CBSE Proficiency Test in Mathematics - 2011

(SAMPLE PAPER)

General Instructions: (All questions are compulsory.)

The questions are divided into three sections:
1. Section I: Questions 1 to 11 are Multiple Choice Questions. Each multiple choice question has four options out of which only ONE option is correct. Each correct answer earns a credit of 3 marks.
A wrong answer carries a penalty of -1 mark.
2. Section II: Questions 12 to 15 are Numerical Questions. Each correct answer earns a credit of 5 marks. There is no negative marking for these questions.
3. Section III: Questions 16 to 17 are Column-matching Questions. In these questions, there are 3 items in the left column (Column I) and 5 options in the right column (Column II). You have to match each item in Column I with ALL the correct options in Column II. For each item in Column I, you earn 2 marks if all correct matches in Column II are indicated, and no incorrect matches are indicated. There is no negative marking for these questions.

• For all types, an unanswered question earns no mark.

1. The sum of all the numbers between 1 and 1000, which are divisible by 5 but not by 2 is:
(A) 101100
(B) 50000
(C) 50050
(D) 10100

2. The annual salary of Mr. Nair for the year 2010 is Rs. 40,000. Every year his salary increases by Rs. 4,000. At the beginning of the year 2010 he had borrowed a sum of Rs. 44,000 from a bank. Given the following information determine the number of years he will take to repay the principal and the interest to the bank.

(a) The interest due for payment is Rs. 3,600 at the end of the year 2010 and increases by Rs. 800 every year thereafter and (b) each year he is going to pay the bank 20% of his annual income towards loan repayment.

3. From a point A on a straight road the angle of elevation of the top of a vertical tower situated on the roof of a vertical building on the same road is q. The angle of elevation of the bottom of the tower from a point B on the road is again q. The height of the building is 50 metres. If AB : BY is 2 : 5, where Y is the base of the building, what is the height of the tower?

4. In a game, a number is chosen at random from the set f1;2;3; : : : ;28;29;30g. What is the probability that the number chosen is a product of exactly two different prime numbers?

(A) 7/30
(B) 1/6
(C) 4/15
(D) 1/5

5. Column I lists certain geometric shapes and Column II describes certain properties of geometric shapes. For each item in Column I, choose ALL the correct options in Column II.

Column I:
(i) Parallelogram
(ii) Rhombus
(iii) Rectangle

Column II:
(A) Diagonals bisect each other.
(B) Diagonals are perpendicular to each other.
(C) The figure includes at least one pair of equal sides.
(D) A circle drawn through any three vertices always passes through the fourth vertex.
(E) the pair of lines obtained by joining the midpoints of the opposite sides are always perpendicular to each other.

Courtesy: CBSE.GOV.IN