- Question-1
- Explanation

John is supposed to walk from his house to park every morning. One morning he is in real hurry and wants to save atleast 1/3^{rd} of the time. By how much percentage he should increase his speed.

a).100% b)33% c) 66% d) 50%

**Answer:**

d) 50%

Let the distance between his house and park be 100 metres.

Let’s assume he takes 30 minutes daily. Hence his speed would be 100/30.

One day, if he wishes to save 1/3^{rd} of 30 minutes, that is 10 minutes, he should cover the distance in 20 minutes in which case his speed would be 100/20.

Required increment in speed = (Required increment in speed / Original Speed) * 100 % = ((100/20 – 100/30)/100/30)* 100% = 50%

- Question-3
- Explanation

Can you give a simple formula to find average of sum of squares of first n natural numbers?

**Answer: d) **

(n + 1) (2n + 1) /6 can be used to calculate the average of sum of first n natural numbers.

- Question-3
- Explanation

Given Log_{ x} (ab) and log_{x }(a/b), how you will find log_{x }a_{ }

**Answer: d) **

**: _{ }**Log

_{ x}(ab) can be written as log

_{x }(a) + log

_{x }(b) ……..equation 1.

log_{x }(a/b) can be written as log_{x }(a) – log_{x }(b) ……..equation 2.

Solving equation 1 and 2 we will get log_{x }(a) = Log_{ x} (ab) + log_{x }(a/b)/ 2)

- Question-4
- Explanation

Consider a rhombus with diagonals of lengths d1 and d2. What could be its area?

**Answer:**

Area of the rhombus = ½(d1 * d2)

- Question-5
- Explanation

Can you quickly tell the ratio of the volume of a cylinder of height h to that of another cylinder of unit height but with same radius?

**Answer: **

Height h is the answer.

Reason: Volume V1 of Cylinder of height h and radius r, V1 = II^{r2} h

Volume V2 of another Cylinder of unit height of same radius r,

V2 = IIr^{2}h /9by substituting 1 for h) Now answer is V1/V2 = h.