## Wednesday, 17 May 2017

1 .

 A.   16 : 17 B.   17 : 16 C.   23 : 21 D.   21 : 23
2 . 2.What is the approximate per cent increase in the number of ball bearings manufactured by Company P in the year 2013, from the previous year?

 A.   143% B.   157% C.   122% D.   59%
3 . 3.What is the average number of ball bearings manufactured by all companies together in the year 2009?

 A.   3360000 B.   336000000 C.   3360000000 D.   None of these
4 . 4. The number of ball bearings manufactured by Company Q in the year 2009 is approximately what per cent of the total number of ball bearings manufactured by it in all the years together?

 A.   24% B.   32% C.   11% D.   17%
5 . 5. How many more ball bearings need to be manufactured by Company S in the year 2013 to make the ratio of the number of ball bearings manufactured by Company S to that of those manufactured by Company U in the year 2013 as 54 : 83?

 A.   80000000 B.   2500000 C.   34000000 D.   5000000
6 . Directions (Q. 6-10): In each of the following questions two equations are given. You have to solve them and give answer as:

I. ${2p^2}$ - 7p + 3 = 0

II. ${4q^2}$ + 3q - 1= 0

 A.   if p < q B.   if p > q C.   if p ≤q D.   if p = q or no relation can be established
7 . I. ${2p^2}$ - 169 = 0

II.${q^2}$ - 289 + 195 = 0

 A.   if p < q B.   if p > q C.   if p ≤ q D.   if p = q or no relation can be established
8 . I.${p^2}$-5p+6=0
II. q${q^2}$ - 3q + 2 = 0

 A.   if p < q B.   if p > q C.   if p ≤ q D.   if p ≥ q
9 . I. 4${p^2}$ - p - 3 = 0
II. 2${q^2}$ + q - 1 = 0

 A.   if p < q B.   if p > q C.   if p ≥ q D.   if p = q or no relation can be established
10 . I. ${p^2}$ + 11p + 30 = 0

II. ${q^2}$- 11q + 30 = 0

 A.   if p < q B.   if p > q C.   if p ≥q D.   if p = q or no relation can be established
1 .
 Answer : Option B Explanation : The required ratio=$32\over30.4$=$323\over304$=$17\over16$=17:16
2 .
 Answer : Option A Explanation : The required percent increase=$53.0-21.8\over21.8$x100≈143%
3 .
 Answer : Option B Explanation : The required average (in crores)=$36.6+18.1+38.7+43.6+24.1+40.5\over6$=$201.6\over6$= 33.6 crores = 33,60,00,000
4 .
 Answer : Option D Explanation : The required per cent $36.5\over51.6+36.5+43.5+18.1+23.5+35.35.7$x100=$36.5X100\over208.9$≈17.4%
5 .
 Answer : Option D Explanation : To get the ratio (as mentioned in the question part) the total production of the company S in 2013 needs to be=$41.5\over83$x54=27 croresHence, (27 cr - 26.5 cr =) 0.5 crore more ball bearings need to be manufactured by the company S in the year 2013.
6 .
 Answer : Option B Explanation : p > qI. ${2p^2}$ - 6p - p + 3 = 02p(p - 3) -1(p - 3) = 0; (2p - 1)(p- 3) = 0p = $1\over2$,3p > qII.${4q^2}$+ 4q - q - 1 = 0; 4q(q + 1) -1(q + 1) = 0(4q - 1)(q + 1) = 0;q = $1\over4$,-1
7 .
 Answer : Option C Explanation : I. p ≤q; ${2p^2}$ = 169p = ± 13  ;II. q${2q^2}$ - 15q - 13q + 195 = 0q(q - 15) - 13(q - 15) = 0(q - 13)(q - 15) = 0q = 13, 15
8 .
 Answer : Option D Explanation : p ≥qI. ${p^2}$ - 3p - 2p + 6 = 0p(p - 3) -2(p - 3) = 0(p - 2)(p - 3) = 0;p = 2, 3II. ${q^2}$ - 2q - q + 2 = 0q(q - 2) -1(q - 2) = 0(q - 1)(q - 2) = 0q = 1, 2
9 .
 Answer : Option D Explanation : I. 4${p^2}$ - 4p + 3p - 3 = 04p(p -1)+ 3(p - 1) = 0(4p + 3) (p - 1) = 0p = 1, $-3\over4$ II. 2${q^2}$ + 2q - q - 1 = 02q(q + 1) -1(q + 1) = 0(q + 1)(2q - 1) = 0;q = $1\over2$,-1
10 .
 Answer : Option A Explanation : p < q${p^2}$ + 6p + 5p + 30 = 0p(p + 6) +5(p + 6) = 0(p + 5) (p + 6) = 0p = -5, -6II. ${q^2}$ - 6q - 5q + 30 = 0q(q - 6) -5(q - 6) = 0(q - 6) (q - 5) = 0;q = 5, 6