GATE Questions

Q:

Let K and L be events on the same sample space, with P (K) = 0.8 and P (B) = 0.6. Are these two events are disjoint ?

A) TRUE B) FALSE
Answer & Explanation Answer: B) FALSE

Explanation:

These two events cannot be disjoint because P(K) + P(L) > 1.


P(AꓴB) = P(A) + P(B) - P(AꓵB).


An event is disjoint if P(A ꓵ B) = 0. If K and L are disjoint P(K ꓴ L) = 0.8 + 0.6 = 1.4


And Since probability cannot be greater than 1, these two mentioned events cannot be disjoint.

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Subject: Probability
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Q:

A 200 m long train passes a motorcycler, running in the same direction at 12 km/hr, in 15 second and a jeep travelling in the same direction in 20 s. At what speed is the car travelling (length of both the motorcycler and jeep is negligible)?

A) 36 kmph B) 32 kmph
C) 29 kmph D) 24 kmph
 
Answer & Explanation Answer: D) 24 kmph

Explanation:

Let the speed of the train be 'S' kmph

From the given data,

Distance = Length of train = D = 200 mts = 200 x 18/5 kms

Time = 10 sec

given speed of the motorcycler = 12 kmph

Relative speed as they are moving in the same direction = (S - 12) kmph

(S- 12) = 200 x 18515S - 12 = 48S = 60 kmph 

Hence, the speed of the train = S = 60 kmph

Now,

Let the speed of the jeep be 'x' kmph

60 - x = 200 x 1852060 - x = 36x = 60 - 36x = 24 kmph

 

Therefore, the speed of the jeep = x = 24 kmph.

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Filed Under: Time and Distance
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10 4543
Q:

A can complete a piece of work in 12 days and B is 60% more efficient than A. In how many days B will complete the same work  ?

A) 8.7 hrs B) 5.2 hrs
C) 5 hrs D) 7.5 hrs
 
Answer & Explanation Answer: D) 7.5 hrs

Explanation:

Ratio of times taken by A and B = 160 : 100
A can do the work in 12 days
Let B can do the work in "D" days
=> 160:100 = 12 : D
=> D = 12 x 100/160 = 7.5 hrs

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Filed Under: Time and Work
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3 4543
Q:

Which gymnospermic plant cures rheumatism?

A) Ephedra B) Pinus
C) Araucaria D) Gnetum
 
Answer & Explanation Answer: D) Gnetum

Explanation:

Oil from Gnetum spp a gymnosperm belonging to the family Gnetaceae is used to relieve the effects of rheumatism

The lianas and shrubs of Gnetum are found in the rain forests of the western ghats.

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Filed Under: General Science
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3 4542
Q:

Simple interest on a certain sum at 7% per annum for 4 years is Rs. 2415. What will be the compound interest on the same principal at 4% per annum in two years?

A) Rs. 704 B) Rs. 854
C) Rs. 893 D) Rs. 914
 
Answer & Explanation Answer: A) Rs. 704

Explanation:

We know that,

S.I. = PTR100 P = S.I x 100T x RAnd also,C.I = P1 + R100n- 1

From given data, P = Rs. 8625

Now, C.I  = 86251+41002-1= 862526252-1= 8625676625-1= 8625 x 51625C.I = Rs. 703.80

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Filed Under: Compound Interest
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Q:

82.5% of 2360?

A) 1960 B) 1954
C) 1947 D) 1931
 
Answer & Explanation Answer: C) 1947

Explanation:

Given 82.5% of 2360

 82.5100 x 2360 = 0.825 x 2360 = 1947

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Filed Under: Percentage
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6 4534
Q:

Find the lowest common multiple of 24, 36 and 40?

A) 360 B) 420
C) 240 D) 120
 
Answer & Explanation Answer: A) 360

Explanation:

To find the LCM of 24, 36 and 40

24 = 2 x 2 x 2 x 3

36 = 2 x 2 x 3 x 3

40 = 2 x 2 x 2 x 5 

Now, LCM of 24, 36 and 40 = 2 x 2 x 2 x 3 x 3 x 5

= 8 x 9 x 5

= 72 x 5

= 360

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Filed Under: HCF and LCM
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19 4534
Q:

Which of these is unique to flowering plants?

A) double fertilization B) an embryo surrounded by nutritive tissue
C) haploid gametophytes D) pollen production
 
Answer & Explanation Answer: A) double fertilization

Explanation:

In flowering plants one sperm nucleus fertilizes the egg and the other sperm nucleus fuses with two other nuclei found within the ovule, thus forming triploid endosperm.

 

Hence, double fertilization is unique to flowering plants.

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Filed Under: Biology
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