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A small sphere rolls down without slipping from the top of a track in a vertical plane. The track has an elevated section and a horizontal part. The horizontal part is 1.0 m above the ground and the top of the track is 2.4 m above the ground. Find the distance on the ground with respect to point B [which is vertically below the end A of the track as shown in fig.] where the sphere lands. During its flight as a projectile, does the sphere continue to rotate about its centre of mass? Explain.

Chemistry

Multiple Choice Question
The difference between heats of reaction at constant pressure and constant volume for the reaction
2C₆H₆(I) + 15O₂(g)

12CO₂(g) + 6H₂O(I) at 25^oC in kJ mol^-1 is

(a)

-7.43

(b)

+3.72

(c)

-3.72

(d)

+7.43

Mathematics

Column Matching
The set of value(s) of k

R for which

(i)	kx² - (k + 1)x + 2k - 1 = 0 has no real roots	(a)	{1, -2}
(ii)	x² - 2(4k - 1)x + 15k² - 2k - 7 > 0 for each x	(b)	(- , -17) (1, )
(iii)	Sum of the roots of x² + (2 - k - k²)x - k² = 0 is zero	(c)	{-4}
(iv)	The roots of x² + (2k - 1)x + k² + 2 = 0 are in the ratio 1 : 2	(d)	(2, 4)

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