2024 · Q61
A question is given followed by two statements I and II. Consider the Question and the Statements and mark the correct option. Question : What is the integral value of k for which the expression 4x² - kx + 1 is positive?
Statement Ik < −2
Statement IIk > -4 Which one of the following is correct in respect of the above Question and the Statements?
Elementary MathematicsAlgebra
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question cannot be answered even by using both the Statements together
Explanation
4x²−kx+1 > 0 for all x needs discriminant k²−16 < 0, i.e. −4 < k < 4, so integral k ∈ {−3,…3}. Statement I (k < −2) then pins k = −3 uniquely, while Statement II (k > −4) leaves seven possibilities. So the question is answerable with statement I alone but not statement II alone — option A. Note: this key is disputed — verify against the official UPSC key.