K(N) denotes the no of ways in which N can be expressed as a difference of two perfect squares. Which of the following is maximum?
K(110) K(105) K(216) K(384)
@IaMfused said:A, B and C in order, toss a coin. The one who gets a head first wins. Find their respective probabilities of winning. 4/7,2/7,1/7Can anyone explain this??
A can win if - he gets a head 1st time, he gets head 2nd time while others get tails ...
=> 1/2 + 1/2*1/2^3 + 1/2*1/2^6...
=> 1/2 / (1-1/2^3)
=> 1/2*8/7 = 4/7
for B => 1/2^2 + 1/2^2*1/2^3+.... = 1/2^2 / (1-1/2^3) = 1/4*8/7 = 2/7
for C => 1-4/7-2/7 = 1/7
@vbhvgupta where is the which part
=> 1/2 + 1/2*1/2^3 + 1/2*1/2^6...
=> 1/2 / (1-1/2^3)
=> 1/2*8/7 = 4/7
for B => 1/2^2 + 1/2^2*1/2^3+.... = 1/2^2 / (1-1/2^3) = 1/4*8/7 = 2/7
for C => 1-4/7-2/7 = 1/7
@vbhvgupta where is the which part
@krum said:A can win if - he gets a head 1st time, he gets head 2nd time while others get tails ...=> 1/2 + 1/2*1/2^3 + 1/2*1/2^6...=> 1/2 / (1-1/2^3)=> 1/2*8/7 = 4/7for B => 1/2^2 + 1/2^2*1/2^3+.... = 1/2^2 / (1-1/2^3) = 1/4*8/7 = 2/7for C => 1-4/7-2/7 = 1/7
Thanks for the detailed answer.
Please explain......
If x is a composite no is the statement given below true?
If there r 3 factors not greator than (2)^1/2 , then there r 3 factors not less than (2)^1/2
@vbhvgupta said:Can you check now??
K(N)=(a+b)(a-b)
we basically need to check for number of ways N can be expressed as product of 2 numbers = number of factors of N / 2
out of 110, 105, 216, 384
216 and 384 have 16 factors each, so both
we basically need to check for number of ways N can be expressed as product of 2 numbers = number of factors of N / 2
out of 110, 105, 216, 384
216 and 384 have 16 factors each, so both
@krum said:K(N)=(a+b)(a-b)we basically need to check for number of ways N can be expressed as product of 2 numbers = number of factors of N / 2out of 110, 105, 216, 384216 and 384 have 16 factors each, so both
Ans is D.....Source: Time material
@vbhvgupta said:K(N) denotes the no of ways in which N can be expressed as a difference of two perfect squares. Which of the following is maximum?K(110) K(105) K(216) K(384)
its 384..
@vbhvgupta said:K(N) denotes the no of ways in which N can be expressed as a difference of two perfect squares. Which of the following is maximum?K(110) K(105) K(216) K(384)
K(384) :D
f(a+b)=F(a)+F(b) and f(5)=12. Find F(12)
:D
A man went out between 5 and 6 and returned between 6 and 7 and found that the hands of the clock have interchanged positions.
(a) At what time did he leave ?
(b) At what time did he return ?
(a) At what time did he leave ?
(b) At what time did he return ?
A train travels at a particular speed for a duration of one hour, after which one of its engine malfunctions reducing its speed to 3/5th of the actual speed before the occurrence of fault in engine. It travels at this speed for 2 hours to reach at its destination. If the fault had occurred 50 miles later on, the train would have reached its destination 45 minutes early. Find the distance traveled by the train??
@Estallar12
Given, F(a+b) = F(a) + F(b)....F(5)= 12..
Now, F(5) = F(1) + F(4), or, F(1) + F(1) + F(3), or, F(1) + F(1) + F(1) + F(2)....
=>Thus, F(5) = 5*F(1), or, F(1) = 12/5...
F(12) = F(10)+F(2)
=>2F(5) + 2F(1)
=>2*[F(5)+F(1)]
=>144/5..
PS:: All the very best 4 CAT to all fellow puys.. 
@Estallar12 said:A man went out between 5 and 6 and returned between 6 and 7 and found that the hands of the clock have interchanged positions.(a) At what time did he leave ?(b) At what time did he return ?
left at 5:a
return at 6:b
return at 6:b
equate hour hand at 5:a to minute hand when it was 6:a
150 + a/2 = 6b
similarly
180 + b/2 = 6a
solve two equations..we ll get a and b :P
150 + a/2 = 6b
similarly
180 + b/2 = 6a
solve two equations..we ll get a and b :P
@Estallar12 said:f(a+b)=F(a)+F(b) and f(5)=12. Find F(12)
it clearly shows that function will be of type Kx
f(x) = kx
f(x) = kx
f(5) = k(5) = 12
k = 12/5
f(12) = 12/5 *12 = 144/5
@Estallar12 said:f(a+b)=F(a)+F(b) and f(5)=12. Find F(12)
I thought the function f, and function F are different 😐
Ye clock wale ques ka koi formula hota h kya
Q ) what is the angle between hr hand and minute hand at 4:16 ??
Koi mod laga k formula h to plz provide link OR explain long approach se bachna h mujhe .
An angle is 2/3 of its supplement.
Find it. :P