GATE Questions

---

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.

The Maharana Mewar Award is a Rajasthan State Award.

This award has been instituted to honour work of permanent value to those who consider it their duty, like the Diwan of Shri Eklingji still do, to benefit society through services in the field of education, literature, social services, philanthropy and character building activities.

Here pairs interchanged are

2, 4 

3, 8

5, 6

Unchanged are 0, 1, 7, 9

Principal = Rs.(100 x 5400)/(12 x 3)= Rs. 15000.

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.

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