JAMIA 2026 — Mathematics PYQ

Definition of a Polynomial:

An algebraic expression is considered a polynomial if all the powers (exponents) of its variable(s) are non-negative integers (i.e., whole numbers like $0,1,2,3,\dots$).

If an expression contains a variable with a fractional exponent, a negative exponent, or a variable inside a radical sign (like a square root), it is not a polynomial. Note that constants or coefficients can be fractional or irrational ($\sqrt{2},\sqrt{7}$, etc.); the rule only applies strictly to the exponents of the variable $x$.

Let's evaluate each option based on this rule:

• Option (a): $x^2+\sqrt{7}x$

  • The exponents of the variable $x$ are $2$ and $1$. Both are non-negative integers. The square root is only on the constant coefficient ($\sqrt{7}$).

  • Result: It is a polynomial.

• Option (b): $\sqrt{x}+5x$

  • We can rewrite the term $\sqrt{x}$ as $x^{\frac{1}{2}}$.

  • The expression becomes: $x^{\frac{1}{2}}+5x^1$.

  • Here, the exponent of the first term is $\frac{1}{2}$, which is a fraction and not an integer.

  • Result: It is NOT a polynomial.

• Option (c): $x^2+3x+\sqrt{7}$

  • The exponents of $x$ are $2$ and $1$. The constant term is $\sqrt{7}$.

  • Result: It is a polynomial.

• Option (d): $x^2+\sqrt{3}x+\sqrt{7}$

  • The exponents of $x$ are $2$ and $1$. The square roots are only on the coefficients ($\sqrt{3}$ and $\sqrt{7}$).

  • Result: It is a polynomial.

Correct Answer

The correct option is (b) $\sqrt{x}+5x$.