When the policeman arrives, the thief has traveled 6 meters.

So, the time taken by the policeman to catch the thief along the circular track = 6/1.5 = 4 seconds.

The total distance covered by the policeman = 12 meters.

Thus, the minimum distance is when the policeman takes the route via the center i.e. he travels a length of 2 x 5 = 10 meters.

The minimum time taken = 10/3 seconds.

The minimum distance covered by the thief = 1.5 x (10/3) = 5 meters

Hence, option 3.

 x = 4⁴ x 5⁶ x 6⁵ x 7¹⁰ x 8⁸

⇒ x = 2³⁷ x 3⁵ x 5⁶ x 7¹⁰ = (2 x 3) (2³⁶ x 3⁴ x 5⁶ x 7¹⁰)

Power of 2 can take values of 0, 2 , 4 , . . . , 36 = 19

Power of 3 can take values of 0, 2,4 = 3

Power of 5 can take values of 0, 2,4, 6 = 4

Power of 7 can take values of 0, 2,4, 6, 8, 10 = 6

Total number of factors = 19 x 3 x 4 x 6 = 1368

If x is a prime number greater than 1, then x is not a factor of (x - 1)!

There are 29 primes up to 110. 4 is also one such number.

Hence, option 4.

Let the speed of the stream be v kmph.

Speed of boat in still water is 24 kmph.

Hence, the speed of boat upstream is (24 – v) kmph and the speed of boat down stream is (24 + v) kmph.

Putting v = 6 kmph:

Thus, the speed of boat in still water is 4 times as fast as the speed of the stream.

The minimum value of a quadratic expression ax² + bx + c (when a > 0) occurs at x = -b / 2a and its minimum value is -(b² - 4ac) / 4a

The minimum value of the equation is = [4(3)(-23) - (11)²]/12 = -397 / 12

Hence, option 4.

Area of each slab = 72 / 50 m² = 1.44 m²

Length of each slab =√1.44 =1.2m =120cm

Let the total population of the town be x.

The number of people who read XYZ = 0.37x - 8000

0.37x+0.37x - 8000 + 0.27x = x

⇒ x = 8,00,000

Hence, option 1.

x² + x - 2 < 0

⇒ (x - 1) (x + 2) < 0

⇒ (x - 1) < 0 and (x + 2) > 0 or (x - 1) > 0 and (x + 2) < 0

⇒ x < 1, x > -2 or x > 1, x < -2 which is not possible.

∴ -2 < x < 1

⇒ (x - 1) < 0 and (x + 2) > 0 

Hence, option 3.

When the minute hand travels 60 minutes, the hour hand travels 5 minutes.

The minute hand travels 55 minutes more than the hour hand in an hour.

In 54 minutes, the Minute hand travels = (54 x 55/ 60) = 49.5

Hence, option 3.

Let the number of hours worked by B be x.

The hours worked by A = (12 - x)

The manhours of work finished by A = (12 - x - 2) x 0.6 + 2

∵ (12 - x - 2) x 0.6 + 2 = x

⇒ x = 5

The total manhours of work done by them in a day = 2 * x = 2 * 5 = 10

Thus, the number of days required to finish the work = 120/10 =12 days

Hence, option 2.