Numbers
NUMBERS
QUESTION & ANSWERS
(a) 8452*7156*2143*1567
(1)2 (2)4 (3)6 (4)8
(b)248 x749x948
(1)2 (2)4 (3)6 (4)8
(c)34n x92nx6n,
where n is any natural number.
(1)2 (2)4 (3)6 (4)8
(a) Which of the following numbers is divisible by both 4 and 9?
(1)2368 (2)2736 (3)3954 (4)3814
(b) Which of the following numbers is divisible by both 8 and 9?
(1)2458 (2)2244 (3)2448 (4)3968
(c) Which of the following numbers is divisible by 6?
(1)2842 (2)2425 (3)2547 (4)2730
(d) Which of the following numbers is divisible by both 11 and 12?
(1)4830 (2)2640 (3)3584 (4)4686
(e) Which of the following numbers is divisible by both 15 and 24?
(1)4680 (2)3630 (3)2460 (4)5460
3.
(a) Which of the following numbers is divisible by 36?
(1)3368 (2)3672 (3)2542 (4)2850
(b) Which of the following numbers is divisible by both 32 and 2?
(1)3732 (2)5280 (3)4120 (4)5242
(c) Which of the following numbers is divisible by both 12 and 18?
(1)7524 (2)3654 (3)3027 (4)5136
(d) Which of the following numbers is divisible by 25?
(1)3075 (2)2150 (3)5000 (4)All the above
4. In each of the following numbers, what should be the missing digit in the indicated place such that the number is a multiple of 11?
(a)945678_
(1)3 (2)2 (3)7 (4)5
(b)37679_
(1)4 (2)7 (3)5 (4)2
15.find the least and greatest three digit number which when increased by 6 are exactly divisible by 9,27 and 15 ?
(1)192 and 939 (2)192 and 993 (3)129 and 932 (4)129 and 993
16. Find the least number to be added to 2700 so that a remainder of 2 is left when the resulting number is divided by 18,12 and 20.
(1)1 (2)2 (3)32 (4)42
17.A number when divided successively by 7 and 5 leaves a remainders of 6 and 4. find the remainder when the smallest such number is divided by 20.
(1)18 (2)14 (3)9 (4)15
18. Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5.
(1)187 (2)197 (3)207 (4)219
19. Find the smallest number which when divided by 3,5,7 and 9 leaves respective remainders of 2,4,6 and 8.
(1)344 (2)343 (3)314 (4)328
20.Find the greatest number which divides 6155 and 4935 leaving remainders of 5 and 15 respectively.
(1)1230 (2)1240 (3)1235 (4)2470
21. Find the greatest number which divides 83, 125 and 209 leaving remainders in each case.
(1)19 (2)17 (3)42 (4)23
22. Two numbers have a H.C.F of 16 and a product of two numbers is 2560. find the L.C.M of the two numbers.
(1)140 (2)150 (3)160 (4)170
23.Two numbers have an H.C.F of 8 and a L.C.M of 1960. Find the number of such possible pairs.
(1)One (2)Two (3)Three (4)Four
24.Find the smallest number which should be multiplied with 520 to make it a perfect square.
(1)130 (2)120 (3)55 (4)35
25.Find the least number with which 16200 should be multiplied with to make it a perfect cube.
(1)36 (2)48 (3)45 (4)360
26.Find the number of divisors of 1764 excluding 1 and itself.
(1)18 (2)27 (3)25 (4)12
27. In how many ways can 3663 be resolved into two factors?
(1)6 (2)8 (3)12 (4)18
28.For what values of n are the following statements are true?
(a)5^2n -1 is divisible by 8 for
(1)Even values of n (2)Odd values of n (3)all values of n (4)can't say
(b)8^n +1 is divisible by 3 for
(1)Odd values of n (2)even values of n (3)all values of n (4) can't say.
29.If x^2+ax+3 is divisible by x-2, find a.
(1)-3/4 (2)-7/2 (3)-3/4 (4)-7/4
30. If 4x^2+4x+b is divisible by x+2, find b
(1)-8 (2)-6 (3)-4 (4)-10
31.Find the remainder when 2^76 is divided by 15
(1)1 (2)3 (3)7 (4)11
32.Find the remainder when 2^66 is divided by 65.
(1)1 (2)17 (3)33 (4)64
33.Find the sum of all the distinct possible remainders when 3n is divided by 5, where n is an integer?
(1)20 (2)10 (3)18 (4)21
34.find the largest power of 3 in 120
(1)58 (2)51 (3)48 (4)40
35.Find the number of zeroes at the end of 400.
(1)84 (2)74 (3)99 (4)89
(1)2842 (2)2425 (3)2547 (4)2730
(d) Which of the following numbers is divisible by both 11 and 12?
(1)4830 (2)2640 (3)3584 (4)4686
(e) Which of the following numbers is divisible by both 15 and 24?
(1)4680 (2)3630 (3)2460 (4)5460
3.
(a) Which of the following numbers is divisible by 36?
(1)3368 (2)3672 (3)2542 (4)2850
(b) Which of the following numbers is divisible by both 32 and 2?
(1)3732 (2)5280 (3)4120 (4)5242
(c) Which of the following numbers is divisible by both 12 and 18?
(1)7524 (2)3654 (3)3027 (4)5136
(d) Which of the following numbers is divisible by 25?
(1)3075 (2)2150 (3)5000 (4)All the above
4. In each of the following numbers, what should be the missing digit in the indicated place such that the number is a multiple of 11?
(a)945678_
(1)3 (2)2 (3)7 (4)5
(b)37679_
(1)4 (2)7 (3)5 (4)2
(c)7_56369
(1)2 (2)3 (3)4 (4)1
(1)2 (2)3 (3)4 (4)1
(d)65428_1
(1)1 (2)2 (3)3 (4)4
(e)129_
(1)4 (2)3 (3)6 (4)8
5. What should be the least number to be added to the following numbers to make them divisible by 9?
(a)51234
(1)6 (2)4 (3)3 (4)5
(1)1 (2)2 (3)3 (4)4
(e)129_
(1)4 (2)3 (3)6 (4)8
5. What should be the least number to be added to the following numbers to make them divisible by 9?
(a)51234
(1)6 (2)4 (3)3 (4)5
(b)96346
(1)8 (2)0 (3)9 (4)7
(c)79325
(1)8 (2)7 (3)1 (4)6
(d)123456
(1)6 (2)3 (3)5 (4)4
(e)491
(1)4 (2)5 (3)3 (4)6
6. Express the following numbers as product of powers of prime factors
(a)16800
(1)8 (2)0 (3)9 (4)7
(c)79325
(1)8 (2)7 (3)1 (4)6
(d)123456
(1)6 (2)3 (3)5 (4)4
(e)491
(1)4 (2)5 (3)3 (4)6
6. Express the following numbers as product of powers of prime factors
(a)16800
(1)2^5*5^2*3*7 (2)2^5*5*3*7 (3)2^4*5^2*3*7 (4)2^5*5^2*3^2*7
(b)676
(1)2^2*13^2 (2)2^3*13 (3)2*13^3 (4)None of these
(c)4477
(1)11^2*37 (2)11*37^2 (3)11*37 (4)None of these
(d)2860
(1)11*13*2^2*5 (2)11*13^2*2*5 (3)11*13*2*5^2 (4)11^2*13*2*5
(e)2160
(1)2^5*3^3*5 (2)2^4*3^3*5 (3)2^6*3^3*5 (4)2^5*3^2*5^2
7. Simplify the following
(a)221*775+343*425
(1)336200 (2)328100 (3)316600 (4)317050
(b)3 5/6+6 1/7-2 1/3-1 1/2
(1)6 1/7 (2)6 1/21 (3)6 1/14 (4)6 5/28
8. Find the square roots of the following perfect squares
(a)18769
(1)131 (2)133 (3)137 (4)139
(b)222.01
(1)14.3 (2)14.1 (3)14.7 (4)14.9
(c)8836
(1)92 (2)94 (3)96 (4)98
9. A number when divided by 162 leaves a remainder of 29. find the remainder when the same number is divided by 27.
(1)2 (2)3 (3)4 (4)5
10.Express 0.48bar71 as fraction.
(1)4823/9000 (2)4823/9900 (3)4893/9990 (4)None of these.
11. Which of the following pairs of numbers are relative primes?
(a)24,25 (b)133,285 (c)210,255 (d)15,91 (e)123,164
(1)only (a) (2)Only (a), (d) and (e) (3)Only (a) and (d) (4)Only (d) and (e)
12. Find the respective L.C.M and H.C.F of the following.
(a)18,27,36
(1)108,9 (2)108,3 (3)144,3 (4)144,9
(b)81,216
(1)944,3 (2)648,27 (3)5256,3 (4)5256,9
(c)9/13, 7/11, 3/8
(1)189, 1/1144 (2)63, 1/1144 (3)1/1144, 189 (4)1/1144, 378
(d)5/6, 13/9, 7/12
(1)455/3, 1/36 (2)385/3, 1/18 (3)1/36, 385/3 (4)1/18, 385/3
(e) 14, 25
(1)350,1 (2)175,1 (3)525,1 (4)875,1
13. Four bells toll at intervals of 10 seconds, 15 seconds, 20 seconds and 30 seconds respectively. If they toll together at 10.00 a.m., at what time will they toll together for the first time after 10 a.m.?
(1)10:01 a.m. (2)10:02 a.m. (3)10:00:30 a.m. (4)10:00:45 a.m.
14. Find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case.
(1)386 (2)391 (3)388 (4)397
(1)10:01 a.m. (2)10:02 a.m. (3)10:00:30 a.m. (4)10:00:45 a.m.
14. Find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case.
(1)386 (2)391 (3)388 (4)397
15.find the least and greatest three digit number which when increased by 6 are exactly divisible by 9,27 and 15 ?
(1)192 and 939 (2)192 and 993 (3)129 and 932 (4)129 and 993
16. Find the least number to be added to 2700 so that a remainder of 2 is left when the resulting number is divided by 18,12 and 20.
(1)1 (2)2 (3)32 (4)42
17.A number when divided successively by 7 and 5 leaves a remainders of 6 and 4. find the remainder when the smallest such number is divided by 20.
(1)18 (2)14 (3)9 (4)15
18. Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5.
(1)187 (2)197 (3)207 (4)219
19. Find the smallest number which when divided by 3,5,7 and 9 leaves respective remainders of 2,4,6 and 8.
(1)344 (2)343 (3)314 (4)328
20.Find the greatest number which divides 6155 and 4935 leaving remainders of 5 and 15 respectively.
(1)1230 (2)1240 (3)1235 (4)2470
21. Find the greatest number which divides 83, 125 and 209 leaving remainders in each case.
(1)19 (2)17 (3)42 (4)23
22. Two numbers have a H.C.F of 16 and a product of two numbers is 2560. find the L.C.M of the two numbers.
(1)140 (2)150 (3)160 (4)170
23.Two numbers have an H.C.F of 8 and a L.C.M of 1960. Find the number of such possible pairs.
(1)One (2)Two (3)Three (4)Four
24.Find the smallest number which should be multiplied with 520 to make it a perfect square.
(1)130 (2)120 (3)55 (4)35
25.Find the least number with which 16200 should be multiplied with to make it a perfect cube.
(1)36 (2)48 (3)45 (4)360
26.Find the number of divisors of 1764 excluding 1 and itself.
(1)18 (2)27 (3)25 (4)12
27. In how many ways can 3663 be resolved into two factors?
(1)6 (2)8 (3)12 (4)18
28.For what values of n are the following statements are true?
(a)5^2n -1 is divisible by 8 for
(1)Even values of n (2)Odd values of n (3)all values of n (4)can't say
(b)8^n +1 is divisible by 3 for
(1)Odd values of n (2)even values of n (3)all values of n (4) can't say.
29.If x^2+ax+3 is divisible by x-2, find a.
(1)-3/4 (2)-7/2 (3)-3/4 (4)-7/4
30. If 4x^2+4x+b is divisible by x+2, find b
(1)-8 (2)-6 (3)-4 (4)-10
31.Find the remainder when 2^76 is divided by 15
(1)1 (2)3 (3)7 (4)11
32.Find the remainder when 2^66 is divided by 65.
(1)1 (2)17 (3)33 (4)64
33.Find the sum of all the distinct possible remainders when 3n is divided by 5, where n is an integer?
(1)20 (2)10 (3)18 (4)21
34.find the largest power of 3 in 120
(1)58 (2)51 (3)48 (4)40
35.Find the number of zeroes at the end of 400.
(1)84 (2)74 (3)99 (4)89
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