There are two examinations, A and B in a subject which are evaluated out of 30 and 70 marks, respectively. In order to pass the course the student has to get at least 40% in total and at least 40 % in B. The following are the marks of the students S1 to S4. The only student/s to have passed is/are Students A B S1 12 28 S2 10 29 S3 16 27 S4 05 29
S1
Pass Course Criteria Analysis
To pass the course, a student must meet two conditions:
- Get at least 40% of the total marks.
- Get at least 40% in Examination B.
Let's first calculate the minimum marks required for each condition.
The maximum marks for Examination A are 30, and for Examination B are 70. The total maximum marks for the course is \(30 + 70 = 100\).
Minimum total marks required to pass:
\( 40\% \text{ of } 100 = \frac{40}{100} \times 100 = 40 \text{ marks} \)
Minimum marks required in Examination B to pass:
\( 40\% \text{ of } 70 = \frac{40}{100} \times 70 = \frac{2800}{100} = 28 \text{ marks} \)
So, a student passes if they score at least 40 total marks AND at least 28 marks in Exam B.
Student Performance Evaluation
Now, let's evaluate each student based on these criteria. We will calculate their total marks and check if they meet both passing conditions.
| Student | Marks in A (out of 30) | Marks in B (out of 70) | Total Marks (out of 100) | Total Marks ≥ 40? | Marks in B ≥ 28? | Passed? |
|---|---|---|---|---|---|---|
| S1 | 12 | 28 | \(12 + 28 = 40\) | Yes (\(40 \ge 40\)) | Yes (\(28 \ge 28\)) | Yes |
| S2 | 10 | 29 | \(10 + 29 = 39\) | No (\(39 < 40\)) | Yes (\(29 \ge 28\)) | No (Failed Total) |
| S3 | 16 | 27 | \(16 + 27 = 43\) | Yes (\(43 \ge 40\)) | No (\(27 < 28\)) | No (Failed in B) |
| S4 | 05 | 29 | \(05 + 29 = 34\) | No (\(34 < 40\)) | Yes (\(29 \ge 28\)) | No (Failed Total) |
From the evaluation, only Student S1 meets both passing conditions (Total marks ≥ 40 and Marks in B ≥ 28).
Identifying Passing Students
Based on the analysis:
- S1 passed because the total marks (40) are ≥ 40 and marks in B (28) are ≥ 28.
- S2 failed because the total marks (39) are < 40, even though marks in B were sufficient.
- S3 failed because marks in B (27) are < 28, even though total marks were sufficient.
- S4 failed because the total marks (34) are < 40, even though marks in B were sufficient.
Therefore, the only student who passed the course is S1.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
