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 sum of first p terms of an Α.P. is ap2+bp, find its common difference.

Question 2

2. In the given fig. , S and T are points on the sides PQ and PR, respectively of ΔPQR, such that PT = 2 cm, TR = 4 cm and ST is parallel to QR. Find the ratio of the areas of ΔPST and ΔPQR.

Question 3

3. In the given figure, ΔAHK is similar to ΔABC. If AK = 10 cm, BC = 3.5 cm and HK = 7 cm, find AC.

Question 4

4. If α, β are the zeroes of a polynomial, such that α + β = 6 and αβ = 4, then write the polynomial.

Question 5

5. Has the rational number 441(22 . 57 . 72) a terminating or a non-terminating decimal representation?

Question 6

6. If cosec θ = 2x and cot θ = 2x, find the value of 2(x2-1x2)

Question 7

7. A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting a red face card.

Question 8

8. The slant height of frustum of a cone is 4 cm and the perimeters (circumferences) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.

[Use π = 227]

Question 9

9. If A(1, 2), B(4, 3) and C(6, 6) are the three vertices of the parallelogram ABCD, find the coordinates of the fourth vertex D.

Question 10

10. If P(2, p) is the mid-point of the line segment joining the points A(6, − 5) and B(− 2, 11), find the value of p.

Section A Section B Section C Section D