GATE Questions

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Since they can do 19 programs in 19 hours, Then 52 programs in 52 hours respectively.
And a 15 min interval
Total time they take to do 52 programs is 52 hours 15 minutes.

Total no of ways = (14 – 1)! = 13!

Number of favorable ways = (12 – 1)! = 11!

So, required probability = 11!×3!13! = 39916800×66227020800 = 24625

Given 5:6 :: 7:10 :: 6:5

We know that compound ratio is calculated as
a:b :: c:d :: e:f
(axcxe):(bxdxf)

=> (5x7x6):(6x10x5)
=> (210):(300)
= 7:10

Daughter of your mother's father's mother => Maternal grandmother => Renu's Aunt.

Hence, Laxmi is Renu's Aunt and Vishal is Renu's Uncle.

Given 30% of 500

$$\begin{gathered} = 30100 x 500 \\ = 30 x 5 \\ = 150 \end{gathered}$$

Hence, 30% of Rs. 500 = Rs. 150.

Why Water Is Not an Element :

An element is a substance consisting of only one type of atom. Water consists of two types of atoms: hydrogen and oxygen.

water is both a molecule and a compound :

A compound forms whenever two or more atoms form chemical bonds with each other. The chemical formula for water is H2O, which means each molecule of water consists of one oxygen atom chemically bonded to two hydrogen atoms.

Thus, water is a compound.

It's also a molecule, which is any chemical species formed by two or more atoms chemically bonded to each other. The terms molecule and compound mean the same thing and can be used interchangeably.

Hence, water is both a molecule and a compound.

As given Kapil's 8th birthday was celebrated 2 years ago,

Kapil’s present age = 8 + 2 = 10 years.

Father's age is twice of Kapil’s age after 10 years.
=> F + 10 = 2 (K + 10) = 2 (10+ 10)
F = 30years,

Avanthi's age =1/6(F) = 30/6 = 5 years.

Here the given series follows a pattern that,

2² - 0 = 4  

3² - 1 = 8  

4² - 2 = 14

5² - 3 = 22

6² - 4 = 32

Hence, the missing number is 32

Method 2 ::

The difference between 4 and 8 is 4, the difference between 8 and 14 is 6, the difference between 14 and 22 is 8. So the next difference between 22 and the next number will be 10 since it follows (4,6,8,10 - add +2 each time)

Hence, 22 + 10 = 32 is the missing number.