GATE Questions and Answers with Explanation

Q:

If $a^{2} + b^{2} = c^{2}$ , then $\frac{1}{l o g_{c + a} (b)} + \frac{1}{l o g_{c - a} (b)} = ?$

A) 1	B) 2
C) 4	D) 8

Answer & Explanation Answer: B) 2

Explanation:

Given $a^{2} + b^{2} = c^{2}$

Now $\frac{1}{\log_{c + a} (b)} + \frac{1}{\log_{c - a} (b)}$

= $\log_{b} (c + a) + \log_{b} (c - a)$

= $\log_{b} (c^{2} - a^{2})$

= $2 \log_{b} (b) = 2$

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Filed Under: Logarithms
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31 11951

Q:

Chief component of first generation computer was

A) Vacuum tubes	B) integrated circuits
C) transisters	D) None of the above

Answer & Explanation Answer: A) Vacuum tubes

Explanation:

chief_component_of_first_generation_computer_was1538216221.jpg image

The chief component in the first generation computers are Vacuum tubes.

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16 11939

Q:

Two numbers are in the ratio 3 : 7. If 6 be added to each of them, then they are in the ratio 5 : 9. Find the numbers ?

A) 11 & 17	B) 7 & 17
C) 9 & 21	D) 13 & 23

Answer & Explanation Answer: C) 9 & 21

Explanation:

Let the two numbers be x and y

Given x : y = 3 : 7 .....(1)

Now, x+6 : y+6 = 5 : 9 .....(2)

From (1), x = 3y/7

From (2), 5y - 9x = 24

=> 5y - 9(3y/7) = 24

=> y = 21

=> From(1), x = 9

Hence, the two numbers be 9 and 21

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Filed Under: Ratios and Proportions
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36 11907

Q:

A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

A) 7:4	B) 11:4
C) 4:7	D) 8:3

Answer & Explanation Answer: D) 8:3

Explanation:

Let the speed of the boat upstream be p kmph and that of downstream be q kmph

Time for upstream = 8 hrs 48 min = $8 \frac{4}{5}$ hrs

Time for downstream = 4 hrs

Distance in both the cases is same.

=> p x $8 \frac{4}{5}$ = q x 4

=> 44p/5 = 4q

=> q = 11p/5

Now, the required ratio of Speed of boat : Speed of water current

= $\frac{q + p}{2} : \frac{q - p}{2}$

=> (11p/5 + p)/2 : (11p/5 - p)/2

=> 8 : 3

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Filed Under: Boats and Streams
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25 11902

Q:

If a carrier wave of 1000 kHz is used to carry the signal, the length of transmitting antenna will be equal to _____ ?

A) 300 m	B) 30 m
C) 3 m	D) 0.3 m

Answer & Explanation Answer: A) 300 m

Explanation:

h = $straight c over straight v$ = 3 × 10⁸/10⁶ = 300 m

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Filed Under: Physics
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39 11895

Q:

Moving from one website to another is called

A) Browsing	B) Attaching
C) Downloading	D) Uploading

Answer & Explanation Answer: A) Browsing

Explanation:

Moving from one website to another is called Browsing.

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42 11874

Q:

Karthik read $\frac{6}{13}$ th of a book in 1st week and $\frac{5}{9}$ th of the remaining book in 2nd week. If there were 100 pages unread after 2nd week, how many pages were there in the book ?

A) 404	B) 415
C) 418	D) 420

Answer & Explanation Answer: C) 418

Explanation:

Let the total book be 1

Then, in the 1st week $\frac{6}{13}$ th of book is read

i.e remaining pages = $1 - \frac{6}{13} = \frac{7}{13}$

in 2nd week he read $\frac{5}{9}$ th of it

i.e $\frac{5}{9} \times \frac{7}{13} = \frac{35}{117}$
Remaining pages after 2nd week = $\frac{7}{13} - \frac{35}{117} = \frac{28}{117}$

But given remaining pages after 2nd week = 100

$\frac{28 x}{117} = 100$

--> x = 418

The total pages in the book are 418

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Filed Under: Decimal Fractions
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17 11873

Q:

Light : Blind

A) Tongue : Sound	B) Voice : Vibration
C) Language : Deaf	D) Speech : Dumb

Answer & Explanation Answer: D) Speech : Dumb

Explanation:

Here the two pair of words related in such a way that, a blind can't see the light. Similarly, a dumb cannot speech.

Hence, Light : Blind :: Speech : Dumb.

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Filed Under: Analogy
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10 11871

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