GATE Questions and Answers with Explanation

Q:

Lami's theorem is applicable only for

A) Non-Concurrent forces	B) Coplanar forces
C) Coplanar and concurrent forces	D) Any type of forces

Answer & Explanation Answer: C) Coplanar and concurrent forces

Explanation:

The Lami's theorem states that " If three forces coplanar and concurrent forces acting on a particle keep it in equilibrium, then each force is proportional to the sine of the angle between the other two and the constant of proportionality is the same." This theorem is derived from the Sine rule of triangles.

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Filed Under: Arithmetical Reasoning
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12 10399

Q:

5% of a number is 25% more than another number. The difference between the numbers is 96. Then find the value of the numbers?

A) 102 & 6	B) 99 & 3
C) 104 & 8	D) 100 & 4

Answer & Explanation Answer: D) 100 & 4

Explanation:

Let the first number be x and the second number be y.

Given

5% of x = (25% of y) + y

=> 5x/100 = 5y/4

=> x = 25y ......(1)

and also given that, x - y = 96

=> x = 96 + y .....(2)

From (1)&(2)

25y = 96 + y

=> 24y = 96

=> y = 4

From (1)

x = 96 + 4 = 100

Hence, the numbers are 100 & 4.

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Filed Under: Percentage
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15 10371

Q:

The term biodiversity refers to

A) Range of genetic variation within a population	B) Total number of different species within a habitat
C) Both A & B	D) None of the above

Answer & Explanation Answer: C) Both A & B

Explanation:

The term biodiversity refers to the variety of life on Earth at all its levels, from genes to ecosystems, and the ecological and evolutionary processes that sustain it.

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Filed Under: General Science
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9 10361

Q:

Divide Rs.118000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6 ?

A) A = 48000 B = 40000 C = 30000	B) A = 30000 B = 40000 C = 48000
C) A = 30000 B = 48000 C = 40000	D) A = 40000 B = 48000 C = 30000

Answer & Explanation Answer: B) A = 30000 B = 40000 C = 48000

Explanation:

Compound ratio of A:B:C
A:B = 3:4
B:C = 5:6
----------
A:B:C = 15:20:24

We can divide Rs.118000 in this ratio.

Share of A = 15/59 x 118000 = 30000

Share of B = 20/59 x 118000 = 40000

Share of C = 24/59 x 118000 = 48000

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Filed Under: Partnership
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4 10359

Q:

Yellow color of urine is due to presence of

A) Bile juice	B) Urochrome
C) Lymph	D) Cholesterol

Answer & Explanation Answer: B) Urochrome

Explanation:

Yellow_color_of_urine_is_due_to_presence_of1554294141.jpg image

The yellow color of urine is due to the presence of a yellow pigment, urochrome.
The color of normal urine is usually light yellow to amber.

Generally the greater the solute volume the deeper the color.

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Filed Under: Biology
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34 10346

Q:

Exercise is to Gym as Eating is to

A) Dieting	B) Fitness
C) Restaurent	D) Food

Answer & Explanation Answer: C) Restaurent

Explanation:

The given words are related in such a manner that, for exercise we go to gym. Simmilarly, for eating we go to restaurent.

Hence, Exercise : Gym :: Eating : Restaurent.

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Filed Under: Analogy
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9 10345

Q:

The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles ?

A) 2413 sq.m	B) 1234 sq.m
C) 4312 sq.m	D) 2143 sq.m

Answer & Explanation Answer: C) 4312 sq.m

Explanation:

Let the radii of the smaller and the larger circles be 's' m and 'l' m respectively.

$2 πs$ = 264 and $2 πl$ = 352

s = $\frac{264}{2 π}$ and l = $\frac{352}{2 π}$

Difference between the areas = $π l^{2} - π s^{2}$

= $π (\frac{176^{2}}{π^{2}} - \frac{132^{2}}{π^{2}})$

= $\frac{1762}{π} - \frac{1322}{π}$

= (176 - 132)(176 + 132) / $π$

= (44 x 308) / (22/7) = 4312 sq.m

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Filed Under: Volume and Surface Area
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18 10339

Q:

John sells his laptop to Mark at a loss of 20% who subsequently sells it to Kevin at a profit of 25%. Kevin after finding some defect in the laptop, returns it to Mark but could recover only Rs.4.50 for every Rs. 5 he had paid. Find the amount of Kevin’s loss if John had paid Rs. 1,75,000 for the laptop ?

A) Rs.16,500	B) Rs.17,500
C) Rs.14,200	D) Rs.15,520

Answer & Explanation Answer: B) Rs.17,500

Explanation:

Let’s assume John bought the laptop for Rs. 100
He then sells it to Mark at a loss of 20% => Rs. 80,
Who consequently sells it to Kevin at a profit of 25% => Rs. 100
Then, Kevin sells it back to Mark for Rs. 90 (Rs.4.50 for every Rs. 5 that he had paid initially), so he suffers a loss of Rs. 10
Therefore, for Rs. 100 there is a loss of Rs. 10,
Then for Rs. 1,75,000 there will be a loss of Rs. 17,500.

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Filed Under: Profit and Loss
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15 10330

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