In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children?
In that 50% of families having 3 children
i.e., 50×3 = 150 (No. of children)
→ Likes that 30% have 2 children = 30×2 = 60
→ 20% have 1 children = 20×1 = 20
Probability of choosing a children the family have two children
= 60/(150+60+20) = 60/230 = 6/23
In a class of 200 students, 125 students have taken Programming Language course, 85 students have taken Data Structures course, 65 students have taken Computer Organization course; 50 students have taken both Programming Language and Data Structures, 35 students have taken both Data Structures and Computer Organization; 30 students have taken both Data Structures and Computer Organization, 15 students have taken all the three courses.How many students have not taken any of the three courses?
PL = 125
DS = 85
CO = 65
PL & DS = 50
DS & CO = 35
CO & PL = 30
PL & DS & CO = 15
⇒ Not taken any course = 200 – (60 +15+15+35+15+15+20)
= 200 – 175
Two straight lines are drawn perpendicular to each other in X-Y plane. If α and β are the acute angles the straight lines make with the X-axis, then α+β is ______.
We know a + α + β = 180
α + β = 180 – 90
α + β = 90
The total revenue of a company during 2014-2018 is shown in the bar graph. If the total expenditure of the company in each year is 500 million rupees, then the aggregate profit or loss (in percentage) on the total expenditure of the company during 2014-2018 is ______.
Total expenditure = 500 million/year = 500 × 5 = 2500 million
Revenue total (from the graph)
= 400 + 500 + 600 + 700 + 800
= 3000 million
Profit = 3000 – 2500 = 500
⟹ 500/2500 = 20% profit
The figure below shows an annular ring with outer and inner radii as b and a, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum n number of circles can be painted, then the unpainted area available in annular space is ______.
π[(b2 – a2) + π/4(b – a)2]
π[(b2 – a2) – π/4(b – a)2]
π[(b2 – a2) – n(b – a)2]
π[(b2 – a2) + n(b – a)2]
Area of non-painted between 2 circles area of part 1 = πb2 – πa2 = π(b2 – a2)
Radius of painted circles = b-a/2
Area of painted circle = π(b-a/2)2
For n circles = nπ(b-a/2)2
Non-painted area = π[b2 – a2– n/4(b – a)2]
Goods and Services Tax (GST) is an indirect tax introduced in India in 2017 that is imposed on the supply of goods and services, and it subsumes all indirect taxes except few. It is a destination-based tax imposed on goods and services used, and it is not imposed at the point of origin from where goods come. GST also has a few components specific to state governments, central government and Union Territories (UTs).
Which one of the following statements can be inferred from the given passage?
GST includes all indirect taxes.
GST is imposed at the point of usage of goods and services.
GST does not have a component specific to UT.
GST is imposed on the production of goods and services.
Select the word that fits the analogy:
Cook : Cook :: Fly : _____
The drawn of the 21st century witnessed the melting glaciers oscillating between giving too much and too little to billions of people who depend on them for fresh water. The UN climate report estimates that without deep cuts to man-made emissions, at least 30% of the northern hemisphere’s surface permafrost could melt by the end of the century. Given this situation of imminent global exodus of billions of people displaced by rising seas, nation-states need to rethink their carbon footprint for political concerns, if not for environmental ones.
Which one of the following statements can be inferred from the given passage?
Nation-states are responsible for providing fresh water to billions of people.
Billions of people are affected by melting glaciers.
Nation-states do not have environmental concerns.
Billions of people are responsible for man-made emissions.
There are multiple routes to reach from node 1 to node 2, as shown in the network.
The cost of travel on an edge between two nodes is given in rupees. Nodes ‘a’, ‘b’, ‘c’, ‘d’, ‘e’, and ‘f’ are toll booths. The toll price at toll booths marked ‘a’ and ‘e’ is Rs.200, and is Rs.100 for the other toll booths. Which is the cheapest route from node 1 to node 2?
1 – f – e – 2 ─ 100 + 100 + 200 = 400
1 – f – b – 2 ─ 100 + 0 + 200 = 300 ⇾ shortest [Answer]
1 – b – 2 ─ 300 + 200 = 500
1 – a – c ─ 2 – 200 + 100 + 100 = 400
Raman is confident of speaking English _____ six months as he has been practicing regularly_____the last three weeks.
If P = 3, R = 27, T = 243, then Q+S = ______.
P=31, Q=32, R=33, S=34, T=35
Q+S = 32 + 34 = 9+81 = 90
His knowledge of the subject was excellent but his classroom performance was ______.
fair / fare
faer / fair
fare / fare
fare / fair
Which one of the following is the area under the curve for the interval [0, 1] on the x-axis?
We know that area of a rectangle = length * breadth = L * B
Area of rectangle (1) = L*B = (1/3) * 2 = (2/3)
Area of rectangle (2) = L*B = (3/4 – 1/3 ) * 3 = (5/4 )
Area of rectangle (3) = L*B = (1 – 3/4) * 1 = 1/4
Therefore Total area = Area(1+2+3) = (2/3) + (5/4) + (1/4) = 26/12 = 13/6
Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.
Statement 1 and Statement 3
Statement 1 and Statement 2
Statement 2 and Statement 4
Statement 3 and Statement 4
Statement 1: All students are inquisitive. Statement 3: No student is inquisitive
From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome. The player should use all the five plates exactly once. The plates can be rotated in their plane.
Option 2: A,D,R,A,R from these we can form RADAR which is a palindrome.
Option 3: A,D,Z,E,D from these letters we can’t form a palindrome.
Option 4: A,D,I,L,Y from these letters we can’t form a palindrome.
Some others believe that “what gets measured, gets gamed”.
One possible reason for the difference in the beliefs is the work culture in organizations. In organizations with good work culture, metrics help improve outcomes.
However, the same metrics are counterproductive in organizations with poor work culture.
Which one of the following is the CORRECT logical inference based on the information in the above passage?
Metrics are useful in organizations with poor work culture
Metrics are useful in organizations with good work culture
Metrics are always counterproductive in organizations with good work culture
Metrics are never useful in organizations with good work culture
Option B: Metrics are useful in organizations with good work culture. Which is correct and relevant to the considered sentence.
Option C: Metrics are always counterproductive in organizations with good work culture. Which is incorrect because we can’t always guarantee good work culture.
Option D: Metrics are never useful in organizations with a good work culture. Incorrect metrics will help to make a good work culture.
Equal number of boys and girls qualified
Equal number of boys and girls appeared for the test
The number of boys who appeared for the test is less than the number of girls who appeared
The number of boys who qualified the test is less than the number of girls who Qualified
60% can be written as ⅗. Which means among 5 qualified persons three of them are girls.
So, The number of boys qualified is less than the number of girls qualified.
Probability of first ball is green = 3/5
If the first ball is green then we are not replacing so the probability of the second ball being orange is = 2/4.
Probability of first ball green and second ball orange is =3/5 * 2/4 = 6/20
Case 2: The first ball is orange
Probability of first ball is orange =2/5
If the first ball is orange then we are replacing it with another orange ball/ so the number balls will remain the same.
Probability of second ball is orange = 2/5
Probability of first ball is orange and second ball is also orange = 2/5*2/5 = 4/25
Therefore, Total probability = (6/20 + 4/25) = 23/50.
The line joining P and R is parallel to the line joining Q and S.
P is placed on the side opposite to the corner T.
S and U cannot be placed on the same side.
Which one of the following statements is correct based on the above information?
P cannot be placed at a corner
S cannot be placed at a corner
U cannot be placed at a mid-point
R cannot be placed at a corner
The Image is satisfying all given conditions. From this we can say that S cannot be placed at the corner. By satisfying all given conditions we can draw in different ways but in all cases S cannot be placed at the corner.
What is the least number of additional straight ropes needed to create the desired plots? A single rope can pass through three poles that are aligned in a straight line.
Therefore least number of additional ropes required = 3.
Out of a group of 21 persons, 9 eat vegetables, 10 eat fish and 7 eat eggs : 5 persons eat all three. How many persons eat at least two out the three dishes?
Listening to music has no effect on learning and a positive effect on physical exercise.
Listening to music has a clear positive effect on physical exercise. Music has a positive effect on learning only in some students.
Listening to music has a clear positive effect both on physical exercise and on learning.
Listening to music has a clear positive effect on learning in all students. Music has a positive effect only in some students who exercise.
From the first statement “Listening to music during exercise improves exercise performance and reduces discomfort. “ It is clear that listening to music has a positive effect on physical exercise.
From the statement “Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. “ it is clear that only on some students music has a positive effect.
A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like _______.
as worse as
as well as
as better as
as nicest as
Given Initial ratio : 3:13:6
Total number of students initially = 3x+13x+6x = 22x
From the given question, we can write 3x+18 = 15y —–I
13x+18 = 35y—–II
6x+18 = 21y——III
I – II => -10X = -20Y
Put IV in III => 6(2y) + 18 = 21y
12y + 18 = 21y
9y = 18
y = 2 —–V
Substitute V in I => 3x + 18 = 30
3x = 12
x = 4
Number of initial students = 22x = 22(4) = 88
The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ₹ 1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.
The ratio of the selling price in Year 2 to the selling price in Year 3 is ______.
According to the given data:
Year Cost/unit Number of units Cost Price
1 ₹ 3 100 300
2 ₹ 2 200 400
3 ₹ 1 300 300
Cost Price = Cost/unit x Number of units
Net Profit = Selling Price – (Cost Price + (Tax% x selling price )
296 = SP – (400 + (13/100) x SP)
=>296 = 0.87SP – 400
=> 0.87SP = 696
=> SP = ₹ 800
210 = SP – (300 + (15/100) x SP)
=> 210 = 0.85SP – 300
=> 0.85SP = 510
=> SP = ₹ 600
The ratio of selling price in Year 2 to the selling price in year 3 = 800:600
A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.
Expand the given equation:
x2+1/4 – x –x2 -9/4 +3x = x+2
=> -2 + 2x = x + 2
X = 4
Observation I: S is taller than R.
Observation II: Q is the shortest of all.
Observation III: U is taller than only one student.
Observation IV: T is taller than S but is not the tallest.
The number of students that are taller than R is the same as the number of students shorter than _______.
Number of students taller than R = Number of students shorter than S = 3
(i) Everybody in the class is prepared for the exam.
(ii) Babu invited Danish to his home because he enjoys playing chess.
Which of the following is the CORRECT observation about the above two sentences?
(i) is grammatically incorrect and (ii) is ambiguous
(i) is grammatically correct and (ii) is ambiguous
(i) is grammatically correct and (ii) is unambiguous
(i) is grammatically incorrect and (ii) is unambiguous
ii). Babu invited Danish to his home because he enjoys playing chess.
This statement is ambiguous as there is no guarantee that Danish knows playing chess.
|Items||Cost (₹)||Profit %||Marked Price (₹)|
The discount on item Q, as a percentage of its marked price, is ______.
Number of boys = 7x
Number of girls = 3x
Total number of students = 10x
So the possible value should multiple by 10.
Answer is 50.
Which one of the following is NOT a convex polygon?
A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like _______.
Which one of the following options maintains a similar logical relation in the above sentence?
Doctor is to surgery as writer is to book.
There are 5 bags having identical sets of 10 distinct chocolates. one chocolate is drawn from each bag, probability to find at least 2 chocolate is identical
The total number of such selections possible = 10*10*10*10*10 = 10^5.
We need to select such that at least two of them are identical.
We can count the number of ways with no chocolate being repeated and subtract it from total possible ways to get the required probability.
The number of ways to select all different/distinct = 10*9*8*7*6
Required number of selections= 10^5-10*9*8*7*6 = 69760
Required probability = 69760/10^5 = 0.69760
Which one of the following statements summarizes the passage?
AOM are addressing the problem superficially.
The proposed AOM addresses the core problems that cause obesity.
AOM are addressing the core problems and are likely to succeed.
If obesity reduces, poverty will naturally reduce, since obesity causes poverty.
Statement I: All bacteria are microorganisms.
Statement II: All pathogens are microorganisms.
Conclusion I: Some pathogens are bacteria.
Conclusion II: All pathogens are not bacteria.
Based on the above statements and conclusions, which one of the following options is logically CORRECT?
Only conclusion I is correct
Only conclusion II is correct
Neither conclusion I nor II is correct
Either conclusion I or II is correct
Based on the given statements, select the most appropriate option to solve the given question, What will be the total weight of 10 poles each of same weight?
(I) One fourth of the weight of a pole is 5 kg
(II) The total weight of these poles is 160 kg more than the total weight of two poles.
Statement I alone is not sufficient
Statement II alone is not sufficient
Statement II alone is not sufficient
Both statements I and II together are not sufficient.
One fourth of the weight of a pole is 5Kg. ⇒ Weight of pole is 4×5 = 20Kg
Weight of 10 poles each of same weight = 10×20 = 200 Kg
∴Statement I alone is sufficient.
Let, Weight of each pole = W Kg
10W = 2W + 160
⇒ 8W = 160
W = 20Kg
∴ Weight of each pole = 20 Kg
∴ Weight of 10 poles = 10×20 Kg = 200 Kg
∴ Statement II alone is sufficient.
Option (C) is the answer.
Either I or II alone is sufficient.
Consider a function f(x) = 1 – |x| on -1 ≤ x ≤ 1. The value of x at which the function attains a maximum and the maximum value of the function are
In the given function, it is given as
-|x| ⇒ To obtain the maximum of this function we have to minimize the value -|x| and the minimum value is 0.
∴ Maximum value of f(x) is at f(0) and i.e., f(x) = 1
Maximum value is 1 at x=0.
A generic term that include various items of clothing such as a skirt, a pair of trousers and a shirt is
Choose the statement where underlined word is used correctly.
The industrialist load a personnel jet.
I write my experience in my personnel diary.
All personnel are being given the day off.
Being religious is a personnel aspect.
We __________________ our friend’s birthday and we ______________ how to make it up to him.
Completely forgot – – – don’t just know
Forgot completely – – – don’t just know
Completely forgot – – – just don’t know
Forgot completely – – – just don’t know
In a triangle PQR, PS is the angle bisector of ∠QPR and ∠QPS = 60º. What is the length of PS?
√(q2 + r2)
∠QPS = 60º
and PS is angle bisector of ∠QPR
⇒ ∠QPS = ∠SPR = 60º
and ∠QPR = 120º
Let, PS = s
Area of ΔPQR = Area of ΔPQS + Area of ΔSPR
1/2 qr Sin∠QPR = 1/2 rs Sin∠QPS + 1/2 sq∠SPR
1/2 qr Sin 120º = 1/2 rs Sin 60º + 1/2 sq 60º
1/2 qr Sin × √3/2 = 1/2 rs × √3/2 + 1/2 × √3/2
qr = rs + sq
∴ s = qr/q+r
PS = qr/q+r
Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.
Since the report lacked needed information, it was of no use to them.
The report was useless to them because there were no needed information in it.
Since the report did not contain the needed information, it was not real useful to them
Since the report lacked needed information, it would not have been useful to them.
(C) not really useful
(D) would not have been