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 = 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