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. If the height of a vertical pole is 3times the length of its shadow on the ground, then the angle of elevation of the Sun at that time is ______.

Question 2

2. A bag contains cards numbered from 1 to 25. A card is drawn at random from the bag. The probability that the number on this card is divisible by both 2 and 3 is

Question 3

3. Two different coins are tossed simultaneously. The probability of getting at least one head is ____.

Question 4

4. Two concentric circles are of radii 5 cm and 3 cm. Length of the chord of the larger circle (in cm), which touches the smaller circle is _______.

Question 5

5. In figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its sides AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = x cm, BC = 7 cm, CR = 3 cm and AS = 5 cm, find x.

Question 6

6. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is _______.

Question 7

7. A rectangular sheet of paper 40 cm × 22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is _______.

Question 8

8. The next term of the A.P. 7,28,63,√... is

Section A Section B Section C Section D