Series RTEQ.P. Code 12/1/-1
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Periodic Test 3
Time allowed : 1½ HoursMaximum Marks : 40
General Instructions :
Read the following instructions carefully and follow them :
(i)This question paper contains 20 questions. All questions are compulsory.
(ii)This question paper is divided into four sections – A, B, C and D.
(iii)In Section A, Question numbers 1 to 10 carry 1 mark each.
(iv)In Section B, Question numbers 11 to 14 are very short answer (VSA) type questions carrying 02 marks each.
(v)In Section C, Question numbers 15 to 18 are short answer (SA) type questions carrying 03 marks each.
(vi)In Section D, Question numbers 19 to 20 are long answer (LA) type questions carrying 05 marks each.
(vii)Draw neat figures wherever required. Take π = 22/7 wherever required, if not stated.
(viii)Use of calculators is not allowed.
SECTION A
This section comprises 10 questions of 1 mark each.
1.1
Find the circumference of a circle of radius 7 cm. (π = 22/7)
2.1
Find the area of a circle of radius 7 cm. (π = 22/7)
3.1
A circle has radius 5 cm and a chord is 3 cm from the centre. How long is the chord?
4.1
An arc subtends 45° at a point on the circle. What angle does it subtend at the centre?
5.1
Find the area of a triangle with sides 3, 4 and 5 cm.
6.1
Find the area of a parallelogram with base 9 cm and height 4 cm.
7.1
Where is the circumcentre of a right-angled triangle?
8.1
Find the length of a semicircular arc of radius 14 cm. (π = 22/7)
9.1
What do the opposite angles of a cyclic quadrilateral add up to?
10.1
Find the area of a quadrant of a circle of radius 14 cm. (π = 22/7)
SECTION B
This section comprises 4 very short answer (VSA) type questions of 2 marks each.
11.2
A circle has diameter 26 cm and a chord of 24 cm. Find the distance of the chord from the centre.
12.2
Use Heron's formula to find the area of a triangle with sides 13, 14 and 15 cm.
13.2
In a cyclic quadrilateral, ∠A = 3x° and ∠C = (2x + 20)°. Find x, ∠A and ∠C.
14.2
A clock's minute hand is 14 cm long. What area does it sweep in 15 minutes? (π = 22/7)
SECTION C
This section comprises 4 short answer (SA) type questions of 3 marks each.
15.3
A chord of a circle of radius 14 cm subtends 60° at the centre. Find (a) the chord length, (b) the length of the minor arc, (c) the area of the minor sector. (π = 22/7)
16.3
An equilateral triangle has side 6 cm. Find its area (a) using (√3/4)a² and (b) using Heron's formula, and show they agree.
17.3
Using the theorem that the angle at the centre is double the angle at the circumference, prove that the angle in a semicircle is 90°.
18.3
A circular park of radius 21 m has a path 7 m wide around the outside. Find the area of the path. (π = 22/7)
SECTION D
This section comprises 2 long answer (LA) type questions of 5 marks each.
19.5
In a circle of radius 10 cm, chord AB subtends 90° at the centre O. Find (a) the length of AB, (b) its distance from O, (c) the area of the minor sector, (d) the area of ΔAOB, (e) the area of the minor segment. (π = 3.14)
20.5
A triangle with sides 7, 24 and 25 cm is inscribed in a circle. (a) Show that it is right-angled. (b) Find the circumradius. (c) Find the area of the triangle. (d) Find the area of the circumcircle. (e) Find the area of the circle outside the triangle. (π = 3.14)
✦ ✦ ✦