SAMPLE QUESTION PAPER (2021-22)
MATHEMATICS
TERM II
CLASS 12
Time: 2 Hrs Max. Marks: 40
GENERAL INSTRUCTIONS
1. This question paper contains three sections – A, B and C. Each section is compulsory.
2. Section A has 6 short answer type (SA1) questions of 2 marks each.
3. Section B has 4 short answer type (SA2) questions of 3 marks each.
4. Section C has 4 long answer type (LA) questions of 4 marks each.
5. There is an internal choice in some of the questions.
6. Question 14 is a case-based problem having 2 sub-parts of two marks each.
SECTION A
1. Evaluate
OR
2. Solve the following differential equation
3.
4. A and B are two events such that P(A) ≠ 0. Find P (B | A), if
(i) A is a subset of B (ii) A ∩ B = Ø
5. Find the area bounded by the curve y2 = 8x and the line x = 4.
6. Find the value of k, if the lines
SECTION B
7. Find the area of the region bounded by the line y = 3x + 2, the X-axis and the ordinates x = -1 and x = 1.
8. Evaluate
OR
Evaluate
9. Three persons A, B and C apply for a job of Manager in a private company. Chances of their selection (A, B and C) are in the ratio 1:2:4. The probabilities that A, B and C can introduce changes to improve profits of the company are 0.8, 0.5, and 0.3 respectively. If the change does not take place, find the probability that it is due to the appointment of C.
10. Solve the following differential equation
OR
Solve the following differential equation
SECTION C
11. Show that the differential equation
12.
13. Find the distance of the point (1, -2, 3) from the plane x – y + z = 5 measured parallel to the line, whose direction cosines are proportional to (2, 3, -6)
OR
CASE BASED / DATA BASED
14. A doctor is to visit a patient. From the post experience, it is known that the probabilities that he will come by train, bus, scooter and by other means of transport are respectively 3/10, 1/5, 1/10 and 2/5. The probability that he will be late are ¼, 1/3 and 1/12, if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late.
On the basis of above information, answer the following questions.
(i) Find the probability that he is late.
(ii) Find the probability that he come by scooter given that he is late and also find the probability that he comes late given that he comes by other means of transport.