Number Theory
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MULTIPLE CHOICE QUESTIONS INTRODUCTION TO NUMBER THEORY ……………………………………………………………………………………..
1. Small trees are to be planted in rows such that each row contains equal but odd number of tree. If there are total of 3500 plants then the no of possible way is 1. 24 2. 8 3. 16 4. 112
2. A number of statements are given below with respect to two numbers 2835 and 2800. Chose the correct staement among the following: a) 2835 and 2800 have equal number of divisor b) 2835 has a total of 18 distinct factor c) 2835 and 2800 have equal number of odd divisor d) 2800 has a total of 23 even factors e) 2835*2800 have 41 distinct facors 1. 2. 3. 4.
b and d a ,c and e b, c and e a and b
3. 32400 is decomposed into N pair of factor such that each pair when Multiplied together yields 32400 itself. Then the maximum value of N is: 1. 37 2. 38 3. 39 4. 41
4. The no 111111111111 is perfectly divisible by: 1. 11 2. 37 3. 407 4. all of the above
5. What is the remainder when 234*235*236*237*238*239 is divided by 120? 1. 119 2. 1 3. 0 4. 2
6. Let a three digit number be in form of xyz such that 2x is arithmetic mean of y and z , also y is arithmetic mean of x and z ,then the no can be 1. 131 2. 357 3. 471 4. 253 7. If the number 78 in decimal base system is represented as 243 in some other base Notation then 442 in the other base notation is eqivalent to: 1. 122 in decimal system 2. 172 in octal system 3. 7A in hexadecimal system 4. all of the above 5. none of these 8. How many zeros are ther at the end of 126! 1. 25 2. 30 3. 31 4. 29 9. Assume n to be a positive integer and p and q are prime number. It is also given That n is greater than 2 and p, q is greater than 6 then which of the following statement is true: a) Seventh power of n substracted by n ( n^7-n ) is necessarily divisible by 42. b) Square of p substracted by square of q ( p^2 - q^2 ) is necessarily divisible by 48 c) (p-1)!+1 is divisible by p d) (pq-1)!+1 is divisible by pq 1. 2. 3. 4.
a , b and d a and c c and d a, b and c
10. There are 16 ways in which students of a class can be grouped such that each Group contains equal number of student. Then the minimum no of student in the Class is: 1. 120 2. 180 3. 150 4. 80
MULTIPLE CHOICE QUESTIONS INTRODUCTION TO NUMBER THEORY ……………………………………………………………………………………..
1. Small trees are to be planted in rows such that each row contains equal but odd number of tree. If there are total of 3500 plants then the no of possible way is 1. 24 2. 8 3. 16 4. 112
2. A number of statements are given below with respect to two numbers 2835 and 2800. Chose the correct staement among the following: a) 2835 and 2800 have equal number of divisor b) 2835 has a total of 18 distinct factor c) 2835 and 2800 have equal number of odd divisor d) 2800 has a total of 23 even factors e) 2835*2800 have 41 distinct facors 1. 2. 3. 4.
b and d a ,c and e b, c and e a and b
3. 32400 is decomposed into N pair of factor such that each pair when Multiplied together yields 32400 itself. Then the maximum value of N is: 1. 37 2. 38 3. 39 4. 41
4. The no 111111111111 is perfectly divisible by: 1. 11 2. 37 3. 407 4. all of the above
5. What is the remainder when 234*235*236*237*238*239 is divided by 120? 1. 119 2. 1 3. 0 4. 2
6. Let a three digit number be in form of xyz such that 2x is arithmetic mean of y and z , also y is arithmetic mean of x and z ,then the no can be 1. 131 2. 357 3. 471 4. 253 7. If the number 78 in decimal base system is represented as 243 in some other base Notation then 442 in the other base notation is eqivalent to: 1. 122 in decimal system 2. 172 in octal system 3. 7A in hexadecimal system 4. all of the above 5. none of these 8. How many zeros are ther at the end of 126! 1. 25 2. 30 3. 31 4. 29 9. Assume n to be a positive integer and p and q are prime number. It is also given That n is greater than 2 and p, q is greater than 6 then which of the following statement is true: a) Seventh power of n substracted by n ( n^7-n ) is necessarily divisible by 42. b) Square of p substracted by square of q ( p^2 - q^2 ) is necessarily divisible by 48 c) (p-1)!+1 is divisible by p d) (pq-1)!+1 is divisible by pq 1. 2. 3. 4.
a , b and d a and c c and d a, b and c
10. There are 16 ways in which students of a class can be grouped such that each Group contains equal number of student. Then the minimum no of student in the Class is: 1. 120 2. 180 3. 150 4. 80
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