Series RTEQ.P. Code 76/1/0
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Periodic Test 5
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
How are the tangents drawn at the two ends of a diameter of a circle related to each other?
2.1
Tangents PA and PB from an external point P touch a circle with centre O at A and B, with ∠APB = 60°. Find ∠AOB.
3.1
The radius of a circle is 15 cm and a point P is 17 cm from the centre. Find the length of the tangent from P.
4.1
What is the maximum number of tangents parallel to a given secant of a circle?
5.1
What is a line called that intersects a circle at two distinct points?
6.1
From the top of a 50 m high tower the angle of depression of a car on the ground is 45°. How far is the car from the foot of the tower?
7.1
A 10 m high pole is supported by a rope of length 20 m from its top to the ground. Find the angle the rope makes with the ground.
8.1
The length of the shadow of a pole is √3 times its height. Find the angle of elevation of the Sun.
9.1
A vertical pole has height h and the observer is at a horizontal distance d from its foot. If the angle of elevation of the top is θ, write the relation between h, d and θ.
10.1
What is the relation between the angle of depression of an object from the top of a tower and the angle of elevation of the top of the tower from the object?
SECTION B
This section comprises 4 very short answer (VSA) type questions of 2 marks each.
11.2
Tangents TP and TQ are drawn from an external point T to a circle with centre O, and ∠PTQ = 40°. Find ∠OPQ.
12.2
The length of the tangent from a point Q to a circle is 16 cm and the radius of the circle is 12 cm. Find the distance of Q from the centre.
13.2
A slide is 3 m high and is inclined at 60° to the ground. Find its length. (Use √3 = 1.732)
14.2
A tree breaks and its top touches the ground at a distance of 9 m from its foot, making an angle of 30° with the ground. Find the original height of the tree. (Use √3 = 1.732)
SECTION C
This section comprises 4 short answer (SA) type questions of 3 marks each.
15.3
A circle is inscribed in a triangle ABC right angled at B, with AB = 15 cm and BC = 8 cm. Find the radius of the circle.
16.3
Prove that a parallelogram circumscribing a circle is a rhombus.
17.3
From a point on a bridge 4.5 m above the water, the angles of depression of the two opposite banks of a river are 30° and 45°. Find the width of the river. (Use √3 = 1.732)
18.3
The angle of elevation of the top of a 15 m high building from a point on the ground is 45°, and that of the top of a tower standing on the building is 60°. Find the height of the tower. (Use √3 = 1.732)
SECTION D
This section comprises 2 long answer (LA) type questions of 5 marks each.
19.5
Two parallel tangents touch a circle with centre O at A and B. A third tangent touches the circle at C and meets the parallel tangents at P and Q. Prove that ∠POQ = 90°.
20.5
From the top of a 60 m high building, the angles of depression of the top and the bottom of a tower are 30° and 60° respectively. Find the height of the tower and its horizontal distance from the building. (Use √3 = 1.732)
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