Class 12 PT II Question Paper 2023-24 Maths

PERIODIC TEST
QUESTION PAPER
Question Paper for CBSE Board, KV Schools,
State Board following NCERT Syllabus

PT 1 | PT 2

Question Paper based on NCERT Syllabus
CBSE Board Question Paper / KV Schools Question Paper
UT-2 (2023-24)
Class: XII Max. Marks: 40
Subject: -Mathematics Time: 90 minutes
General Instructions:
1. This question paper contains five sections – A, B, C, D and E. Each part is compulsory.
2. Section A has 8 multiple choice type questions of 1 mark each and 1 assertion reasoning question of 1 mark each.
3. Section B has 2 questions of 2 marks each.
4. Section C has 3 questions of 3 marks each,
5. Section D has 2 questions of 5 marks each
6. Section E has 2 case based questions of 4 marks each
7. There is an internal choice in some of the questions.

Q.NO Section A Marks
Q (1-10) are multiple choice type questions. Select the correct option
1 𝑥
𝑒 (1+𝑥)
1
∫ 2 𝑥 dx equals to
𝑐𝑜𝑠 (𝑒 𝑥)

a) tan(ex) + c b) cot(ex) + c c) tan(x ex) + c d) - cot(ex) + c
2 The number of arbitrary constants in the particular solution of a differential equation of 1
third order is:
a) 3 b) 2 c) 1 d) 0

3 π 3π 1
The area bounded by the curve 𝑦 = 𝑠𝑖𝑛 2𝑥 , x-axis and the lines 𝑥 4 and 𝑥 = 4
is:
(a) 1 sq. units (b) 2 sq. units (c) 4 sq. units (d) 32 sq. units
4 4
𝑥 +1
1
∫ 2 dx equals to
𝑥 +1

3 3
𝑥 𝑥
a) 3 + 𝑥 − 𝑥 + 𝑐 b) 3 − 𝑥 − 𝑥 + 𝑐
3
𝑥
c) 3 + 𝑥 − 2𝑥 + 𝑐 d) none of these

5 𝑎 1
1 π
The value of “a” if ∫ 2 𝑑𝑥 = 8
0 4+𝑥
a) 2 b) 1 c) 0 d) none of these

6 2 1
The area bounded by the parabola 𝑦 8𝑥 , the x-axis and the latus rectum is:
16 23 32 16 2
(a) 3 (b) 3
(c) 3 (d) 3
7 1

The degree of the differential equation is
a)4 b) 3 c) 1 d) not defined
8 𝑥 𝑥 1
Given, ∫ 𝑒 (tan 𝑡𝑎𝑛 𝑥 + 1 ) sec 𝑠𝑒𝑐 𝑥 𝑑𝑥 = 𝑒 𝑓(𝑥) + 𝑐. Then f(x) is

a) sec 𝑠𝑒𝑐 𝑥 tan 𝑡𝑎𝑛 𝑥 b) sec 𝑠𝑒𝑐 𝑥 c) 𝑥 d) none of these

In the given question, a statement of assertion (A) is followed by a statement of Reason (R).
9 Choose the correct answer out of the following choices.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true but R is not the correct explanation of A.
c) A is true but R is false.
d) A is false but R is true.

1
2

Assertion (A): ∫ 𝑙𝑜𝑔 1−𝑥 𝑑𝑥 = 0
1
( )
1+𝑥

−2
𝑎
Reason (R): ∫ 𝑓(𝑥) 𝑑𝑥 = 0 if 𝑓(− 𝑥) = 𝑓(𝑥)
−𝑎

Section B
2
10 𝑑𝑦 1+𝑦 2
Find the particular solution of the differential equation 𝑑𝑥 = 2 given that 𝑦 = 1 when
1+𝑥
𝑥=0
11 1−sin𝑠𝑖𝑛 𝑥
2
Evaluate ∫ 2 𝑑𝑥
𝑐𝑜𝑠 𝑥

Section C
12 π/2 π 3
𝑥sin𝑠𝑖𝑛 𝑥
Evaluate ∫ sin 𝑠𝑖𝑛 2𝑥 𝑙𝑜𝑔⁡(tan 𝑡𝑎𝑛 𝑥) 𝑑𝑥 or ∫ 1+ 𝑥
𝑑𝑥
0 0
2 2
13 𝑥 𝑦 3
Find the area of the region bounded by the ellipse 16
+ 9 =1
14 2 3
(
Find the general solution of the differential equation 𝑦 𝑑𝑥 – 𝑥 + 2𝑦 𝑑𝑦 = 0 )
Section D
𝑥+3
15 Evaluate: ∫ 2
𝑑𝑥 5
5−4𝑥−𝑥

𝑑𝑦
Solve the differential equation (𝑥 − 𝑦) 𝑑𝑥 = 𝑥 + 2𝑦
16 5
Or
𝑑𝑦
Find the general solution of the differential equation 𝑥 𝑑𝑥 + 𝑦 − 𝑥 + 𝑥𝑦 𝑐𝑜𝑡𝑥 = 0 (𝑥≠0)

Section E (CASE BASED QUESTIONS)
17 Three children Amit(A), Sumit(B) and Rohit(C) are playing in a park with toy telephones and 1x4=4
had tightly caught the wires joining telephones to form a triangle as shown in figure:
Based on the above information
answer the following questions:
(i) Find the equation of line representing
the wire AB.
(ii) Find the equation of line representing
the wire BC.
(iii) Find the equation of line representing
the wire AC.
(iv) Find the area of triangle ABC using
integration

18 Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is 1x4=4

directly proportional to the number of children who have not been administered the drops. By
the end of 2nd week half the children have been given the polio drops. How many will have been
given the drops by the end of 3rd week can be estimated using the solution to the differential
𝑑𝑦
equation 𝑑𝑥 = 𝑘(50 − 𝑦) where x denotes the number of weeks and y the number of children

who have been given the drops.

(i) State the order of the above given differential equation.
(ii) Which method of solving a differential equation can be used here?
𝑑𝑦
(iii) Find the solution of the differential equation 𝑑𝑥 = 𝑘(50 − 𝑦)

(iv) Find the value of c in the particular solution given that y(0)=0 and k = 0.049.

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