Online quizzes: Mathematics

Question 1: Find the value of the box with the question mark.

online quizzes: Math

Answer: 

First, observe, the value in the first box of the second row is nothing but the average values of the two boxes in the first row. The same pattern follows for the rest of the rows. Since the average value of 25 and 13 is 19. The answer is 19.

Question 2: How to write 1 using 10 digits (0 to 9)?

Answer:
There are two ways to solve this problem. First,  one can try to write 1 as a summation of two fractions like the following.

 ,

Here all 10 digits (0,1,2,3,4,5,6,7,8,9) are present in the right hand expression.
The second way of writing 1 using 10 digits is the following.

, [ Using the fact that the 0th power of a number is 1]

Question 3: How to write 10 using five nines?

Answer:
We can write in the following ways.

 ,         ,      ,         

Question 4: How many ones are there between 1 to 100?

Answer: 21
List of numbers is the following.
{1,10,11,12,13,14,15,16,17,18,19,21,31,41,51,61,71,81,91,100}
Now, count the total number of ones that are there. 

Question 5:
Given that,    ,  then find the value of the following expression.



Answer:
 ,    

This implies that the roots of the given quadratic equation are x=1. So putting x=1, we find the required answer to be 2.