Duration: 1 hour
Section A: Each question carries 1 mark
Question 1: Consider the first 7 multiples of 6. Find their mean.
Question 2: For the data given below, find the median. The weight in grams of bars of chocolates is as follows:
137, 145, 122, 153, 118, 159, 164, 111
Question 3: A cone has a base diameter of 14 cm and a slant height of 25 cm. Find its height.
Section B: Each question carries 2 marks
Question 1: A circle is circumscribed about an equilateral triangle of side length 18cm. Find the radius of the circle.
Question 2: Given that two chords of a circle are parallel, then prove that if a diameter of the circle bisects one chord, it also bisects the other chord.
Question 3: The number of girl child per family was recorded for 1000 families with 3 children. The data obtained was as follows:
|Number of Girls||0||1||2||3|
|Number of families||112||314||382||192|
Question 4: In a certain city, out of 30 days of the month, it rains on 8 days. Find the probability that on a given day selected, it does not rain.
Section C: Each question carries 3 marks
Question 1: The average Olympiad score of 10 students who are selected to represent the school for a Math quiz is 85. If one more student whose score is 88 is added to this group of 10 students, then now what is the average score of this group of 11 students?
Question 2: Derive the formula for area of an equilateral triangle of side ‘a’ in terms of the side of length a only.
Section D: Each question carries 4 marks
Question 1: Mr. Mehra’s field is in the shape of an irregular quadrilateral. The sides taken in clockwise direction measure 26 m, 27 m, 7 m and 24 m. The two sides measuring 7 m and 24 m form a right angle. Find the area of the field.
Question 2: Two points of a parallelogram are (1,2) and (2,5). The base of the parallelogram is parallel to the x axis and is 4 units long. Find the co-ordinates of the other two points of this parallelogram and also find the length of the other pair of parallel sides of the parallelogram. What would the area of this parallelogram be?