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: 8

Explanation:

9321 = 3 x 13 x 239 = 31 x 13 1 x 239 1 ; add one to all the powers ie.,

(1+1) x (1+1) x (1+1)= 8 ;

we get eight factors.

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: 961 x 961

Explanation:

We know that  a m × a n = a m + n 

? 31 31 - 27 =  31 4 = 961 x 961.

Correct Answer: 0

Explanation:

15 23 + 23 23 = 19 - 4 23 + 19 + 4 23  

 The remainder on dividing by 19 will be  - 4 23 + 4 23= 0.

Correct Answer: 26

Explanation:

The pattern is three consecutive numbers and then three consecutive numbers missing.Then four consecutive numbers and then four consecutive numbers missing.Then five consecutive numbers and then five consecutive numbers missing.

 

The next number=20+6=26

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: 152 to 164

Explanation:

A+7B=112

it is clear that A = 14, then it becomes A>=B, but A is smallest angle) given
so, range of A is 0.0001 to 13.9999 ( I am taking upto 4 decimal places)
so, range of B becomes 14 to 16 ( after rounding off to 4 decimal places)
so, range of C becomes 152 to 164 ( after rounding off to 4 decimal places)

Correct Answer: i

Explanation:

We know that,

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