1
GATE CSE 2003
+1
-0.3
$$A$$ system of equations represented by $$AX=0$$ where $$X$$ is a column vector of unknown and $$A$$ is a square matrix containing coefficients has a non-trival solution when $$A$$ is.
A
non-singular
B
singular
C
symmetric
D
Hermitian
2
GATE CSE 2003
+1
-0.3
$$\mathop {Lim}\limits_{x \to 0} \,{{Si{n^2}x} \over x} = \_\_\_\_.$$
A
$$0$$
B
$$\infty$$
C
$$1$$
D
$$-1$$
3
GATE CSE 2003
+2
-0.6
A uni-processor computer system only has two processes, both of which alternate $$10$$ $$ms$$ $$CPU$$ bursts with $$90$$ $$ms$$ $${\rm I}/O$$ bursts. Both the processes were created at nearly the same time. The $${\rm I}/O$$ of both processes can proceed in parallel. Which of the following scheduling strategies will result in the least $$CPU$$ utilization (over a long period of time) for this system?
A
First come First served scheduling
B
Shortest remaining time first scheduling
C
Static priority scheduling with different priorities for the two processes
D
Round robin scheduling with a time quantum of $$5$$ $$ms.$$
4
GATE CSE 2003
+2
-0.6
Suppose we want to synchronize two concurrent processes P and Q using binary semaphores S and T. The code for the processes P and Q is shown below.

Process P:

while(1){
W:
Print '0';
Print '0';
X:
}


Process Q:

while(1){
Y:
Print '1';
Print '1';
Z:
}

Synchronization statements can be inserted only at points W, X, Y, and Z.

Which of the following will always lead to an output starting with 001100110011

A
P(A) at W, V(S) at X, P(T) at Y, V(T) at Z, S and T initially 1
B
P(A) at W, V(T) at X, P(T) at Y, V(S) at Z, S initially 1 and T initially 0
C
P(S) at W, V(T) at X, P(T) at Y,V(T) at Z, S and T initially 1
D
P(S) at W, V(S) at X, P(T) at Y, V(T) at Z, S initially 1 and T initially 0
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