The unit digit of term (864 – 464) will be.
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Solution
unit digit of 864 = 6
unit digit of 464 = 6
so unit digit of term is 6-6=0
The remainder when (91 + 92 + 93 +………… +98) is divided by 6.
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Solution
By dividing 9 there is always '3' remainder. total terms are 8.
∴ = remainder = 0
What is the maximum value of ‘m’ such that 7m divides 21! completely ?
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Solution
In 21! there are three 7
So maximum value of m = 3.
What digit should come at the place of “a” if the number “83274a” is divisible by 8 ?
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Solution
To be divisible by 8 → Last three digits should be multiple of 8.
∴ a = 4
Which of the following can not be a perfect square of a integer number ?
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Solution
Perfect square of any integer number, never ends with 2
What will be the remainder when 6768 is divided by 68 ?
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Solution
= remainder = 1 (negative remainder method)
The unit digit of the following term will be?
264102 + 264103
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Solution
(264)102 + (264)103
⇒ (4)2 + (4)3 dividing the powers by 4.
⇒ 6 + 4 taking only unit digits.
⇒ 0
What will be the remainder when 289 is divided by 89?
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Solution
Short trick = Where p is a prime number then remainder will be 2.
So, remainder = 2.
The product of four consecutive even numbers will always be divisible by which highest number ?
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Solution
The first four even numbers are 2, 4, 6, 8
Multiple then = 2 × 4 × 6 × 8 = 384.
Find the total number of prime numbers from 1 to 100.
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Solution
25 by counting