1
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Let $${E_1}$$ and $${E_2}$$ be two entities in an E-R diagram with simple single-valued attributes, $${E_1}$$ and $${E_2}$$ are two relationships between $${E_1}$$ and $${E_2}$$, Where $${E_1}$$ is one-to-many and $${E_2}$$ is many-to-many. $${E_1}$$ and $${E_2}$$ do not have any attributes of their own. What is the minimum number of tables required represent this situation in the relation model?
A
$$2$$
B
$$3$$
C
$$4$$
D
$$5$$
2
GATE CSE 2005
MCQ (Single Correct Answer)
+1
-0.3
Let $$f$$ be a function from a set $$A$$ to a set $$B$$, $$g$$ a function from $$B$$ to $$C$$, and $$h$$ a function from $$A$$ to $$C$$, such that $$h\left( a \right) = g\left( {f\left( a \right)} \right)$$ for all $$a \in A$$. Which of the following statements is always true for all such functions $$f$$ and $$g$$?
A
$$g$$ is onto $$ \Rightarrow $$ $$h$$ is onto
B
$$h$$ is onto $$ \Rightarrow $$$$f$$ is onto
C
$$h$$ is onto $$ \Rightarrow $$ $$g$$ is onto
D
$$h$$ is onto $$ \Rightarrow $$ $$f$$ and $$g$$ are onto
3
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider the following system of equations in three real variables $$x1, x2$$ and $$x3$$ :
$$2x1 - x2 + 3x3 = 1$$
$$3x1 + 2x2 + 5x3 = 2$$
$$ - x1 + 4x2 + x3 = 3$$
This system of equations has
A
no solution
B
a unique solution
C
more than one but a finite number of solutions
D
an infinite number of solutions
4
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider the set $$H$$ of all $$3$$ $$X$$ $$3$$ matrices of the type $$$\left[ {\matrix{ a & f & e \cr 0 & b & d \cr 0 & 0 & c \cr } } \right]$$$

Where $$a, b, c, d, e$$ and $$f$$ are real numbers and $$abc$$ $$ \ne \,\,0$$. Under the matrix multiplication operation, the set $$H$$ is:

A
$$a$$ group
B
$$a$$ monoid but not $$a$$ group
C
$$a$$ semigroup but not $$a$$ monoid
D
neither $$a$$ group nor $$a$$ semigroup
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