post your answers........
16. find the lowest of three nos. as described: if the cube of the first no exceeds the product by 2, the cube of 2nd no. is smaller than therir product by 3, and the cube of the third no. exceeds their product by 3.
A) 3^1/3 b)9^1/3 c)2 d)any of these
17. find the Gcd of (2^100 -1, 2^120 -1)
a) 2^20 -1 b)2^40 – 1 C)2^60 -1 d)2^10 -1
18. find the gcd of (111111....1111 hundred ones ; 1111....111 sixty ones)
A) 1111....forty ones b)11111.....twenty five ones
C) 11111.... twenty ones d) none of these
19. find the number of numbers between 200 and 300, both included, which are not divisible by 2, 3, 4 and 5.
(a) 27 (b) 26 (c) 25 (d) none of these
20. 12^55/3^11 + 8^48/16^18 will give the digit at unit's place as
(a) 4 (b) 6 (c) 8 (d) 0
21. Let N be the product of five different odd prime numbers. If N is the five-digit number abcab, 4 < a < 8, how many values of N are possible?
a. 1 b. 2 c. 3 d. 4 e. more than 4
22. Which of the following numbers can be written as the sum of the squares of three odd numbers?
a. 4445 b. 1233 c. 3339 d. 5021
23. The product P of three positive integers is 9 times their sum, and one of the integers is the sum of the other two. The sum of all possible values of P is
a 702 b. 540 c. 336 d. 1404
24. What is the remainder when (81)^21 + (27)^21 + (9)^21 + (3)^21 + 1 is divided by (3)^20 + 1
a. 0 b. 61 c. 1 d. 121
25. A three-digit number in base 10 is written in base 9 and base 11 to give two numbers N1 and N2,respectively. What is the probability that N1and N2 are also three-digit numbers?
a. 0.42 b. 0.67 c. 0.55 d. 0.88 e. 0.33
26. What is the sum of the sum of the sum of the digits of 55!?
a. 27 b. 36 c. 5 d. 9
27 .If , then the value of S is
a. 588 b. 373 c. 256 d. 504
28. Let N = 2^15 × 3^12. How many factors of N^2 are less than N but do not divide N completely?
29. How many two-digit positive integers are there which are one and a half times larger than the product of their digits?
a. 0 b. 1 c. 2 d. 3
30. N is a number such that 200 < N < 300 and it has exactly 6 positive divisors. How many different values of N are possible?
a. 12 b. 13 c. 14 d. 15
Sunday, November 29, 2009
Practice questions in Number System PART 1. (Answers are given)
Hi students, practice these questions based on number system, answers are given below the questions. please leave a comment
1. The sum of the first 100 numbers, 1 to 100 is divisible by
(1) 2, 4 and 8 (2) 2 and 4 (3) 2 only (4) None of these
Correct Answer - (3)
2. What is the minimum number of square marbles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm?
(1) 176 (2) 187 (3) 54043 (4) 748
Correct Answer - (2)
3. What is the remainder when 9^1 + 9^2 + 9^3 + …. + 9^8 is divided by 6?
(1) 3 (2) 2 (3) 0 (4) 5
Correct Answer - (3)
4. What is the reminder when 91 + 92 + 93 + …… + 99 is divided by 6?
(1) 0 (2) 3 (3) 4 (4) None of these
Correct Answer - (2)
5. Find the value of 1.1! + 2.2! + 3.3! + ……+n.n!
(1) n! +1 (2) (n+1)! (3) (n+1)!-1 (4) (n+1)!+1
Correct Answer - (3)
6. ‘a’ and ‘b’ are the lengths of the base and height of a right angled triangle whose hypotenuse is ‘h’. If the values of ‘a’ and ‘b’ are positive integers, which of the following cannot be a value of the square of the hypotenuse?
(1) 13 (2) 23 (3) 37 (4) 41
Correct Answer - (2)
7. Two numbers when divided by a certain divisor leave remainders of 431 and 379 respectively. When the sum of these two numbers is divided by the same divisor, the remainder is 211. What is the divisor?
(1) 599 (2) 1021 (3) 263 (4) Cannot be determined
Correct Answer - (1)
8. What is the least number that should be multiplied to 100! to make it perfectly divisible by 350?
(1) 144 (2) 72 (3) 108 (4) 216
Correct Answer - (2)
9. A certain number when successfully divided by 8 and 11 leaves remainders of 3 and 7 respectively. What will be remainder when the number is divided by the product of 8 and 11, viz 88?
(1) 3 (2) 21 (3) 59 (4) 68
Correct Answer - (3)
10. What is the total number of different divisors including 1 and the number that can divide the number 6400?
(1) 24 (2) 27 (3) 27 (4) 68
Correct Answer - (2)
11. When 26854 and 27584 are divided by a certain two digit prime number, the remainder obtained is 47. Which of the following choices is a possible value of the divisor?
(1) 61 (2) 71 (3) 73 (4) 89
Correct Answer - (3)
12. How many times will the digit ‘0′ appear between 1 and 10,000?
(1) 4000 (2) 4003 (3) 2893 (4) 3892
Correct Answer - (3)
13. What number should be subtracted from x^3 + 4x^2 – 7x + 12 if it is to be perfectly divisible by x + 3?
(1) 42 (2) 39 (3) 13 (4) None of these
Correct Answer - (1)
14. What is the value of M and N respectively? If M39048458N is divisible by 8 and 11; Where M and N are single digit integers?
(1) 7, 8 (2) 8, 6 (3) 6, 4 (4) 5, 4
Correct Answer - (3)
15. How many zeros contained in 100!?
(1) 100 (2) 24 (3) 97 (4) Cannot be determined
Correct Answer - (2)
16. When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?
(1) 11 (2) 17 (3) 13 (4) 23
Correct Answer - (3)
17. What is the total number of different divisors of the number 7200?
(1) 20 (2) 4 (3) 54 (4) 32
Correct Answer - (3)
18. When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?
(1) 10 (2) 7 (3) 192 (4) None of these
Correct Answer - (2)
19. A person starts multiplying consecutive positive integers from 20. How many numbers should he multiply before the will have result that will end with 3 zeroes?
(1) 11 (2) 10 (3) 6 (4) 5
Correct Answer - (3)
20. How many four digit numbers exist which can be formed by using the digits 2, 3, 5 and 7 once only such that they are divisible by 25?
(1) 4! - 3! (2) 4 (3) 8 (4) 6
Correct Answer - (2)
1. The sum of the first 100 numbers, 1 to 100 is divisible by
(1) 2, 4 and 8 (2) 2 and 4 (3) 2 only (4) None of these
Correct Answer - (3)
2. What is the minimum number of square marbles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm?
(1) 176 (2) 187 (3) 54043 (4) 748
Correct Answer - (2)
3. What is the remainder when 9^1 + 9^2 + 9^3 + …. + 9^8 is divided by 6?
(1) 3 (2) 2 (3) 0 (4) 5
Correct Answer - (3)
4. What is the reminder when 91 + 92 + 93 + …… + 99 is divided by 6?
(1) 0 (2) 3 (3) 4 (4) None of these
Correct Answer - (2)
5. Find the value of 1.1! + 2.2! + 3.3! + ……+n.n!
(1) n! +1 (2) (n+1)! (3) (n+1)!-1 (4) (n+1)!+1
Correct Answer - (3)
6. ‘a’ and ‘b’ are the lengths of the base and height of a right angled triangle whose hypotenuse is ‘h’. If the values of ‘a’ and ‘b’ are positive integers, which of the following cannot be a value of the square of the hypotenuse?
(1) 13 (2) 23 (3) 37 (4) 41
Correct Answer - (2)
7. Two numbers when divided by a certain divisor leave remainders of 431 and 379 respectively. When the sum of these two numbers is divided by the same divisor, the remainder is 211. What is the divisor?
(1) 599 (2) 1021 (3) 263 (4) Cannot be determined
Correct Answer - (1)
8. What is the least number that should be multiplied to 100! to make it perfectly divisible by 350?
(1) 144 (2) 72 (3) 108 (4) 216
Correct Answer - (2)
9. A certain number when successfully divided by 8 and 11 leaves remainders of 3 and 7 respectively. What will be remainder when the number is divided by the product of 8 and 11, viz 88?
(1) 3 (2) 21 (3) 59 (4) 68
Correct Answer - (3)
10. What is the total number of different divisors including 1 and the number that can divide the number 6400?
(1) 24 (2) 27 (3) 27 (4) 68
Correct Answer - (2)
11. When 26854 and 27584 are divided by a certain two digit prime number, the remainder obtained is 47. Which of the following choices is a possible value of the divisor?
(1) 61 (2) 71 (3) 73 (4) 89
Correct Answer - (3)
12. How many times will the digit ‘0′ appear between 1 and 10,000?
(1) 4000 (2) 4003 (3) 2893 (4) 3892
Correct Answer - (3)
13. What number should be subtracted from x^3 + 4x^2 – 7x + 12 if it is to be perfectly divisible by x + 3?
(1) 42 (2) 39 (3) 13 (4) None of these
Correct Answer - (1)
14. What is the value of M and N respectively? If M39048458N is divisible by 8 and 11; Where M and N are single digit integers?
(1) 7, 8 (2) 8, 6 (3) 6, 4 (4) 5, 4
Correct Answer - (3)
15. How many zeros contained in 100!?
(1) 100 (2) 24 (3) 97 (4) Cannot be determined
Correct Answer - (2)
16. When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?
(1) 11 (2) 17 (3) 13 (4) 23
Correct Answer - (3)
17. What is the total number of different divisors of the number 7200?
(1) 20 (2) 4 (3) 54 (4) 32
Correct Answer - (3)
18. When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?
(1) 10 (2) 7 (3) 192 (4) None of these
Correct Answer - (2)
19. A person starts multiplying consecutive positive integers from 20. How many numbers should he multiply before the will have result that will end with 3 zeroes?
(1) 11 (2) 10 (3) 6 (4) 5
Correct Answer - (3)
20. How many four digit numbers exist which can be formed by using the digits 2, 3, 5 and 7 once only such that they are divisible by 25?
(1) 4! - 3! (2) 4 (3) 8 (4) 6
Correct Answer - (2)
try to solve these number system questions PART 1 ???
Hi solve these questions and post your answers.
1. If 8 are written 88 times side by side, we shall get a large number of 88 digits. What is the remainder when 7 divide this large number?
a. 1 b. 4 c. 3 d. 5
2. How many four-digit numbers are there with less than 6 different prime factors?
a. 1224 b. 8476 c. 9000 d. 7613
3. A = 1111……………..1(46 times) and M = 2222………………..2(64 times). What is the remainder when AM is divided by 18?
a. 6 b. 16 c. 4 d. none of these
4. A is the product of ten consecutive two-digit numbers. Y is the highest power of 5 in A. what can be the maximum value of Y?
a. 4 b. 3 c. 2 d. 1
5. How many different factors of 105 end with zero?
a. 5 b. 16 c. 25 d. none of these
6. A = 10! + 12! + 14! + 16! +…………100!. The highest power of 2 in A is
a. 9 b. 7 c. 10 d. none of these
7. A is the product of first 100 multiples of 8, i.e. A = 8 16 24 ………..800. How many zeros would be there at the end of A?
a. 10 b. 12 c. 11 d. none of these
8. A = 155216, how many factors of A are there?
a. 217 b. 47089 c. 46656 d. none of these
9. The remainder when 25! is divided by 107 is
a. 2 b. 4 106 c. 6 106 d. 2 106
10. You write first 56 even numbers, how many times will you be writing the digit 2?
a. 12 b. 11 c. 16 d. 17
11. Product of 11 irrational number would always be
a. Irrational b. Rational
c. Can be anything rational or irrational d. none of these
12. You are selecting 10 numbers randomly out of the first 100 odd numbers. Sum of these 10 odd numbers is A. How many different values of A are possible?
a. 100C10 b. 1801 c. 1800 d. 901
13. A is a natural number. H.C.F. of A+10, A+15, A+20, A +25 and A+26 is
a. A b. A+1 c. 1 d. depends on the value of A
14. A = 626! – 625! . How many consecutive zeros would be there at the end of A?
a. 156 b. 160 c. 1 d. none of these
15. A (x) = 10 –x. what is the LCM of A (2), A (3), A (4), A (5) AND A (-1)?
a. A (2) b. A (3) c. A (5) d. A (-1)
1. If 8 are written 88 times side by side, we shall get a large number of 88 digits. What is the remainder when 7 divide this large number?
a. 1 b. 4 c. 3 d. 5
2. How many four-digit numbers are there with less than 6 different prime factors?
a. 1224 b. 8476 c. 9000 d. 7613
3. A = 1111……………..1(46 times) and M = 2222………………..2(64 times). What is the remainder when AM is divided by 18?
a. 6 b. 16 c. 4 d. none of these
4. A is the product of ten consecutive two-digit numbers. Y is the highest power of 5 in A. what can be the maximum value of Y?
a. 4 b. 3 c. 2 d. 1
5. How many different factors of 105 end with zero?
a. 5 b. 16 c. 25 d. none of these
6. A = 10! + 12! + 14! + 16! +…………100!. The highest power of 2 in A is
a. 9 b. 7 c. 10 d. none of these
7. A is the product of first 100 multiples of 8, i.e. A = 8 16 24 ………..800. How many zeros would be there at the end of A?
a. 10 b. 12 c. 11 d. none of these
8. A = 155216, how many factors of A are there?
a. 217 b. 47089 c. 46656 d. none of these
9. The remainder when 25! is divided by 107 is
a. 2 b. 4 106 c. 6 106 d. 2 106
10. You write first 56 even numbers, how many times will you be writing the digit 2?
a. 12 b. 11 c. 16 d. 17
11. Product of 11 irrational number would always be
a. Irrational b. Rational
c. Can be anything rational or irrational d. none of these
12. You are selecting 10 numbers randomly out of the first 100 odd numbers. Sum of these 10 odd numbers is A. How many different values of A are possible?
a. 100C10 b. 1801 c. 1800 d. 901
13. A is a natural number. H.C.F. of A+10, A+15, A+20, A +25 and A+26 is
a. A b. A+1 c. 1 d. depends on the value of A
14. A = 626! – 625! . How many consecutive zeros would be there at the end of A?
a. 156 b. 160 c. 1 d. none of these
15. A (x) = 10 –x. what is the LCM of A (2), A (3), A (4), A (5) AND A (-1)?
a. A (2) b. A (3) c. A (5) d. A (-1)
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