Class 11 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: XI 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 4 multiple choice type questions of 1 mark each and 2 assertion reasoning question of 1
mark each and 6 very short questions of 1 mark each.
3. Section B has 4 questions of 2 marks each.
4. Section C has 2 questions of 3 marks each,
5. Section D has 2 questions of 5 marks each
6. Section E has 1 case based question of 4 marks.
7. There is an internal choice in some of the questions.

Q.NO Section A Marks
Q (1-4) are multiple choice type questions. Select the correct option
1 Slope of a line which cuts off intercepts of equal length on the axes is 1
(A) − 1 (B) 0 (C) 2 (D) 2
2 If the focus of parabola is (0, -3) and its directrix is y = 3, then its equation is 1
(a) x2 = - 12y (b) x2 = 12y (c) y2 = - 12x (d) y2 = 12x
3 The length of the foot of perpendicular drawn from the point P (3, 4, 5) on Y - axis is 1
(A) 10 (B) 34 (C) 113 (D) 5 2
4 |𝑥| 1
𝑥
is equal to
A) 0 B) 0.5 C) 1 D) does not exists
In the given questions (Q No.5 and Q No. 6), a statement of assertion (A) is followed by a
statement of Reason (R). 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.

5 Assertion (A): Equation of the horizontal line having distance ‘a’ from the x-axis is either 1
y = a or y = –a.
Reason (R): Equation of the vertical line having distance b from the y-axis is either
x = b or x = –b.
6 Assertion (A): The point (– 4, 5, – 6) lies in the VI octant. 1
Reason (R): The three coordinate planes divide the space into eight equal parts known
as octants.

Very Short Answer Type Questions
7 Find the equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 1
8 Find the distance between the lines 3x + 4y = 9 and 6x + 8y = 15. 1

9 Find the area of the circle centred at (1, 2) and passing through (4, 6). 1
10 Find the length of latus rectum of the ellipse 3x2 + y2 = 12. 1
11 If the origin is the centroid of a triangle ABC having vertices A (a, 1, 3), B (– 2, b, – 5) 1
and C (4, 7, c), find the value of a.
3
12 𝑥 −8 1
Evaluate 𝑥−2

Section B
13 Find angles between the lines 3 x + y = 1 and x + 3 y = 1 2

14 2 2 2
For the ellipse 9𝑥 + 16𝑦 = 144, find the vertices and eccentricity.
15 Find the equation of the set of points which are equidistant from the points (1, 2, 3) 2
and (3, 2, –1).
16 sin𝑠𝑖𝑛 (2+𝑥) −𝑠𝑖𝑛⁡(2−𝑥) 2
Evaluate the limit : 𝑥

Section C
Three vertices of a parallelogram ABCD are
17 3
( 3, − 1, 2 ) , 𝐵 ( 1, 2, − 4 ) 𝑎𝑛𝑑 𝐶 ( − 1 , 1, 2 ). Find the coordinates of the
fourth vertex.
Suppose
18 f(x)= {𝑎 + 𝑏𝑥, 𝑥 < 1 4, 𝑥 = 1 𝑏 − 𝑎𝑥, 𝑥 > 1 3
And if 𝑓(𝑥) = f(1) what are possible values of a and b ?

Section D
19 Find the equation of the circle which passes through the points (2, 3) and (4, 5) 5
and the centre lies on the straight line y – 4x + 3 = 0.
Or
A rod of length 12 cm moves with its ends always touching the coordinate axes.
Determine the equation of the locus of a point P on the rod, which is 3 cm from
the end in contact with the x-axis.
20 In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and 5
length of altitude from the vertex A.
Or
Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the
line to be a plane mirror.
Section E
21 Case study based : 1+1+
+1+1

Consider the lampshade in above figure and answer the questions given below:
(i). Name the curve formed by the image of lampshade.
(ii). Find the equation of the image of lampshade with vertex (0, ±3) and foci (0, ±5)
(iii). Find he length of transverse axes of image of lampshade.
(iv). Find the length of latus rectum of image of lampshade.

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