Duration: 1 hour
Section A: Each question carries 1 mark
Question 1: According to Euclid’s division lemma, for two positive integers a and b, there exist q and r which are unique integers such that a= ________.
Complete the statement.
Question 2: How many real zeros would the following polynomial curve have?
Question 3: Is the following equation a quadratic equation?
Question 4: The distance between the points (-1,5) and (2,-3) on the co-ordinate gird would be = ___________?
Question 5: How many tangents can a circle have?
Section B: Each question carries 2 marks
Question 1: Sara takes 18 minutes to run around a circular jogging track while Suzy takes 12minutes for the same jog. If they start off together from the same point and in the same direction, then after how many minutes will they meet again at the starting point?
Question 2: The zeros of a quadratic polynomial are -3 and 2. Find the polynomial.
Question 3: Sam takes 2 hours to row 20 Km downstream. However he is able to row only 4 Km in the same time if he rows upstream. Find his rowing speed in still water and also find the speed of the current.
Question 4: In an arithmetic progression, the 17th term exceeds the 10th term by 7. Find the common difference of the progression.
Section C: Each question carries 3 marks
Question 1: Two of the zeros of the polynomial x^4-6x^3-26x^2+138x-35 are 2+√3 and 2-√3. Find the remaining zeros of this polynomial.
Question 2: If Jack gives Rs. 100 to Jill, she becomes twice as rich as him. However, if Jill gives Rs. 10 to Jack, he would become 6 times as rich as her! How much money do they each have presently?
Question 3: Find the first term and the common difference of an arithmetic progression whose third term is 16 and the 5th term is smaller than the 7th term by 12.
Question 4: Two aircrafts start from the same airport. One flies north and the other flies west. The north bound aircraft is cruising at a speed of 1000 km per hour and the west bound aircraft is cruising at a speed of 1200 km per hour. Find the distance between the two aircrafts 1 and a half hour after take-off.