GATE Questions

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We Know that sum of the n natural numbers =n(n+1)2

Then sum of 50 natural numbers= 50(51)2= 1250

Average of the 50 natural numbers = 125050 = 25.5

Let assume the value of a,b &c that will satisfy the equation.
so a=1,b=1,c= -1 or a=1,b= -1 &c=1 or a= -1,b=1,c=1
here all three cases satisfy the equation
assume any one a=1,b=1,c= -1

Hence (a+b)(b+c)(c+a)=(1+1)(1-1)(-1+1) = 0

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.

When modifiers are misplaced or put in the wrong place, things can get quite confusing. A modifier adds detail or limits or changes the meaning of another word or phrase. 

Here Option A) "Covered in fluffiness, the couple played with the kitten" is the ony sentence contains a misplaced modifier. In the sentence, it gives the meaning that the couple are fluffy not the kitten.

Let the man's rate upstream be x kmph and that downstream be y kmph.

Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

		x x 8	4		= (y x 4)
			5

	44	x =4y
	5

y =	11	x.
	5

Required ratio =		y + x		:		y - x
		2				2

=		16x	x	1		:		6x	x	1
		5		2				5		2

   = 8 : 3.

A greenhouse gas is a gas in an atmosphere that absorbs and emits radiant energy within the thermal infrared range. This process is the fundamental cause of the greenhouse effect. 

Carbon dioxide is a main greenhouse gas, found in car exhaust pipes.
Methane and nitrous oxide is another type of greenhouse gas.

Oxygen is the only clean gas out there because we need it to survive. Therefore, the only gas that is not a greenhouse gas is Oxygen.

To convert a fraction into decimal, just take the number on top which we called the numerator and divide it by the number at the bottom which we called the denominator.

2/3

How it comes :

$2÷3=0$ bring down the decimal point.

$20÷3=6$ and carry the remainder $2$ to make $20$

$20÷3=6$ and carry the remainder $2$ to make $20$

$20÷3=6$ and carry the remainder $2$ to make $20$

etc...

This gives the recurring decimal 0.6666...

If we round off to two decimals , then it becomes 0.67.

Hence, decimal fraction of 2/3 = 0.67.