GATE Questions

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These two events cannot be disjoint because P(K) + P(L) > 1.

P(AꓴB) = P(A) + P(B) - P(AꓵB).

An event is disjoint if P(A ꓵ B) = 0. If K and L are disjoint P(K ꓴ L) = 0.8 + 0.6 = 1.4

And Since probability cannot be greater than 1, these two mentioned events cannot be disjoint.

To find the LCM of 24, 36 and 40

24 = 2 x 2 x 2 x 3

36 = 2 x 2 x 3 x 3

40 = 2 x 2 x 2 x 5 

Now, LCM of 24, 36 and 40 = 2 x 2 x 2 x 3 x 3 x 5

= 8 x 9 x 5

= 72 x 5

= 360

Given Dileep and Narender started a business.

Dileep invested 8000 for 12 months

Let Narender invested 'p' for 6 months

At the end of the year, their profit ratio is 1 : 1.

Hence,

8000 x 12 : p x 6

p : 16000

p/16000 = 1/1

=> p = 16,000

Hence, Narender invested amount is Rs. 16,000.

Carbon dioxide is present under pressure in soft drinks.

15! - 14! - 13!

= (15 × 14 × 13!) - (14 × 13!) - (13!)

= 13! (15 × 14 - 14 - 1)

= 13! (15 × 14 - 15)

= 13! x 15 (14 - 1)

= 15 × 13 × 13!

Now, the distance covered by Chennai express in 2 hrs = 60 x 2 = 120 kms

Let the Charminar Express takes 't' hrs to catch Chennai express

=> 80 x t = 60 x (2 + t)

=> 80 t = 120 + 60t

=> t = 6 hrs

Therefore, the distance away from Hyderabad the two trains meet = 80 x 6 = 480 kms.

Instructions per second (IPS) is a measure of a computer's processor speed. CPU speed of a personal computer is 32 KIPS (Kilo Instructions per second).

Diamond is the hardest substance available on Earth.

Diamond is the hardest substance available on Earth due to the giant molecular structure of diamond in which each carbon atom is covalently bonded to four other carbon atoms. A covalent bond is very strong and requires a large amount of energy to break itself, and diamond has many covalent bonds.