# Intercollegiate Math Quiz

On April the 2nd 2016, I was in my Alma mater Don Bosco Institute of Technology, Kurla, for the intercollegiate math quiz organized by the math club, Domain (Don bOsco Math Activity INitiative). I was the member of this math club from 2012 to 2014 and was the vice chairman in my third year of engineering, 2012 to 2013. It was a joy to see our little Math club growing to such a big entity and inspiring students from other colleges to establish their own math club.

The quiz had four levels. First three levels were done on paper. Each level had math questions and also some general knowledge questions related to math and mathematicians. After each level, some of the teams were eliminated. There were also spot questions asked in between two levels and spot prizes were awarded to those who answered them correctly. At the end of three levels, five teams were selected for the final level.

At the end of four rounds, Anand Chitrao and Akshay Sant from Ruia College, Matunga were the winners by a huge margin. We congratulate them for their success.

The question and answers for the rapid fire round are as below…

1. If A=B and B=C then A=C, what is his property called?

Ans: Transitive Property

1. On whose life was the movie “A Beautiful Mind” starring Russell Crowe was made?

Ans: John Nash

1. For a triangle of uniform density, where will its center of mass lie?

Ans: Centroid

1. Set of numbers which can form the lengths of a right angled triangle is also known as what?

Ans: Pythagorean Triplet

1. If toffee costs Rs. 100 less than a pastry and the total bill was 101, what is the price of that toffee?

Ans: Rs. 0.5

1. Word radiation comes from which geometric term?

1. If y is inversely proportional to x, which curve do you find on the y vs x graph?

Ans: Rectangular Hyperbola

1. When will the equation x^n + y^n = C represent a square?

Ans: When n tends to infinity

1. If I take 80 minutes each to run three of the sides of a square ground and 1 hr 20 min for the last side, what is the ratio of my speed in the last leg to that of the first three?

Ans: 1

1. Hypothetically if iron is twice as dense as copper what will be heavier, a kilo of iron or a kilo of copper?

Ans: They both weigh the same

1. What sentence is called the Liar’s Paradox?

Ans: I am lying

1. If a bacterium doubles its population every minute, and takes 45 minutes to occupy a quarter of the bottle, after how many minutes will they fully occupy the entire bottle?

Ans: 2 minutes

1. If frog jumps a slope which is 10 feet long, covers 3 feet in every jump and slips down 2 feet, how many jumps will it require to jump over the top?

Ans: 8

1. Who is known as the man who knew infinity?

Ans: Srinivasa Ramanujan

1. Which geometric shape has the minimum surface area for a given volume?

Ans: Sphere

1. Which shape is used for making dish antenna and solar thermal collector?

Ans: Paraboloid

1. Which curve represents the path which requires minimum time for a body to reach from point A to point B under gravity?

Ans: Cycloid

1. What number is 10^100?

Ans: Googol

1. Which conic section do you get when you cut the cone parallel to its axis?

Ans: Hyperbola

1. A guy walks 10 km due north in a straight line and ends up 5 km further away from North pole than he originally was, how is that possible?

Ans: He was 2.5 km away from North Pole initially

1. What number is known as the Golden Ratio?

Ans: 1.618

1. In a lucky draw contest there are 100 people participating including me, I cheated and put my name in the box 5 times. What is the probability that my name will come up?

Ans: 5/104

1. Who is believed to be the first to prove that irrational numbers exists?

Ans: Hippasus of Metapontum

1. If two matrices are multiplied and the resultant matrix is n times the second matrix which was multiplied, what is n known as?

Ans: Eigen value

1. In numerical integration which rule approximates the curve as a straight line?

Ans: Trapezoidal Rule

1. If the derivative of a function is 0, it can either be maxima, minima or ______?

Ans: Point of Inflection

1. Which geometric shape has the least perimeter for the given area?

Ans: Circle

1. Which curve do you get if you cut a cone parallel to its edge?

Ans: Parabola

1. Which point marks the center of the circle which touches all the three sides of the triangle?

Ans: Incenter

1. In a 30-60-90 triangle, what is the ratio of side opposite to 60 degree to the side opposite to 30 degree?

Ans: Sqrt(3)

1. Who is known as the father of geometry?

Ans: Euclid

1. What geometrical shape do we get by connecting two opposite Mobius strips?

Ans: Kline bottle

1. Which geometrical shape does the equation x + y = 5 represent in three dimensions?

Ans: Plane

1. Which medal is often described as the “Nobel Prizeof Mathematics“?

Ans: Fields medal

1. Which conic section do we get if we cut a cone through its vertex?

Ans: Pair of straight lines

1. In numerical integration, which rules approximate a curve to parabola?

Ans: Simpson’s rules

1. Which curve shows brachistochrone property?

Ans: Cycloid

1. How is 1000 written in Roman numerals?

Ans: M

1. What number is 10^Googol?

Ans: Googolplex

1. Which matrix is its own inverse?

Ans: Identity matrix

1. Which natural number is doubled when added to its reciprocal?

Ans: 1

1. What is the sum of the first 100 odd natural numbers?

Ans: 10000

1. What is the name of the point which is the center of a circle which passes through all the three vertices of the triangle?

Ans: Circumcircle

1. What are the diagonal elements of a skew symmetric matrix?

Ans: 0

1. For a cube of volume 27 units, what is the length of its longest diagonal?

Ans: 3 * sqrt(3)

1. Who is known as the father of computer?

Ans: Charles Babbage

1. For a radioactive element, what curve describes the quantity of the material left with time?

Ans: Logarithmic curve

1. If set A is a collection of all the integers with absolute value less than 100, what is the sum of those integers?

Ans: 0

1. A bookworm eats it way through a book at the rate 1 inch per hour, how long will it take to eat its way from the front of volume one of the book to the back of volume three, each volume being half inch long (Volumes are kept in order)?

Ans: 30 minutes

1. Who invented Principle of calculation machine with progressive transmission of tens?

Ans: Pafnuty Chebyshev

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