GATE Questions

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In the real numbers, zero does not have a reciprocal because no real number multiplied by 0 produces 1 (the product of any number with zero is zero).

Hence, 0 doesn't have any multiplicative inverse.

Given that, upstream distance = 7 kms

Upstream speed = 7/42 x 60 = 10 kms

Speed of the stream = 3 kmph

Let speed in still water = M kmph, then

Upstream speed = M - 3 = 10

=> M = 13 kmph.

BIOS in computers stands for Basic Input Output System.

BIOS is a set of computer instructions in firmware which control input and output operations.

Cruise = a sea voyage for pleasure. All other words are related to ‘journey on land, sea with an aim’.

Let the distance be 'd' kms.

According to the given data,

$$\begin{gathered} d30 - d50 = 4060 hrs \\ => 6d = 300 \\ => d = 50 kms. \\ \end{gathered}$$

Given speed of jogger = 9 kmph
Speed of train = 45 kmph
As they are in same direction,
Relative speed = 45 - 9 = 36 kmph = 36x5/18 = 10 m/s
Distance = 240 + 120 = 360 mts
Time = distance/speed = 360/10 = 36 sec.

Intermolecular forces :

The forces of attraction present in between the molecules or atoms or compounds is termed as intermolecular forces.


The molecule HCl is composed of hydrogen and chlorine atom. There is high difference in electronegativities therefore, it is polar in nature. The H end of HCl is permanently slightly positive charge. The Cl end of HCl has a permanent slight negative charge. the "H" in one molecule is attracted to the "Cl" in a neighbor. The intermolecular force is weak compared to a covalent bond. But this dipole-dipole interaction is one of the stronger intermolecular attractions.

It also has hydrogen bonding and dispersion forces. 

Dispersion forces are the weakest forces which are present in between all molecules or atoms.
Hydrogen bonds are present in molecules having at least one H-A bond where A is the strong electronegative atom (mainly F, Cl and N).

The distance is constant in this case.

Let the time taken for travel with a speed of 10 kmph be 't'.

Now the speed of 15 kmph is 3/2 times the speed of 10 kmph.

Therefore, time taken with the speed of 15 kmph will be 2t/3 (speed is inversely proportional to time)

Extra time taken = t - 2t/3 = t/3

=> 1pm - 11am = 2hrs

=> t/3 = 2h

=> t = 6 hrs.

Now, Distance = speed x time = 10 x 6 = 60 kms

Time he takes to reach at noon = 6 - 1 = 5 hrs

Now, Speed = 60/5 = 12 kmph.