# CDS Exam 2016 Mathematics Sample Paper Part – 7

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69. The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of semicircle whose diameter is equal to the side of the square. (Round off your answer to t, decimal places)

(A) 77.14 cm

(B) 47.14 c

(C) 84.92 cm

(D) 23.57 cm

70. A metallic sphere of radius 12 cm melted and drawn into a wire, whose radius of cross section s 16 cm. What is the length of the wire?

(A) 45 cm

(B) 1.8 cm

(C) 90 cm

(D) None of these

71. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, al the three pipes are opened A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of the solution R n the liquid in the tank after 3 mi flutes?

(A) 5/11

(B) 6/1 1

(C) 7/11

(D) 8/11

72. A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water d the tank in:

(A) hours

(B) 7 hours

(C) 8 hours

(D) 14 hours

73. A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank s filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:

(A) 6 hours

(B) 10 hours

(C) 15 hours

(0) 30 hours

74. How much time will the leak tale to empty the full cistern?

I. The cistern is normally filled m 9 hours.

II. It take one hour more than the usual time to fill the cistern because of la leak in the bottom.

(A) I alone sufficient while II alone not sufficient to answer

(B) Both l and II are necessary to answer

(C) Either I or II alone sufficient to answer

(D) Both I and II are not sufficient to answer

75. How long will it take to empty the tank if both the inlet pipe A and the outlet pipe B are opened simultaneously?

I. A can fill the tank in 16 minutes.

II. B can empty the full tank in 8 minutes.

(A) I alone sufficient while II alone not sufficient to answer

(B) Both I and li are necessary to answer

(C) Both I and II are necessary to answer

(D) Both I and II are not sufficient to answer

76. The method used to compute average or central value of the collected data is considered as

(A) measures of positive variation

(B) measures of central tendency

(C) measures of negative skewness

(D) measures of negative variation

77. The mean or average used to measure central tendency is called

(A) sample mean

(B) arithmetic mean

(C) negative mean

(D) population mean