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Mathematics : A.P.

by Sanyam Kapoor -
The number of terms of an A.P. is even; the sum of odd terms is 24, of the even terms is 30, and the last term exceeds the first by 10\frac{1}{2}, find the number of terms and the series.

Thank You!
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Maths - trigonometric identities

by Harish J Mohan -
If sinα + cosα = (√7)/2; where 0<α<π/6, then tan(α/2) is equal to :-
A)√7-2
B)2-√7
C)(1/3)(√7-2)
D)(1/3)(2-Thank You 
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Fluid mechanics problem

by Amit Koikkarah Aji -
Water level is maintained upto a fixed height H.The vessel is kept on a horizontal plane.At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel.(Figure in attachment).
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coordinate geometry

by chanchal kumar -
If G is the centroid and I the in-centre of the triangle, with vertices A(-36,7), B(20,7) and C(0,-8), then, find the value of GI.
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