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General Aptitude - 5 - GATE Chemistry MCQ


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20 Questions MCQ Test GATE Chemistry Mock Test Series - General Aptitude - 5

General Aptitude - 5 for GATE Chemistry 2024 is part of GATE Chemistry Mock Test Series preparation. The General Aptitude - 5 questions and answers have been prepared according to the GATE Chemistry exam syllabus.The General Aptitude - 5 MCQs are made for GATE Chemistry 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for General Aptitude - 5 below.
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General Aptitude - 5 - Question 1

40% of deaths on city roads may be attributed to drunken driving. The number of degree needed to represent this as a slice of a pie chart is

Detailed Solution for General Aptitude - 5 - Question 1

40% of 360o = (40/100) * 360o =144o
Therefore Number of degrees needed to represent, 40% in a pie chart is 144o

General Aptitude - 5 - Question 2

Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?

Detailed Solution for General Aptitude - 5 - Question 2

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General Aptitude - 5 - Question 3

The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is

Detailed Solution for General Aptitude - 5 - Question 3

We have total 900 three digit numbers from 100-999.
We have numbers in which 1 is immediate right to 2 are 210-219, 121, 221, 321, 421, 521, 621, 721, 821, 921.
So we have numbers in which 1 is never immediate right of 2 = 900 - 19 = 881 numbers

General Aptitude - 5 - Question 4

A person moving through a tuberculosis prone zone has a 50% probability of becoming infected.However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?

Detailed Solution for General Aptitude - 5 - Question 4

Probability of being infected = 0.5
Probability of developing disease = 0.3
Only when a person develops disease he will show symptoms of it and whenever a disease is developed we can expect symptoms to be shown.
So, Probability of not showing symptoms = 1 − 0.3 = 0.7
Probability of being infected and not showing any symptoms = 0.5 × 0.7 = 0.35
(or)
P(infected) = 0.5,
P(No.of disease / Infected) = 0.7 × 0.5 = 0.35

General Aptitude - 5 - Question 5

P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?

Detailed Solution for General Aptitude - 5 - Question 5

Q's one hour work = 
R's one hour work = 
Since Q has taken 2 days sick leave, he has worked only 5 days on the end of seventh day.
Work completed by Q on 7th day= (5x12) 
Work completed by R on 7th day=(7x18) 
Ratio of their work
=

General Aptitude - 5 - Question 6

If logx (5/7) = -1/3, then the value of x is

Detailed Solution for General Aptitude - 5 - Question 6

5/7 = x-1/3 ⇒ 7/5 = x1/3

⇒ x = (7/5)3 = 343 / 125

General Aptitude - 5 - Question 7

A rule states that in order to drink beer one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking beer. What must be checked to ensure that the rule is being followed ?

Detailed Solution for General Aptitude - 5 - Question 7

In this question the rule states that "in order to drink beer the person must be over 18 years of age". So we will consider the following options according to the rule:
For P it is given that his/her age is 16 years and since he/she is below 18 years of age, they cannot have beer so we have to check P's drink to see if the rule is followed.
For Q it is given that his/her age is 25 years and the rule states nothing about what anyone above 18 years cannot drink therefore there is no restriction on him/her. We do not need to check his/her drink.
For R it is given that he/she is having a milkshake. Now for milkshake also the rule puts no restriction therefore there is no need to check his/her age.
and finally for S it is given that he/she is having a beer and now since the rule clearly states that if anyone is having beer then he/she must be over 18 years of age therefore we need to check S's age.
So the correct option is Option B) We need to check P's drink and S's age

General Aptitude - 5 - Question 8

500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329). Physics (186).Mathematics (295). Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

Detailed Solution for General Aptitude - 5 - Question 8

Method 1
There are 500 students in total.
Only Chemistry: 329 - ( 217 + 83 ) = 29
Only Mathematics : 295 - ( 217 + 63 ) = 15
Only Physics : 186 - ( 83 + 63 ) = 40
Finally :
500 - ( 29 + 15 + 40 + 83 + 63 + 217 ) = 500 - 447 = 53 students.
Method 2
Total number of students
= n(P) + n(C) + n(M) − n(P∩C) − n(P∩M)− n(C∩M) + n(P∩C∩M)
⇒ 500  =329 + 295 + 186 − 217 − 83 − 63 + x
⇒ x = 53.

General Aptitude - 5 - Question 9

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot.

Q. Which of the following is the steepest path leaving from P?

Detailed Solution for General Aptitude - 5 - Question 9

Form the given Locations and contour lines
Path from P to Q = 575 to 500 = 75 m deep
Path from P to R = 575 to 425 = 150 m deep
Path from P to S = 575 to 525 = 25 m deep
Path from P to T = 575 to 525 = 25 m deep
Therefore P to R is the steepest path 62 among all the paths

General Aptitude - 5 - Question 10

If, the value of abc is _____

Detailed Solution for General Aptitude - 5 - Question 10

Given,

General Aptitude - 5 - Question 11

Fill in the missing value

Detailed Solution for General Aptitude - 5 - Question 11

Middle number is the average of the numbers on both sides.(Left and Right)
Average of 6 and 4 is 5
Average of (7 + 4) and (2 + 1) is 7
Average of (1 + 9 + 2) and (1 + 2 + 1) is 8
Average of (4 + 1) and (2 + 3) is 5
Therefore, Average of (3) and (3) is 3

The number appearing in the centre line is average of the sum of numbers appearing on left  and right of numbers.

Hence, the unknown number is given by 3 + 3 / 2 = 3

General Aptitude - 5 - Question 12

Given (9 inches)1/2 = (0.25 yards) 1/2, which one of the following statements is TRUE?

Detailed Solution for General Aptitude - 5 - Question 12

Take square on both side, we get

9 inches = 0.25 yards

Why not option (A) ?

Let me give you an example

(3m)2=9m2

It means that if number gets squared then the units also get squared. Above is an example of a square having side 3m, the area of this square would be 9m2.

Similarly,

(9 m)½ = 3 m½

Hence, if I have

(9 inches)½ = (0.25 yards)½

If I take the square root, then we get

3 inches½ = 0.5 yards½

and not 3 inches = 0.5 yards

So option (A) is wrong

General Aptitude - 5 - Question 13

M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?

Detailed Solution for General Aptitude - 5 - Question 13

So the adjoining figure for solution

General Aptitude - 5 - Question 14

The number that least fits this set: (324, 441, 97 and 64) is _____.

Detailed Solution for General Aptitude - 5 - Question 14

18= 324
21= 441
8= 64
X2 ! =  97
All the above are perfect squares but 97 is a prime number.

General Aptitude - 5 - Question 15

Find the area bounded by the lines 3x + 2y = 14, 2x - 3y = 5 in the first quadrant.

Detailed Solution for General Aptitude - 5 - Question 15

The total area of the triangle which is bounded by the 2 given lines in the first quadrant

= 1/2 x 14/3 x 7

=  98 / 6

= 16.33 sq units

And area bounded with x axis and the lines in the 1st quadrant   

= 1/2 x ( 4.67 - 2.5)

= 1.08 sq units

So area bounded with y axis  =  total area in 1st quadrant - area in 1st quadrant bounded by the lines and the   x axis

= 16.33 - 1.08      

= 15.25 sq units

General Aptitude - 5 - Question 16

A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a slope of −0.02. What is the value of y at x = 5 from the fit?

Detailed Solution for General Aptitude - 5 - Question 16

The equation of a line is
y = mx + c where m is the slope & c is the y-intercept
Now, In this question x is replaced with lnx
So, the equation of line becomes,
y = mlnx + c
or, y = -0.02lnx + c
We have given with abscissa which is essentially x-intercept. So, now we have to find ‘c’ the y-intercept.
for, y=0, lnx = 0.1 (given in the question)
Putting the value,
0 = -0.02 × 0.1 + c
or, c = 0.002
So, the equation of line becomes,
y = -0.02lnx + 0.002
putting x = 5 (asked in the question)
y = -0.002ln5 + 0.002 = -0.002 × 1.6 + 0.002 = -0.03
(ln5 = 1.6)

General Aptitude - 5 - Question 17

A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.

Detailed Solution for General Aptitude - 5 - Question 17

Total number of cubes = 9 × 3 = 27
∴Total number of faces = 27 × 6 = 162
∴Total number of non-visible faces = 162 - 54 = 108

∴ Number of visible faces / Number of non visible faces = 54/108 = 1/2

General Aptitude - 5 - Question 18

Two and a quarter hours back, when seen in a mirror, the reflection of a wall clock without number markings seemed to show 1:30. What is the actual current time shown by the clock?

Detailed Solution for General Aptitude - 5 - Question 18

Present time is given  by

= 10: 30 + 2 : 15

= 12 : 45

General Aptitude - 5 - Question 19

A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?

Detailed Solution for General Aptitude - 5 - Question 19

Let’s assume that the piece from which rectangle is made, has length x mm.

Perimeter of rectangle = x

∴ Breadth of rectangle = x/6 and length of rectangle = 2x/6 = x/3

⇒ Area of rectangle = x/6 × x/3 = x2/18

Perimeter of square = 340 – x

Length of square = (340 – x)/4 = 85 – x/4

⇒ Area of square =(85 − x/4)2

Total area =(85 − x/4)2 + x2/18 = f(x)

Now, f′(x)=2×(85 − x/4)× − 1 + 2x/18 = 0

Solving, we get: x = 180

Length of square = 85 – x/4 = 85 – 45 = 40 mm

General Aptitude - 5 - Question 20

It takes 10s and 15s, respectively, for two trains travelling at different constant speeds to completely pass a telegraph post. The length of the first train is 120 m and that of the second train is 150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is _____.

Detailed Solution for General Aptitude - 5 - Question 20

Speed = length / time

⇒ length = speed x time

120 = 10 x s1 ⇒ s= 12

150 = 15 x s⇒ s2 = 10

|s1 - s2| = 2

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