यदि (A) में (7) तत्व हैं, तो (\mathcal{P}(A)) में विषम संख्या के तत्वों वाले subsets कितने हैं?
If (A) has (7) elements, how many subsets in (\mathcal{P}(A)) have an odd number of elements?
Explanation opens after your attempt
Correct Answer
B. (64)
Concept
For an (n)-element set, the number of odd subsets is \(2^{n-1}\), so \(2^6=64\). In exams, even and odd subsets are equal in number.
Why this answer is correct
The correct answer is B. (64). For an (n)-element set, the number of odd subsets is \(2^{n-1}\), so \(2^6=64\). In exams, even and odd subsets are equal in number.
Exam Tip
किसी (n)-तत्वीय समुच्चय में odd subsets की संख्या \(2^{n-1}\) होती है, अतः \(2^6=64\)। परीक्षा में even और odd subsets बराबर होते हैं।
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