Correct Answer: 2

Explanation:

Let n = 4 q + 3. Then 2 n = 8 q + 6   = 4(2 q + 1 ) + 2.

Thus, when 2n is divided by 4, the remainder is 2.

Correct Answer: 2

Explanation:

Since 653xy is divisible by 5 as well as 2, so y = 0.
Now, 653x0 must be divisible by 8.
So, 3x0 must be divisible by 8. This happens when x = 2
x + y = (2 + 0) = 2.

Correct Answer: 31

Explanation:

Let the three consecutive odd numbers be x, x+2, x+4

Then,

x + x + 2 + x + 4 = 93

=> 3x + 6 = 93

=> 3x = 87

=> x = 29 => 29, 31, 33 are three consecutive odd numbers.

 

Therefore, the middle number is 31.

Correct Answer: 12

Explanation:

we can do this by trial and error method.

Putting x = 2,we get 2²(2² - 1) = 12.
checking with other integers, the above equation always gives a value which is a multiple of 12,
So, x²(x² - 1) is always divisible by 12.

Correct Answer: 1

Explanation:

The mutiplicative inverse of a number is nothing but a reciprocal of a number.

Now, the product of a number and its multiplicative inverse is always equal to 1.

 

For example :

Let the number be 15

Multiplicative inverse of 15 = 1/15

The product of a number and its multiplicative inverse is = 15 x 1/15 = 1.

Correct Answer: 5

Explanation:

By trial and error method, we get
2880/3 = 960 is not a perfect square
2880/4 = 720 is not a perfect square
2880/5 = 576 which is perfect square of 24
Hence, 5 is the least number by which 2880 must be divided in order to make it into a perfect square.

Correct Answer: i

Explanation:

We know that,

$$\begin{gathered} i 2 = - 1 \\ i 3 = i 2 x i = - 1 x i = - i \\ i 4 = i 2 x i 2 = - 1 x - 1 = 1 \\ Hence , i 233 = i 4 x 58 + 1 = i 232 x i 1 = 1 x i = i \end{gathered}$$

Correct Answer: 400

Explanation:

The value of 4 in 475 means the place value of 4 in 475 and not its face value. Face value means the digit itself though it is at any place in the given number. But place value means the value of digit in its place in the given number.

 

Here the place value of 4 in 475 can be determined by as 4 is in 100's place in 475.

Hence, the place value of 4 in 475 is 4x100 = 400.

Correct Answer: 555681

Explanation:

Given number is 987 = 3 x 7 x 47.

So, required number must be divisible by each one of 3, 7, 47.

None of the numbers in 553681 and 555181 are divisible by 3. While 556581 is not divisible by 7.
Correct answer is 555681.

Correct Answer: 21

Explanation:

A prime number is a whole number greater than 1 whose only factors are 1 and itself.

 

Factors of 5 are 1, 5

Factors of 11 are 1, 11

Factors of 21 are 1, 3, 7, 21

Factors of 37 are 1, 37.

 

Hence, according to the definition of a prime number, 21 is not a prime number as it has more than two factors.