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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,990

#312. If

verify

.

#313. Show that

.

#314. Two dice are thrown together. What is the probability of getting a total of 8 or a product of 12?

#315. Prove that

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,990

#316. Prove that

#317.If a line passes through the midpoint of AB where A is (3,0) and B is (5,4) and makes an angle of 60° with tehe x-axis, find its equation.

#318. The angle of elevation of a tower at a point is 45° . After going 20 meters towards the foot of the tower, the angle of elevation of the tower becomes 60° . Claculate the height of the tower.

#319. Find the equation of the straight line joining the point of intersection of

3x - y + 9 = 0 and 2y = x - 4 = 0 to the point of intersection of 2x + y = 4 and

2y = x + 3.

#320.The vertices of a triangle are A(1,8), B(-2,4), and C(8, -5). m and N are the midpoints of AB and AC. Show that MN is parallel to BC and

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,990

#321. In an Arithmetic progression,

Find the first term and the common difference.

#322. A cylndrical pillar is 3.5 meters in diameter and 20 meters high. Find its volume.

#323. Find the point which divides the line joining the points (-2, 6) and (3, 6) internally in the ratio 3:2.

#324. Prove that the points (9,0), (1,4), and (11,-1) are collinear.

#325. If sin θ = cos θ, where θ is an acute angle, find the value of 2tan² θ - sin² θ - 1.

#326. The mean of 100 items is 48 and their standard deviation is 10. Find the sum of all the items and also the sum of the squares of all the items.

#327. The sum of the three digits in a three digit number is 24. Twice the tenth digit is equal to the sum of the digits in the other two places. if 198 is added to the number, then the digits would be in the reversed order. Find the number.

#328 : Factorize:-

#329. If

find

.

#330. The mid-points of three sides of a triangle are (5, -3), (-5, 3), and (6, 6). Find the equations of the sides of the traingle.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,990

331. Find a and b if

is a factor of

.

#332. Find the values of a and b if 9x-2) is a common factor of

#333. If (x-7) and (x-4) are factors of

find the values of p and q.

#334. If (x-1), (x+2), and (x-2) are the factors of

find a, b, and c.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,990

#335, Two dices contain the numbers from 1 to 6 and 1 to 6. By using these 6 numbers all calendar dates from 01 to 31 must be displayed by rearranging the dices in any way. What are the six numbers each dice contains?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,049

# 328

By the rational root theorem:

Can only have these rational roots {-1/1,-1/2,-2/2,-2/1,1,1/2,2}

plugging them in we get roots of -2,1/2 and 1

Which means the factorization is of the form

*Last edited by bobbym (2009-10-18 01:51:17)*

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,990

Outststading!!!

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,049

Hi ganesh;

*Last edited by bobbym (2009-06-12 20:58:49)*

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,990

I shall let you know soon!

Character is who you are when no one is looking.

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**Fruityloop****Member**- Registered: 2009-05-18
- Posts: 120

Thank you for the interesting and challenging puzzles Ganesh.

*Last edited by Fruityloop (2009-06-18 06:01:04)*

The eclipses from Algol (an eclipsing binary star) come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,049

*Last edited by bobbym (2009-06-22 01:19:21)*

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,954

hi ganesh

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**LearnMathsFree: Videos on various topics.New: Integration Problem | Adding FractionsPopular: Continued Fractions | Metric Spaces | Duality**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,990

Hi zetafunc,

The solution #321 is correct! Well done!

Character is who you are when no one is looking.

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