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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 46,162

Hi bobbym,

51. Find the equation of the straight line passing through the point (3,4) and has intercepts which are in the ratio 3:2.

52.If the straight line passing through the points (h,3) intersects the line 7x - 9y - 19 = 0 at right angle, then find the value of 'h'.

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: 46,162

Hi bobbym,

52. I missed the point on the problem. It is (4,1).

53. A card is drawn at random from a well-shuffled pack of cards. Find the probability that it will be a spade or king.

54. The first term of a Geometric Progression exeeds the second term by 2 and the sum to infinity is 50, find the Geometric Progression.

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: 46,162

Hi bobbym,

The solution 53 (probability = 4/13) is correct. Good work!

55. The largest of 50 measurement is 3.84 kilogram. If the range is 0.46 kilogram, find the smallest measurement.

56. If A and B are mutually exclusive events such that

, then find .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: 46,162

Hi bobbym,

The solutions 55 and 56 are perfect. Remarkable!

57. The angle of elevation of the top of a tower as seen by an observer is

. The observer is at a distance of meters from the tower. If the eye level of the observer is 1.5 meters above the ground level, find the height of the tower.58. Find the volume of a sphere-shaped metallic shot-put having diameter of 8.4 centimeters.

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: 46,162

Hi bobbym,

The solutions 57 and 58 are correct. Excellent

59. Find the square root of the following polynomial.

.60. Find the value of 'k' so that the equation

has real and equal roots.

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: 46,162

Hi bobbym,

The solutions 59 and 60 are correct. Marvelous!

61. A rectangular field is 20 meters long and 14 meters wide. There is a path of equal width all around it having an area of 111 square meters. Find the width of the path on the outside.

62. Find the equation of the perpendicular bisector of the straight line segment joining the points (3,4) and (-1,2).

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: 46,162

Hi bobbym,

The solutions 61 and 62 are correct. Immaculate!

63. Given

, find .64. If the values of

, findi)

ii) P(A' U B').

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: 46,162

Hi bobbym,

The solution 63 (both parts) are correct. Marvelous!

65. Find the sum of the series :

66. Find the values of 'a' and 'b' if the following polynomial is a perfect square.

.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: 46,162

Hi bobbym,

The solutions 65 and 66 are correct. Brilliant!

67. A car left 30 minutes later than the scheduled time. In order to reach its destination 150 kilometers away, it has to increase its speed by 25 kilometers per hour from its usual speed. Find its usual speed.

68. If

are the roots of the equation , form an equation whose roots are .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: 46,162

Hi bobbym,

The solutions 67 and 68 are correct. Stupendous!

69. Using the concept of slope, show shat the points (-2,-1), (4,0), (3,3), and (-3,2) taken in order form a parallelogram.

70. Find the equation of the straight lines passing through the point (2,2) and the sum of the intercepts is 9. (Two solutions).

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: 46,162

Hi bobbym,

The solutions 69 and 70 are correct. Spectacular!

71. Find two consecutive odd natural numbers, the sum of whose squares is 202.

72. The ratio of volumes of two cones is 4:5 and the ratio of the radii of their bases is 2:3. Find the ratio of their vertical heights.

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: 46,162

Hi bobbym,

The solutions 71 and 72 are correct. Excellent!

73. The mean and standard deviation of 20 items are found to be 10 and 2 respectively. At the time of checking, it was found that an item 12 was wrongly entered as 8. Calculate the correct mean and standard deviation.

74. A box contains 10 white, 6 red, and 10 black balls. A ball is drawn at random. Find the probability that the ball drawn is white or red.

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: 46,162

Hi bobbym,

The solutions 73 and 74 are correct. Marvelous!

75. Find the range and coefficient of range of the following data:

41.2, 33.7, 29.1, 34.5, 25.7, 24.8, 56.5, 12.5.

76. Three rotten eggs are mixed with 12 good ones. One egg is chosen at random. What is the probability of choosing a rotten egg?

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

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