Quantitative Aptitude Practice Paper for State Public Service Commission (PCS) Competitive Exams includes 26 Objective questions with answers .

**Ques.** Ratio of the earnings of A and B is 4 : 7. If the earnings of A increase by 50% and those of B decrease by 25%, the new ratio of their earnings becomes 8 : 7. What are A’s earnings?

(a) Rs. 25,000

(b) Rs. 26,000

(c) Rs. 29,000

(d) Rs. 24,000

**Ques.** 400 mts long train crosses a pole in half a minute. What is its speed?

(a) 102 kmph

(b) 48 kmph

(c) 96 kmph

(d) None of these

**Ques.** Two pipes A and B can separately fill a tank in 12 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start, pipe A is turned off. How much time will it take to fill the tank?

(a) 11 min

(b) 12 min

(c) 6 min

(d) 8 min

**Ques.** The sum of all 4 digit numbers that can be formed by using the digits 2, 4, 6, 8 (repetition of digits not allowed) is

(a) 133320

(b) 533280

(c) 53328

(d) None of these

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**Ques.** The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 is

(a) y – x + 1 = 0

(b) y – x – 1 = 0

(c) y – x + 2 = 0

(d) y – x – 2 = 0

**Ques.** 10 men and 15 women finish a work in 6 days. One man alone finishes that work in 100 days. In how many days will a woman finish the work?

(a) 125 days

(b) 150 days

(c) 90 days

(d) 225 days

**Ques.** Consider the following statements

(1) Mode can be computed from histogram

(2) Median is not independent of change of scale

(3) Variance is independent of change of origin and scale

Which of these is/are correct

(a) (1), (2) and (3)

(b) Only (2)

(c) Only (1) and (2)

(d) Only (1)

**Ques.** Karl Pearson’s coefficient of correlation between *x* and *y* for the following data is

x : |
3 | 4 | 8 | 9 | 6 | 2 | 1 |

y : |
5 | 3 | 7 | 7 | 6 | 9 | 2 |

(a) 0.480

(b) – 0.480

(c) 0.408

(d) – 0.408

**Ques. **160% of 16000 = ?

(a) 25600

(b) 100

(c) 10

(d) 2560

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**Ques.** The numbers of arrangements of the letters of the word SALOON, if the two O’s do not come together, is

(a) 360

(b) 720

(c) 240

(d) 120

Ques. Find the missing number: 3, 23, 43, ?, 83, 103

(a) 33

(b) 53

(c) 63

(d) 73

**Ques.** What least number must be subtracted fromeach of the numbers 14, 17, 34 and 42 so that the remainders may be proportional?

(a) 4

(b) 3

(c) 2

(d) 9

**Ques.** If the sum of the 10 terms of an A.P. is 4 times to the sum of its 5 terms, then the ratio of first term and common difference is

(a) 1 : 2

(b) 2 : 1

(c) 2 : 3

(d) 3 : 2

A

**Ques.** A specific range of numbers within which a population mean should lie is

(a) the range.

(b) the confidence coefficient.

(c) the confidence interval.

(d) the confidence level.

**Ques.** If f(x) = |x – 2| and g(x) = f(f(x)), then for x > 20, g’ (x) equals

(a) –1

(b) 1

(c) 0

(d) none of these

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**Ques.** The number which exceeds its positive square root by 12 is

(a) 9

(b) 16

(c) 25

(d) None of these

**Ques. **In a quadrilateral ABCD, the diagonals AC and BD intersect at O. Let OA = 2, OB = 2, OC = 3, OD = 4 and AB = 3. The area of the quadrilateral is

(a) 55/4

(b) 117/8

(c) 173/12

(d) none of the these

**Ques.** The number of words which can be formed from the letters of the word MAXIMUM, if two consonants cannot occur together, is

(a) 4 !

(b) 3! x 4!

(c) 7 !

(d) None of these

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**Ques.** The mean weight per student in a group of seven students is 55 *kg* If the individual weights of 6 students are 52, 58, 55, 53, 56 and 54; then weights of the seventh student is

(a) 55*kg*

(b) 60*kg
*(c) 57

*kg*

(d) 50

*kg*

**Ques.** If sum of infinite terms of a G.P. is 3 and sum of squares of its terms is 3, then its first term and common ratio are

(a) 3/2, ½

(b) 1, ½

(c) 3/2, 2

(d) None of these

**Ques. **A team of 25 men is supposed to do a work in 44 days. After 18 days, 2 more men were employed and the work finished 1 day earlier. How many days would it have been delayed if 2 more men were not employed?

(a) 1 day

(b) 2 days

(c) 1.5 days

(d) None of these

**Ques. **There are 2 kinds of milk powder with different fat and protein contents. When these 2 kinds of milk powder are mixed in various proportion, the protein and fat concentration of the mixtures was found to be (5%, 8%), (6%, 6%) and (8%, x%) respectively. Then x =

(a) 2

(b) 3.5

(c) 4

(d) 4.5

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**Ques.** Karl Pearson’s coefficient of rank correlation between the ranks obtained by ten students in Mathematics and Chemistry in a class test as given below is

Rank in Mathematics : | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Rank in Chemistry : | 3 | 10 | 5 | 1 | 2 | 9 | 4 | 8 | 7 | 6 |

(a) 0.224

(b) 0.204

(c) 0.240

(d) None of these

**Ques.** A market with 3900 operating firms has the following distribution for firms arranged according to various income groups of workers

Income group |
No. of firms |

150-300 | 300 |

300-500 | 500 |

500-800 | 900 |

800-1200 | 1000 |

1200-1800 | 1200 |

**Ques.** If a histogram for the above distribution is constructed the highest bar in the histogram would correspond to the class

(a) 500-800

(b) 1200-1800

(c) 800-1200

(d) 150-300

**Ques. **196 × 948 ÷ 158 = ?

(a) 1156

(b) 1200

(c) 1188

(d) 1176

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**Ques.** In a mixture of 60 litres, the ratio of milk and water is 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is:

(a) 30 litres

(b) 70 litres

(c) 40 litres

(d) 60 litres

**Ques.** The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the other two are

(a) 2 and 9

(b) 3 and 8

(c) 4 and 7

(d) 5 and 6

**Ques.** A bag contains 2 white and 4 black balls. A ball is drawn 5 times with replacement. The probability that at least 4 of the balls drawn are white is

(a) 8/141

(b) 10/243

(c) 11/243

(d) 8/41

**Ques.** If Quartile Deviation is 16, the most likely value of S.D. will be

(a) 24

(b) 42

(c) 10

(d) None of these

**Ques.** The mean proportional between 234 and 104 is:

(a) 16

(b) 40

(c) 54

(d) None of these

**Ques.** In what time a sum will become three times of itself at the rate of 10% per annum?

(a) 10year

(b) 15year

(c) 20year

(d) 25year

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**Ques.** The total expenditure incurred by an industry under different heads is best presented as a

(a) Bar diagram

(b) Pie diagram

(c) Histogram

(d) Frequency polygon

**Ques.** If the mean of the distribution is 2.6, then the value of *y* is

Variate | 1 | 2 | 3 | 4 | 5 |

Frequency f of | 4 | 5 | y | 1 | 2 |

(a) 24

(b) 13

(c) 8

(d) 3

**Ques. **In how many different ways can the letters of the word ‘ARISE’ be arranged ?

(a) 90

(b) 60

(c) 180

(d) 120

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**Ques.** A boatman can row to a place 48 km distant and back, in 14 hrs. If he can row 4 km with the stream in the samas 3 km against it, the speed of the stream (in km/hr) is

(a) 1

(b) 2.2

(c) 3

(d) 0.5