What is the remainder when 1523+2323 is divided by 19 ?

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: 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: 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: 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: Vr / (12 - V)

Explanation:

We have to rearrange the equation to make R the subject.

Start by cross multiplying by (r + R); V (r + R) = 12R

Multiply out the bracket Vr + VR = 12R

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: 168

Explanation:

The pattern is -4, +9,-16, +25, -36

The next number=119+49=168

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,

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

Correct Answer: 6 and 12 both

Explanation:

6 n 2 + 6 n = 6 n n + 1, which is always divisible by 6 and 12 both, since n(n+1) is always even.