Education
Class 10 Mathematics Chapters 9 & 10 Grand Test | Model Paper | Punjab Board 2027
Class 10 Mathematics Grand Test 2027 based on the Punjab Board 2027 Model Papers is available for Chapters 9 and 10. This board-pattern test covers Tangent and Angles of a Circle and Practical Geometry of Circles and includes objective, short-answer, long-answer and construction-based questions. It is designed to help Class 10 students prepare effectively for the Punjab Board Mathematics 2027 examination and practice important concepts according to the latest board-style paper pattern.
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11. At least how many chords are needed to locate the centre of the circle?
14. In fig (B), radial segment is:
15. In fig (C) m∠ATR = __________.
Model PAPER
2027
MATHEMATICS
CHAPTER
WISE
WISE
Roll No. (in Figures): ………………………………
(in Words): ………………………………….
Unit 9: Tangent and Angles of a Circle
Time : 20 Minutes
Unit 10: Practical Geometry of Circles
Marks: 15
OBJECTIVE TYPE
ABCD
1ABCD
2ABCD
3ABCD
4ABCD
5ABCD
ABCD
6ABCD
7ABCD
8ABCD
9ABCD
10ABCD
ABCD
11ABCD
12ABCD
13ABCD
14ABCD
15ABCD
Note: Four possible answers A, B, C and D to each question are given.
The choice which you think is correct, fill that circle in front of that question with
Marker or Pen ink. Cutting or filling two or more circles will result in zero mark in
that question.
Q1. 15
1. ________ tangents can be drawn to a circle from a point outside the circle:
2. In circle, radius and tangent are:
3. The angle subtended by the arc at the centre of the circle is called:
4. Any two angles in the same segment of the circle are:
5. If OC is the radial segment in a circle,
MN is a tangent, then
6. Point P is 13 cm from the centre of a circle if the radius is 5cm,
what is length of tangent from point P to the circle?
7. A circular running track subtends angle of 65° at the centre.
What angle does it subtend at a point on the boundary?
8. If arc length is 10π and the θ = 120° what is radius?
9. There are ________ types of arcs.
10. The point where two tangents meet outside a circle forms:
Fig (A)
12. The angle between the radius and a tangent at the point of contact is:
13. In figure (A), the circle is passing through the points.
Fig (B)
Fig (C)
Here is Subjective Part of Punjab Board Model paper 2027.
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(i) What is the significance of the point where the two right
bisectors of the chords of a circle meet?
Roll No. (in Figures): ………………………………………………..
(in Words): ………………………………………………..
Unit 9: Tangent and Angles of a Circle
Time : 2:10 Hours
Unit 10: Practical Geometry of Circles
Marks: 60
SUBJECTIVE TYPE (PART – I)
Q2. Write short answers to any six (6) questions:
(6 × 2 = 12)
(i) A circular garden has a walking path forming a quadrilateral
inscribed in it. If one angle is 87°, what is opposite angle?
(ii) Find θ, when
ℓ = 3cm, r = 2.2 cm
(iii) Find θ, when
ℓ = 5.6cm, r = 2 cm
(iv) Find ℓ and area of sector, when
r = 1.7 cm, θ = 0.25 radian
(v) Find ℓ and area of sector, when
r = 3 cm, θ = 45°
(vi) Uzma cut a pizza of radius 14 cm into 8 equal slices.
What is the area of one slice (sector)?
(vii) A triangular frame within a semicircular gate joins the
ends of the diameter to the peak. What is the angle formed at the peak?
(viii) A circular birthday cake has a radius of 15 cm.
A slice has an arc length of 10cm. What is the area of this slice?
(ix) A sector cut from a circle of radius 5cm has a perimeter
of 16cm, Find area of this sector.
Q3. Write short answers to any SIX (6) questions:
(6 × 2 = 12)
(i) Define the tangent to a circle:
(ii) If two tangents, PA and PB are drawn from a point P
to the circle with centre O. What can we concluded about their lengths?
(iii) If two circles of radii
r1 = 11 and
r2 = 7 touch internally,
what is the distance of their centres?
(iv) What is the measure of an angle subtended in a semi-circle?
(v) What is the measure of the angle in a segment greater than a semi-circle?
(vi) A circle has a radius of 10cm and a central angle of 60°.
Find the arc length.
(vii) The perimeter of a sector is 25 cm and its arc length is 9cm.
Find the radius of circle.
(viii) What is geometric property used to locate the centre of a circle?
(ix) How many points on the circumference are required to find the
center, and why?
Q4. Write short answers to any SIX (6) questions:
(6 × 2 = 12)
Fig.
(ii) In fig how is radius of the circle defined?
(iii) What constraint is placed on the length of chords to complete
a circle without finding its centre?
(iv) What is the geometrical relationship between the chord of an
arc and a line passing through the mid point of the arc?
(v) What is the first step to draw a tangent to a given circle
from a point P when P is on the circumference?
(vi) Describes the steps to draw a tangent to circle with centre
“O”, from a point P, which is outside the circle.
(vii) According to steps for drawing two tangents meeting at a
30° angle, what is the purpose of drawing the diameter first?
(viii) Can a tangent be drawn from a point located inside the circle?
(ix) What is a point of tangency?
(PART – II)
Note: Attempt any two (02) questions.
(2 × 8 = 16)
Q5. (a)
Two circular gears touch each other externally for proper rotation
in a machine. The radii of the two circular gears are 5cm and 7cm.
What is the distance between their centres if they touch externally?
4
(b)
An inner holder touches the outer cylindrical container internally.
If the outer container has radius 8 cm and the inner holder has radius
6 cm, find the distance between their centres.
4
Q6. (a)
In the diagram P, Q and R are points on the circumference of a circle
and the line segment PQ is the diameter.
Find the angles x and y.
4
Fig.
(b)
S, T, U and V are points on the circumference of a circle.
Find the angles x and y.
4
Q7. (a)
A sector cut from a circle of radius 5cm has a perimeter of 16cm.
Find area of this sector.
4
(b)
Take any three non-collinear points
P,Q,R and construct a circle passing
through these points.
4
(PART – III)
Note: Attempt any one (01) question.
(1 × 8 = 8)
Q8. (a)
Draw an arc ABC and complete a circle by finding its centre.
4
(b)
Take any three non-collinear points (locations of the lamp posts in
the park), construct a circle passing through all these points.
4
(a)
Draw a circle with radius 1.5 cm, Draw tangents to this circle that
meet an angle of 30°.
4
(b)
Draw tangent to PQR at point P,
when P is endpoint of the arc.
4
