All questions of Venn Diagrams for UPSC CSE Exam

Hospital consists of nurse and patient but nurse and patient are of two different nature.

To find the number of even integers n, where 100 < n="" />< 1000,="" we="" can="" count="" the="" number="" of="" even="" hundreds,="" tens,="" and="" ones="" />

For the hundreds digit, there are 9 possible even digits: 2, 4, 6, 8, 10, 12, 14, 16, and 18.

For the tens digit, there are 10 possible even digits: 0, 2, 4, 6, 8, 10, 12, 14, 16, and 18.

For the ones digit, there are 5 possible even digits: 0, 2, 4, 6, and 8.

Therefore, the total number of even integers n is 9 * 10 * 5 = 450.

Note that we include the number 100 in this count because it is an even integer.

Understanding the Problem
To solve the problem, we need to set up variables for the number of students in each category of elective subjects.
Given Data
- Total students = 360
- Students not taking any subject = 72
- Students taking Green Supply Chain (G) = 120
- Students taking Corporate Governance (C) = 124
- Students taking all three subjects = 12
- Let:
- x = Students taking G and C but not Global Climate Change (X)
- y = Students taking G and X but not C
- z = Students taking X and C but not G
Relationships between the groups
- According to the problem:
- \( x = 2y \)
- \( x = z \)
- \( y = 12 \) (since 12 students take all three subjects)
Calculating Students in Each Category
Using the relationships:
- \( y = 12 \) (students taking all three)
- \( x = 2y = 2 \times 12 = 24 \)
- \( z = x = 24 \)
Calculating Total Students Taking Each Subject
Using the inclusion-exclusion principle:
- Total taking G and C = \( 120 + 124 - (x + y + z + 12) \)
Set the equation:
- \( 120 + 124 - (24 + 12 + 24 + 12) = 360 - 72 \)
- Solve for students taking Global Climate Change only:
Final Calculation
Total students studying:
- \( G + C + X - G \cap C - G \cap X - C \cap X + G \cap C \cap X = 288 \)
Thus, the students studying Global Climate Change only = \( 360 - 72 - (students in G + C + both) = 104 \).
Conclusion
The number of students studying Global Climate Change & Business only is:
Answer: 104 (Option B).

Given Information:
- Shyam visited Ram during his brief vacation.
- In the mornings, they both would go for yoga.
- In the evenings, they would play tennis.
- They indulge only in one activity per day, either yoga or tennis.
- There were days when they were lazy and stayed home all day long.
- There were 24 mornings when they did nothing.
- There were 14 evenings when they stayed at home.
- In total, they did yoga or played tennis on 22 days.

Approach:
- Let's assume the number of days Shyam stayed with Ram is x.
- We need to find the value of x.

Solution:

Mornings:
- There were 24 mornings when they did nothing.
- Since there are 7 days in a week, the number of weeks they did nothing in the mornings = 24/7 = 3 weeks.
- So, the number of mornings they did yoga or played tennis = 7 - 3 = 4 mornings per week.
- Therefore, the total number of mornings they did yoga or played tennis = 4 * (x/7) = 4x/7.

Evenings:
- There were 14 evenings when they stayed at home.
- Similarly, the number of evenings they did yoga or played tennis = 7 - 14/7 = 7 - 2 = 5 evenings per week.
- Therefore, the total number of evenings they did yoga or played tennis = 5 * (x/7) = 5x/7.

Total number of days they did yoga or played tennis:
- According to the given information, the total number of days they did yoga or played tennis = 22.
- So, the equation is 4x/7 + 5x/7 = 22.
- Combining like terms, we get 9x/7 = 22.
- Multiplying both sides by 7/9, we get x = (22 * 7) / 9.
- Simplifying, x = 154/9.
- Since x represents the number of days, we round it up to the nearest whole number.
- Therefore, the number of days Shyam stayed with Ram is 17.

Final Answer:
- Shyam stayed with Ram for 17 days.
- None of the given options (a, b, c, d) matches the correct answer.

Bcoz Judge is different from thieves and criminal

All mothers are women and some mothers and some women may be engineers.

Given Data:
- 22% of families own agricultural land
- 18% of families own a mobile phone
- 1600 families own both agricultural land and a mobile phone
- 68% of families neither own agricultural land nor a mobile phone

Calculating the Total Number of Families:
1. Let the total number of families be x.
2. Families owning agricultural land = 22% of x = 0.22x
3. Families owning a mobile phone = 18% of x = 0.18x
4. Families owning both agricultural land and a mobile phone = 1600
5. Families owning either agricultural land or a mobile phone = (0.22x + 0.18x) - 1600
6. Families owning neither agricultural land nor a mobile phone = 68% of x = 0.68x
7. Families owning either agricultural land or a mobile phone = x - 0.68x = 0.32x
8. Families owning either agricultural land or a mobile phone = (0.22x + 0.18x) - 1600
0.32x = 0.22x + 0.18x - 1600
0.32x = 0.4x - 1600
1600 = 0.08x
x = 20000
Therefore, the total number of families living in the village is 20000 families. Hence, the correct answer is option A.

And C.

Club A is a sports club that focuses on various sports activities such as football, basketball, and volleyball. It has a well-equipped gymnasium, outdoor fields, and courts for different sports. Club A organizes regular tournaments and competitions for its members and also offers coaching and training programs.

Club B is a music club that caters to individuals interested in music and performing arts. It has a music studio with various musical instruments, practice rooms, and a performance stage. Club B offers music lessons, band practice sessions, and organizes concerts and showcases for its members. It also provides opportunities for members to collaborate and form bands or music groups.

Club C is an academic club that focuses on intellectual and academic pursuits. It offers study groups, tutoring sessions, and workshops to help members excel in their studies. Club C also organizes academic competitions, debates, and guest lectures to enhance members' knowledge and skills. It provides a supportive and stimulating environment for members to engage in intellectual discussions and develop critical thinking abilities.

Overall, these three clubs provide diverse opportunities for individuals to engage in sports, music, and academic pursuits, catering to different interests and passions.

Some questions are asked in examination and some in practice but examination and practice are different from each other.

Bus and Train are different from each other but some travelers travel by bus and some travel by train.

Bonus and Dividend are different from each other. But both these are parts of profit.

Understanding the Problem
To solve the problem, we need to analyze the distribution of students in various majors and how they impact the total count.

Given Data
- Total students: 60
- Students majoring in both Mathematics and Physics: 6
- Students majoring in both Physics and Biology: 15
- No students majoring in both Mathematics and Biology.

Calculating Majors
Let:
- M = Students majoring only in Mathematics
- P = Students majoring only in Physics
- B = Students majoring only in Biology
- MP = Students majoring in both Mathematics and Physics (6)
- PB = Students majoring in both Physics and Biology (15)
The total number of students can be expressed as:
M + P + B + MP + PB = 60.
Substituting the values:
M + P + B + 6 + 15 = 60
M + P + B = 39.

Average Marks Analysis
The average marks for students majoring in Mathematics is 45, and for Biology, it is 60. The combined average for these two groups is 50.
Using the average formula:
\[
\text{Combined Average} = \frac{(M \times 45) + (B \times 60)}{M + B} = 50.
\]
After simplification:
\[
(M \times 45) + (B \times 60) = 50(M + B).
\]
This leads to:
\[
(M \times -5) + (B \times 10) = 0 \Rightarrow 10B = 5M \Rightarrow B = \frac{M}{2}.
\]

Maximizing Physics Majors
Substituting \(B = \frac{M}{2}\) into \(M + P + B = 39\):
\[
M + P + \frac{M}{2} = 39 \Rightarrow \frac{3M}{2} + P = 39.
\]
Assuming \(M + P + 6 + 15 \leq 60\), we want to maximize \(P\).
From \(B = \frac{M}{2}\), let \(M = 2k\), then \(B = k\):
\[
\frac{3(2k)}{2} + P = 39 \Rightarrow 3k + P = 39 \Rightarrow P = 39 - 3k.
\]
To maximize \(P\), minimize \(k\). The smallest \(k\) can be is 0 (no Biology students), yielding:
\[
P = 39 \text{ (impossible since it exceeds total students)}.
\]
Testing \(k = 1\):
\[
P = 39 - 3(1) = 36 \text{ (still exceeds total)}.
\]
Continuing, when \(k=3\):
\[
P = 39 - 9 = 30 \text{ (valid)}.
\]
Thus, the maximum students majoring ONLY in Physics is 15, leading to the final answer.

Conclusion
The maximum possible number of students majoring ONLY in Physics is:

Answer: 15

All the pigeons are birds while dog is different from these.

All these three games are different from each other.

All these three elements are different from each other

All the three are different professions.

Sea is a part of Earth while Sun is different from these two.

A teacher may or may not be a writer and musician. Similarly a musician may or may not be a teacher and writer and so a writer may or may not be a teacher and musician.

All the three are different from each other.

All the three are different from each other.

Mercury and Zinc both are different from one another but belong to metal.

Haryana is in India and India is in the World.

Bulb and Lamp are different from each other but light is obtained from both.