GATE Questions and Answers with Explanation

Q:

In what time a 360 m. long train moving at the speed of 44 km/hr will cross a 140 m. long bridge ?

A) 36 sec	B) 39 sec
C) 41 sec	D) 43 sec

Answer & Explanation Answer: C) 41 sec

Explanation:

Speed = 44 kmph x 5/18 = 110/9 m/s

We know that, Time = distance/speed

Time = (360 + 140) / (110/9)

= 500 x 9/110 = 41 sec.

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Filed Under: Time and Distance
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12 6820

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 6810

Q:

The bonds in the compound MgSO4 can be described as

A) covalent	B) ionic
C) both A & B	D) None of the above

Answer & Explanation Answer: C) both A & B

Explanation:

Here the given compound is MgSO4.

In the given compound, Sulphur (S) and Oxygen (O) are two non metals and Magnesium (Mg) is a metal.

In this compound, Sulphur and Oxygen reacts to form covalent bond and the metal Magnesium reacts with both non metals Sulphur and Oxygen to form ionic bonds.

Hence, in the given compound MgSO4 there are both covalent and ionic bonds.

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Filed Under: Chemistry
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1 6805

Q:

Mr. X sold two properties P1 and P2 for Rs 1,00,000 each. He sold property P1 for 20% less than what he paid for it. What is the percentage of profit of property P2, so that he is not in gain or loss on the sale of two properties?

A) 33.33%	B) 29.97%
C) 25%	D) 22.22%

Answer & Explanation Answer: A) 33.33%

Explanation:

Let 'A' be the cost price of property P1.

Then from the given data, the selling price of P1 = Rs. 1,00,000

He got 20% loss on selling P1

$\Rightarrow A - \frac{20 A}{100} = 100000 \Rightarrow A = 1, 25, 000$

Therefore, the amount he lossed on selling P1 = 25,000

As ge he got no loss or gain on sale of P1 and P2, the gain on selling P2 = 25,000

But the selling price of P2 = 1,00,000 => Cost price of P2 = 75,000

Hence, the profit percentage on P2 = $\frac{Gain}{CP} x 100 = \frac{25000}{75000} x 100 = \frac{100}{3} = 33.33 %$

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Filed Under: Profit and Loss
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10 6801

Q:

A train is moving and crossing a man who is running on a platform of 100 m at a speed of 8 kmph in the direction of the train, in 9 sec. If the speed of the train is 74 kmph. Find the length of the train ?

A) 202 mts	B) 188 mts
C) 165 mts	D) 156 mts

Answer & Explanation Answer: C) 165 mts

Explanation:

Let the length of the train = L mts

Relative speed of train and man = 74 - 8 = 66 kmph = 66 x 5/18 m/s

=> 66 x 5/18 = L/9

=> L = 165 mts.

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Filed Under: Problems on Trains
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22 6799

Q:

Solve this logical Math puzzle?

logical_thinking_puzzle1536132282.jpg image

Answer

Let that something be 'x'

From the given data,

x + x/5 = 21

5x + x/5 = 21

6x = 21 x 5

=> x = 17.5

Hence, that something is x = 17.5.

Workspace

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Subject: Math Puzzles Exam Prep: AIEEE , Bank Exams , CAT , GATE , GRE
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9 6792

Q:

How much does a clock lose per day, if its hands coincide ever 65 minutes ?

A) 1440/143 min	B) 184/13 min
C) 1425/18 min	D) 541/9 min

Answer & Explanation Answer: C) 1425/18 min

Explanation:

55 min. spaces are covered in 60 min.
60 min. spaces are covered in ((60/55) x 60) min = 720/11 min.
Loss in 65 min. = (720/11 - 65 ) = 5/11
Loss in 24 hrs = (5/11 x 1/65 x 24 x 60)min = 1440/143 min.

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Filed Under: Calendar
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21 6787

Q:

On her deathbed, a grand mother called upon his three grand sons and told them to distribute all her assets worth Rs. 52,500 in the ratio of 1/35 : 1/21 : 1/15 amongst themselves. Find the smallest share amongst the three portions ?

A) Rs. 5422	B) Rs. 10,500
C) Rs. 12,800	D) Rs. 15,000

Answer & Explanation Answer: B) Rs. 10,500

Explanation:

The ratio of distribution should be:
21 x 15 : 15 x 35 : 35 x 21
= 315 : 525 : 735
= 3 : 5 : 7
The smallest share will be of worth:
3/15 x 52,500 = Rs. 10,500

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Filed Under: Ratios and Proportions
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