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

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