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

Infinity Learn · Accepted Answer

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 $$20$$ $$=$$ $$1$$.Thus, 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,…, n. If the total number of wrong answers is 4095, then value of n is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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,…, n. If the total number of wrong answers is 4095, then value of n is