UPSC Conducts Special Class Railway Apprentices (SCRA) Examination for selection of candidates to be appointed as Special Class Railway Apprentices in Mechanical Department of Indian Railways. Candidates who are preparing for the UPSC SCRA Exam in the forthcoming year can find out what kind of questions were asked in this exam in the year 2013. Some of the questions asked in Mathematics Paper III of UPSC SCRA Exam 2013 are as follows:

1. If A = {1, 2, 3} and B = {1, 2} and C = {4, 5, 6}, then what is the number of elements in the set A x B x C ?

(a) 8
(b) 9
(c) 15
(d) 18

2. There are unlimited number of identical balls of four different colours. How many arrangements of at most 6 balls can be made by using them? [to be arranged in a single row only]

(a) 1365
(b) 2730
(c) 5460
(d) None of the above

3. Let Z be the set of integers and ‘0’ be a binary operation of Z defined by a 0 b = a + b – ab for all a, b ε Z. What is the inverse of an element a (≠ 1) ε Z?

(a) a/(a – 1)
(b) a/(1 – a)
(c) (a – 1)/a
(d) None of the above

4. If x² – x  + 1 = 0, then what is the value of

(a) 8
(b) 10
(c) 12
(d) None of the above

5. If (x + 1) (x + 2) (x + 3) (x + 6) = 3x², then the equation has

(a) all imaginary roots
(b) all real roots
(c) two rational and two irrational roots
(d) two imaginary and two irrational roots

Click here to go through full question paper on official website of UPSC.

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