TANCET 2025 Solved Papers

Concept:A data-sufficiency statement is sufficient only when it gives a unique value of the required unknown. Use the given relation $y=3x^2-4x+2$ and check each statement separately.Explanation:Statement (1): $3x^2-4x+2=0$. Its discriminant is $b^2-4ac=(-4)^2-4(3)(2)=-8$. Since the discriminant is negative, the equation has no real root. So it does not give a unique value of $x$. Hence Statement (1) alone is not sufficient.Statement (2): $3x-4=0$ directly gives $x=\frac{4}{3}$. This is a unique value. Substituting it in $y=3x^2-4x+2$ gives $y=3\left(\frac{4}{3}\right)^2-4\left(\frac{4}{3}\right)+2=2$. So Statement (2) alone is sufficient.Answer:Option B: Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.