In a green view apartment, the houses of a row are numbered consecutively from 1 to 49. Assuming that there is a value of 'x' such that the sum of the numbers of the houses preceding the house numbered 'x' is equal to the sum of the numbers of the houses following it. Then, what will be the value of 'x' ?
Answer: C From the given information, Sum of the first (x-1) natural numbers = Sum of natural number from (x+1) to 49. So, (x-1)(x)/2 = 49*50/2 - (x)(x+1)/2 => 2x2 = 49*50 => x = 7*5 = 35.
Q. No. 32:
How many subsets of {1,2,3,..............,11} contains at least one even integer ?
Answer: C Given, set = {1,2,3,........,11} The total number of subsets = 211 The number of subsets which contains no even number = 26 The number of subsets which contains at least one even number => 211 - 26 = 2048 - 64 = 1984.
Q. No. 33:
The mean salary in ICM ltd. was Rs 1500, and the standard deviation was Rs 400. A year later each employee got a Rs 100 raise. After another year each employee's salary (including the above mentioned raise) was increased by 20%. The standard deviation of the current salary is :
Answer: B Mean salary was Rs 1500 Standard deviation = Rs 400 After 1 year all the employees got a uniform rise of Rs 100. So, there will be no change in standard deviation. After another year, every employee's salary was increased by 20%. So, standard deviation will be increased by 20%. Standard deviation = 400 * 120/100 = Rs 480.