Research Aptitude Test

Result

Research Aptitude Test - 12

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Weekly Quiz Competition

Question 1
2 / -0.5

Two liquids A and B are mixed in such a proportion that they form an ideal solution who 's total vapor pressure is exactly three times that of the partial pressure of A. If PA ºand PB ºare the vapor pressures of pure A and B respectively, then the total vapor pressure of the solution is given by Options:

A

B

C

D

Solution

You must Know: Total Pressure P_T = P_A + P_B Where P_A is Partial Pressure

And P_A = P °_A X_A where P °_A = Vapor Pressure and XA = Mole Fraction of A

Similarly, for P_B = P °_B X_B

We Know X_A + X_B = 1 ------- -—Sum of Mole Fractions

Given: P_T = 3 P_A = P_A + P_B

= 3 P °_A X_A --------- 3

So, 2P_A = P_B

2P °_A X_A = P °_B X_B --------- 1

X_A + X_B = 1 --------- 2

From 1 &2 we get X_A = P °_B / (2P °_A + P °_B )

Put X_A in 3 We Get Ans as

P_T = 3 P °_A P °_B / (2 P °_A a+ P °B)
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. The strange behaviour of the woman puppet was:

A
definitely because someone was moving it with sticks or strings.

B
definitely because there were magnets fixed in the heads of all three puppets.

C
could be because of magnets in the heads of all three puppets or someone moving them with sticks or strings.

D
just a random thing. Since we were children then, we thought it was happening in a particular way.

Solution

Magnetic Attraction &Repulsion Properties must be used.
Question 3
2 / -0.5

If log₁₀2 = 0.3010, the value of log₁₀5 is

A
A. 0.3241

B
B. 0.6911

C
C. 0.6990

D
D. 0.7525

Solution

log₁₀ 5 = log₁₀ (10/2) = log₁₀ 10 - log₁₀ 2.

= 1-log₁₀ 2 = (1 - 0.3010) = 0.6990
Question 4
2 / -0.5

The value of (log₉27 + log₈32) is

A
A. 4

B
B. 7

C
C. 7/2

D
D. 19/6

Solution

log₉ 27 + log₈ 32
Question 5
2 / -0.5

If log₅(x²+ x) - log₅(x+ 1) = 2, then the value of x

A
A. 5

B
B. 32

C
C. 25

D
D. 10

Solution

log₅ (x² + x) - log₅ (x+ 1) = 2

or log₅ x = 2 or x = 5² = 25.
Question 6
2 / -0.5

Sum the series to infinity

A
A. 8/15

B
B. 7/17

C
C. 7/15

D
D. 8/17

Solution
Question 7
2 / -0.5

Find the 9th term of the H.P. 6, 4, 3 ............

A
A. 7/5

B
B. 6/5

C
C. 5/6

D
D. None of these

Solution

The given sequence is 6,4,3,...... which is H.P

The sequence of reciprocals of its terms is 1/6 , 1/4 , 1/3 , ... . which is an A.P

∴ 9^th term of H.P is 6/5
Question 8
2 / -0.5

If x > 1, y > 1 , z >1 are in G.P., then are in

A
A. A.P.

B
B. H.P.

C
C. G.P.

D
D. None of these

Solution

∵ x, y, z are in G.P.

∵ y² = xz

Taking log on both sides

2 log y = log x + log z

⇒ 2 + 2 log y = (1 + log x) + (1 log z)

⇒ 2 (1 + log y) = (1 + log x) + (1 + log z)

⇒ 1 + log x, 1 + log y, 1 + log z, are in A.P.
Question 9
2 / -0.5

How many straight lines can be formed from 8 non-collinear points on the X-Y plane?

A
A. 28

B
B. 56

C
C. 18

D
D. 19860

Solution

To draw a line we have to choose two points So, ^B C₂ as 28 ways
Question 10
2 / -0.5

In how many ways can the letters of the word PATNA be rearranged?

A
A. 60

B
B. 120

C
C. 119

D
D. 59

Solution

This can be in 5!/2! ways

5!/2! = 60