Mean x = Sum of nos. / Count of numbers = 1078/11 = 98
Median y = Middle term when number are arranged in ascending order = 97
Mode z = Number which is present maximum number of times = 87
x^2 + 3xyz + 2y^2 + 3 z*2 = (98)^2 + 3*98*97*87 + 2*(97)^2 + 3*(87)^2 = 2532195
MILLENNIUM
Lets arrange the letters alphabetically = E II LL MM NN U
Words starting with E = 9!/(2!*2!*2!*2!) = 22680
Words starting with I = 9!/(2!*2!*2!) = 45360
Words starting with L = 9!/(2!*2!*2!) = 45360
Words starting with ME = 8!/(2!*2!*2!) = 5040
Words starting with MIE = 7!/(2!*2!) = 1260
Words starting with MII = 7!/(2!*2!) = 1260
Words starting with MILE = 6!/(2!) = 360
Words starting with MILI = 6!/(2!) = 360
Words starting with MILLEI = 4!/(2!) = 12
Words starting with MILLEM = 4!/(2!) = 12
Words starting with MILLENI = 3! = 6
Words starting with MILLENM = 3! = 6
Words starting with MILLENNIM = 1
and the required word is the next one MILLENNIUM
Sum of all = 121718
Words starting with lm = 8!/(2!*2!) = 10080
Words starting with ln = 8!/(2!) = 20160
Words starting with ls = 8!/(2!*2!) = 10080
Words starting with luc = 7!/(2!*2!) = 1260
Words starting with lue = 7!/(2!) = 2520
Words starting with lui = 7!/(2!*2!) = 1260
Words starting with lumc = 6!/(2!*2!) = 180
Words starting with lume = 6!/(2!) = 360
Words starting with lumic = 5!/(2!*2!) = 30
Words starting with lumie = 5!/(2!) = 60
Words starting with luminc = 4!/(2!) = 12
Words starting with luminec = 3! = 6
Words starting with luminee = 3! = 6
Words starting with luminen = 3! = 6
Words starting with luminescen = 1
An Indian State name (excluding union territories) is randomly picked. What is the probability that that name of the picked Indian State starts with a vowel?
A 2 digit number between 11 to 50 (both inclusive) is randomly picked.
What is the probability that the picked number is such a prime number whose sum of digits is an odd number?
1st Match
Mean of 11 scores = 354/11 = 32.18
Sum of squared difference from mean for each number = (33-32.18)^2 + (24-32.18)^2 + ......+ (26-32.18)^2 = 815.6364
Average of Squared difference (Variance) = 815.6364/11 = 74.1487
Population Standard Deviation = Square root of variance = 74.1487^1/2 = ~8.610
2ns Match
Mean of 11 scores = 410/11 = 37.27273
Sum of squared difference from mean for each number = (13-37.27)^2 + (44-37.27)^2 + ......+ (7-37.27)^2 = 7326.18
Average of Squared difference (Variance) = 7326.18/11 = 666.016
Population Standard Deviation = Square root of variance = 666.016^1/2 = ~25.807
Difference between Population standard deviation of 2nd match and 1st match = 25.807 - 8.610 = ~17.197
Any factor of this number should be of the form 31^a * 17^b * 7^c * 3^d * 2^e * 89 ^f
For the factors of this number to be an even number e should be non 0
a can take values 0, 1, 2, 3
b can take values 0, 1
c can take values 0, 1
d can take values 0, 1, 2
e can take values 1, 2, 3, 4
f can take values 0, 1
A man goes down stream with a boat to some destination and returns upstream to his original place in 15 hours. If the speed of the boat in still water and downstream are 10km/hr and 14km/hr respectively, the distance of the destination from the starting place in KMs is