NIMCET 2007 — Computer PYQ

Step 1: Construct the Matrix

The problem states that we have a $3\times 3$ matrix $A$ filled with consecutive integers row-wise starting from $0$ (i.e., $\{0,1,2,\dots \}$).

Since indices $i$ and $j$ run from $1$ to $3$, the elements of the matrix $A$ are arranged as follows:

$$A=\left(\begin{array}{ccc}{A}_{11}& amp;A_{12}& amp;A_{13}\\ A_{21}& amp;A_{22}& amp;A_{23}\\ A_{31}& amp;A_{32}& amp;A_{33}\end{array}\right)=\left(\begin{array}{ccc}0& amp;1& amp;2\\ 3& amp;4& amp;5\\ 6& amp;7& amp;8\end{array}\right)$$

Step 2: Understand the Condition

The inner loop checks the condition:

$$i+j=4$$

If this condition is met, the variable $t$ is updated using the formula:

$$t=5+A_{ij}$$

Let's find all pairs of $(i,j)$ where $i$ and $j$ range from $1$ to $3$ that satisfy $i+j=4$:

• For $i=1$: $j=3⟹1+3=4$

• For $i=2$: $j=2⟹2+2=4$

• For $i=3$: $j=1⟹3+1=4$

These elements represent the anti-diagonal (secondary diagonal) of the matrix.

Step 3: Trace the Loop Execution

Initially, $t=0$.

1. When $i=1,j=3$:

   • Condition $1+3=4$ is true.

   • Matrix element $A_{13}=2$.

   • Update $t$:

     $$t=5+A_{13}=5+2=7$$

2. When $i=2,j=2$:

   • Condition $2+2=4$ is true.

   • Matrix element $A_{22}=4$.

   • Update $t$:

     $$t=5+A_{22}=5+4=9$$

3. When $i=3,j=1$:

   • Condition $3+1=4$ is true.

   • Matrix element $A_{31}=6$.

   • Update $t$:

     $$t=5+A_{31}=5+6=11$$

For all other combinations of $i$ and $j$, the condition $i+j=4$ is false, so the value of $t$ remains unchanged.

Conclusion

The final value of $t$ output by the instructions is 11.

Correct Answer: (c) 11