GATE Questions

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Here, x = 20 and y = - 20
Therefore, the net % change in value
=x + y + xy100 %
= 20 + -20 + 20 × -20100%  or  - 4%

Since the sign is negative, there is a decrease in value by 4%.

If Vijay gives 'x' marbles to Ajay then Vijay and Ajay would have V - x and A + x marbles.
V - x = A + x --- (1)
If Ajay gives 2x marbles to Vijay then Ajay and Vijay would have A - 2x and V + 2x marbles.
V + 2x - (A - 2x) = 30 => V - A + 4x = 30 --- (2)
From (1) we have V - A = 2x
Substituting V - A = 2x in (2)
6x = 30 => x = 5.

The Surface tension pulls the surface of the drop equally at all points thus produces the spherical shape having the minimum surface area. This surface tension is the "skin" of a body of water that makes the molecules stick together.

Let the number of sides be n. 

The number of diagonals is given by ⁿC₂ - n  

^{Therefore, n}C₂ - n = 44, n>0 

ⁿC₂ - n = 44

n² - 3n - 88 = 0 

n² -11n + 8n - 88 = 0  

As n>0, n will not be -8. Therefore, n=11.

Let the number of failed students be x

=> Number of passed students = 4x 

So total number of students was 5x

From the given data,

If total number of students be 5x – 35

=> 4x-35-9/x+9 = 2/1

=> 4x – 44 = 2(x + 9)

=> 4x – 2x = 18 + 44

=> x = 31

Total number = 31×5

= 155

$$\begin{gathered} 3 \\ 32 + 3 = 12 \\ 5 \\ 52 + 5 = 30 \end{gathered}$$

Let x and y be the respective km's travelled by man via taxi and by his own car.
Given x + y = 90 => x = 90 - y
But according to the question,
7x + 6y = 595
7(90-y) + 6y = 595
=> 630 - 7y + 6y = 595
=> y = 630 - 595 = 35
=> x = 90 - 35 = 55
Therefore, the distance travelled by taxi is 55 kms.

Astronomy is the study of planets and heavenly bodies. Historically, astronomy has focused on observations of heavenly bodies. It is a close cousin to astrophysics. Succinctly put, astrophysics involves the study of the physics of astronomy and concentrates on the behavior, properties and motion of objects out there.