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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

1. The sum of three terms of an Arithmetic Progression is -6 and their product is 90. Find the three terms.

2. A cylindrical jar of diameter 14 centimeters and depth 20 centimeters is half-full of water. 300 leadshots of same size are dropped into the jar and the water level raises by 2.8 centimeters. Find the diameter of each leadshot.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

Hi bobbym,

The Solution '1' is correct. The solution '2' is 1.4 centimeters.

Excellent!

3. A girl of height 150 centimeters stands in front of a lamp post and casts a shadow of length

centimeters on the ground. Find the angle of elevation of the top of the lamp posr.4. Find the sum of all the natural numbers between 400 and 600 which are divisible by 11.

(Solution 2 : Diameter = 1.4 centimeters).

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

hi,

The solutions 3 and 4 are correct. Excellent!

5. Find the values of a and b if the polynomial is a perfect square.

6. If

are the square roots of and , then find p.It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

Hi bobbym,

The solution 5 is correct. Excellent!

7. Find the angle on inclination of the line passing through the points (1,2) and (2,3).

8. Compute :-

.Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

Hi bobbym,

The solutions 7 and 8 are correct. Good work!

9. If the total surface area of a sphere is

square centimeters, then find its radius.10. Three coins are tossed simultaneously. Find the probability of getting at least two heads.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

Hi bobbym,

The solutions 9 and 10 are correct. Excellent!

11. If the product of three consecutive terms in Geometric Progression is 216 and the sum of their products in pairs is 156, find them.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

Hi bobbym,

Good work, bobbym!

12. Find the total area of 14 squares whose sides are 11 centimeters, 12 centimeters, 13 centimeters, ....... and 24 centimeters respectively.

13. Solve the equation

where 1 + x ≠ 0, 2 + x ≠ 0 and 4 + x ≠ 0 using quadratic formula.Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

Hi bobbym,

The solutions 12 and 13 are correct. Marvelous!

14. Find the sum of

up to eight terms.15. Find the equation of the straight lines whose x and y intercepts are

and .Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

Hi bobbym,

The solutions 14 and 15 are correct. Marvelous!

16. Find the point of intersection of the lines

and .17. Find the center and the radius of the sphere given by x² + y² + z² - 6x + 8y - 10z + 1 = 0.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

Hi bobbym,

I request that the problems 16 and 17 are omitted.

I am posting the amended problems.

16. Find the quotient and remainder using synthetic division when

is divided by (x - 1).17. If the sum and product of one of the roots of the quadratic equation

are both equal to 10, then find the values of a and c.Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

Hi,

18. A solid sphere of diameter 42 centimeters is melted and recast into a number of identical cones, each of diameter 7 centimeters and height 3 centimeters. Find the number of cones so formed.

19. Find the square root of

.Have a Remarkable Sunday!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

Have a good Sunday too!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

Hi bobbym,

The solution 18 and 19 are correct. Brilliant!

20. Radius and slant height of a solid right circular cone are in the ratio 3:5. If the curved surface area is

square centimeters, then find the total surface area..

21. Two dice are rolled and the product of the outcomes (numbers) are found. What is the probability that the product so found is a prime number?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,611

Hi bobbym,

I accept your solution 21. Good work!

Regarding 20, I request you to check the solution once again. I feel the problem is worded rightly.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline