Numbers Questions

We know that am×an=am+n 

∴3131-27 = 314 = 961 x 961.

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.

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.

The weight will be 250g plus (1.55 - 0.65)/0.10 units of 100g

250 + 900 = 1150

This is the maximum weight that can be sent at that price. But, weights exceeding

250 + 800 will also get charged this amount (that is what the ‘part thereof’ implies).

Hence a package weighing 1145 will be charged $1145

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

The next number=119+49=168

We know that,

$$\begin{gathered} i2 = -1 \\ i3 = i2 x i = -1 x i = -i \\ i4 = i2 x i2 = -1 x -1 = 1 \\ Hence, i233 =i4 x 58 + 1 = i232 x i1 = 1 x i = i \end{gathered}$$