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If 11 points X1, X2, ..., X11 are chosen on a straight line in that order (but not necessarily evenly spaced), and Y is an arbitrary point on the line and S is the sum of the distances YX1, YX2, ..., YX11, then S is minimized when the point Y is
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• at X11
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• midway between X1 and X11
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• midway between X5 and X7
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• at X6
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• midway between X2 and X10

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TCS Other Question
.A cow and a horse are bought for Rs.200000. The cow is sold at a profit of20% and the horse is sold at a loss of 10%. The overall gain is Rs. 4000.The cost pric of the cow is:
a.Rs 130000
b.Rs 80000
c.Rs 70000
d.Rs 120000 Cubes C1, C2, C3... and spheres S1, S2, S3... are defined in the following way.
• S1 has radius 1cm.
• For each n > 0, Cn is inscribed in Sn and Sn+1 is inscribed in Cn (i.e. C1 is inscribed in S1, S2 is inscribed in C1, C2 is inscribed in S2 and so on).
Let Vn be the sum of the volumes of the first n cubes C1, C2,..., Cn. Then as n → ∞ Vn approaches
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• 4(1+3√3)/13
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• 2(1+3√3)/13
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• ∞, i.e. Vn is unbounded
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• 1(1+3√3)/13
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• 6(1+3√3)/13