General Aptitude - 5 - GATE Chemistry MCQ

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

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

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

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 7^th day= (5x12) 
Work completed by R on 7^th day=(7x18) 
Ratio of their work
=

5/7 = x^-1/3 ⇒ 7/5 = x^1/3

⇒ x = (7/5)³ = 343 / 125

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

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.

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

Given,

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

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 m^½

Hence, if I have

(9 inches)^½ = (0.25 yards)^½

If I take the square root, then we get

3 inches^½ = 0.5 yards^½

and not 3 inches = 0.5 yards

So option (A) is wrong

So the adjoining figure for solution

18² = 324
21² = 441
8² = 64
X² ! =  97
All the above are perfect squares but 97 is a prime number.

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

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)

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

Present time is given  by

= 10: 30 + 2 : 15

= 12 : 45

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

Speed = length / time

⇒ length = speed x time

120 = 10 x s₁ ⇒ s₁ = 12

150 = 15 x s₂ ⇒ s₂ = 10

|s₁ - s₂| = 2