JAMIA 2026 — Mathematics PYQ

Given the equation:

$${}^7{C}_x{=}^7{C}_{x-1}$$

Here, $n=7$, $a=x$, and $b=x-1$.

• Case 1: $a=b$

  $$x=x-1$$

  $$0=-1$$

  (This is impossible, so we reject this case).

• Case 2: $a+b=n$

  $$x+(x-1)=7$$

  $$2x-1=7$$

  $$2x=7+1$$

  $$2x=8$$

  $$x=\frac{8}{2}$$

  $$x=4$$

Conclusion

The value of $x$ is $4$.

Therefore, the correct option is (d).