Mathematics - Online Test

y=4at

Squaring both sides,we get

y2=16a2t2

Putting the value of at2 i.e. at2=y216a in  x = at2 we get,

16ax=y2

or y2=4(4a)x

which is nothing but equation of parabola.

First we will find the number of four digit numbers that can be formed using the digits 0,1,2,3,4,5,6,7,8,9  with repetition .

The first place can be filled by any of the 9 digits other than 0, and the second, third and the fourth places each  can be filled by any of the ten digits

Hence the total number of ways of forming a four digit number = 9×10×10×10=9000

Now we will find the number of four digit numbers in which nall the digits are distinct 

The first place can be filled by any of the 9 digits other than 0, and the second, can be filled by any of the remaining 9 digits since repetition is not possible

Similarly  third and the fourth places each  can be filled by 8 and 7 digits respectively

Hence the total number of ways of forming a four digit number  with distinct digits b= 9×9×8×7=4536

The total number of numbers from 1000 to 9999 (both inclusive) that do not have 4 different digits=9000−4536=4464