JAMIA 2026 — Computer PYQ

1. Find possible values of $X$:

$X$ is a 3-digit binary number with two $1$s and one $0$ (leading digit cannot be $0$).

• $110_2=1\times 2^2+1\times 2^1+0\times 2^0=4+2+0=6$

• $101_2=1\times 2^2+0\times 2^1+1\times 2^0=4+0+1=5$

So, Decimal value of $X=5$ or $6$.

2. Check the options for $(Y{)}_s$:

Since all options start with $1$, let $Y=1d_0$ in base $s$.

$$\text{Decimal Value}=1\times s^1+d_0\times s^0=s+d_0$$

(Condition: Digits must be strictly less than the base $s$)

• Option (a) 10: $Y=10⟹d_0=0⟹\text{Value}=s+0=s$

  • If $\text{Value}=5⟹s=5$ (Valid, since digits 1, 0 < 5)

  • If $\text{Value}=6⟹s=6$ (Valid, since digits 1, 0 < 6)

• Option (b) 12: $Y=12⟹d_0=2⟹\text{Value}=s+2$

  • If $\text{Value}=5⟹s+2=5⟹s=3$ (Valid, since digits 1, 2 < 3)

• Option (c) 13: $Y=13⟹d_0=3⟹\text{Value}=s+3$

  • If $\text{Value}=5⟹s=2$ (Invalid, digit $3$ cannot exist in base $2$)

  • If $\text{Value}=6⟹s=3$ (Invalid, digit $3$ cannot exist in base $3$)

• Option (d) 14: $Y=14⟹d_0=4⟹\text{Value}=s+4$

  • If $\text{Value}=6⟹s=2$ (Invalid, digit $4$ cannot exist in base $2$)

Correct Answer

Option (a) 10 (or b) are mathematically valid. In standard exams, (a) is preferred as $(5{)}_{10}=(10{)}_5$ and $(6{)}_{10}=(10{)}_6$.