SOLVED PAPER 2021 (CDS) (I) (Elementary Mathematics)

Total Questions: 100

91. Consider the following data with regard to production of cars (in lakhs) :

 

Year 2015Year 2016
Country A3538
Country B4547
Country C8893
Country D7579
Country E5860.9

In which of the countries, the production of cars has increased by more than or equal to 5% in 2016 over 2015?

Correct Answer: (c) A, C, D and E
Solution:

92. The following table shows the marks of 90 students in a test of 80 marks:

 

MarksNumber of students
1-105
11-208
21-3010
31-4013
41-5018
51-6017
61-7012
71-807

The percentage of students who have obtained less than or equal to 50% marks is

Correct Answer: (b) 40%
Solution:

93. What is the median of the following data?

2, 3, -1, 2, 6, 8, 9

Correct Answer: (b) 3
Solution:

94. What is the arithmetic mean of the first ten composite numbers?

Correct Answer: (d) 11.2
Solution:

95. The marks obtained by 5 students are 21, 27, 19, 26, 32. Later on 5 grace marks are added to each students. What are the average marks of the revised marks of the students?

Correct Answer: (b) 30
Solution:

96. Let p be the mean of m observations and q be the mean of n observations, where p ≤ q. If the combined mean of (m + n) observations is c, then which one of the following is correct ?

Correct Answer: (c) p ≤ c ≤ q
Solution:


97. (Questions 97-100) Consider the following data with regard to different types (I, II, III, IV, V) of multivitamin tablets produced in a company (in lakhs).

 

YearIIIIIIIVV
200016080709075
200120015085160100
200213535449585
20032409512080120
20041801108595115
200521015010092110

Which product is produced least over the years 2000-2005?

Correct Answer: (b) Type III
Solution:Total production of each tablets over the years 2000 - 2005.
Type I
160 + 200 + 135 + 240 + 180 + 210 = 1125
Type II
80 + 150 + 35 + 95 + 110 + 150 = 620
Type III
70 + 85 + 44 + 120 + 85 + 100 = 504
Type IV
90 + 160 + 95 + 80 + 95 + 92 = 612
Type V
75 + 100 + 85 + 120 + 115 + 110 = 605
Hence, the required product is type III.

98. In which one of the following pairs of years, the difference in total number of tablets produced between them is minimum?

Correct Answer: (a) (2003, 2005)
Solution:The total number of tablets produced in the year
2000 is 160 + 80 + 70 + 90 + 75 = 475
The total number of tablets produced in the year
2001 is 200 + 150 + 85 + 160 + 100 = 695
The total number of tablets produced in the year
2002 is 135 + 35 + 44 + 95 + 85 = 394
The total number of tablets produced in the year
2003 is 240 + 95 + 120 + 80 + 120 = 655
The total number of tablets produced in the year
2004 is 180 + 110 + 85 + 95 + 115 = 585
The total number of tablets produced in the year
2005 is 210 + 150 + 100 + 92 + 110 = 662
The difference in total number of tablets produced
between 2003 and 2005 is 662 - 655 = 7
The difference in total number of tablets produced
between 2001 and 2005 is 695 - 662 = 33
The difference in total number of tablets produced
between 2003 and 2004 is 665 - 585 = 70
The difference in total number of tablets produced
between 2000 and 2002 is 475 - 394 = 81

Hence, the difference in total number of tablets
produced is minimum between 2003 and 2005.

99. The ratio of percentage drop in total production in 2004 compared to 2001 to that in 2000 compared to 2001, is

Correct Answer: (c) ½
Solution:


100. In which year, the production of Type I is more than the sum of the production of Type III and Type IV ?

Correct Answer: (c) 2003
Solution:The number of tablets of Type I
produced in the year 2001 = 200

The total number of tablets of Type III
and IV together produced in the year
200 = 185 + 160 = 245

The number of tablets of Type I
produced in the year 2002 = 135

The total number of tablets of Type III
and IV together produced in the year
2002 = 44 + 95 = 139

The number of tablets of Type I
produced in the year 2003 = 240

The total number of tablets of Type III
and IV together produced in the year
2003 = 120 + 80 = 200

The number of tablets of Type I
produced in the year 2004 = 180

The total number of tablets of Type III
and IV together produced in the year
2004 = 100 + 92 = 192

Hence, for the year 2003, the production
of Type I is more than the total production
of tablet of the type III and Type IV together.