Q. Determine all possibilities for the solution set of a homogeneous system of 4 equations in 4 unknowns.

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Q. Determine all possibilities for the solution set of a homogeneous system of 6 equations in 5 unknowns.

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Q. Determine all possibilities for the solution set of a homogeneous system of 5 equations in 4 unknowns and the rank of the system is 3.

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Q. Determine the number of derangements of (2, 4, 6, 1, 3, 5) that end with integer 2, 4 and 6 in some order?

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Q. A nursery teacher has 5 pencil boxes to give out to her five students. Determine the probability that at least one student gets their name tag?

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Q. Farhan has received 9 gifts from 9 different people. In how many ways can Farhan receives the gifts such that no one gives him real gifts?

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Q. There are 7 groups in a picnic who has brought their own lunch box, and then the 7 lunch box are exchanged within those groups. Determine the number of ways that they can exchange the lunch box such that none of them can get their own.

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Q. Computational complexity of derangements is of __________

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Q. There are 5 different-colored boxes in a room each with a distinct cover. Find out the number of ways so that these covers can be put on the boxes such that none of the boxes can have right covers on it? (Assume that all the covers must be on the boxes).

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Q. A postman can put 12 letters into their respective envelopes such that exactly 5 will go into the right envelope. Find the number of ways of doing this work.

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Q. Determine the number of ways In a single competition a singing couple from 5 boys and 5 girls can be formed so that no girl can sing a song with their respective boy?

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Q. What is the sum of all 6 digit numbers which can be formed using the digits 2, 3, 5, 6 and 9 exactly once?

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Q. Determine the average of all four digit numbers that can be made using all the digits 2, 3, 5, 7 and 11 exactly once?

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Q. In a blindfolded game, a boy can hit the target 8 times out of 12. If he fired 8 shots, find out the probability of more than 4 hits?

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Q. A fair coin is tossed 15 times. Determine the probability in which no heads turned up.

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Q. When a programmer compiles her code there is a 95% chance of finding a bug every time. It takes three hours to rewrite her code when she finds out a bug. Determine the probability such that she will finish her coding by the end of her workday. (Assume, a workday is 7 hours)

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Q. Determine the probability when a die is thrown 2 times such that there are no fours and no fives occur?

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Q. In earlier days, there was a chance to make a telephone call would be of 0.6. Determine the probability when it could make 11 successes in 20 attempts of phone call.

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Q. By the expression \(\left(\frac{x}{3} + \frac{1}{x}\right)^5\), evaluate the middle term in the expression.

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Q. Evaluate the expression (y+1)⁴ – (y-1)⁴.

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