Research Aptitude Test

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Research Aptitude Test - 17

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Weekly Quiz Competition

Question 1
2 / -0.5

The velocity of the nitrogen molecule in room temperature air is:

A
Zero

B
10 m s-1

C
15m s -1

D
500 m s -1

E
5000 m s -1

Solution

Nitrogen molecule is 28 neuclons ×1.67 ×10-27 kg/neucleon = 4.68 д10-26 kg. So the average speed of a gas molecule is about 500 m/sec .
Question 2
2 / -0.5

When I was a child, there used to be a fair in my town during the Diwali and Eid festivities. Among the many things I saw was a strange puppet show. There were three puppets, one of a man, another of a woman and the third one of a rakshasa (demon). Whenever the rakshasa was brought close to the woman, she would turn her face away. But when the man was brought close to her, she would turn back and face the man.

I and my friends looked at this show and argued for hours what caused the woman to turn her face. Choose one or more of the options below about my childhood experience above:

Q. One of my friends stayed back one day at the show and kept looking at the puppets for a long time. He asked the manager of the show to move the puppets in certain ways. The manager as a kind person and with my friend insisting, he agreed to do what my friend asked for. But he did not the friend if there were magnets in the puppets. But the next day, the friend told us that he was sure that there were magnets inside the puppets 'faces. What did he ask the manager to do and what could he have Seen? He must see the effect after asking for moving the puppets

A
backwards towards each other.

B
at different speeds.

C
up and down.

D
On the same plane, but in different directions.

Solution

Backwards towards each other.

By this His Friend can get to know the Poles if Magnets were there which Confirms Presence of Magnets in it.
Question 3
2 / -0.5

If 2^2x-1= 1/8^x-3, the value of x is:

A
A. 3

B
B. 2

C
C. 0

D
D. -2

Solution

If 2^2x-1 = 1/8^x-3 , ⇒ 2^2x-1 = 1/(2³ )^(x-3)

⇒ 2^2x-1 = 1/2^3x-9 ⇒ 2^2x-1 = 2^9-3x

∴ 2x - 1 = 9 - 3x or 5x = 10 or x = 2
Question 4
2 / -0.5

then x is equal to:

A
A. 125

B
B. 64

C
C. 27

D
D. 9

Solution

On squaring both sides, we get

5 + ∛x = 9 or ∛x = 4.

Cunning both sides, we get

x = (4 x 4 x 4) = 64.
Question 5
2 / -0.5

If a^x = b^y = c^z and b² = ac, then y equals:

A
xz/x+z

B
xz/2(x-z)

C
xz/2(z-x)

D
2xz/(x+z)

Solution

Let a^x = b^y = c^z = k.

Then a = k^1/x , b = k^1/y and c = k^1/z .

b² = ac ⇒k2/y = k^1/x k^1/2

y = 2xz
x+z
Question 6
2 / -0.5

If x = y^a , y = z^b and z = x^c , then the value of abc is:

A
4

B
3

C
2

D
1

Solution

x = y^a = (z^b )^a = z^ab = (x^c )^ab = x^abc ∴abc = 1.
Question 7
2 / -0.5

How many natural numbers between 300 to 500 are multiples of 7?

A
A. 29

B
B. 28

C
C. 27

D
D. None of these

Solution

Between 300 and 500 the first term divisible by 7 is 301 and last term divisible by 7 is 497

So, here a = 301, d = 7

L = a + (n - 1) d

497 = 301 + (n-1) x 7

⇒ 7n = 203

⇒ n = 29
Question 8
2 / -0.5

The 4^th and 10^th term of an GP are 1/3 and 243 respectively. Find the 2nd term.

A
3

B
1

C
1/27

D
1/9

Solution

It is given that

ar³ = 1/3 ……(i)

ar⁹ = 243 ……(ii)

From (i) and (ii) we get

r⁶ = 729

r = 3

From (i) and (ill) we get

Second term will be 1/27
Question 9
2 / -0.5

The 7^thand 21^stterms of an AP are 6 and -22 respectively. Find the 26^thterm.

A
A. -34

B
B. -32

C
C. -12

D
D. -10

Solution

It is given that a + 6d = 6 and a + 20d = -22

⇒ 14d = -28, d = -2,

⇒ a = 18

26^th term will be -32
Question 10
2 / -0.5

Find the number of terms of the series 1/81, 1/27, 1/9........ . - 729.

A
A. 11

B
B. 12

C
C. 10

D
D. 13

Solution

It. is given that

GP is 1/81 , -1/27 , 7/9, …..-729

Here ar^n-1 = 729

(-3)^n-1 = 3¹⁰ , n = 11

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Re-Attempt Weekly Quiz Competition

Research Aptitude Test - 17

Result

Research Aptitude Test - 17

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SHARING IS CARING

Question 1

Zero

10 m s-1

15m s -1

500 m s -1

5000 m s -1

Solution

Question 2

backwards towards each other.

at different speeds.

up and down.

On the same plane, but in different directions.

Solution

Question 3

A. 3

B. 2

C. 0

D. -2

Solution

Question 4

A. 125

B. 64

C. 27

D. 9

Solution

Question 5

xz/x+z

xz/2(x-z)

xz/2(z-x)

2xz/(x+z)

Solution

Question 6

4

3

2

1

Solution

Question 7

A. 29

B. 28

C. 27

D. None of these

Solution

Question 8

3

1

1/27

1/9

Solution

Question 9

A. -34

B. -32

C. -12

D. -10

Solution

Question 10

A. 11

B. 12

C. 10

D. 13

Solution

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