Math and Logic Questions
1. The street of a city are arranged like the lines of a chessboard , there are m street running north and south and n east and west . Find the no. ways in which a man can travel from N.W to the S.E corner, going by the shortest possible distance.
2. How many different arrangement can be made out of the letters in the ex-pression a^3b^2c^4 when written at full length?
Ans. 1260.
3. How many 7-digit numbers exist which are divisible by 9 and whose last but one digit is 5?
4. You continue flipping a coin until the number of heads equals the number of tails. I then award you prize money equal to the number of flips you conducted .How much are you willing to pay me to play this game?
5. Consider those points in 3-space whose three coordinates are all nonnegative integers, not greater than n. Determine the number of straight lines that pass through n of these points.
6 Four figures are to be inserted into a six-page essay, in a given order. One page may contain at most two figures. How many different ways are there to assign page numbers to the figures under these restrictions?
7. How many (unordered) pairs can be formed from positive integers such that, in each pair, the two numbers are coprime and add up to 285?
8. ( 1+ x) ^ n – nx is divisible by
A. x B. x.x C. x.x.x. D. None of these
9. The root of the equation (3-x)^4 + (2-x)^4 = (5-2x)^4 are
a. ALL REAL B. all imaginary C. two real and 2 imaginary D. None of these
10. The greatest integer less than or equal to ( root(2)+1)^6 is
A. 196 B.197 C.198 D.199.
11. How many hundred-digit natural numbers can be formed such that only even digits are used and any two consecutive digits differ by 2?
12. If x1 , x2, x3 are the root of x^3-1=0 , then
A. x1+x2+x3 not equal to 0 B. x1.x2.x3 not equal to 1 C.(x1+x2+x3)^2 = 0 D. None of these
13. How many different ways are there to arrange the numbers 1,2,...,n in a single row such that every number, except the number which occurs
2. How many different arrangement can be made out of the letters in the ex-pression a^3b^2c^4 when written at full length?
Ans. 1260.
3. How many 7-digit numbers exist which are divisible by 9 and whose last but one digit is 5?
4. You continue flipping a coin until the number of heads equals the number of tails. I then award you prize money equal to the number of flips you conducted .How much are you willing to pay me to play this game?
5. Consider those points in 3-space whose three coordinates are all nonnegative integers, not greater than n. Determine the number of straight lines that pass through n of these points.
6 Four figures are to be inserted into a six-page essay, in a given order. One page may contain at most two figures. How many different ways are there to assign page numbers to the figures under these restrictions?
7. How many (unordered) pairs can be formed from positive integers such that, in each pair, the two numbers are coprime and add up to 285?
8. ( 1+ x) ^ n – nx is divisible by
A. x B. x.x C. x.x.x. D. None of these
9. The root of the equation (3-x)^4 + (2-x)^4 = (5-2x)^4 are
a. ALL REAL B. all imaginary C. two real and 2 imaginary D. None of these
10. The greatest integer less than or equal to ( root(2)+1)^6 is
A. 196 B.197 C.198 D.199.
11. How many hundred-digit natural numbers can be formed such that only even digits are used and any two consecutive digits differ by 2?
12. If x1 , x2, x3 are the root of x^3-1=0 , then
A. x1+x2+x3 not equal to 0 B. x1.x2.x3 not equal to 1 C.(x1+x2+x3)^2 = 0 D. None of these
13. How many different ways are there to arrange the numbers 1,2,...,n in a single row such that every number, except the number which occurs