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.
OR
2.
3. Suppose, a girl throws a die. If she gets 1 or 2, she tosses a coin three times and notes the number of tails. If she gets 3, 4, 5 or 6, she tosses a coin once and notes whether a ‘head’ or ‘tail’ is obtained. If she obtained exactly one ‘tail’, what is the probability that she threw 3, 4, 5 or 6 with the die?
Let E1 be the event that the girl gets 1 or 2, E2 be the event that the girl gets 3, 4, 5 or 6 and A be the event that the girl gets exactly a ‘tail’
Then, P(E1) = 2/6 = 1/3
And P(E2) = 4/6 = 2/3
P(A/E1) = P (getting exactly one tail, when a coin is tossed three times = 3/8
P(A/E2) = P (getting exactly a tail, when a coin is tossed once) = ½
Now, required probability,
P(E2/A) = [P(E2). P(A/E2)] / [P(E1).P(A/E1) + P(E2).P(A/E2)]
= {2/3 . ½} / {1/3.3.8 + 2/3.1/2}
= {1/3}/{1/8 + 1/3} = 8/11
4. If a die is thrown and a card is selected at random from a deck of 52 playing cards. Find the probability of getting an even number on the die and a spade card.
Let the event A and B are getting an even number on die and getting spade card, respectively.
Therefore, P(A) = 3/6 = ½
And P(B) = 13/52 = ¼
Now, both are independent events
Therefore P(A∩B) = P(A) x P(B) = ½ x ¼ = 1/8
5. Solve the differential equation
6.
SECTION B
7.
8.
9. Find the particular solution of the differential equation (1 + e2x) dy + (1 + y2) ex dx = 0, given that y = 1, when x = 0.
OR
Solve the following differential equation y2 dx + (x2 – xy + y2) dy = 0
10. Find the shortest distance between lines
OR
SECTION C
11.
12. Find the area of region bounded by the curve y2 = 4x and the line x = 4.
OR
Find the area of the region bounded by the parabola x2 = 4y and the line x = 4y – 2.
13.
CASE BASED / DATA BASED
14. In an office three employees Vinay, Sonia and Iqbal process incoming copies of a certain form. Vinay process 50% of the forms. Sonia processes 20% and Iqbal the remaining 30% of the forms. Vinay has an error rate of 0.06, Sonia has an error rate of 0.04 and Iqbal has an error rate of 0.03.
Based on the above information, answer the following questions.
(i) Find the total probability of committing an error in processing the form.
Ans. Let E1 = Event that incoming copies are processed by Vinay
E2 = Event that incoming copies are processed by Sonia
E3 = Event that incoming copies are processed by Iqbal
And A = Error rate made by the persons.
Then, we have
P(E1) = 0.5, P(E2) = 0.2, P(E3) = 0.3
P(A/E1) = 0.06, P(A/E2) = 0.04 and P(A/E3) = 0.03
Required Probability = P(A)
=P(E1) P(A/E1) + P(E2) P(A/E2) + P(E3)P(A/E3)
= 0.5 x 0.06 + 0.2 x 0.04 + 0.3 x 0.03
= 0.030 + 0.008 + 0.009 = 0.047
(ii) The manager of the company wants to do a quality check. During inspection, he selects a form at random from the days output of processed forms. If the form selected at random has an error, then find the probability that the form is not processed by Vinay.
