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Thank you for the interesting and challenging puzzles Ganesh.]]>

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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

]]>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.]]>

.

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.

]]>.

#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

,

verify

.

#313. Show that

.

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

#315. Prove that

#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.

]]>?

#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?]]>