A question is given followed by two statements I and II. Consider the Question and the Statements and mark the correct option.<br><br>Question : What is the integral value of k for which the expression 4x^2-kx+1 is positive ?<br><br>Statement-I : k \lt -2<br><br>Statement-II: k \gt -4<br><br>Which one of the following is correct in respect of the above Question and the Statements?
- A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone ✓
- B. The Question can be answered by using either Statement alone
- C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- D. The Question cannot be answered even by using both the Statements together
Correct Answer: A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
Explanation
For 4x^2-kx+1 \gt 0 to hold for all real x, the discriminant must be negative: k^2 - 16 \lt 0 \implies -4 \lt k \lt 4. The integers in this range are -3, -2, -1, 0, 1, 2, 3. Statement I (k \lt -2) narrows this to a unique integer k = -3. Statement II (k \gt -4) leaves multiple possibilities. Thus, Statement I alone is sufficient.
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