GATE Questions

Q:

In a mixture, the ratio of juice and water is 4 : 3. By adding 6 litre water the ratio of juice and water will be 8 : 7. What is the amount of juice in the original mixture ?

A) 38 lit B) 96 lit
C) 48 lit D) 52 lit
 
Answer & Explanation Answer: C) 48 lit

Explanation:

Let the amount of juice and water in original mixture '4x' litre and '3x' litre respectively.

According to given data,

4x/3x+6 =8/7

28x=24x+48

28x–24x=48

4x = 48

x = 12

Amount of juice = 4x = 4×12 = 48 litre.

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Filed Under: Alligation or Mixture
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Q:

The price of 2 oranges, 3 bananas and 4 apples is Rs. 15. The price of 3 oranges, 2 bananas and 1 apple is Rs. 10. What will be price of 4 oranges, 4 bananas and 4 apples  ?

A) Rs. 10 B) Rs. 15
C) Rs. 20 D) Rs. 25
 
Answer & Explanation Answer: C) Rs. 20

Explanation:

Let the Oranges be 'O', Bananas be 'B' and Apples be 'A'

From the given data,

 

2O + 3B + 4A = 15 ...... (I)

3O + 2B + A = 10 ..... (II)

On adding (I) and (II),

5O + 5B + 5A = 25

O + B + A = 5

4O + 4B + 4A = 20.

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Filed Under: Simplification
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Q:

Which compound contains both ionic and covalent bonds?

A) NaNO3 B) CaSO4
C) NH4Cl D) All of the above
 
Answer & Explanation Answer: D) All of the above

Explanation:

Here all the given compounds have both ionic and covalent bonds.

 

NaNO3 - In Sodium nitrate, Nitrate is covalently bonded as nitrogen is bonded with 3 oxygen atoms. And this nitrate is ionically bonded with sodium.

 

CaSO4 - In Calcium sulphate, sulphate is covalently bonded as sulphur is bonded with 4 oxygen atoms. And this sulphate is ionically bonded with calcium.

 

NH4Cl - In Ammonium chloride, ammonium is covalently bonded as nitrogen is bonded with 4 hydrogen atoms. And this ammonium is ionically bonded with chlorine.

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Q:

A woman says, "If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum." The woman's husband age is ?

A) 45 B) 24
C) 42 D) 54
 
Answer & Explanation Answer: D) 54

Explanation:

By trial and error method from the given options,

as 54 - 45 =  (1/11) x (45+54)  = 99/11  = 9

Hence this satisfies the given conditions.

Then the woman's husband age is 54.

 

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Q:

A box contains 90 screws each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg, then the weight of the empty box is ?

A) 10.5 kgs B) 12 kgs
C) 9.6 kgs D) 11.5 kgs
 
Answer & Explanation Answer: D) 11.5 kgs

Explanation:

Screws weight = 90x100 = 9000gms
bolts weight = 100 x 150 = 15000gms
weight = screws + bolts => 24000 gms =>24 kg
Given entire box weight = 35.5kg
empty box = entire box weight - weight => 35.5kg - 24kg => 11.5kg
so the empty box is 11.5kg.

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Q:

The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is  ?

A) 2(6!) B) 6! x 7
C) 6! x ⁷P₆ D) None
 
Answer & Explanation Answer: C) 6! x ⁷P₆

Explanation:

We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.

Hence required number of ways = 6! x ⁷P₆

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Filed Under: Permutations and Combinations
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Q:

A water tank in a village is normally filled in 8 hours but takes 2 hours longer to fill because of a leak in its bottom. If the tank is full, in how many hrs will the leak empty it ? 

A) 34 hrs B) 36 hrs
C) 38 hrs D) 40 hrs
 
Answer & Explanation Answer: D) 40 hrs

Explanation:

The time taken by the leak to empty the tank = 18 - 110 = 5 - 440 = 140

Therefore, the leak empties the tank in 40 hours.

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Q:

What is the gram formula mass of Li2SO4?

A) 101.2487 B) 109.9446
C) 111.2687 D) 106.5871
 
Answer & Explanation Answer: B) 109.9446

Explanation:

The term gram formula mass is synonymous with molecular mass. So, to get this, we must add molar mass of all the elements in this compound.

 

Given compound is Lithium Sulphate - Li2SO4

Elemental calculation ::

Li  -  Lithium   -   6.941    -     2   -   13.88200 %
S  -  Sulfur     -    32.065   -    1   -   32.065 %
O  -  Oxygen   -   15.9994  -    4   -   63.9976 %

Now, total = 12.6264 + 29.1647 + 58.2090 = 109.9446 

 

Hence, the gram formula mass of Li2SO4 = 109.9446.

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Filed Under: Chemistry
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