## 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.

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.

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?

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

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

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

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 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.

The digits of a positive integer, are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number.

The marks obtained by a student of Class XI in first and second terminal examination are 76 and 61, respectively. Find the maximum marks he should get in the annual examination to have an average of at most 70 marks.