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 crores Hence, (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 > q I. ${2p^2}$ - 6p - p + 3 = 0 2p(p - 3) -1(p - 3) = 0; (2p - 1)(p- 3) = 0 p = $1\over2$,3 p > q
II.${4q^2}$+ 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 = 0 q(q - 15) - 13(q - 15) = 0 (q - 13)(q - 15) = 0 q = 13, 15
| | | 8 . | Answer : Option D | Explanation : | p ≥q I. ${p^2}$ - 3p - 2p + 6 = 0 p(p - 3) -2(p - 3) = 0 (p - 2)(p - 3) = 0; p = 2, 3 II. ${q^2}$ - 2q - q + 2 = 0 q(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 = 0 4p(p -1)+ 3(p - 1) = 0 (4p + 3) (p - 1) = 0 p = 1, $-3\over4$ II. 2${q^2}$ + 2q - q - 1 = 0 2q(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 = 0 p(p + 6) +5(p + 6) = 0 (p + 5) (p + 6) = 0 p = -5, -6 II. ${q^2}$ - 6q - 5q + 30 = 0 q(q - 6) -5(q - 6) = 0 (q - 6) (q - 5) = 0; q = 5, 6
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