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Class 10 Mathematics
CBQ Practice

Competency Based Questions · 3 chapters · 6 CBQ sets

Question types:Case StudySource BasedAssertion–Reason
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Ch 5

Arithmetic Progressions

2 sets
CBQ 1Case StudySeating Arrangement in a Stadium4 marks

Read the passage

A stadium has rows of seats arranged such that the first row has 20 seats, the second row has 24 seats, the third row has 28 seats, and so on. The number of seats in successive rows forms an Arithmetic Progression (AP). The stadium management wants to plan seating for 15 rows in total. The groundskeeper is asked to calculate the total capacity and identify seat counts in specific rows so that the ticketing team can assign blocks.
1

What is the common difference of the AP formed by the number of seats?

1M
(A)2
(B)4
(C)6
(D)8
2

How many seats are there in the 10th row?

1M
(A)52
(B)56
(C)60
(D)64
3

What is the total number of seats in the first 5 rows?

1M
(A)120
(B)140
(C)160
(D)180
4

Find the total seating capacity of the stadium if there are 15 rows.

1M
CBQ 2Assertion–Reason1 mark
A
Assertion

The sequence 3, 7, 11, 15, ... is an Arithmetic Progression with common difference 4.

R
Reason

In an Arithmetic Progression, the difference between any two consecutive terms is always constant and equal to the first term.

(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
Ch 6

Triangles

2 sets
CBQ 1Case StudyShadow and Height of a Tower4 marks

Read the passage

Ramesh, a surveyor, is measuring the height of a tall tower using the concept of similar triangles. He observes that a vertical pole of height 6 m casts a shadow of 4 m on the ground. At the same time, the tower casts a shadow of 28 m. Ramesh knows that when sunlight falls at the same angle, the triangles formed by the pole and its shadow and by the tower and its shadow are similar. He uses the property of similar triangles: corresponding sides are proportional, to find the height of the tower. He also needs to verify certain conditions using Pythagoras theorem.
1

Which criterion of similarity is applicable in this situation?

1M
(A)SSS (Side-Side-Side) Similarity
(B)AA (Angle-Angle) Similarity
(C)SAS (Side-Angle-Side) Similarity
(D)RHS Similarity
2

What is the height of the tower?

1M
(A)36 m
(B)40 m
(C)42 m
(D)48 m
3

If the triangle formed by the tower has a base of 28 m and height 42 m, what is its hypotenuse (approximately)?

1M
(A)48.5 m
(B)50.1 m
(C)49.5 m
(D)51.2 m
4

State the Basic Proportionality Theorem (Thales' Theorem) and explain how it applies to a triangle where a line is drawn parallel to one side.

1M
CBQ 2Assertion–Reason1 mark
A
Assertion

If in two triangles, the corresponding angles are equal, then the triangles are congruent.

R
Reason

Two triangles are similar if their corresponding angles are equal (AA criterion), but similar triangles are not necessarily congruent.

(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
Ch 10

Circles

2 sets
CBQ 1Case StudyTangents from an External Point4 marks

Read the passage

An architect is designing a circular garden with centre O and radius 7 m. A straight pathway is to be built from an external point P, which is 25 m from the centre O. The pathway touches the circular garden at exactly one point. The architect wants to find the length of the pathway (tangent) and also verify some properties about the angle between the radius and the tangent at the point of contact. Another pathway is drawn from the same point P touching the circle at point Q. The architect needs to confirm properties of these two tangents from the external point P.
1

What is the length of the tangent PA from external point P to the circle?

1M
(A)18 m
(B)20 m
(C)24 m
(D)25 m
2

The angle between the radius OA and the tangent PA at point A is:

1M
(A)45°
(B)60°
(C)90°
(D)180°
3

If PA and PB are two tangents from external point P to a circle with centre O, which of the following is TRUE?

1M
(A)PA > PB
(B)PA < PB
(C)PA = PB
(D)PA and PB are perpendicular to each other
4

Prove that the lengths of tangents drawn from an external point to a circle are equal.

1M
CBQ 2Assertion–Reason1 mark
A
Assertion

A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

R
Reason

The tangent at any point of a circle is perpendicular to the radius through the point of contact because the tangent touches the circle at exactly one point.

(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

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