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**ganesh****Moderator**- Registered: 2005-06-28
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Answers to #269, and #271:-

Both correct, JaneFairfax!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#273. Let

. What are the numbers N is divisible by?#274. What is the number of distinct triangles that can be formed with integral value sides, the perimeter of the triangle being 14 units?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#275. Sam has forgotten his friend's seven digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number nine appears once. If Sam were to use trial and success method to call his friend, what is the minimum number of trials he has to make in order to be certain to succeed?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
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Answer to #275:

I get a bigger number as the solution. **I request you to post all the steps involved in arriving at the solution.**

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#276. What is the least value of n such that

#277. There are two positive numbers such that their Arithmetic Mean is 10 and their Geometric Mean is 8. Find the two numbers, and find their Harmonic Mean.

#278. The first three terms of a Geometric Progression are x, x+3, x+9. Find the value of x and also find the sum of the first eight terms.

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#279. What is the number of solutions the equation 2x+y=40 has such that both x and y are positive integers and

?#280. The length, breadth, and height of a room are in the ratio 3:2:1. By what percentage would the area of the four walls increase or decrease if the breadth and height are halved and the length is doubled?

#281. What is the value of

if

?

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#282. If x = -0.5, which of the following has the least value?

(1)

(2)

(3)

(4)

(5)

#283. Which among the following has the greatest value?

#284. Consider a sequence where the

term is. What is the value of

?

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#285. A square is inscribed in a circle (The diagonals of the square are equal in length to the diameter of the circle). A circle is then inscribed in the square (the side of the square is equal in length to the diameter of the circle), as given in the rough diagram below. What is the ratio of the area of the larger circle to the smaller circle?

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

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
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Answer to #285:-

Absolutely right, JaneFairfax!

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#286. Consider the set

. How many Arithmetic Progressions can be formed with the elements of S that start with 1 and end with 1000 and have atleast 3 elements?Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#287. Consider the following sets, Universal Set U, sets A and B,

.

What is

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#288. If the sum of the first 10 terms of an Arithmetic Progression with first erm p and common difference q is 4 times the sum of the first 5 times, then what is the ratio p:q equal to?

#289. If the roots of the equation

,

what is the value of m?

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#290. What is the sum of the first 50 terms of the series

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

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
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Answer to #290:-

You are correct, JaneFairfax!

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#291. What is the value of

#292. What is the value of

#293. What is the value of x if

#294. In a triangle ABC, the length of the sides in centimeters are

#295. What is the value of

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

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
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Answers to #291, 3292, and #293:-

All the answers are correct, JaneFairfax!

#296. What is the value of

#297. If A(2,3), B(1,4), C(0,-2), and D(x,y) are the vertices of a parallelogram, what is the value of (x,y)?

#298. What is the value of

if?

#299. What is the value of x if

?#300. What is the coefficient of

in the expansion of?

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#301. If

are the binomial coefficients in the expansion of,

then what is the value of

?

#302. If the binomial coefficients of three consecutive terms in the expansion of

are 220, 495, and 792 respectively, what is the value of n?Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#303. There are three Clubs A, B, and C in a town with 40, 50, and 60 members respectively. 10 people are members of all the three clubs, and 70 are members of only one club. How many people are members of exactly two clubs?

#304. Fou cities P, Q, R, and S are the four vertices of a square. Each city is connected to every other city by a direct road and none of theseroads intersect each other. What is the maximum possible number of routes available from one city to te diagonally opposite city?

#305. In how many ways can eight Directors, the Vice-Chairman and the Chairman of a company be seated at a round table, if the Chairman has to sit between the Vice-Chairman and a director?

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#306. A square is drawn by joining the midpoints of the sides of a given square. A third square is drawn by joining the midpoints of the second square.This process is continued indefinitely. If a side of the first square is 8 centimeters, what is the sum of areas of all the squares in square centimeters?

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#307. What is the probability of getting five heads and seven tails in 12 flips of a balanced coin?

#308. If p be the length of the perpendicular from the origin to the straight line ax + by = p and

, then what is the angle between the perpendicular and the positive direction of the x-axis?#309. The straight line ax + by + c = 0 and the coordinate axes form an isosceles triangle under what condition?

#310. A wire 34 centimeters long is bent in the form of a quadrilateral of which each angle is 90° . What is the maximum area enclosed by the quadrilateral?

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#311. If

are the roots of the equation , what is the value of ?#312. if A and B are any two events such that

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

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