Matrix Arrangement for Cat Sheet 4
- Jul 10
- 6 min read
Updated: Jul 24
Practicse Question
Matrix Arrangement CAT Case 1
The year is 1942. General Harold Alexander is leading British troops in the battle of El Alamein in Africa in World War-II. It is important for the General to repulse the Nazi attack on the town of Port Said else the Nazis would capture Suez Canal. General Alexander is planning to attack the Nazi troops led by General Romel. However, Nazi troops laid a total of 5 mines in a square of 5 × 5 units such that there is exactly one mine in each row and one mine in each column. If the British troops step on the small square with a mine with it, the mine would explode.The five columns are denoted by C1, C2, C3, C4 and C5, as shown. Similarly, the five rows are denoted by R1, R2, R3, R4 and R5, as shown.We can see that the cell R2C2 has ‘2’ written in it. It means that there are 2 cells with mines among the cells that share either a side with R2C2 or are diagonally opposite to that cell. The cells with a number written in it do not contain any mine. This diagram is partially filled and the other cells either contain a mine or have some number written in them.
Q.1 Out of the 20 cells in which numbers are written, the numbers written in how many cells can be uniquely determined?
Answer Here TITA
Q.2 Out of the 5 cells with mines, the coordinates (i.e., the row number and the column number) of how many cells can be uniquely determined?
a.5
b.4
c.3
d.2
Q.3 What can be said about the cell R5C4?
a.It has a number written in it and that number is 1.
b.It has a number written in it and that number is 2.
c.It has a mine in it.
d.Nothing conclusive can be said about the cell.
Q.4 How many cells have 1 written in them?
a.9
b.11
c.12
d.cannot be determined
Q.5 How many mines out of the five are placed in such a way that two or more cells containing the mines share either a side or are diagonally opposite to each other?
a.0
b.2
c.3
d.Nothing conclusive can be said
Matrix Arragement for CAT Case 2
Refer to the data below and answer the questions that follow.Shiva runs a coaching institute where he teaches all subjects to the students of primary school. Ten students have been enrolled in one such coaching batch and Shiva has conducted a class test on five different subjects for these students. The results of the students in this class test have been tabulated by Shiva using a grading system. In the grading system, A, B, C, D, and F grades fetch 8, 6, 4, 2, and 0 grade points respectively. The Grade Point Average (GPA) is the arithmetic mean of the grade points obtained in the five subjects. For example, if a student has received A, A, B, D, and C grades in five different subjects, his or her GPA is \({(8 + 8 + 6 + 2 + 4) \over {5}}\) = 5.6. Only ‘F’ grade is considered a failing grade. The tabular representation of these ten students’ grades and their GPAs are shown below (the names of the students in the table have been written in alphabetical order from top to bottom):
| P.T. | Mathematics | Science | Drawing | Spelling | GPA |
Abhinav |
| A |
| C |
| 3.6 |
Bobita | C |
| C |
| C | 3.2 |
Chahel | F | C | A |
|
| 5.2 |
Dahana |
| F | D |
|
| 1.2 |
Ekansh | B | D | B |
|
| 3.2 |
Faiza |
|
|
|
| F | 5.6 |
Gopi |
|
|
| F | D | 4 |
Harini |
| C | C |
|
| 2 |
Indrajeet |
|
|
|
| D | 5.6 |
Jagat |
| B | B |
|
| 3.2 |
Shiva noticed that when he scrolls through this table no two vertically consecutive cells contain the same grade.Some additional facts are also known about the students' grades. These are as follows:1. Faiza did not score grade C in any subject.2. Indrajeet did not score grade D twice.3. Jagat failed in at most one subject.4. Exactly two students have passed in all the subjects.5. No student failed (i.e. received ‘F’ grade) in Science.
Q.6 How many students failed in Spelling?
Q.7 Who scored maximum grade points in P.T.?
Faiza
Gopi
Indrajeet
Both Faiza and Indrajeet
Q.8 Identify the pair of students who passed in all five subjects.
a.Bobita and Dahana
b.Bobita and Abhinav
c.Abhinav and Indrajeet
d.Bobita and Indrajeet
Q.9 Statement A: Gopi and Indrajeet received the same grade points in Mathematics.Statement B: Gopi and Indrajeet received the same grade points in P.T.
a.Statement A only
b.Statement B only
c.Both Statement A and Statement B
d.Neither Statement A nor Statement B
Q.10 Statement A: Gopi and Indrajeet received the same grade points in Mathematics.Statement B: Gopi and Indrajeet received the same grade points in P.T.
a.Statement A only
b.Statement B only
c.Both Statement A and Statement B
d.Neither Statement A nor Statement B
Q.11 Which of the two statements below is/are definitely false?Statement A: Chahel received 8 grade points in Drawing.Statement B: Indrajeet received the same grade point in Drawing as Chahel received in Spelling.
a.Statement A only
b.Statement B only
c.Both Statement A and Statement B
d.Neither Statement A nor Statement B
Matrix Arrangement for CAT Case 3
The principal of Loreto Convent School provided one ticket to each student of Class 12th. Each ticket had a 3 × 3 grid such that the 3 columns were named as A, B and C from left to right whereas the 3 rows were named as a, b and c from top to bottom. Each student had to fill the grid with digits from 1 to 9 such that each cell contains a distinct number. Each student filled their ticket’s grid and later it was found that no two tickets had the same three digits in any row or column as compared to any other student. For example, if a row contained 1, 2 and 3 in one of the student’s ticket, then no other student’s ticket had all of 1, 2 and 3 together in a row or column. Also, cell in row a and column A is denoted as aA, that in row a and column B is denoted as aB and so on. A maximum possible number of students filled the grid. One of the students, Sanjeev, filled the grid in his ticket as shown below.
Q.12 In how many ways can a student fill the grid such that both the diagonals of his ticket have the same digits and in the same cells as in Sanjeev’s ticket?
Q.13 If digits 4 and 6 are in column A and digit 4 is in row c, then in how many ways can a student fill his ticket’s grid such that the digits 1, 5 and 9 are exactly in the same cell and in the same order as in Sanjeev’s grid?
Q.14 In how many ways can a student fill his ticket’s grid having its diagonal filled with digits 3, 5 and 7 in the same cells as in Sanjeev’s grid and each of the other three digits less than 5 interchanged places with each other whereas the other three digits more than 5 interchanged places with each other?(Arrangement has been done in such a way that no digit except 3, 5 and 7 was at the same place as of Sanjeev’s grid.)
a.1
b.2
c.3
d.None of these
Q.15 What can be the maximum possible number of cells, in the grid of some other student’s ticket, having the same digits as in Sanjeev’s grid?
Matrix Arrangement for CAT Case 4
Five football players of India were asked to rank 5 football teams - P, Q, R, S and T - of other countries from 1 to 5 as per their performances in last year’s tournament, where rank 1 being the highest and rank 5 being the lowest. Team P was ranked same by all the five players while team Q was ranked same by exactly 4 players. Team R was given the same rank by 3 players and another same rank by 2 players. Team S was given the same rank by 3 players and two different ranks by the other 2 players and team T was ranked same by only 2 players and ranked different by the other 3. At the end, each team was assigned a final rank equivalent to the rank that was assigned to that team by maximum number of players. All five teams had different final ranks and final ranks of teams P, Q and R were 1, 2 and 3 respectively. Also, team R was ranked 4 by exactly two players. Each player had given a different ranking to each of the five teams.
Q.16 Which of the following ranks were given by a player to team Q?
a.3
b.4
c.5
d.4 or 5
Q.17 How many players can rank team S as 4?
Q.18 Find the sum of the two ranks given to the team S, which were different from the same rank given by the three players?
a.6
b.8
c.7
d.5
Q.19 Which of the following is the correct order of teams, when arranged in increasing order of the sum of the ranks given to them by the 5 players?
a.P,Q,R,S,T
b.P,Q,R,T,S
c.P,Q,T,R,S
d.Sum is same for two or more teams
Answers For Matrix Arrangement
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
20 | A | B | B | B | 5 | A | D | A | 4 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | |
D | 4 | 13 | B | 6 | C | 1 | C | B |
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