1995 General Studies, all questions

UPSC Prelims 1995 · General Studies

Question 137: Basic Numeracy

The value of (a – m)(b – m) … (y – m)(z – m) is

am26 + am25 + abm24 + … + a.b.c … z
bm26 – am25 + abm24 + … – a.b.c … z
c0
dIndeterminate

AnswerThe answer is (c).

The product runs through all 26 letters from a to z, and m is one of them. So one factor is (m - m) = 0, which makes the whole product zero whatever the other letters are. The expansions in options (a) and (b) belong to a product that has no such factor. Remember: any product containing a zero factor is zero.

Why each option is right or wrong
  • (a) Not the expansion here; a zero factor kills the product.
  • (b) Same: the expansion ignores the zero factor (m - m).
  • (c) Right: 0.
  • (d) The value is determinate: it is zero.

Explanation: written by UPSC Grade, not by UPSC.

Practise this paper timedPrevious questionNext question

Source: UPSC, Civil Services (Preliminary) Examination 1995, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.