*** Problems

Jai Ganesh · 2009-03-05 03:51:19

#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

?

Jai Ganesh · 2009-03-05 04:07:38

#246. What is the argument of

?

#247. What is the value of

if
?

Jai Ganesh · 2009-03-05 18:12:12

#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?

Jai Ganesh · 2009-03-05 20:43:37

#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:-

.

Jai Ganesh · 2009-03-05 20:50:52

#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.

Jai Ganesh · 2009-03-06 02:32:50

#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

?

Jai Ganesh · 2009-03-07 02:30:25

#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?

Jai Ganesh · 2009-03-07 19:02:18

#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°?

Jai Ganesh · 2009-03-08 01:43:54

#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?

Jai Ganesh · 2009-03-09 02:35:02

#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?

Jai Ganesh · 2009-03-11 08:01:53

#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

?

Kurre · 2009-03-11 08:17:50

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

Jai Ganesh · 2009-03-11 17:08:55

Answer to #276:-
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?

Jai Ganesh · 2009-03-13 02:15:24

#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?

Jai Ganesh · 2009-03-14 21:48:34

#286. Solve:-

.

#287. Solve for x:-

.

Jai Ganesh · 2009-03-14 21:53:35

#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

.

Jai Ganesh · 2009-03-15 00:16:45

#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.

Jai Ganesh · 2009-03-17 07:34:37

#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.

Jai Ganesh · 2009-03-18 22:33:03

#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

.

Jai Ganesh · 2009-03-19 08:49:10

#301. Divide the polynomial

by the polynomial

and give the quotient and the remainder.

Jai Ganesh · 2009-03-22 03:03:36

#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.

Jai Ganesh · 2009-03-25 04:12:44

#304. What is teh value of r if

?

#305. What is the value of x if

?

Jai Ganesh · 2009-03-25 05:06:37

#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?

Jai Ganesh · 2009-03-27 07:42:10

#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.

Jai Ganesh · 2009-03-27 07:44:46

#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.

Math Is Fun Forum

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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