Time allowed: 180 minutes; Maximum Marks: 90

General Instructions:
1)  All questions are compulsory.
2) The question paper consists of thirty questions divided into 4 sections A, B, C and D. Section A comprises of ten questions of 01 mark each, Section B comprises of five questions of 02 marks each, Section C comprises ten questions of 03 marks each and Section D comprises of five questions of 06 marks each.
3)  All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.
4)  There is no overall choice. However, internal choice has been provided in one question of 02 marks each, three questions of 03 marks each and two questions of 06 marks each. You have to attempt only one of the alternatives in all such questions.
5)  In question on construction, drawing should be near and exactly as per the given measurements.
6) Use of calculators is not permitted.

Section A Section B Section C Section D

Question 1

1. The common difference of the A.P. 1p, 1−pp, 1−

Question 2

2. In Fig. 1, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA ⊥ PB, then the length of each tangent is:

Question 3

3. In Fig.2, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm, then the radius of the circle (in cm.) is:

Question 4

4. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30°. The distance of the car from the base of the tower (in m.) is:

Question 5

5. The probability of getting an even number, when a die is thrown once, is :

Question 6

6. A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime-number less than 23, is :

Question 7

7. In Fig. 3, Find the area of triangle ABC (in sq. units) is:

Question 8

8. If the difference between the circumference and the radius of a circle is 37 cm, then using π = 227, the circumference (in cm) of the circle is:

(A) 154

(B) 44

(C) 14

(D) 7

Section A Section B Section C Section D