GATE Questions and Answers with Explanation

Q:

What is the maximum velocity with which a body of mass 'm' must enter a vertical loop of radius 'R'so that it can complete the loop?

A) 0 B) gR C) $\sqrt{2} g R$ D) $\sqrt{5 g R}$

A) A	B) B
C) C	D) D

Answer & Explanation Answer: D) D

Explanation:

To complete the vertical loop, the minimum speed required at the lowest point = $\sqrt{5 g R}$ .

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Q:

Sriram was conducting an experiment in which the average of 11 observations came to be 92, while the average of first five observations was 89, and that of the last five was 86. What was the measure of the 6th observation ?

A) 134	B) 137
C) 139	D) 141

Answer & Explanation Answer: B) 137

Explanation:

This can be done as,

(11 × 92) - (5 × 89) - (5 × 86)

= 1012- 445 - 430 = 137

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Q:

The capacity of a tank is 2400 $m^{3}$ . A pump can be used both for filling and emptying the tank. The emptying capacity of the pump is 10 $m^{3}$ /minute higher than its filling capacity. And also, the pump needs 8 minutes less to empty the tank than to fill it. Find the filling capacity of the pump.

A) 46 cub.m/min	B) 44 cub.m/min
C) 48 cub.m/min	D) 50 cub.m/min

Answer & Explanation Answer: D) 50 cub.m/min

Explanation:

Let filling capacity of the pump be 'F' $m^{3} / \min$

Then, the filling capacity of the pump will be (F + 10) $m^{3} / \min$

From the given data,

$\frac{2400}{F} - \frac{2400}{F + 10} = 8 \Rightarrow 2400 [\frac{F + 10 - F}{F (F + 10)}] = 8 \Rightarrow F^{2} + 10 F - 3000 = 0 \Rightarrow F = 50 m^{3} / \min$

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Filed Under: Pipes and Cistern
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Q:

If a trader sold two cars each at Rs. 404415 and gains 15% on the first and loses 15% on the second, then his profit or loss percent on the whole is ?

A) 1.44 %	B) 2.02 %
C) 1.04 %	D) 2.25 %

Answer & Explanation Answer: D) 2.25 %

Explanation:

SP of each car is Rs. 404415, he gains 15% on first car and losses 15% on second car.

In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100

= (15)(15)/100 % = 2.25%

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Q:

If the boat goes 7 kms upstream in 42 min and speed of the stream is 3 kmph, then the speed of the boat in still water ?

A) 14 kmph	B) 13 kmph
C) 12 kmph	D) 11 kmph

Answer & Explanation Answer: B) 13 kmph

Explanation:

Given that, upstream distance = 7 kms

Upstream speed = 7/42 x 60 = 10 kms

Speed of the stream = 3 kmph

Let speed in still water = M kmph, then

Upstream speed = M - 3 = 10

=> M = 13 kmph.

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Q:

K and L start a business jointly. K invests Rs.16000 for 8 months and L remains in the business for 4 months. Out of the total profit L claims 2/7th share. How much money is contributed by L?

A) Rs. 13,204	B) Rs. 14,521
C) Rs. 12,800	D) Rs. 15,000

Answer & Explanation Answer: C) Rs. 12,800

Explanation:

Given share of L is 2/7 th of profit. Then, their profits are divided in to 5:2 ratio.

Ratio of K and L is

$\frac{16000 \times 8}{x \times 4} = \frac{5}{2}$

x = Rs. 12,800.

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Q:

A by product of involuntary muscle contraction and relaxation is

A) Oxygen	B) Water
C) Heat	D) Nitrogen

Answer & Explanation Answer: C) Heat

Explanation:

A_by_product_of_involuntary_muscle_contraction_and_relaxation_is1537166589.jpg image

When a muscle is contracted and relaxed some amount of heat is released as a by product.

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Filed Under: Chemistry
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Q:

Find the one which does not belong to that group ?

A) Architect	B) Blacksmith
C) Sculpture	D) Tailor

Answer & Explanation Answer: A) Architect

Explanation:

All except Architect are manufactures.

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Filed Under: Analogy
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