Quiz 1

since it is 100^8 converting it in the power of 2.
so 100^8=(100000000)^2
now,
100000000^2-111112^2  a^2-b^2=(a+b)(a-b)
=(100000000-111112)(100000000+111112) =99888888*100111112

99888888*100111112 so 9+9+8+8+8+8+8+8=66 66 is divisible by 3 but not 9 so ans should be ->3^1

Probability of raining on a particular day is 20/365
(No. of favorable days/total no of days), for a leap year
its probability is 20/266.
Now we have P=20/365, Q=20/366, R=20/365.... now
verify options, only option (3) is correct

probability is 1-p(drawing four socks which ar different)
p(drawing four socks different) (20/20)*(18/19)*(16/18)*(14/17)=>224/323
so probability is 1-224/323=>99/323

In 64 squares, there are:

(1) 4 at-corner squares, each has ONLY 2 squares each
having a side in common with...
(2) 6*4 = 24 side squares, each has ONLY 3 squares such
that each has a side in common with...
(3) 6*6 = 36 inner squares, each has 4 squares such that
each has a side in common with...
So we have the calculation:

P = (4/64)*(2/63) + (24/64)*(3/63)+ (36/64)*(4/63)
P = 1/18

In four shots he can hit once,twice,thrice,all hit
the probability
of hitting the target isp(1hit out of 4)+P(2hit out of
4)+p(3hit out of 4)+p(All hit)
it is total probability-probability of not hitting yhr target
=>1-(3/4*3/4*3/4*3/4)
=>175/256

Total ways of selecting 3 dots out of 15 is 15C3 = 455
If 3 dots are collinear then triangle may not be
formed.
Now look at the above diagram. If we select any 3 dots
from the red lines they may not form a triangle.
They are 3 x 5C3 = 30. If we select the three letters from
blue lines, they may not form a triangle. They are in total
5 ways. Also there are 6 others lines which don\\\'t form
a triangle.
Also another two orange lines. Total = 30 + 5 + 6 + 2 = 43.
So we can form a triangle in 455 - 43 = 412.
So answer could be 412/455.

1 pyramid can show 4 different kind of arrangements

1,2,4=7
1,2,6=9
1,4,6=11
2,4,6=12

So, out of 4 outcomes

3 are odd and 1 is even.

In question given two pyramids are thrown.
So, to make some of their faces as even

Condition 1: some of both individual faces of each pyramid is odd

3/4 * 3/4
=9/16

Condition 2: some of both individual faces of pyramid is even
1/4 + 1/4
=1/16

Total such conditions = 9/16 + 1/16
= 10/16
= 5/8

P(s)=2/3, P(m)=1/3
The probability of scoring 3 = 5c3*(2/3)^3*(1/3)^2
=5*2*((2/3)^3*(1/3)^2)

it was p>99
since p is an even number..so it can,t be divisible by odds
e is the probability of p to be divisible by even numbers..
means there are only even numbers in sample space..
n for w all whole numbers are allowed(odds also)
the
possible number of values of p are same in both cases but
sample space(for w)=2(sample space for e)

so it is clear that w=e/2

mod of x-4 should be 0 to 4 and also mod of y-4 should be
0 to 4.So first think all the possible value of x so that
x-4=0 and think all the possible value of so that y-4=4.
So to make |x-4|=0 and |y-4|=4 value of x and y is 1.
(4,0),2.(4,8).simillarly to make |y-4|=0 and |x-4|=4 value
of (x,y) is 3.(0,4),4.(0,8).to make |x-4|=1 and |y-4|=3, values
are 5.(3,1),6.(3,7),7.(5,1),8.(5,7) and |x-4|=3,|y-4|=1 values
are9.(1,3),10.(7,3),11.(1,5),12.(7,5).for |x-2|=2 and |y-2|=2
values are 13.(2,2),14.(2,6),15.(6,6),16.(6,2). so total 16.