GATE Questions

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Let workdone 1 boy in 1 day be b

and that of 1 girl be g

From the given data,

4(5b + 3g) = 23

20b + 12g = 23 .......(a)

2(3b + 2g) = 7

6b + 4g = 7 ........(b)

Solving (a) & (b), we get

b = 1, g = 1/4

Let number og girls required be 'p'

6(7 x 1 + p x 1/4) = 45

=> p = 2.

Hence, number of girls required = 2

The Word LOGARITHMS  contains 10 letters.

To find how many 4 letter words we can form from that = P410 =10x9x8x7 = 5040.

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.

In an algebraic expression, like terms are terms that contain the same variables raised to the same powers. Calculating x-squared plus x-squared is a matter of combining like terms. 

Now x^2 + x^2 = 2x^2

Hence, x-squared plus x-squared is equal to 2 times x squared.

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.

Sucrose is not a monosaccharide.

Monosaccharides are simple carbohydrates molecules that cannot be broken down into smaller molecules of other carbohydrates.

Glucose, galactose and fructose are examples of Monosaccharides.

Energy is measured in units called Joules.

Joule is unit of work or energy in the International System of Units (SI) which is equal to the work done by a force of one newton acting through one metre.

1 Joule  =  10⁷ ergs or 0.7377 foot-pounds.