# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #276 2009-03-05 03:51:19

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#242. What is the coefficient of

in the expansion of
?

#243. If the coefficient of x in the exapnsion of

is 270, then what is the value of k?

#244. What is the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of  three parallel lines?

#245. What is the value of r if

?

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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## #277 2009-03-05 04:07:38

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#246. What is the argument of

?

#247. What is the value of

if
?

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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## #278 2009-03-05 18:12:12

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#248. Find the least positive integer n such that

.

#249.Find the equation of the ellipse whose foci are (1,0) and (-1,0) and whose eccentricity is

.

#250. A ladder 10 meters long rests against a vertical wall. If the bottom of the ladder slides away from the wall at the rate of 1 meter/second, how fast is the top oif the ladder sliding down the wall when the bottom of the wall is 6 meters from the wall?

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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## #279 2009-03-05 20:43:37

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#251. If the polynomials

and
leave the same remainder when divided by (x-3), what is the value of a?

#252. If the quotient on dividing

by (x+3) is
, find the value of a.

#253. Find the Greatest Common Divisor of

and
.

#254. Simplify:-

.

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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## #280 2009-03-05 20:50:52

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#255. Find the 5[sup]th[/sup] term of the Geometric Progression whose 3[sup]rd[/sup] term is

and 7[sup]th[/sup] term is
.

#256. The sum of a Geometric Progression to infinite terms is 2 and the sum of their squares to infinite terms is

. Find the series.

#257. Three numbers are in Arithmetic Progression and their sum is 15. If 1, 3, and 9 are added to them, the numbers form a Geometric Progression. Find the numbers.

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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## #281 2009-03-06 02:32:50

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#258. If the first, second, and last terms of an Arithmetic Progression are a, b, and c respectively, then what is the number of terms in the Arithmetic progression?

#259. What is the value of n if

?

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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## #282 2009-03-07 02:30:25

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#260. If

and
, then what is the value of
?

#261. What is the value of k for which (x+2) is a factor of

?

#262. Let f(n) denote the sum of the first n terms of an Arithmetic Progression. Then, what is
f(n+3) -3f(n+2) + 2f(n+1) equal to?

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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## #283 2009-03-07 19:02:18

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#263. A water tank has the shape of an inverted circular cone with radius 2 meters at the top and height 4 meters. If water is be pimped into the tank at the rate of 2 meter³/minute, find the rate at which the water level is rising when the water is 3 meters deep.

#264. The distance x meters travelled by a vehicle in time t seconds after the brakes are applied is given by

.
Determine
(i) the speed of the vehicle in Kilometers/hour at the instant the brakes are applied.
(ii) the distance travelled by the vehicle before it stops.

#265. Two sides of a triangle have lengths 12 meters and 15 meters. The angle between them is increasing at the rate of 2°/minute. How fast is the length of the third side increasing when the angle between the sdies of fixed lengths is 60°?

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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## #284 2009-03-08 01:43:54

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#266. A watermelon is cut into two pieces in the ratio 3:5 by weight. The bigger of the two is further cut in the ratio of 5:7 by weight. Find the ratio of each of the three pieces.

#267. The sides of a right angled triangle are a, a+x, and a+2x with both a and x positive. What is the ratio of a to x?

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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## #285 2009-03-09 02:35:02

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#268. If p:q = r:s = t:u = 2:3, then what is (mp+nr+ot) : (mq+ns+ou) equal to?

#269. If x:y = 3:4, then what is (7x+3y) : (7x-3y) equal to?

#270. If a:b:c = 2:3:4 and 2a - 3b + 4c = 33, then what is the value of c?

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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## #286 2009-03-11 08:01:53

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#271. If

, then what is the value of
.

#272. What is the value of k for which (x+2) is a factor of

?

#273. What is the value of x if sin²x - 2sinx + 1 = 0?

#274. What is the Least Common Multiple of 3x²-x, 3x²+x, and 9x²-1?

#275. Let f(n) denote the sum of first n terms of an Arithmetic Progression. What is f(n+3) - 3f(n+2) + 2f(n+1) equal to?

#276. If p and q are the roots of the equation

, what is the value of p[sup]2[/sup]+q[sup]2[/sup]?

#277. what is the logarithm of 19683 to the bases 3√3?

#278. What are the values of A and B if

?

#279. Simplify:-

.

#280. If x and y are acute angles, then what is the value of x + y if

?

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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## #287 2009-03-11 08:17:50

Kurre
Member Registered: 2006-07-18
Posts: 280

### Re: *** Problems

Last edited by Kurre (2009-03-11 08:18:44)

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## #288 2009-03-11 17:08:55

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

Perfect, Kurre! #281. What is the value of the expression

if
and 90° < θ < 180°.

#282. If a(cos 45°cos15° - sin45°sin15°) = 1, what is the value of a?

#283. Given

, what is the value of θ?

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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## #289 2009-03-13 02:15:24

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#284. What is the value of

?

#285. If tan θ + sin θ  = m and tan θ - sin θ =n, then what is the value of m[sup]2[/sup]-n[sup]2[/sup] in terms of m and n?

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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## #290 2009-03-14 21:48:34

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#286. Solve:-

.

#287. Solve for x:-

.

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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## #291 2009-03-14 21:53:35

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#288. If the n[sup]th[/sup] term of an Arithmetic Progression is (2n+1), find the sum of the first n terms of the Arithmetic Progression.

#289. Find the sum of mn terms of an Arithmetic Progression given

.

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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## #292 2009-03-15 00:16:45

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#290. Find all the zeros of the polynomial

if two of its zeros are √2 and -√2.

#291.If the polynomial

is divided by another polynomial
,
the remainder obtained is x+a. Find k and a.

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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## #293 2009-03-17 07:34:37

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#292. If x² - 1 is a factor of

,
show that a + c + e = b + d = 0.

#293. Deceompose into partial fractions:-

.

#294. The area of the curved surface of a cylinder is 4,400 square centimeters and the circumference of its base is 110 centimeters. Find the volume of the cylinder.

#295. A hollow sphere of internal and external diameters 4 cm and 8 cm respectivelyis melted and cast into a cone of diamter 8 cm. Find the height of the cone.

#296. Find the four numbers in Geometric Progression whose sum is 85 and their product is 4096.

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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## #294 2009-03-18 22:33:03

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#297. Find the values of a and b if

is a perfect square.

#298. Find the values of a and b if

is divisible by (x + 2) and (x - 1).

#299. Simplify:-

.

#300. If p, q are the roots of the equation x[sup]2[/sup] - 3x - 4 = 0, form the equation whose roots are

.

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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## #295 2009-03-19 08:49:10

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#301. Divide the polynomial

by the polynomial

and give the quotient and the remainder.

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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## #296 2009-03-22 03:03:36

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#302. Solve the following non-homogeneous system of linear equations by determinant method:-

.

#303. Solve by matrix inversion method:
x + y + z = 9
2x + 5y + 7z = 52
2x + y - z = 0.

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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## #297 2009-03-25 04:12:44

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#304. What is teh value of r if

?

#305. What is the value of x if

?

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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## #298 2009-03-25 05:06:37

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#306. What is the value of

?

#307. If the coefficients of the (2r+1)[sup]th[/sup] and the (r + 2)[sup]th[/sup] terms in the expansion of

are equal, what is the value of r?

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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## #299 2009-03-27 07:42:10

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#308. Find the area of the quadrilateral whose vertices are (-1, -6), (-3, 9), (5, -8), and (3, 9).

#309. Find the equation of the perpendicular bisector of the line joining the points (1,7) and (-3,3).

#310. The angles of elevation of the top of a tower from two points at distances a and b from the base and in the same straight line with it are complimentary. Find the height of the tower in terms of a and b.

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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## #300 2009-03-27 07:44:46

Jai Ganesh Registered: 2005-06-28
Posts: 43,477

### Re: *** Problems

#311. Two dice are rolled once. Find the probability of getting an even number on the second die or the total of the face numbers being 10.

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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