GATE Questions

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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.

1/K + 1/L + 1/M = 1/8 (Given)
Also given that K = 2L and L = 2M
=> 1/2L + 1/L + 2/L = 1/8
=> (1 + 2 + 4)/2L = 1/8
=> 2L/7 = 8
=> L = 28 hours.

We know that 1 yard = 3 feet. 

A yardstick which is used for measurement has 3 feet long but it cannot walk.

Total number of chairs = (3 + 5 + 4) = 12.

Let S be the sample space.

Then, n(s)= Number of ways of picking 2 chairs out of 12

= 12×11/2×1 = 66

Let n(E) = number of events of selecting 2 chairs for selecting no white chairs.

=> 8C2 = 8×7/2×1 = 28

Therefore required probability = 28/66 = 14/33.

SP of first article = 1000

Profit = 20%

CP = 100100+P×SP= 5000/6 = 2500/3

SP of second article = 1000

Loss = 20%

CP = 100100-L×SP= 5000/4 = 1250

Total SP = 2000

Total CP = 25003+ 1250 = 6250/3

CP is more than SP, he makes a loss.

Loss = CP-SP = (6250/3)- 2000 = 250/3

Loss Percent =250362503×100= 4%

We know that, Elements in the same group of the periodic table have similar characteristics.

Here Magnesium and Strontium shared some similar properties because they both belong to the same group. Sr is the chemical symbol for strontium which is a group two element; it has atomic number of 38. 

Speed of the boat upstream = 36/9 = 4 kmph

Speed of the boat in downstream = 36/6 = 6 kmph

Speed of stream = 6-4/2 = 1 kmph

From above diagram
AC represents the hill and DE represents the tower

Given that AC = 100 m

angleXAD = angleADB = 30° (∵ AX || BD )
angleXAE = angleAEC = 60° (∵ AX || CE)

Let DE = h

Then, BC = DE = h, AB = (100-h) (∵ AC=100 and BC = h), BD = CE

tan 60°=AC/CE => √3 = 100/CE =>CE = 100/√3 ----- (1)

tan 30° = AB/BD => 1/√3 = 100−h/BD => BD = 100−h(√3)
∵ BD = CE and Substitute the value of CE from equation 1
100/√3 = 100−h(√3) => h = 66.66 mts

The height of the tower = 66.66 mts.