# Quiz at GanitCharcha

Welcome to GanitCharcha's Quiz page. Our quizzes are not made to test one or to help one test how much Mathematics on a given topic he/she knows, rather it is purposefully designed to help people feel motivated to learn. Our quizzes will help to paint the construction of one's own mathematical understanding while instilling love for the subject. Under the broad name of Quiz, one can also find different types of Math problems to challenge his/her math mind.

## Quiz : On the works of mathematician Srinivasa Ramanujan

1
What is Hardyâ€“Ramanujan number which is the smallest number that can be expressed as the sum of two cubes in two different ways?

2
Given a positive integer $x$, prime counting function ($f$) outputs number of primes that are less than $x$. Now, the value $f(x) - f(x/2)$ will only change if we obtain another prime which means that $x$ itself is prime. Therefore, $f(x) - f(x/2) \geq n$, if $x \geq R_{n}$ and these $R_{n}$'s are all primes and is referred as Ramanujan Primes. (http://en.wikipedia.org/wiki/Ramanujan_prime)

The smallest Ramanujan Prime number greater than 10 is

3
Who is the first Indian to be elected as the fellow of the Royal Society?

4
Who is the first Mathematician to be elected as the fellow of the Royal Society?

5
The problem of finding the solutions for $a$, $b$, $m$, $n$ and $x$, $y$ such that $a^{3} + b^{3} = m^{3} + n^{3} = x^{3} + y^{3}$ is known as

6
Ramanujan was awarded Bachelor of Science by Research in 1916 (latter referred as Ph.D) for his work on

7
A positive integer which has more divisors than any smaller positive integer is called

8
The first five Highly Composite Numbers are

9
Which one is not a highly composite number?

10
Apart from Number Theory and Mathematical Analysis, Ramanujan has great contributions in the area of

11
Ramanujan worked extensively with the following two English Mathematicians.

12
A positive integer on a given base if is divisible by the sum of it's digits on the same base, is called a Harshad number.
Which one is not a Harshad number

13
In the December 1914 issue of the English magazine 'Strand', a King's college student saw the following puzzle and narrated it to Ramanujan. In a long street there are $n$ number of houses where $n$ is greater than 50 and less than 500. And houses are numbered from left to right as 1, 2, 3, .. so on to $n$. The problem is to find a house with number $x$ such that the sum of the house numbers to the left of it equals the sum of the house numbers to its right. Ramanujan while was cooking vegetables in a frying pan gave the most general soloution to the whole class of problems not just the one with the constraint $50 < n < 500.$ Who is the King's college student who narrated the problem to Ramanujan?

14
In the December 1914 issue of the English magazine 'Strand', a King's college student saw the following puzzle and narrated it to Ramanujan. In a long street there are $n$ number of houses where $n$ is greater than 50 and less than 500. And houses are numbered from left to right as 1, 2, 3, .. so on to $n$. The problem is to find a house with number $x$ such that the sum of the house numbers to the left of it equals the sum of the house numbers to its right. Ramanujan while was cooking vegetables in a frying pan gave the most general soloution to the whole class of problems not just the one with the constraint $50 < n < 500.$ What is the solution for this specific instance of the problem?

Number of positive integers that are less than a given integer $x$ and can be expressed as sum of two square numbers is proportional to $x$ divided by square root of $ln(x)$, i.e., $\frac{x}{\sqrt{ln(x)}}$.
And the constant of proportionality as $x$ grows to infinity is called Landau-Ramanujan constant and its value is