All India (2)

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. If 1 is a root of the equations ay2 + ay + 3 = 0 andy2+ y + b = 0 then ab equals:

Question 2

2. The sum of first 20 odd natural numbers is:

Question 3

3. In Fig. 1, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is:

Question 4

4. In Fig 2, a circle touches the side DF of ΔEDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm, then the perimeter of ΔEDF (in cm) is:

Question 5

5. If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:

Question 6

6. If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is:

Question 7

7. The length of shadow of a tower on the plane ground is 3times the height of the tower. The angle of elevation of sun is:

Question 8

8. If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are:

Question 9

9. The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are:

Question 10

10. Two dice are thrown together. The probability of getting the same number on both dice is:

Section A Section B Section C Section D