U.G.C. NET Exam. December 2023 Paper II (COMPUTER SCIENCE)

Total Questions: 100

91. The cost function of total food is:

Correct Answer: (c) Z = 12x + 20y
Solution:

The cost function for the total food, we need to consider the cost per gram of each type of food (X and Y) and the quantities (X and Y) of each type.
Given-
Food X costs Rs 12 per gram.
Food Y costs Rs 20 per gram.
The cost function (z) calculated as follows.
Follows-
Z = Cost of food X + cost of food Y
Z = (Cost per gram of food X Quantity of food X) +
(Cost per gram of food Y * quantity of food Y)
Z = (12* x) + (20* Y)
so the correct option is Z = 12x + 20 Y

92. Which of the following constrains when formulating the LPP?

Correct Answer: (d) 6x + 8y ≥ 100, 7x + 12y ≥ 120, x, y ≥ 0
Solution:

The correct constraint when formulating the Liner Programming Problem (LPP) based on the given information is
6x + 7y = 100, 8x + 12y ≥ 120, x, y ≥ 0
The constraint 7x + 12y ≥ 120 implies that the total units of vitamin E from food X and Y combined must be greater than or equal to 120, which is also correct as it meets the minimum requirement of 120 units. Therefore, the constraints 6x + 8y ≥ 100,

7x +12y ≥ 120, x, y ≥ 0 +   is valid for formulation the LPP based on the given scenario.

93. Which of the following are quantities (in grams) of food X and Y respectively when the cost of food is minimum :

Correct Answer: (b)
Solution:

So, the quantities 15 and 5/4 do satisfy the constraints
and the cost is Rs - 205, However, we can't conclude
that this is the minimum cost without further analysis.

94. The dual of the formulated LPP is :

Correct Answer: (a)
Solution:

95. The minimum cost of food is:

Correct Answer: (a) 205
Solution:

To find the minimum cost of food that meets the daily requirements for vitamin D and E. We need to set up the following option problemminimize the cost - 12x + 20y
Subject to the constraints-
6x + 8y  ≥100 (minimum requirement for vitamin D)
7x + 12y ≥ 120 (minimum requirement for vitamin E)
Solving this linear programming problem- We find the minimum cost is Rs- 205.s

96. Answer the following question

Correct Answer: (c) 4
Solution:

97. Answer the following question

Correct Answer: (a)
Solution:

98. Which of the following join is used to get all the tuples of relation X and Y with Null values of corresponding missing values?

Correct Answer: (d) Full outer join
Solution:

To get all the types of relation X and Y with null values for corresponding missing values, you would use a full outer join. This join type returns all records when there is match in either the left (X) or right (Y) table recodes. If there is no match, the missing side will contain null.

99. Number of tuples by applying right outer join on relation X and Y is/ are:

Correct Answer: (d) 4
Solution:

To perform a right outer join on the relations X and Y. We need to match tuples based on the common attributes 's' and include all tuples from Y and matching tuples from x. If there is no match in X for a tuples in Y, Null values are included for attributes of X
in the result.

100. Number of tuples obtained by applying Cartesian product over X and Y are:

Correct Answer: (a) 16
Solution: