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C. Competency-based questions: HOTS Century #Interdisciplinary
Skills
1. In a city there are two factories A and B. Each factory produces toys for boys and girls. There are three
types of toys produced in both the factories, type I, II and III (manual, electric, remote controlled). For boys the
number of toys of types I, II and III respectively are 80, 70 and 65 in factory A and 85, 65 and 72 are in factory
B. For girls the number of units of types I, II and III respectively are 80, 75, 90 in factory A and 50, 55, 80 are
in factory B.
a. If P represents the matrix of number of units of each type produced by factory A for both boys and girls,
then P is given by
Boys Girls I II III I II III Boys Girls


I 85 50 Boys 50 55 80  Boys 80 75 90 I 80 80

i.   ii.   iii.   iv.  
II 65 55  Girls 85 65 72  Girls 80 70 65  II 70 75 






III 72 80  III 65 90 


b. The total production of toys of each type for boys is given by the matrix
I II III I II III I II III I II III
i. ii. iii. iv.
  165 130 137    130 165 137    165 135 137    137 135 165 
2. A city municipal council noted the number of malaria cases in two zones in 2022. The information is given
as follows:
Table 1
Age (in years) 5-15 15-25 25-35 25-45 45-55 55-65
No. of cases 6 11 21 23 14 5
Table 2

Age (in years) 5-15 15-25 25-35 25-45 45-55 55-65
No. of cases 8 16 10 42 24 12
a. The mean of the given data is

i. 26.2 ii. 32.4
iii. 33.5 iv. 35.4
b. The upper limit of modal class is

i. 15 ii. 25
iii. 35 iv. 45
Assertion and Reasoning Questions:
Direction: Questions 3-4, consist of two statements – Assertion (A) and Reasoning (R). Answer these questions
by selecting the appropriate option given below:
a. Both A and R are true and R is the correct explanation of A.
b. Both A and R are true but R is not the correct explanation of A.
c. A is true but R is false.
d. A is false but R is true.

3. Assertion (A): Word embeddings in NLP are represented as vectors.
Reason (R): Vectors are not useful for understanding the context of words.

4. Assertion (A): Mean is always equal to the mode.
Reason (R): Mean, median, and mode are different measures of central tendency.

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