Latest Questions, General Mathematics

Question: `4^(61) + 4^(62) + 4^(63) + 4^(64)` is divisible by :
A
3

B
11

C
13

D
17

Note: Not available
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Question: The unit digit in the sum` (264)^(102) + (264)^(103)` is :
A
0

B
4

C
6

D
8

Note: Not available
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Question: If` p = 3/5, q = 7/9` and` r = 5/7`, then
A
`p < q < r`

B
`q < r < p`

C
`p < r < q`

D
`r < q < p`

Note: `p = 3/4 = 0.6, q = 7/9 = 0.777, i.e.r = 0.714` Clearly, `0.6 <0.714 < 0.777 i.e p< r < q.
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Question: The number of prime factors of`(6)^(10) xx (7)^(17) xx (55)^(27)` is :
A
54

B
64

C
81

D
91

Note: `(6)^(10) xx (7)^(17) xx (55)^(27)` `= 2^(10) xx 3^(10) xx 7^(17) xx 5^(27) xx 11^(27)` :. The total number of prime factors `= (10 + 10 + 17 + 27 + 27) = 91`
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Question: which of the following numbers is a multiple of 11 ?
A
`978626`

B
`112144`

C
`447355`

D
`869756`

Note: `(6 + 6 + 7) - (2 + 8 + 9) = 0,` So, 978626 is divisible by 11
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Question: which of the following numbers is a multiple of 11 ?
A
`978626`

B
`112144`

C
`447355`

D
`869756`

Note: `(6 + 6 + 7) - (2 + 8 + 9) = 0,` So, 978626 is divisible by 11
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Question: The number of prime factors in` (1/6)^(12) xx (8)^(25) xx (3/4)^(15)` is :
A
33

B
37

C
52

D
None

Note: `(1/6)^(12) xx (8)^(25) xx (3/4)^(15)` `= 1/(2^(12) xx 3^(12)) xx (2^3)^(25) xx 3^(15)/(2^15 xx 2^15)` `= (2^75 xx 3^15)/(2^42 xx 3^12)` `= 2^33 xx 3^3` :. Total number of prime factors `= (33 + 3) = 36`
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Question: `(51 + 52 + 53 + ______ + 100) = ?`
A
`(51 xx 52)/2`

B
`(52 xx 53)/2`

C
`(100 xx 50)/2`

D
`3775`

Note: Not available
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Question: A number when divided by 32 leaves the remainder 29. This number when divided by 8 will leave the remainder :
A
3

B
5

C
7

D
29

Note: Let the given number be x. The when divided by 32. suppose gives the quotient k. Then, `x = 32 k + 29 = 8 xx (4 k + 3) + 5` Thus, when x is divided by 8. it gives `(4 k + 3)` as quotient and 5 as remainder.
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Question: If` a/b = 4/5` and` b/c = 15/16,` then` (c^2 - a^2)/(c^2 + a^2) = ?`
A
`1/7`

B
`7/25`

C
`3/4`

D
None

Note: `a/c = a/b xx b/c = 4/5 xx 15/16 = 3/4` `:. (c^2 - a^2)/(c^2 + a^2)` `= (1 - a^2/c^2)/(1 + a^2/c^2)` `= (1 - 9/16)/(1 + 9/16)` `= 7/16 xx 16/25` `= 7/25`
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Question: `4^(61) + 4^(62) + 4^(63) + 4^(64)` is divisible by :

Question: The unit digit in the sum` (264)^(102) + (264)^(103)` is :

Question: If` p = 3/5, q = 7/9` and` r = 5/7`, then

Question: The number of prime factors of`(6)^(10) xx (7)^(17) xx (55)^(27)` is :

Question: which of the following numbers is a multiple of 11 ?

Question: which of the following numbers is a multiple of 11 ?

Question: The number of prime factors in` (1/6)^(12) xx (8)^(25) xx (3/4)^(15)` is :

Question: `(51 + 52 + 53 + ______ + 100) = ?`

Question: A number when divided by 32 leaves the remainder 29. This number when divided by 8 will leave the remainder :

Question: If` a/b = 4/5` and` b/c = 15/16,` then` (c^2 - a^2)/(c^2 + a^2) = ?`