) what is the number of multisets of size 4 that can be constructed from n distinct elements so that at least one element occurs exactly twice?
(b) How many multisets can be constructed from n distinct elements?

4
GATE CSE 2000
Subjective
+5
-0
Let $$S = \left\{ {0,1,2,3,4,5,6,7} \right\}$$ and $$ \otimes $$ denote multiplication modulo $$8$$, that is, $$x \otimes y = \left( {xy} \right)$$ mod $$8$$

(a) Prove that $$\left( {0,\,1,\, \otimes } \right)$$ is not a group.
(b) Write $$3$$ distinct groups $$\left( {G,\,\, \otimes } \right)$$ where $$G \subset s$$ and $$G$$ has $$2$$ $$\,\,\,\,\,\,$$elements.

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