GATE Questions and Answers with Explanation

Q:

In a G - 20 meeting there were total 20 people representing their own country. All the representative sat around a circular table. Find the number of ways in which we can arrange them around a circular table so that there is exactly one person between two representatives namely Manmohan and Musharraf.

A) 2 x (17!)	B) 2 x (18!)
C) (3!) x (18!)	D) (17!)

Answer & Explanation Answer: B) 2 x (18!)

Explanation:

A person can be chosen out of 18 people in 18 ways to be seated between Musharraf and Manmohan. Now consider Musharraf, Manmohan, and the third person, sitting between them, as a single personality, we can arrange them in 17! ways but Musharraf and Manmohan can also be arranged in 2 ways.

Required number of permutations = 18 x (17!) x 2 = 2 x 18!

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2 10475

Q:

5 men and 4 women are to be seated in a row so that the women occupy the even places . How many such arrangements are possible?

A) 2880	B) 1440
C) 720	D) 2020

Answer & Explanation Answer: A) 2880

Explanation:

There are total 9 places out of which 4 are even and rest 5 places are odd.

4 women can be arranged at 4 even places in 4! ways.

and 5 men can be placed in remaining 5 places in 5! ways.

Hence, the required number of permutations = 4! x 5! = 24 x 120 = 2880

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Q:

From a container of wine, a thief has stolen 15 litres of wine and replaced it with same quantity of water. He again repeated the same process. Thus, in three attempts the ratio of wine and water became 343 : 169. The initial amount of wine in the container was:

A) 75 litres	B) 100 litres
C) 150 litres	D) 120 litres

Answer & Explanation Answer: D) 120 litres

Explanation:

$\frac{w i n e (l e f t)}{w i n e (a d d e d)} = \frac{343}{169}$

It means $\frac{w i n e (l e f t)}{w i n e (i n i t i a l a m o u n t)} = \frac{343}{512}$ (since 343 + 169 = 512)

Thus, $343 x = 512 x {(1 - \frac{15}{k})}^{3}$

$\frac{343}{512} = {(\frac{7}{8})}^{3} = {(1 - \frac{15}{k})}^{3}$

$(1 - \frac{15}{k}) = \frac{7}{8} = (1 - \frac{1}{8})$

Thus the initial amount of wine was 120 liters.

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Filed Under: Alligation or Mixture
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29 7470

Q:

From a tank of petrol, which contains 200 litres of petrol, the seller replaces each time with kerosene when he sells 40 litres of petrol(or its mixture). Everytime he sells out only 40 litres of petrol(pure or impure). After replacing the petrol with kerosen 4th time, the total amount of kerosene in the mixture is

A) 81.92L	B) 96L
C) 118.08L	D) None of these

Answer & Explanation Answer: C) 118.08L

Explanation:

The amount of petrol left after 4 operations

= $200 \times {(1 - \frac{40}{200})}^{4}$

= $200 \times {(\frac{4}{5})}^{4}$

= $200 \times (\frac{256}{625})$

= 81.92 litres

Hence the amount of kerosene = 200 - 81.92 = 118. 08 litres

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Q:

The smallest Union Territory of India is

A) Lakshadweep	B) Pondicherry
C) Daman and Diu	D) Dadar and Nagar Haveli

Answer & Explanation Answer: A) Lakshadweep

Explanation:

Lakshadweep has an area of only about 32 sq km.

The_smallest_Union_Territory_of_India_is1554209119.jpg image

The area of Pondicherry, Daman and Diu and Dadar and Nagar Haveli are about 492 sq km and 491 sq km respectively.

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Filed Under: Indian Geography
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40 19839

Q:

The enzyme that is necessary to bring about clotting of blood is

A) peptidase	B) amylase
C) lipase	D) thrombokinase

Answer & Explanation Answer: D) thrombokinase

Explanation:

The clotting of blood is a chain reaction initiated by the enzyme thrombokinase produced by the platelets. This causes prothrombin to be converted into thrombin in the presence of $C a^{+ +}$ ion.

Thrombin combines with fibrinogen to produce fibrin threads which entangles the corpuscles to form the clot.

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Filed Under: Biology
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Q:

The main element used in the vulcanisation of rubber is

A) nickel	B) copper
C) sulphur	D) graphite

Answer & Explanation Answer: C) sulphur

Explanation:

In vulcanization, cruder rubber is heated with 3% sulphur at about for $120^{0} C$ for 2-3 hours.

Vulcanised rubber is a vastly improved product.

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Filed Under: Chemistry
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Q:

The purest form of iron is

A) wrought iron	B) steel
C) pig iron	D) nickel steel

Answer & Explanation Answer: A) wrought iron

Explanation:

Wrought Iron is the purest form of iron. It contains 0.12 to 0.25% carbon and so it is the purest form of iron.

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