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 2014. Some of the questions asked in Mathematics Paper III of UPSC SCRA Exam 2014 are as follows:

1. The function ƒ : R → R defined by ƒ(x) = (x-a)(x-b)(x-c) where a, b, c ε R, is

(a) not one-one but onto
(b) one-one but not onto
(c) both one-one and onto
(d) neither one-one not onto

2. If A = {1,2,3,4}, then which of the following is/are the function(s) from A to itself?

I. ƒ1 = {(x, y) l x+y = 5}
II. ƒ2 = {(x, y) l y < x}

Select the correct answer using the code given below.

(a) I only
(b) II only
(c) Both I and II
(d) Neither I nor II

3. If ƒ : R → be given by y = ƒ(x) = (x + 1)² – 1 then ƒ(x) is invertible if

(a) y ≥ -1
(b) -2 ≤ y < -1
(c) -3 ≤ y < -2
(d) None of the above

4. The complex numbers z satisfying z² + lzl = 0 are

(a) 0, i, -i
(b) 0, l, i, -i
(c) 0, l, -l, i, -i
(d) 0, -1

5. If the lines  x+2ay+a=0, x+3by+b=0 and x+4cy+c=0 are concurrent, then a, b, c are in

(a) HP
(b) AP
(c) GP
(d) None of the above

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