(Paper) Central Armed Police Forces (CAPF) Exam (Assistant
Commandant) Solved Paper - 2016 "Mathematics"
119. A vehicle with mileage 15 km/L contains 2 L of fuel. The vehicle gets some defect asa result of which 5 L of fuel gets wasted per hour, when the engine is on. With what minimum speed, the vechile has to move to travel 20 km with the existing amount of fuel, if it travels with a uniform speed?
(a) 100 km/h
(b) 120 km/h
(c) 150 km/h
(d) 200 km/h
120. A device can write 100 digits in 1 min. It starts writing natural numbers. The device is stopped after running it for half an hour. It is found that the last number it was writing, is incomplete. The number is
121. A circular coin of radius 1 cm is allowed to roll freely on the periphery over a circular disc of radius 10 cm. If the disc has no movement and the coin completes one revolution rolling on the periphery over the disc and without slipping, then what is the number of times the coin rotated about its centre?
122. Which one of the followig inequalities is always true for positive real number x, y?
(a) xy > x + y
(b) (x + y) < (x + y)2
(c) x + y < x2 + y2
(d) 1 + x + y < (1 + x + y)2
123. There are two concentric circles. The radii of the two circles are 100 m and 110 m respectively. A wheel of radius 30 cm rolls on the smaller circle and another wheel rolls on the larger circle. After they have completed one revolution, it is found that the two wheels rolled equal number of times on their respective axes. What is the radius of the other wheel?
(a) 31 cm
(b) 32 cm
(c) 33 cm
(d) 34 cm
124. A triangle is formed with vertices (0, 0), (0, 1OO) and (100,100). What is the number of points inside the triangle with integer coordinates?
125. Suppose R is the region bounded by the two curves Y = x2 and Y = 2x 2 - 1 as shown in the following diagram
Two distinct lines are drawn such that each of these lines partitions the regions into at least two parts. If 'n' is the total number of regions generated by these lines, then
(a) 'n' can be 4 but not 3
(b) 'n' can be 4 but not 5
(c) 'n' can be 5 but not 6
(d) 'n' can be 6