Instructions

For the following questions answer them individually

Question 12

A train running at 18 km per hour crosses a mark on the platform in 9 seconds and takes 25 seconds to cross the platform. If P is the length of the train and Q is the length of the platform in meters, then (P, Q) = ___________ .

Question 13

Three pipes P, Q and R can fill a tank in 6 hours. After working at it together for 2 hours, R is closed and both P and Q can fill the remaining part in 7 hours. The number of hours that will be taken by R alone to fill the tank is

Question 16

Given below are two statements :

Statement I: The number of ways to pack six copies of the same book into four identical boxes where a box can contain as many as six books, is 9.

Statement II: The minimum number of students needed in a class to guarantee that there are at least six students whose birthday fall in the same month, is 61 .

In the light of the above statements, choose the **correct** answer from the options given below.

Question 17

Given below are two statements :

Statement I: The ratio of the son's age to the father's age is 1 : 5. The product of their ages is 245. The ratio of the son's age to the father's age after 9 years will be 3 : 5.

Statement II: A milkman adds 30 litres of water to 70 litres of milk. After selling 1/5th of the total quantity, he adds water equal to the quantity he sold. The proportion of water to milk he sells now would be 28 : 72.

In the light of the above statements, choose the **correct** answer from the options given below.

Question 18

If $$x - \frac{1}{x} = y, y - \frac{1}{y} = z, z - \frac{1}{z} = x$$, there which of the following equations are true?

A. $$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0$$

B. $$\frac{1}{x^{2}} + \frac{1}{y^{2}} + \frac{1}{z^{2}} = 8$$

C. $$\frac{1}{xy} + \frac{1}{yz} + \frac{1}{zx} = -3$$

Choose the correct answer from the options given below:

Question 20

Arrange the following numbers in increasing order :

A. $$\sqrt{59} - \sqrt{51}$$

B. $$\sqrt{37} - \sqrt{29}$$

C. $$\sqrt{87} - \sqrt{79}$$

D. $$\sqrt{79} - \sqrt{71}$$

Choose the correct answer from the options given below:

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