The Indian Institute of Technology (IIT) Kanpur will confer a doctorate on former sprint queen PT Usha, who missed a medal by a whisker at the 1984, Los Angeles Olympics. The degree, Doctor of Science (honoris causa – a degree awarded as a mark of esteem) will be conferred on June 16 to mark the 50th convocation of the prestigious institute of the country. This is her second doctorate – in 2002, Kannur University had conferred D.Lit on her.

Relative speed = 60 + 90 = 150 km/hr.

= 150 x 5/18 = 125/3 m/sec.

Distance covered = 1.10 + 0.9 = 2 km = 2000 m.

Required time = 2000 x 3/125 = 48 sec.

The book “Indira Gandhi – A life in Nature”, was launched by Congress president Sonia Gandhi at the Indira Gandhi Memorial in the presence of former ministers, bureaucrats and environmentalists who worked closely with her to frame some of country’s landmarks wildlife and environment laws. Renowned mountaineer Capt Manmohan Singh Kohli recalled how Gandhi once told him “please call me as a daughter of the mountains”. The book has been written by former Union minister Jairam Ramesh and it has been published by Simon & Schuster.

Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of K and L be a and b respectively.
a - b = 15% (100k) => a = b + 15k
=> a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 8720
32.5k = 32.5k/100k x 8720 = 2834

The number of valid votes polled in favour of L is 2834.

175760 =2³ x 2 x 5 x 13³
= 2³ x 2 x 5 x 13³

To make perfect cube, it must be divided by 2 x 5 = 10

Speed in still water = 6 kmph

Stream speed = 1.2 kmph

Down stream  = 7.2 kmph

Up Stream = 4.8 kmph

x/7.2 + x/4.8 = 1

x = 2.88

Total Distance  = 2.88 x 2 = 5.76 kms

Work done by P alone in one day = 1/6th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/6 of the total) = 1/18 of the total. 

Work done by P and Q, working together in one day = 1/6 + 1/18  = 4/18 = 2/9 

They would take 9/2 days = 4 (1/2) days to complete the work working together.