if a^x = b, b^y= c and xyz = 1, then what is the value of c^z?

Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.

∴ The watch gains	❨	2 + 4	4	❩min.	or	34	min. in 170 hrs.
			5			5

Now,	34	min. are gained in 170 hrs.
	5

∴ 2 min. are gained in	❨	170 x	5	x 2	❩hrs	= 50 hrs.
			34

∴ Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p.m. on Wednesday.

Perimeter = Distance covered in 8 min. =	❨	12000	x 8	❩m = 1600 m.
		60

Let length = 3x metres and breadth = 2x metres.

Then, 2(3x + 2x) = 1600 or x = 160.

∴ Length = 480 m and Breadth = 320 m.

∴ Area = (480 x 320) m² = 153600 m².

√l² + b² = √41.

Also, lb = 20.

(l + b)² = (l² + b²) + 2lb = 41 + 40 = 81

⟹ (l + b) = 9.

∴ Perimeter = 2(l + b) = 18 cm.

Let 40% of A =	2	B
	3

Then,	40A	=	2B
	100		3

⟹	2A	=	2B
	5		3

⟹	A	=	❨	2	x	5	❩	=	5
	B			3		2			3

∴ A : B = 5 : 3.

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).

So, in a day, the hands point in the opposite directions 22 times.

B runs 35 m in 7 sec.

∴ B covers 200 m in	❨	7	x 200	❩	= 40 sec.
		35

B's time over the course = 40 sec.

∴ A's time over the course (40 - 7) sec = 33 sec.

In 12 hours, they are at right angles 22 times.

∴ In 24 hours, they are at right angles 44 times.

T.D.	= B.D. x 100 100 + (R x T)
	= Rs. [ 420 x 100 ] 100 + ❨ 15 x 1 ❩ 3
	= Rs. ❨ 420 x 100 ❩ 105
	= Rs. 400.