UGC NET Questions (Paper – 1)

Statements A, C and E are correct: surds are indeed irrational roots, rationalising eliminates surds from denominators and simple index laws such as a⁰ = 1 are frequently used to simplify expressions in aptitude questions. Statement B is false because the rule √a × √b = √(ab) holds only when a and b are non-negative, not for all real numbers. Statement D is also false as the correct product rule is aᵐ × aⁿ = aᵐ⁺ⁿ, not aᵐ⁻ⁿ. Thus, the combination consisting of A, C and E only is correct.

Option A:
Option A is incomplete since it omits E and therefore does not mention how index laws are applied in practice to simplify complex expressions in exam questions. Without E, the connection to aptitude simplification is weaker.

Option B:
Option B is wrong because it includes D, which misstates the product law for exponents, and leaves out E, so it both accepts a wrong algebraic rule and omits a true practical fact. This combination cannot be correct.

Option C:
Option C is correct as it contains exactly those statements that align with standard definitions and simplification techniques while excluding B and D, both of which misapply or overgeneralise algebraic rules. It provides the right conceptual picture for NET-level problems.

Option D:
Option D is incorrect because it includes B, which fails to note that the square-root product rule requires non-negative radicands, and it omits E, again ignoring the exam relevance of simple index laws. This mixture makes the option unsatisfactory.