GATE Questions

---

Let Shilpa's present age is p years

According to question,

p = 4(x+4) – 4(x–4)

p = 4x+16 – 4x+16

p = 32

Shilpa's present age = 32 years

Rajeev is four years older than Shilpa

=> Shilpa's present age = Rajeev's age 4 years before.

=> Rajeev's age 4 years before = 32 years.

Imension of the duster is assumed as 5x5x7 cm3

Volume of the duster below the water layer
= volume of water increased
= πxrxrxh = 3.14×52×2.14 ≈ 168 cm3

Total volume of the duster = 5×5×7 = 175 cm3

Percentage of the duster part below the layer = 168×100/175 = 96%

Percentage of the duster part above the layer = 4%

The given compound is NaHCO3 Sodium bicarbonate which is commonly known as Baking soda.

Oxidation numbers are the charges on ions. When a neutral atom loses electrons it becomes positively charged. When a neutral atom gains electrons it becomes negatively charged.

Here the C represents the oxidation state of carbon in this compound. Compounds are electrically neutral, which is why we set the sum of the oxidation states equal to zero.

Sodium has a +1 oxidation state. Hydrogen has a +1 oxidation state. Oxygen has a -2 oxidation state. There are three oxygen atoms, which means the total oxidation state provided by both oxygen ions is -6. Adding up these oxidation states we get:

1 + 1 + (-6) + C = 0

-4 + C = 0

=> C = 4

This means the oxidation state of carbon in this compound is +4.

Except 142 all are divisible by number '7'.

One fathom = 1.8288 meters = 6 feet

A fathom is a unit of length used especially for measuring the depth of water.

% Profit with respect to A = 40 + 50 + (40 x 50)/100 = 90 + 20 = 110 %.

Let present Anirudh's age be 'A' and Bhavana's age be 'B'

Given seven years, their ratio is 7:9

=> A-7 : B-7 = 7 : 9

=> 9A - 7B = 14 .......(1)

And given,

Chandhu is 12 years older than A nad 12 years younger than B

=> C = A + 12....(2)

=> B = C + 12

=> B = A + 12 + 12 .....(From (2))

=> B = A + 24 ....(3)

Put (3) in (1)

9A - 7(A+24) = 14

9A - 7A - 168 = 14

2A = 182

=> A = 91 years

=> C = A + 12 = 91 +12 = 103 years.

Using pythagarous theorem,
distance travelled by first train = 36x5/18x30 = 300m
distance travelled by second train = 48x5/18x30 = 400m
so distance between them =√( 90000 + 160000) = √250000 = 500mts.