व्यंजक को सर्वनिष्ठ प्रसामान्य समघात और सम्मिलन प्रसामान्य समघात के रूप में लिखिए।
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प्रारम्भिक प्रतिबंधों के साथ, पुनरावृत्ति संबंध
का जनक फलन ज्ञात कीजिए।
सर्वसमिका
को जनक फलनों के प्रयोग से हल कीजिए।
Which of the following statements are true and which are false? Give reasons for your answer.
(i) ‘x2 + y2 - 3 is not divisible by 4.’ is a mathematical statement.
(ii) The number of onto functions from to
is 4!S64.
(iii) The generating function associated with a sequence can never be a polynomial.
(iv) .
(v) Selection sort is faster than insertion sort in worst case.
(vi) , where n is a power of 2, is a linear recurrence relation.
(vii) The generating function of the sequence is (1 - z)-2.
(viii) If g(x) is the generating function for , then (1 - x)g(x) is the generating function for the sequence
where
.
(ix) The number of partitions of 10 with no part larger than 5 is Q105.
(x) The number of integer solutions of the equation in positive integers is
.
How many numbers form 0 to 999 (0 and 999 inclusive) are not divisible by 7 or 11?
अचर गुणांकों वाले एक रैखिक समघात पुनरावृत्ति संबंध का व्यापक हल ज्ञात कीजिए जिसके अभिलक्षणिक मूल 4, -2 और 3 हैं, और बहुकताएँ क्रमशः 2, 1, और 3 हैं। संबंध का एक असमघात भाग भी है जो 3n और 4n का एकघात संचय है।
Compute the time complexity of the merge sort algorithm.
For any natural numbers n and k, prove that .