*** Problems

Jai Ganesh · 2009-02-15 19:00:45

#184. Find the value of x if

.

#185. If one root of

is 4, while the equation

has equal roots, what is the value of q?

#186. If x, y, and z are odd positive integers, then which of the following is not necessarily true?
(1)

is odd.
(2) is even.
(3) is odd.
(4) is even.

Jai Ganesh · 2009-02-16 16:53:01

#187. What is/are the value(s) of

?

#188. The points (2, -2), (8, 4), (4, 6), and (-1, 1) in order are the vertices of which one of the following quadrilaterals?
(1) Square
(2) Rhombus
(3) Rectangle
(4) Trapezium

Jai Ganesh · 2009-02-17 02:44:21

#189. What is the x-coordinate of the point on the tangent of the given curve where the tangent is parallel to the x-axis?

#190. What is the degree of the differential equation

?

Jai Ganesh · 2009-02-19 02:30:07

#191. There are two candles of the same length initially. The first candle can burn for 24 hours while the second can burn for 16 hours. Both of them are lit at the same time. After sometime, it was found that one of the candles was twice as long as the other. For how long had the candles been burning?

#192. If all the natural numbers are written side by side as 12345..... then which digit would be the 131st digit of the number so written?

#193. 5 persons can cut 5 trees in 5 days working 5 hours a day. In how many days can 7 persons cut 7 trees working 7 hours a day?

JaneFairfax · 2009-02-19 09:43:20

Jai Ganesh · 2009-02-19 16:43:52

Answers to #185, #187, #191, #192, and #193:-
All correct, JaneFairfax!!!!

Jai Ganesh · 2009-02-21 01:05:17

#194. If the sum of the squares of the distances of the points (x,y,z) from the points (a,0,0), and (-a,0,0) is 2c², then which one of the following is correct?
(1) x² + a² = 2c² - y² - z²
(2) x² + a² = c² - y² - z²
(3) x² - a² = c² - y² - z²
(4) x² + a² = c² + y² + z²

#195. What is the sum of the series

?

Jai Ganesh · 2009-02-21 01:31:25

#196. If the sum of the squares of the roots of the equation

is 5, then what is the value of p?

JaneFairfax · 2009-02-21 14:34:47

Jai Ganesh · 2009-02-21 17:24:55

Answer to #195:-
Correct, JaneFairfax!

#197. A card is drawn from a pack of 52 cards and a gambler bets that is is a spade or an ace. What are the odds against his winning the bet?

#198. A can hit a target 4 times in 5 shots; B can hit the target 3 times in 4 shots, and C can hit the target 2 times in 3 shots. All the three fire a shot each. What is the probability that at least two shots hit the target?

#199. If U is the Universal set and P is a subset of U, then what is

equal to?

#200. What is the degree of the equation

?

Jai Ganesh · 2009-02-22 20:35:42

#201. If a, b are real, what is the value of

?

#202. If z = 1 + i, what is the inverse of z²?

#203. What are the coordinates of a point equidistant from the points (a,0,0), (0,a,0), (0,0,a), and (0,0,0)?

#204. A line makes 45° with the positive x-axis and makes equal angles with the positive y and z axes respectively. What is the sum of the three angles which the lin makes with the positive x, y, and z axes?

#205. A particle moves in a straight line with a velocity given by v = x + 1 9x being the displacement). What is the time taken by the particle to traverse a distance of 99 meters?

#206. What is the value of cosec(2A) - cot(2A)?

#207. What is the area of the triangle bound by the lines y = 0, x + y = 0 and x + 4 = 0?

#208. A person saves $135 in the first year, $150 in the second year, $165 in the third, thus increasing his saving by $15 every year. After how many years would his total savings be $5500?

#209. What is the equation of the line which passes through (4, -5) and is parallel to the line 3x+4y+5 = 0?

#210. What is the locus of a point which is equidistant from (1,2,3), and (3,2,-1)?

Jai Ganesh · 2009-02-23 17:11:57

#211. If the roots of the equation

are two conseutive integers, then what is the value of
?

#212. What is the common root in the equations

?

#213. If

,
what is the value of
?

#214. If the probability of a defective bolt is 1/10, what are the mean and variance for the distribution of defective bolts in a total of 400?

Jai Ganesh · 2009-02-24 02:01:34

#215. What is the greatest coefficient in the expansion of

?

#216. If the equations 4x + 7y = 10 and 10x + ky = 25 represent coincident lines, what is the value of k?

Jai Ganesh · 2009-02-24 02:21:53

#217. If (x + yi) (3 - 4i) = 5 + 12i, then what is

?

#218. What is the value of

?

Jai Ganesh · 2009-02-24 03:23:32

#219. If the sum of the first n terms of an Arithmetic Progression is Pn+Qn², where P and Q are constants, then what is the common difference of the Arithmetic Progression?

#220. The first term of an Arithmetic Progression of consecutive integers is p²+1. What is the sum of (2p+1) terms of the series?

#221. If 3 + 3a + 3a² + 3a³ + ..... ∞ is equal to

, and a>0, then what is the value of a?

JaneFairfax · 2009-02-24 07:37:05

Jai Ganesh · 2009-02-25 03:12:39

Answer to #221:-
Correct, JaneFairfax!

#222. If the sum of the first 2n terms of the Arithmetic progression 2,5,8, .... is equal to the sum of the sum of the first n terms of the Arithmetic progression 57, 59, 61, ......, then what is n equal to?

#223. If p and q are the roots of the equation ax² = bx = c = 0, then what is the equation whose roots are

?

#224. What is the number of diagonals of a polygon having n sides?

#225. A polygon has 44 diagonals. How many sides does it have?

Jai Ganesh · 2009-02-27 02:28:36

#226. What is the coefficient of the middle term in the expansion of

?

#227. What is the power of x occuring in the seventh term of the expansion of

?

#228. What is the coefficient of

in
?

#229. What is the value of

?

Jai Ganesh · 2009-02-28 03:01:22

#230. What is the value of tan 15° tan 25° tan 45° tan 65° tan 75°?

#231. what is the value of x if

?

#232. What is the value of

?

#233. What is the value of

?

#234. if

, then what is the value of
?

Jai Ganesh · 2009-02-28 18:27:50

#235. What is the area of the smallest square tht would enclose a regular hexagon of side 1 unit?

#236. A right circular cone of height h is cut by a plane parallel to the base at a distance h/3 from the vertex. What is the ratio of the volumes of the resulting cone and the frustum?

Jai Ganesh · 2009-03-01 19:17:48

#237. What value(s) of x is/are the solution of

?

Jai Ganesh · 2009-03-02 02:26:54

#238. What is the number of real roots of the equation

?

#239. Two veseels of equal volume contain milk and water in the ratio 3:2 and m:n. If the contents are poured into a bigger container, what would the ratio of milk to water in the new container be?

Jai Ganesh · 2009-03-04 04:19:49

#240. The daily work of two men is equal to that of three women or that of four youngsters. By employing 14 men, 12 women, and 12 youngsters, a certain work can be finishedin 24 days. if the work has to be completed in 14 days and only men are available as additional labor, how many of them would be required?

JaneFairfax · 2009-03-04 05:21:54

Last edited by JaneFairfax (2009-03-04 07:55:47)

Jai Ganesh · 2009-03-04 16:43:04

Answer to #238:
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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