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## #276 2009-03-05 15:43:04

ganesh
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### Re: *** Problems

Correct, JaneFairfax!

#241. A park rectangular in shape of dimensions 17m x 18m is surrounded by a footpath 1.5 meters wide. In order to provide a proper road on the footpath, a proper foundation is to be laid and the ground is dug to a depth of 12 centimeter and filled completely with gravel. What is the quantity of gravel required in cubic meters?

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## #277 2009-03-06 02:51:19

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#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
?

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## #278 2009-03-06 03:07:38

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#246. What is the argument of

?

#247. What is the value of
if
?

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## #279 2009-03-06 17:12:12

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#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?

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## #280 2009-03-06 19:43:37

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#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:-
.

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## #281 2009-03-06 19:50:52

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#255. Find the 5th term of the Geometric Progression whose 3rd term is

and 7th 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.

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## #282 2009-03-07 01:32:50

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#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

?

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## #283 2009-03-08 01:30:25

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#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?

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## #284 2009-03-08 18:02:18

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#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°?

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## #285 2009-03-09 00:43:54

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#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?

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## #286 2009-03-10 01:35:02

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#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?

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## #287 2009-03-12 07:01:53

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#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 p2+q2?

#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
?

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## #288 2009-03-12 07:17:50

Kurre
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Last edited by Kurre (2009-03-12 07:18:44)

## #289 2009-03-12 16:08:55

ganesh
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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?

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## #290 2009-03-14 01:15:24

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#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 m2-n2 in terms of m and n?

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## #291 2009-03-15 20:48:34

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#286. Solve:-

.

#287. Solve for x:-
.

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## #292 2009-03-15 20:53:35

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#288. If the nth 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

.

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## #293 2009-03-15 23:16:45

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#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.

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## #294 2009-03-18 06:34:37

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#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.

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## #295 2009-03-19 21:33:03

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#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 x2 - 3x - 4 = 0, form the equation whose roots are
.

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## #296 2009-03-20 07:49:10

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#301. Divide the polynomial

by the polynomial

and give the quotient and the remainder.

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## #297 2009-03-23 02:03:36

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#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.

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## #298 2009-03-26 03:12:44

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#304. What is teh value of r if

?

#305. What is the value of x if
?

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## #299 2009-03-26 04:06:37

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#306. What is the value of

?

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

are equal, what is the value of r?

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## #300 2009-03-28 06:42:10

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#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.

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