Question
Download Solution PDFयदि , और z=(110)2, तो 3−y3−z3−3xyz किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFगणना:
x, y, और z को द्विआधारी से दशमलव में बदलें:
⇒ x = (1111)2 = \(1\cdot2^{3}+1\cdot2^{2}+1\cdot2^{1}+1\cdot2^{0}=15\)
⇒ y = (1001)2 = \(1\cdot2^{3}+0\cdot2^{2}+0\cdot2^{1}+1\cdot2^{0}=9\)
⇒ z = (110)2 = \(1\cdot2^{2}+1\cdot2^{1}+0\cdot2^{0}=6\)
अब \(x^{3}-y^{3}-z^{3}-3xyz \) का मान ज्ञात करें
\(15^{3}-9^{3}-6^{3}-3\!\times\!15\!\times\!9\!\times\!6 = 3375-729-216-2430 = 0\)
व्यंजक का परिणाम 0 है। द्विआधारी में, 0 केवल (0)2 है।
इसलिए, सही उत्तर विकल्प 4 है।
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