GATE Questions

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Oxygen in our blood is transported by a protein named Haemoglobin.

In physics, the dynamo theory proposes a mechanism by which a celestial body such as Earth or a star generates a magnetic field.

Earth's crust core contains a large amount of iron and nickel is the evidence of the dynamo theory.

We know that,  Speed = Distance/time

Let the speed of the train be = x kmph

           NORMAL SPEED                           SPEED 5 KMPH MORE

          Distance = 360 Km                         Distance =360
 
          speed    =  X Kmph                        Speed = (x+5)
 
            Time =360/X                              Time =360/(x+15)
          

For the same journey if the speed increased 10 kmph more it will take 1 hour less

Time with original speed - time with increased speed = 1

 => (360/x) - (360/x+10) =  1                               

 =>  (360(x+5)-360x)/x(x+5) =1

 =>   360X + 1800 -360X  = X(X+5)

  =>   X^2 + 5x - 1800 = 0

  X = 40 or -45

 X cannot be negetive value
                  

 X = 40 kmph.

We know that zero can't be in hundreds place. But let's assume that our number could start with zero.

The formula to find sum of all numbers in a permutation is

111 x no of ways numbers can be formed for a number at given position x sum of all given digits

No of 1 s depends on number of digits

So,the answer us

111 x 20 x (0+1+2+3+4+5) = 33300

We got 20 as follows. If we have 0 in units place we can form a number in 4*5 ways. This is for all numbers. So we have substituted 20 in formula.

Now, this is not the final answer because we have included 0 in hundreds place. so we have to remove the sum of all numbers that starts with 0.

This is nothing but the sum of all 2 digits numbers formed by 1 2 3 4 5. Because 0 at first place makes it a 2 digit number.

So the sum for this is 11 x 4 x (1+2+3+4+5).
=660

Hope u understood why we use 4. Each number can be formed in 4x1 ways

So, the final answer is 33300-660 = 32640

DNA fingerprinting is used to identify the parents, thieves and rapists.

When both sides have won the same number of points then: when each side has won one, or two, points, the score is described as "15-all" and "30-all" (or "15-up" and "30-up"), respectively.

However, if each player has won three points, the score is called as "deuce", not "40–all". From that point on in the game, whenever the score is tied, it is described as "deuce", regardless of how many points have been played.

Uttar Pradesh is the Indian state which share the most borders with 9 different states.

Neighbouring States of Uttar Pradesh –

Uttarakhand and Himachal Pradesh in northwest,

Delhi, Haryana and Rajasthan in west,

Madhya Pradesh in south,

Chhattisgarh in southeast,

Bihar and Jharkhand in east.

From statement I,

Time taken by Sriram to complete the work = 40 days

From statement II,

Time taken by Sriram to complete the wok = 30 days

So from both either by statement I or statement II we can find the time to complete the work.