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229.

ABCD is a rectangle with AD = 10. P is a point on BC such that Angle APD = 90°. If DP = 8 then the length of BP is
(A) 6.4
(B) 5.2
(C) 4.8
(D) 3.6
(E) None of the above

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230.

ABCD is a square. P is the midpoint of AB. The line passing through A and perpendicular to DP intersects the diagonal at Q and BC at R. If AB = 2 then PR = ______ ?
A). 1/2
B). √3 /2
C). √2
D). 1
E). None of these

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231.

If [X] denotes the greatest integer less than or equal to X, then
[1/3] + [1/3 + 1/99] + [1/3 + 2/99 ]+................[1/3 + 98/99]
(A) 33
(B) 34
(C) 66
(D) 67
(E) 98

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232.

[1]	An operation “#” is defined by a # b=1 − b/a Conclusion I. (2 # 1) # (4 # 3) = −1 Conclusion II. (3 # 1) # (4 # 2) = −2 Conclusion III. (2 # 3) # (1 # 3) = 0

[2]	A, B, C and D are whole numbers such that A + B + C = 118 B + C + D = 156 C + D + A = 166 D + A + B = 178 Conclusion I. A is the smallest number and A = 21. Conclusion II. D is the largest number and D = 88. Conclusion III. B is the largest number and B = 56

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233.

Four digits of the number 29138576 are omitted so that the result is as large as possible. The largest omitted digit is
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5

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