Research Aptitude Test

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Research Aptitude Test - 5

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Weekly Quiz Competition

Question 1
2 / -0.5

The probability that a student is not a swimmer Is 1/5. Then the probability that out of the five students, exactly four are swimmers, is

A

B

C

D
None of these

Solution

Probability that a student is not a swimmer = 1/5

So, Probability that a student is a swimmer = 1 –1/5 = 4/5

To calculate required probability,

Probability that 4 students are swimmers and 1 is non-swimmer = (4/5) ×(4/5) ×(4/5)×(4/5)×(1/5)

= (4/5)⁴ ×(1/5)

Now, there are many ways to choose which 4 of the 5 students are swimmers.

Ways to choose 4 student out of 5 = ⁵ C₄
So, required probability =
Question 2
2 / -0.5

If the probability of rain on any given day in Pune city is 50%. Then what is the possibility that it rains on exactly 3 days in a 5-day period?

A
8/125

B
5/16

C
8/25

D
2/25

Solution

Probability that it rains on any day = ½and it doesn 't rain = 1 - (½) = ½

Prob. that it rains on exactly 3 days in a 5-day period.

= ⁵ C₃ x (½)³ x (½)²

⁵ C₃ for choosing which three days among given five days. (½)³ for that it rains on three days and (½)² for it doesn ’t rain on the remaining 2 days.
Question 3
2 / -0.5

A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 or 15 is

A
1/5

B
1/6

C
1/7

D
1/9

Solution

Total distinct multiples of 5 and 15 in first 120 natural number = 24
total numbers = 120

Probability = 24/120 = 1/5
Question 4
2 / -0.5

A woman introduces a man as the son of the brother of her mother. How is a man related to a woman?

A
Nephew

B
Son

C
Cousin

D
Uncle

Solution

Hence man is a woman 's Cousin.
Question 5
2 / -0.5

Direction : Read the following information carefully and answer the question below it.

In a certain code, ‘II be pee’ means' roses are blue’: 'silk hee' means ‘red flowers' and ‘pee mil hee’ means 'flowers are vegetables’.

Q. How is ‘red’ written in that code?

A
hee

B
silk

C
be

D
none of these

Solution

In the second and third statements, the common code word is 'hee' and the common word is 'flowers’. So, ‘hee’ stands for 'flowers'. Thus, in the second statement, 'silk- stands for 'red'.
Question 6
2 / -0.5

Direction : Read the following information carefully and answer the question below it.

In a certain code, ‘II be pee ’means 'roses are blue ’: 'silk hee 'means ‘red flowers 'and ‘pee mil hee ’means 'flowers are vegetables ’.

Q. How is ‘roses ’written in that code?

A
il

B
pee

C
be

D
can not be determined

Solution

Since from the given information, we can only find the code for ‘are 'in the first statement, it cannot be determined which of the remaining two codes for ‘roses ’.Explanation:

- The code 'II be pee 'means 'roses are blue '.
- The code 'silk hee 'means 'red flowers '.
- The code 'pee mil hee 'means 'flowers are vegetables '.
- From the given codes, we can see that 'pee 'is common in both the codes that represent 'roses 'and 'flowers '.
- However, the code for 'roses 'and 'flowers 'have different endings ('be 'and 'mil 'respectively).
- So, it is not possible to determine the exact code for 'roses 'based on the given information.
- Therefore, the answer is option D: cannot be determined.
Question 7
2 / -0.5

Direction : Read the following information carefully and answer the question below it.

In a certain code, ‘II be pee ’means 'roses are blue ’: 'silk hee 'means ‘red flowers 'and ‘pee mil hee ’means 'flowers are vegetables ’.

Q. How is ‘vegetables are red flowers ’written in code?

A
mil pee silk hee

B
silk pee hee be

C
il silk mit he

D
can not be determined

Solution

Clearly, the required code will consist of the same codes as in the third statements with the code for ‘red ’i.e. silk added to it.
Question 8
2 / -0.5

Direction : A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that the cube is colored with green color on one set of adjacent faces, red on the second and blue on the third set.

Q. How many cubelets are there which are colored with exactly one color?

A
180

B
150

C
165

D
148

Solution

From each face 5 x 5 = 25 cubelets are painted is one color. Such total = 25 x 6 = 150 cubelets. Further because each face Is having one similar color adjacent face and 3 other different coloured faces hence 5 x 3 = 15 extra cubelets will come from three edges, where adjacent faces of similar color are meeting hence total = 150 + 15 = 165 cube will be then colored in exactly one color
Question 9
2 / -0.5

A man can cover a distance in 1 hr 24min by covering 2/3 of the distance at 4 km/h and the rest at 5km/h. The total distance is

A
2km

B
5km

C
6km

D
10km

Solution

Say Total Distance be d
Speed = distance / time (convert 1 hour 24 minutes to hour)
(2d/3)/4 + (d/3)/5 = 1+ 24/60
So, get d = 6 Km
Extra: - To convert from km/h to m/s multiply km/h with 5/18.
Question 10
2 / -0.5

Choose the correct alternative that will continue the same pattern and fill in the blank spaces.
2, 7, 14, 23, ___47

A
34

B
31

C
38

D
27

Solution

Difference (Next term - Previous term) between two consecutive No. is in AP, i.e.,
Difference between No is 5, 7, 9,11, 13.
So, 23+11=34.