*** Problems

Jai Ganesh · 2009-03-29 05:04:18

#312. If

,
verify
.

#313. Show that

if
.

#314. Two dice are thrown together. What is the probability of getting a total of 8 or a product of 12?

#315. Prove that

.

Jai Ganesh · 2009-03-30 06:04:50

#316. Prove that

.

#317.If a line passes through the midpoint of AB where A is (3,0) and B is (5,4) and makes an angle of 60° with tehe x-axis, find its equation.

#318. The angle of elevation of a tower at a point is 45° . After going 20 meters towards the foot of the tower, the angle of elevation of the tower becomes 60° . Claculate the height of the tower.

#319. Find the equation of the straight line joining the point of intersection of
3x - y + 9 = 0 and 2y = x - 4 = 0 to the point of intersection of 2x + y = 4 and
2y = x + 3.

#320.The vertices of a triangle are A(1,8), B(-2,4), and C(8, -5). m and N are the midpoints of AB and AC. Show that MN is parallel to BC and

.

Jai Ganesh · 2009-04-02 04:02:12

#321. In an Arithmetic progression,

.
Find the first term and the common difference.

#322. A cylndrical pillar is 3.5 meters in diameter and 20 meters high. Find its volume.

#323. Find the point which divides the line joining the points (-2, 6) and (3, 6) internally in the ratio 3:2.

#324. Prove that the points (9,0), (1,4), and (11,-1) are collinear.

#325. If sin θ = cos θ, where θ is an acute angle, find the value of 2tan² θ - sin² θ - 1.

#326. The mean of 100 items is 48 and their standard deviation is 10. Find the sum of all the items and also the sum of the squares of all the items.

#327. The sum of the three digits in a three digit number is 24. Twice the tenth digit is equal to the sum of the digits in the other two places. if 198 is added to the number, then the digits would be in the reversed order. Find the number.

#328 : Factorize:-

.

#329. If

find
.

#330. The mid-points of three sides of a triangle are (5, -3), (-5, 3), and (6, 6). Find the equations of the sides of the traingle.

Jai Ganesh · 2009-04-06 05:05:02

331. Find a and b if

is a factor of
.

#332. Find the values of a and b if 9x-2) is a common factor of

.

#333. If (x-7) and (x-4) are factors of

,
find the values of p and q.

#334. If (x-1), (x+2), and (x-2) are the factors of

,
find a, b, and c.

Jai Ganesh · 2009-06-07 19:50:38

#335, Two dices contain the numbers from 1 to 6 and 1 to 6. By using these 6 numbers all calendar dates from 01 to 31 must be displayed by rearranging the dices in any way. What are the six numbers each dice contains?

bobbym · 2009-06-07 21:28:31

# 328

By the rational root theorem:

Can only have these rational roots {-1/1,-1/2,-2/2,-2/1,1,1/2,2}

plugging them in we get roots of -2,1/2 and 1

Which means the factorization is of the form

Last edited by bobbym (2009-10-18 01:51:17)

Jai Ganesh · 2009-06-07 23:44:11

Outststading!!!

bobbym · 2009-06-12 01:32:22

Hi ganesh;

Last edited by bobbym (2009-06-12 20:58:49)

Jai Ganesh · 2009-06-13 19:08:07

I shall let you know soon!

Fruityloop · 2009-06-17 13:14:11

Thank you for the interesting and challenging puzzles Ganesh.

Last edited by Fruityloop (2009-06-18 06:01:04)

bobbym · 2009-06-22 01:17:55

Last edited by bobbym (2009-06-22 01:19:21)

anonimnystefy · 2011-12-28 03:19:13

hi ganesh

zetafunc · 2015-09-14 03:00:59

Jai Ganesh · 2015-09-14 19:22:21

Hi zetafunc,

The solution #321 is correct! Well done!

Monox D. I-Fly · 2015-12-13 16:17:03

Jai Ganesh · 2015-12-14 01:25:15

Hi Monox D. I-Fly,

The solution #315 is correct! Excellent! Now, I am unable to concentrate on essay type problems! Excuse!

Monox D. I-Fly · 2015-12-14 20:58:07

Too bad I want to prove all the trigonometry identities problem, though.

Jai Ganesh · 2015-12-15 02:30:55

Hope you understand, Monox D. I-Fly!

666 bro · 2019-10-18 21:58:18

Hi
#321 solution is a=9 and d=6

Jai Ganesh · 2019-10-18 23:23:25

Hi,

The solution #321 is correct. Neat work, 666 bro!

666 bro · 2019-11-11 22:51:50

#329 solution is (x+y) ((1-2q)) /(x-y)

666 bro · 2019-11-13 22:08:49

The solution of #262 is -(a+nd)

666 bro · 2020-04-27 21:54:20

The solution of # 314 is (7/36).

Jai Ganesh · 2020-04-28 03:46:41

Hi,

I get

666 bro · 2020-04-28 15:25:20

But I got this is answer in an different way.
Let A and B are two events.
Total number of outcomes=36
A= getting sum of 8
B= getting a product of 12
P(A) = probability of the dices getting sum of 8= (5/36)
P(B) = probability of the dices getting product of 12 = (4/36)
P(A&B) = probability of getting both sum of 8 and product of 12= (2/36)
P(AUB) = probability of getting sum of 8 or getting a product of 12.
so, we should find P(AUB)
Then P(AUB) = P(A) +P(B) -P(A&B)
Now, P(AUB) = (5/36) +(4/36) -(2/36)
= (7/36)
(∴) P(AUB) =(7/36).

Math Is Fun Forum

#301 2009-03-29 05:04:18

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#303 2009-04-02 04:02:12

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#304 2009-04-06 05:05:02

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#305 2009-06-07 19:50:38

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#306 2009-06-07 21:28:31

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#307 2009-06-07 23:44:11

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#308 2009-06-12 01:32:22

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#309 2009-06-13 19:08:07

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#310 2009-06-17 13:14:11

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#311 2009-06-22 01:17:55

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#312 2011-12-28 03:19:13

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#313 2015-09-14 03:00:59

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#314 2015-09-14 19:22:21

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#315 2015-12-13 16:17:03

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#316 2015-12-14 01:25:15

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#317 2015-12-14 20:58:07

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#318 2015-12-15 02:30:55

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#319 2019-10-18 21:58:18

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#320 2019-10-18 23:23:25

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#321 2019-11-11 22:51:50

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#322 2019-11-13 22:08:49

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#323 2020-04-27 21:54:20

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#324 2020-04-28 03:46:41

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#325 2020-04-28 15:25:20

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