All India

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 roots of the equationx2−3x−m(m+3)=0, where m is a constant, are:

Question 2

2. If the common differences of an A.P. is 3, then a20−a15is:

Question 3

3. In figure 1, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70°, then ∠TPQ is equal to ________.

Question 4

4. In Figure 2, AB and AC are tangents to the circle with centre O such that ∠BAC = 40°. Then ∠BOC is equal to ________.

Question 5

5. The perimeter (in cm) of a square circumscribing a circle of radius a cm, is _________.

Question 6

6. The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is _________.

Question 7

7. A tower stands vertically on the ground. From a point on the ground which is 25 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 45°. Then the height (in meters) of the tower is _________ m.

Question 8

8. If P(a2, 4) is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is

Question 9

9. If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance

2AB is equal to __________.

Question 10

10. A card is drawn from a well-shuffled deck of 52 playing cards. The probability that the card will not be an ace is ________.

Section A Section B Section C Section D