CAT Questions

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Rainer Weiss, a professor at the Massachusetts Institute of Technology, and Kip Thorne and Barry Barish, both of the California Institute of Technology, were awarded the Nobel Prize in Physics for the discovery of ripples in space-time known as gravitational waves, which were predicted by Albert Einstein a century ago but had never been directly seen.

Let the required number be 'p'

We know, sum of angles in a triangle are 180 deg

According to given data,

p - p/7 = 180

7p - p = 180 x 7

=> 6p = 1260

=> p = 1260/6 = 210

Biodegradable substances can be broken down into simpler, harmless substances in nature with due course of time by the biological process such as action of microbes. They can be recycled as a part of food chain.

Here, Leather bags are biodegradable.

Here given the required digit number is 4 digit.

It must be divisible by 5. Hence, the unit's digit in the required 4 digit number must be 0 or 5. But here only 5 is available.

x x x 5

The remaining places can be filled by remaining digits as 5 x 4 x 3 ways.

Hence, number 4-digit numbers can be formed are 5 x 4 x 3 = 20 x 3 = 60.