GATE Questions

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Number of books that can be placed in the larger box is given by Volume of Box / Volume of book.
Now, n = 25 x 42 x 60 / 7 x 6 x 5
= 63000 / 210
= 300.
Therefore, 300 books can be in that box.

Let the smallest number be x.
Then larger number = (x + 1365)
x + 1365 = 6x + 15
= 5x = 1350
x = 270
Smaller number = 270.

$$\begin{gathered} 112 × 54 \\ 112 × 1024 \\ = 112 × 1000024 \\ = 1120000/16 \end{gathered}$$

= 70,000.

Let the two digits be x & y

From given data in the question, we get

x + y = 3(x - y)

x + y = 3x - 3y

=> 2x = 4y

x/y = 2/1

For having the 2:1, numbers satisfying are

12, 21, 24, 42, 36, 63, 48, 84

From this 36 is eleminated because it is a perfect square and no others are prime or perfect squares.

Hence, there exists 7 such 2-digit numbers => 12, 21, 24, 42, 63, 48, 84.

Here pairs interchanged are

2, 4 

3, 8

5, 6

Unchanged are 0, 1, 7, 9

Let the side of the square be 's' cm

length of rectangle = (s+5) cm

breadth of rectangle = (s-3)cm

(s+5) (s-3) = 

s2 - 5s - 3s - 15 = s2 

2s = 15

Perimeter of rectangle = 2(L+B) = 2(s+5 + s–3) = 2(2s + 2)

= 2(15 + 2) = 34 cm 

Viruses are responsible for some of the most dangerous and deadly diseases including influenza, ebola, rabies and smallpox.

Despite their potential to kill, these potent pathogens are in fact considered to be non-living.

Reasons:

1. Viruses don't have any cells, like living organisms do. They have protein coats but no organelles or other cellular machinery. Just a little DNA packet.

2. Viruses can't produce new proteins, DNA, or RNA and therefore are unable to reproduce on their own. They need infected cells' machinery to make all of these and produce new virons.

3. Viruses have no metabolic activity. They don't use or convert energy and have no ongoing interior processes. They're basically just inert structures until they impact a potential host cell.

A sponge is a porous material. Rubber is an elastic material. 

Since Rubber is not a Massive or solid and not an inflexible thing, it is elastic.