UPSC sample papers

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

1. 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
Ans: (d)

2. 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
Ans: (a)

3. 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
Ans: (b)

4. 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)
Ans: (d)

5. 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
Ans: (c)

6. 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
Ans: (c)

7. 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
Ans: (c)

Related: NATA Sample Papers

8. 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
Aans: (a)

9. 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.
Ans: (c)

10. 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
Ans: (b)

11. The number which exceeds its positive square root by 12 is
(a) 9
(b) 16
(c) 25
(d) None of these
Ans: (b)

12. 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
Ans: (a)

13. 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) 55kg
(b) 60kg
(c) 57kg
(d) 50kg
Ans: (c)

14. 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
Ans: (a)

15. 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
Ans: (a)

16. 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

17. 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
Ans: (b)

18. 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
Ans: (a)

19. 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
Ans: (c)

20. 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
Ans: (d)

21. If Quartile Deviation is 16, the most likely value of S.D. will be
(a) 24
(b) 42
(c) 10
(d) None of these
Ans: (a)

22. The mean proportional between 234 and 104 is:
(a) 16
(b) 40
(c) 54
(d) None of these
Ans: (d)

23. 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
Ans: (c)

24. 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
Ans: (b)

25. 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
Ans: (c) 