Combinatorics | Number Theory Answers

Out of 250 students who failed in an examination, it was revealed that 128 failed in mathematics, 87 failed in physics and 134 failed in chemistry. 31 failed in mathematics and physics, 54 failed in chemistry and mathematics, 30 failed in chemistry and physics. Find how many candidates failed in:
(a) In all the three subjects (7 marks)
(b) In mathematics but not in physics (2 marks)
(c) In chemistry but not in mathematics (2 marks)
(d) In physics but not in chemistry or in mathematics (2 marks)
(e) In chemistry or in mathematics but not in physics (2 marks)
Hint: Use venn diagram to simplify your work in question 3 above

The number 3797 has an interesting property.Being prime itself,it is possible to continuously remove digits from left to right,and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3. Find the only four-digit prime number with this property.

A mobile operator declared that it will provide a free minute of talk-time for every 2 minutes spent.If you want to talk a total of 7 minutes,for how many minutes will you have to pay?

what is the least common multiple of 20 and 16

Q2 An investigator interviewed 100 students to determine preference for three drinks: Milk(M), Coffee(C), Tea(T). He reported the following: 10 students had all the three drinks M,C,T; 20 had M&C: 30 had C&T; 25 had M&T; 12 had M only; 5 had C only & 8 had T only. Enumerate how many did not take any of the drink.

out of 250 candidates who failed in an examination, it was revealed that 128 failed in mathematics, 87 in physics and 134 in aggregate, 31 failed in mathematics and in physics 54 failed in the aggregate and in mathematics, 30 failed in the aggregate and in physics. find how many candidates failed.
1 in all the three subjects. 2. in mathematics but not in physics. 3. in the aggregate but not in mathematics 4. in physics but not in the aggregate or in mathematics 5. in the aggregate or in mathematics, but not in mathematics

James brought fewer donuts than two dozen of donuts. He wants to evenly share them among 2,3,4 people. No matter how many people he shares them with he Aways have one left over. How many did he buy? What numbers goes in to 24 when factored with 2,3,4 gives remainder of 1

if factorial r = 24 . what is value of r ?

how many numbers of five digits each can be made from the digits 1,2,3,4,5,6,7,8,9, where each number contains exactly one even digit and no digit is used more than once

Let S={a,b}.how many elements does the power set 2s contain?