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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Q:

The marked price of an article is increased by 25% and the selling price is increased by 16.66%, then the amount of profit doubles. If the original marked price be Rs. 400 which is greater than the corresponding cost price by 33.33%, what is the increased selling price?

A) Rs. 380	B) Rs. 420
C) Rs. 460	D) Rs. 440

Answer & Explanation Answer: B) Rs. 420

Explanation:

As given in the question, Marked price is 25% more than the Cost price.

=> C.P of the article = $\frac{3}{4} x 400 = 300$

Now,

Let the original S.P of the article be Rs. P

Now the new S.P = P + $\frac{(16.666 + 13.333)}{300} x P$

=> S.P = $\frac{7 P}{6}$

According to the question,

$\frac{7 P}{6} - 300 = 2 (P - 300)$

=> 5P = 1800

=> P = Rs. 360

Hence, the increased S.P = 360 x 7/6 = Rs. 420.

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Filed Under: Profit and Loss
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Q:

Rearrange the following sentences (A), (B), (C), (D), (E) and (F) in the proper sequence to form a meaningful paragraph.

(A) It causes a lot of physical problems especially for our eyes, body and mind.
(B) Such a lifestyle makes man lazy and excessively dependent on machines.
(C) Innovative products such as computers, laptops, mobile phones,
(D) Harmful radiation causes various terminal diseases.
(E) Technology has advanced rapidly and man cannot seem to live without it now.
(F) iPads have made things easier for us, but it also has its disadvantages.

Which of the following options is the correct arrangement ?

A) E C B A D F	B) E C F A D B
C) D C B A E F	D) D E B A C F

Answer & Explanation Answer: B) E C F A D B

Explanation:

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Filed Under: Logical Sequence of Words
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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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Filed Under: Alligation or Mixture
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Q:

When all the students in a school are made to stand in rows of 54, 30 such rows are formed. If the students are made to stand in rows of 45, how many such rows will be formed ?

A) 22	B) 36
C) 32	D) 26

Answer & Explanation Answer: B) 36

Explanation:

Total number of students = 54 x 30
When arranged in rows of 45, number of rows formed are,
$\frac{54 x 30}{45}$ = 36.

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Filed Under: Average
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Q:

Pointing towards a photograph kiran said to chotu, "I am the only daughter of this lady and her son is your maternal uncle " How is the kiran related to chotu's father ?

A) Cousin	B) Daughter
C) Sister	D) Wife

Answer & Explanation Answer: D) Wife

Explanation:

cpVU4AOGE7K85NoCI0.34923100_1496466517.png image

So, the speaker is the mother of chotu. Kiran is wife of chotu's father. Chotu's father is not shown in the diagram.

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Filed Under: Blood Relations
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Q:

Missing Letter Challenge

A) I	B) M
C) P	D) L

Answer & Explanation Answer: D) L

Explanation:

Here the letters follow the rule (AxZ)+(A+Z)

The number corresponding to the letters are used in the rule

A=1, Z=26 => 26x1 + 1 + 26 = 26+27 = 53 = 053

(LxP)+(L+P) = (12 x16) + 12 + 16 = 192+28 = 220

Similarly (11x12) + 11 + 12 => 132 + 23 = 155

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Q:

80 litres of diesel is required to travel 800 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 1000 kms using 1200 cc engine ?

A) 120 lit	B) 140 lit
C) 110 lit	D) 150 lit

Answer & Explanation Answer: D) 150 lit

Explanation:

To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 80 litres.

=> the amount of diesel required to cover a distance of 1000 kms = 1000 x 80/800 = 100 litres

However, the vehicle uses a 1200 cc engine and it is given that the amount of diesel required varies directly as the engine capacity.

i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.

Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800 x 100 = 150 litres.

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Filed Under: Ratios and Proportions
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