JAMIA 2026 — Reasoning PYQ

Step 1: Analyze the first given condition

• Inputs: $x=10$, $y=30$

• Sum of digits of $x$: $S(10)=1+0=1$

• Sum of digits of $y$: $S(30)=3+0=3$

• Multiply the two sums: $1\times 3=3$

• This matches the output: $f(10,30)=3$

Step 2: Verify with the second condition

• Inputs: $x=60$, $y=21$

• Sum of digits of $x$: $S(60)=6+0=6$

• Sum of digits of $y$: $S(21)=2+1=3$

• Multiply the two sums: $6\times 3=18$

• This matches the output: $f(60,21)=18$

Step 3: Verify with the third condition

• Inputs: $x=21$, $y=11$

• Sum of digits of $x$: $S(21)=2+1=3$

• Sum of digits of $y$: $S(11)=1+1=2$

• Multiply the two sums: $3\times 2=6$

• This matches the output: $f(21,11)=6$

Finding the Value of $f(72,12)$

Since the pattern holds true for all given examples, the general formula is:

$$f(x,y)=S(x)\times S(y)$$

Now, applying this logic to the required numbers:

• Inputs: $x=72$, $y=12$

• Sum of digits of $72$: $S(72)=7+2=9$

• Sum of digits of $12$: $S(12)=1+2=3$

Calculating the final result:

$$f(72,12)=9\times 3=27$$

Correct Answer: (b) 27