CBSE Class 10 Mathematics Previous Year Question Paper 2019 (All India Set-2)

Class X

(CBSE 2019)

Mathematics

All India (Set-2)

General Instructions:

(i) All questions are compulsory.

(ii) The question paper consists of 30 questions divided into four sections – A, B, C and D.

(iii) Section A comprises 6 questions of 1 mark each. Section B contains 6 questions of 2 marks

each. Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4

marks each.

(iv) There is no overall choice. However, an internal choice has been provided in two questions

of 1 mark, two questions of 2 marks, four questions of 3 marks each and three questions

of 4 marks each. You have to attempt only one of the alternative in all such questions.

(v) Use of calculators is not permitted.

Question 1

Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of

the larger circle which touches the smaller circle.

SOLUTION:

Let the two concentric circles be centred at point O.

Also, a > b where a is radius of larger circle and b is radius of smaller circle.

And let PQ be the chord of the larger circle which touches the smaller circle at point A.

Therefore, PQ is tangent to the smaller circle.

OA ⊥ PQ (As OA is the radius of the circle)

Applying Pythagoras theorem in ΔOAP, we obtain

OA2 + AP2 = OP2

Question 2

In Figure 1, PS = 3 cm, QS = 4 cm, ∠PRQ = θ, ∠PSQ = 90°, PQ ⊥ RQ and RQ = 9 cm.

Evaluate tan θ. OR