The squares of a 3×3 chessboard are randomly colored black or white. Let W be the number of white squares and B the number of black squares. The expected value of |B−W| can be expressed as a/b where a and b are co prime positive integers. What is the value of a+b?
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How many randomly assembled people are needed to have a better than 50% probability that at least 1 of them was born in a leap year?
A. 1
B. 2
C. 3
D. 4
E. 5
A 10 km race has 5 water stations set up around the course. What is the minimum number of people that must run in the race in order to guarantee that 10 people stop at the same set of water stations?
Details and assumptions
A racer may stop at none of the water stations. (The set of water stations such a racer stops at 0 station is called the null set.)
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Find the volumme of the largest right circular cone that can be cut out of cuboid of 56*21*14.
16248
Two parallel sides of trapezium are 7 and 17 cms.A line segment parallel to these sides is drawn which divides them trapezium into two equal regions. find the length of this line.
A right angled triangle ABC is right angled at B. The point of contact of the incircle with the hypotenuse divides it in ratio 3:2. If the perimeter is 36 cm,find its inradius.
3
Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in the train approaching the place hears the second shot 10 minutes after the first . Find the speed of train in km/hr (supposing that sound travels at 330m/s)?
a)19.8
b) 58.6
c) 59.4
d)111.80
Let ϕ(n) be the Euler Phi Function. If 1≤n≤1000, what is the smallest integer value of n that minimizes ϕ(n)/n?
Find the total number of points having integral coordinates inside the region enclosed by 2|x| + 3|y| = 18 in the X-Y plane.
please solve question 33
please solve question 28
A number N has 27 factors. Let x represent the maximum number of prime factors of N and y represent the minimum number of prime factors of N. Find the value of y-x?
10 men,8 women and 6 boys together can complete a piece of work in 25 days.for how many days will 19 men,20 women and 30 boys be occupied with three times the work? the work done in a particular time by a man,a woman,and a boy are in the ratio 5:3:2.
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if 15 men or 24 women or 36 boys can do a work in 12 days working 8hr a day,how many men must be associated with 12 women and 6 boys to do another work,2.25 times as great i 30 days working 6 hr per day??
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If x+Y+z=0 then the value of (y-z-x /2)^3 + (z-x-y /2)^3 + (x-y-z /2)^3 =?
(a) 24xyz (b) -24xyz (c)3xyz/8 (d) 3xyz
if 15 men or 24 women or 36 boys can do a work in 12 days working 8hr a day,how many men must be associated with 12 women and 6 boys to do another work,2.25 times as great i 30 days working 6 hr per day??
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The number of terms in an A.P is odd. If the sum of all the terms is 45 and the number of terms is 4 more than the middle term, find the middle term.
please solve question 28
area of rectangle/ area of circle = 2 root(5)/3*pi
==> 1/2*d^2 sin x / pi * d^2/4 = 2 root(5)/3*pi
==> sin x = root 5/3 == > cos x = 2/3
therefore tan x = root 5/2
we need tan x/2.. tan x = 2 tanx/2 / (1 - tan^2 x/2)
root 5/2 = 2x / (1-x^2) solve for x we get x = 1/root 5
So I feel the answer is 1/root 5
How many of the first 1200 natural nos are prime to either 6 or 15?
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