GATE Questions

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According to Pradeep : 20,21 or 22...(1)
According to his brother : not 22....(2)
From (1)&(2), the birthday falls on February 20 or 21.

The mother completes the job in x hours.
So, the daughter will take 2x hours to complete the same job.

In an hour, the mother will complete 1/x of the total job.
In an hour, the daughter will complete 1/2x of the total job.

So, if the mother and daughter work together, in an hour they will complete 1/x + 1/2x of the job.
i.e., in an hour they will complete 3/2x of the job.

The question states that they complete the entire task in 6 hours if they work together.
i.e., they complete 1/6 th of the task in an hour.

Equating the two information, we get 3/2x = 1/6
By solving for x, we get 2x = 18 or x = 9.

The mother takes 9 hours to complete the job.

What has Hands But cannot Clap is a Clock or a Watch.

A Clock technically has 3 hands.

1 Hour Hand Which tells Hours

1 Minute Hand Which tells Minutes

1 Second Hand Which tells Seconds.

But cannot clap with these hands.

All of us, believe that the Solar System evolved from a giant cloud of dust and gas. They believe that this dust and gas began to collapse under the weight of its own gravity. As it did so, the matter contained within this could begin moving in a giant circle, much like the water in a drain moves around the center of the drain in a circle.

At the center of this spinning cloud, a small star began to form. This star grew larger and larger as it collected more and more of the dust and gas that collapsed into it.

Further away from the center of this mass where the star was forming, there were smaller clumps of dust and gas that were also collapsing. The star in the center eventually ignited forming our Sun, while the smaller clumps became the planets, minor planets, moons, comets, and asteroids.

Let the required height of the building be x meter

More shadow length, More height(direct proportion)

Hence we can write as

(shadow length) 40.25 : 28.75 :: 17.5 : x
⇒ 40.25 × x = 28.75 × 17.5
⇒ x = 28.75 × 17.5/40.25
= 2875 × 175/40250
= 2875 × 7/1610
= 2875/230
= 575/46
= 12.5 cm

We know that, Total probability = 1

Given probability of black stones = 1/4

=> Probability of blue and white stones = 1 - 1/4 = 3/4

But, given blue + white stones =  9 + 6 = 15

Hence,

3/4 ----- 15

 1   -----  ?

=> 15 x 4/3 = 20.

Hence, total number of stones in the box = 20.

Leap year means the year that can be divisible by 4. From the above options 2009 is not divisible by 4. So it is not a leap year.