- If sqrt(a),sqrt(b),sqrt(c) are sides of acute angled triangle, then
prove a,b,c are sides of triangle.(a,b,c>0)
- Number of ordered pairs of positive integers (x,y) satisfying,
1/x+1/y=1/2001 is__________________________
- And here's one for you poetic freaks!!
Old Boniface he took his cheer,
Then he bored a hole through a solid sphere,
Clear through the center, straight and strong,
And the hole was just six inches long.
Now tell me, when the end was gained,
What volume in the sphere remained?
Sounds like I haven't told enough,
But I have, and the answer isn't tough!
:-)
- You can see three faces of each of two dice. The total number of
pips on these faces is 27. How many pips can you see on each die?
- The masses of weights in a set are 1 g, 2 g, 3 g, ..., 101 g. The
19-g weight was lost. Is it possible to divide the remaining 100
weights into two groups with the same number of pieces and the same
total weight?
If a `religion' is defined to be a system of ideas that contains unprovable
statements, then Godel taught us that mathematics is not only a religion,
it is the only religion that can prove itself to be one.-- John Barrow
- The population of the island of Pianosa is 100. Some of the inhabitants
always lie, the others always tell the truth. Each islander worships one
of three gods: the Sun god, the Moon god, or the Earth god. One day a
visiting anthropologist asked each inhabitant the following
questions:
1.Do you worship the Sun god?
2.Do you worship the Moon god?
3.Do you worship the Earth god?
There were 60 "yes" answers to the first question, 40 "yes" answers to the
second question, and 30 "yes" answers to the third. How many liars live on
the island?
And then we take the limit as x goes to infinity...AND BEYOND!
-- Prof. Tom Hunter, Swarthmore Math Dept.
- What is the 137th number in the following sequence: 111, 21, 13, 12,
11, 10, 7... ?
- How many grooves are there on one side of a 12 inch 33 1/3 rpm long
playing album?
- In watching a cowboy movie, you may have noticed that the wagon wheels
of a stagecoach sometimes rotate the wrong way: the stagecoach may be
moving left to right across the movie screen while the spokes of the
wheel rotate backwards (counterclockwise). If a movie displays 24 frames
per second, if the wagon wheels are 5 feet tall and have eight spokes
each, and if the horses pull the stagecoach left to right at 20 miles/hour
(32 km/hour), will the wagon spokes be rotating forward or backwards
compared to the direction of the stagecoach? What will the movie audience
perceive as the angular velocity of the wheels?
- What is the fastest way to make a 90 degree turn on a slippery road?
- Two spheres are the same size and weight, but one is hollow. They are
each made of uniform material, though of course not the same material.
If I roll them down an inclined plane starting together, which is going to
reach the bottom faster ?
It is odd, but on the infrequent occasions when I have been called upon
in a formal place to play the bongo drums, the introducer never seems to
find it necessary to mention that I also do theoretical physics.
--Richard Feynman
- Is a round-trip by airplane longer or shorter if there is wind
blowing?
- You have an old-fashioned refrigerator with a small freezer
compartment which could hold seven ice cube trays stacked vertically, but
there are no shelves to separate the trays. You have an unlimited supply
of trays, each of which can make a dozen cubes, but if you stand one on
top of another before it's frozen, it will nest part way into it and you
won't get full cubes from the bottom tray. So, what is the fastest way to
make ice cubes?
- He took an S-shaped tube and wanted to find out whether it would move
clockwise or anti-clockwise, when it sucked in air. The experiment was set up
at the Princeton synchrotron when he was a Graduate student. He kept raising
the power of the pump, till it blew up, earning him a lifetime ban from the
place. Who was this illustrious personality?
- Here is a press release from ISRO:
Dec 7,2000 Prime Minister Meets Indian
Boys Selected...
The Prime Minister, Mr Atal Bihari Vajpayee yesterday (December 6,
2000) met the three students, 15-year old Shaleen Rajendra Hartalka from
Udaipur, 13-year old Tanmay Sanjay Khirwadkar of Nagpur and
10-year old Vikas Sarangadhara of Bangalore, who have been...
What have the boys been selected for?
- When you are using a tester (AC) you have to touch the back with your
finger/hand/any body part. But this not work for a DC tester. Why?
- In the year of the fall of the Byzantine empire, according to Chinese
manuscripts, an extremely bright object appeared in the sky which was
visible during daytime and whose light was enough to read books by at
night. Today it exists as a remnant of that recorded event. What was the
event and what is the remnant?
Q: "How does one measure the height of a building using a
barometer?"
A: Drop the barometer off the building onto someones head, killing them
outright. Wait for the next day's papers and read the part where is says
"A man (39) was killed yesterday when a scientist (26) dropped a
barometer from the top of an [x] foot building".
--Dr N.C. Eastmond, nce@liverpool.ac.uk, in sci.physics
- You are riding on a car. You have a bottle of cold drink. You start
drinking. How much should you drink such that the bottle, when placed on a
horizontal table inside the car, is the least likely to fall? Assume for
calculations that the bottle is cylindrical. The qualitative answer is
independent of shape.
- Connect 12 batteries in a circle, end to end, with no resistances but
their internal ones. Connect two leads of an ideal voltmeter across the
first and the third junction. What will be it's reading?
- Why is it that such different-sized creatures as the flea, the lion
and the human, can jump approximately a meter high (give or take a factor
of two) ?
- You are given two inflated balloons, one is filled partially with
water and the other is empty. Now if both are held above a flame, the empty one
bursts while the other one does not. Why?
- Fill a bottle almost to the brim with water. Now place in a test tube
vertically with the mouth facing downwards. Close the bottle. Now, if you
squeeze the bottle, what happens. (assume the bottle can be squeezed!)
The hypothalamus is one of the most important parts of the brain,
involved in many kinds of motivation, among other functions. The
hypothalamus controls the "Four F's": 1. fighting; 2. fleeing;
3. feeding; and 4. mating.
--Psychology professor in neuropsychology intro course
- This member of the beetle family are usually brown or black and are
around half an inch long. It has two chemicals in its belly that shine when
they are mixed. The inside lining of the belly is white, and this causes the
light from the chemicals to be reflected out. Identify the creature.
- Apart from the fact that it enables them to see their targets better,
(after a hit) why is the dropping of a bird white, when most of their food
intake is darkly pigmented?
- An Arab once wrote a mathematical book called "Hidab al-jabr wal
muqabala". An important word comes from this. What?
"Any technology indistinguishable from magic is insufficiently advanced.
- What happens when you look at the static on a television screen wearing
a pair of spectacles in which one lens is heavily tinted and one is transparent?
- Van Geulen spent most of his life calculating the value of this
constant which is also referred to by his first name. What
is the constant better known as and what is his first name?
- About 20 to 30 % of the population suffer from Autosomal Dominant
Compelling Helio-Ophthalmic Outburst Syndrome. What does it refer
to? (hint: Similar to Acquired Immuno Deficiency Syndrome, perhaps?)
- If you had two bubbles in an infinite ocean (with no external fields),
would they attract or repel? Explain.
As far as the laws of mathematics refer to reality, they are not certain,
as far as they are certain, they do not refer to reality.
--Albert Einstein
- A cannon is mounted at 45 degrees to the horizontal on a flat
plane. At the position of maximum range, a perfectly elastic board is
placed at 45 degrees. When the cannon is fired, the cannonball flies
through the air, strikes the board, and bounces all the way back into the
barrel of the cannon. Now assume that the angle of the board cannot be
raised past 44 degrees (and you have no other degrees of freedom to
adjust). How can you orient the board so that the cannonball once again
bounces back into the barrel?
-
With regard to the medals themselves, I might say that they should each
contain at least 200 dollars worth of gold and be of a fair size, probably
7.5 centimeters in diameter.Because of the international character the
language to be employed it would seem should be Latin or Greek? The design
has still to be definitely determined. It will have to be decided on by
artists in consultation with mathematicians. The suggestions made in the
preceding are tentative and open to consideration on the part of
mathematicians. ...
This is an excerpt from a letter written by a professor in the
University of Toronto a few months before his death. Identify the
person.
- Insects have compound eyes with multiple optical receptors, though the
number of receptors is less than in the human eye. Having a very wide angle
of vision, they cannot stop looking at the sun. How come they do not go
blind from exposure to the sun, given that the sun takes about half a
degree of the field of vision?
- What happens when you dial 3-2-1-2-3-3-3, 2-2-2, 3-9-9,
3-2-1-2-3-3-3, 3-2-1-2-3-1 on your telephone?