In a certain test there are n questions. In this test $$2k$$ students gave wrong answers to at least (n$$ – $$k) questions, where k $$=$$ $$0$$, $$1$$, $$2$$, …, n. If the total number of wrong answers is $$4095$$, then value of n is

Question

In a certain test there are n questions. In this test $$2k$$ students gave wrong answers to at least (n$$ – $$k) questions, where k $$=$$ $$0$$, $$1$$, $$2$$, …, n. If the total number of wrong answers is $$4095$$, then value of n is

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The number of students answering at least r questions incorrectly is $$2n$$−r∴ the number of students answering exactly $$r(1$$≤r≤n−$$1)$$ questions incorrectly is  $$2n$$−r−$$2n$$−$$(r+1)Also$$, the number of students answering all questions wrongly is $$20=1Thus$$, the total number of wrong answers $$is12n$$−$$1$$−$$2n$$−$$2+22n$$−$$2$$−$$2n$$−$$3+32n$$−$$3$$−$$2n$$−$$4+$$….....$$+(n$$−$$1)21$$−$$20+n20$$ $$=2n$$−$$1+2n$$−$$2+$$…$$+20=2n$$−$$1Now$$, $$2n$$−$$1=4095$$⇒$$2n=4096=212$$⇒$$n=12$$

In a certain test there are n questions. In this test $2^{k}$ students gave wrong answers to at least $(n - k)$ questions, where $k = 0, 1, 2, \dots, n$ . If the total number of wrong answers is $4095$ , then value of $n$ is

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In a certain test there are n questions. In this test 2k students gave wrong answers to at least (n – k) questions, where k = 0, 1, 2, …, n. If the total number of wrong answers is 4095, then value of n is

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In a certain test there are n questions. In this test $2^{k}$ students gave wrong answers to at least $(n - k)$ questions, where $k = 0, 1, 2, \dots, n$ . If the total number of wrong answers is $4095$ , then value of $n$ is