GATE Questions and Answers with Explanation

Q:

The Value of $[\log (\tan (1^{0})) + \log (\tan (2^{0})) + \dots \dots + \log (\tan (89^{0}))]$ is

A) -1	B) 0
C) 1/2	D) 1

Answer & Explanation Answer: B) 0

Explanation:

$= [\log \tan (1^{0}) + \log \tan (89^{0})] + [\log \tan (2^{0}) + \log \tan (88^{0})] + \dots \dots + [\log \tan (45^{0})]$

$= \log [\tan (1^{0}) \times \tan (89^{0})] + \log [\tan (2^{0}) \times \tan (88^{0})] + \dots \dots + \log (1)$

$[∵ \tan (90 - θ) = c o t θ a n d \tan (45^{0}) = 1]$

= log 1 + log 1 +.....+log 1

= 0.

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Filed Under: Logarithms
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27 5969

Q:

Heat transfer horizontally within the atmosphere is called

A) Convection	B) Advection
C) Conduction	D) Absorption

Answer & Explanation Answer: B) Advection

Explanation:

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Filed Under: General Science
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8 5968

Q:

There are 600 Kabaddi players 4% wear knee band on one leg. Of the remaining, 25% wear knee bands on both legs. How many players don't wear a knee band ?

A) 426	B) 428
C) 415	D) 432

Answer & Explanation Answer: D) 432

Explanation:

There are 600 Kabaddi players
4% wear knee band on one leg
Remaining players = 600 x 0.96 = 576
Of the remaining, 25% wear knee bands on both leg
and Of the remaining, 75% do not wear knee bands .
So players not wearing knee bands = 0.75 x 576 = 576 x 3/4 = 144 x 3 = 432.

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Filed Under: Percentage
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5 5960

Q:

Anil purchases two books for Rs.100. He sells first at loss of 5% and second al 20% profit. If he gets Overall profit of 5% then what is cost of first book?

A) 58	B) 60
C) 55	D) 45

Answer & Explanation Answer: B) 60

Explanation:

-5-----------------------5-------------------20

5-(-5) = 10

20-5= 15

Ratio of cost price of book1 and book2 = 3:2

Then cost price of book 1 is given by

(3/5) x 100 = Rs. 60.

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Filed Under: Profit and Loss
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20 5960

Q:

A clock is started at 11 a.m. By 600 seconds past 6 p.m, the hour hand has turned through ?

A) 155 degrees	B) 175 degrees
C) 205 degrees	D) 215 degrees

Answer & Explanation Answer: D) 215 degrees

Explanation:

The total angle traced by the hour hand is the angle traced in 7 hours and 10 minutes.
We know that the angle traced by the hour hand in one hour is 30º and in one minute is 1/2º.
Therefore, (30º x 7) + (10 x 1/2º) = 215º is the angle traced by the hour hand.

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Filed Under: Clock puzzles
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15 5958

Q:

Teachers day is celebrated in memory of

A) Dr. Rajendra Prasad	B) Sir Vallabhai Patel
C) Dr. Sarvepalli Radhakrishnan	D) Jawaharlal Nehru

Answer & Explanation Answer: C) Dr. Sarvepalli Radhakrishnan

Explanation:

Every year 5th September is celebrated as Teacher's Day in India, in the memory of Dr. Sarvepalli Radhakrishnan's birthday. He was the first vice-president and second president of India.

Teachers_day_is_celebrated_in_memory_of1536127626.jpg image

After he become the president of India, his students want to celebrate his birthday in grand but he refused and he adviced them to celebrate that day as teachers day. From then, 5th September is celebrated as Teacher's Day.

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Filed Under: General Awareness
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2 5950

Q:

What is the main component of bones and teeth?

A) Calcium Phosphate	B) Calcium Carbonate
C) Calcium Nitrate	D) Calcium Sulphate

Answer & Explanation Answer: A) Calcium Phosphate

Explanation:

The main component of bones and teeth is Calcium Phosphate.

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Filed Under: General Science
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9 5950

Q:

A shop keeper sells an article at a loss of 8%, but when he increases the selling price of the article by Rs. 164 he earns a profit of 2.25% on the cost price. If he sells the same article at Rs. 1760, what is his profit percentage?

A) 2.5%	B) 5%
C) 10%	D) 7.5%

Answer & Explanation Answer: C) 10%

Explanation:

According to the given data,

Let Cost price of the article be 'cp'

Then,

102.25 cp - 92 cp = 164 x 100

10.25 cp = 16400

cp = 1600

Now, if he sells at Rs. 1760

Profit = 1760 - 1600 = 160

Profit% = 160/1600 x 100 = 10%.

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Filed Under: Profit and Loss
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10 5942

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