## The number of his ancestors

A person has 2 parents 4 grandparents, 8 great-grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.

## the sum of squares of the roots of the equation

Find the value of ‘a’ such that the sum of squares of the roots of the equation x^2 – (a – 2)x – (a + 1) = 0 is least?

## The integral value of ‘k’

What is the integral value of ‘k’ for which the quadratic equation x^2 – 6 x + k = 0 have real and distinct roots?

## The most preferable shirt size

A shopkeeper recorded the data regarding the number of shirts sold in the month of September at its factory outlet. The data are given below in table. Study the data and suggest him, the production of which shirt size should he increased to earn the profit? Which measure do you use to find the most preferable shirt size? Size 85 cm 90 cm 95 cm 100 cm Total Frequency 100 600 500 300 1600 a) 85 cm, Mean                      b) 90 cm, Mode               c) 95 cm, Median                   d) 92 cm, Mode

## The heights of students

A class teacher arranges 8 students in a line according to ascending order of their height. The heights of students are given below. 135 cm, 145 cm, 150 cm, 165 cm, 140 cm, 152 cm, 160 cm, 158 cm Later a new student got admitted whose height is 154 cm. What is the median height of students now? Where the new student would be seated? a) 154 cm, in middle b) 158 cm, at 6th place c) 156 cm, at 7th place d) 155 cm at 4th place

## A position on line equidistance from both ends

Two friends Tina and Mina were playing a game. Tina drew a line and marked 4 at one end and 10 at other end. She asked Mina to stand at a position on line which is equidistance from both ends. Where should Mina stand to satisfy Tina’s condition?

## the values of a, b and n

The 3rd , 4th and 5th terms in the expansion of (a + b)n are respectively 84, 280 and 560. Find the values of a, b and n.