Exams › GATE › General Aptitude

In how many ways can cells in a 3 × 3 grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown.

1. 2
2. 9
3. 3
4. 6

Correct answer: 6

Solution

The problem is equivalent to finding the number of permutations of 3 distinct objects, as each shaded cell must occupy a unique position in each row and column. This can be calculated as 3! (3 factorial), which equals 6, representing all possible arrangements of shaded cells.

Related GATE General Aptitude questions

• Which one of the given options is a possible value of x in the following sequence? 3, 7, 15, x, 63, 127, 255
• On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?
• During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85°, the ratio of the Earth-Sun and Earth-Moon distances is closest to
• The probability that a student passes only in Mathematics is 1/3. The probability that the student passes only in English is 4/9. The probability that the student passes in both of these subjects is 1/6. The probability that the student will pass in at least one of these two subjects is
• Rohit goes to a restaurant for lunch at about 1 PM. When he enters the restaurant, he notices that the hour and minute hands on the wall clock are exactly coinciding. After about an hour, when he leaves the restaurant, he notices that the clock hands are again exactly coinciding. How much time (in minutes) did Rohit spend at the restaurant?
• a + a + a +... + a (n times) = a² b and b + b + b +... + b (m times) = ab², where a, b, n and m are natural numbers. What is the value of (m + m + m +... + m (n times))(n + n + n +... + n (m times))?

⚔️ Practice GATE General Aptitude free + battle 1v1 →