Your total paise = 50 paise. But given total paise=75 paise. Also, from the given data it is clear that number of 2 paise stamp is 6 times the.number of 1 paise stamps. I have posted the detailed approach-cum-solution of this problem in the previous page of this thread.
@anytomdickandhary sirplease solve this XAT 2013 questionf(x)=x^4+x^3+x^2+x+1find the remainder when f(x^5) is divided by f(x)options=> 1,4,5,a monomial of x, a polynomial of xI marked polynomial of xTF's key says E but CL and TIME keys say C
Initial workings
f(x) = (x^5 - 1)/(x -1)
=>(x-1)f(x) = (x^5 -1)...................(i)
f(x^5) = x^20 + x^15 + x^10 + x^5 + 1
What next can I do now? (i.e what is that I am thinking now before I proceed)
1. I notice that in f(x^5) above difference is successive powers of terms is 5. So it looks possible that we can represent f(x^5) as (x^5 - 1)*Q + R.
2. based on my conclusion above and eqn (i).... it looks like (x^5 - 1) is the connect between f(x) and f(x^5)
So with intuitive conclusions from point 1 and point 2 I proceed ahead
@paridhi11890Your total paise = 50 paise.But given total paise=75 paise.Also, from the given data it is clear that number of 2 paise stamp is 6 times the.number of 1 paise stamps. I have posted the detailed approach-cum-solution of this problem in the previous page of this thread.
Typo :P
I meant 30 2p stamps and 5 1p stamps... Sorry :embarrassed:
@anytomdickandhary sirplease solve this XAT 2013 questionf(x)=x^4+x^3+x^2+x+1find the remainder when f(x^5) is divided by f(x)options=> 1,4,5,a monomial of x, a polynomial of xI marked polynomial of xTF's key says E but CL and TIME keys say C
The question is => x^20 +x^15 + x^10 + x^5 + 1 divided by x^4 + x^3 + x^2 + x^1 + 1.
I noticed two things: (a) The powers in the dividend are all 5 apart. (b) the divisor can be written as (x^5 - 1)/(x - 1) which means something divisible by x^5-1 will also be divisible by this.
So I set about writing the dividend in terms of x^5 - 1 forms, starting from x^20 and adding back adjustments for the lower powers as needed:
Recently, while I was in a holiday resort in Peru I watched a very interesting spectacle. Two gentleman by the name of Sr. Guittierez and Sr. Lbanez decided to have a Llama race over the mile course on the beach sands. They requested me and some of my other friends whom I had met at the resort to act as the judges. We stationed ourselves at different points on the course, which was marked off in quarter miles. But, the two Llamas, being good friends decided not to part company, and ran together the whole way. However, we the judges, noted with interest the following results The Llamas ran the first three quarters in six and three quarters minutes. They took the same time to run the first half mile as the second half. And they ran the third quarter in exactly the same times as the last quarter. From these results I became very much interested in finding out just how long it took those two Llamas to run the whole mile. Can you find out the answer?
Ram,shyam and hari went out for a 100 km journey.ram and hari started the journey in the ram's car at the rate of 25km/h,while shyam walked at 5 km/h.After sometime hari got off and started walking at the rate of 5kmph and ram went back to pick up shyam.All three reached the destination simaltaneously.The number of the hours required for the trip was .... ??
Ram,shyam and hari went out for a 100 km journey.ram and hari started the journey in the ram's car at the rate of 25km/h,while shyam walked at 5 km/h.After sometime hari got off and started walking at the rate of 5kmph and ram went back to pick up shyam.All three reached the destination simaltaneously.The number of the hours required for the trip was .... ?? how to solve this? it is XAT 2013 question .
meine option based se kiya tha exam mein marked 8 hrs dont know whether it was right or wrong
@hedonistajay answer is 8 only.if u get the complete solution.do share it here.I want to know the full solution coz i tried it many times,still couldn't get it.
@nole I used equations to solve this one... take the distance after covering which harii got off and started walking as x, the rest as ( (100-x), now we know all three reached at the same time, so i equated the times of hari and ram. we get the following equation:
x/25+(100-x)/5 = x/25 +2*4/5(x/30)+ (100-x)/25
solve to get value of x...and then calculate the LHS, to get the number of hours... hope the solution was clear
Ram,shyam and hari went out for a 100 km journey.ram and hari started the journey in the ram's car at the rate of 25km/h,while shyam walked at 5 km/h.After sometime hari got off and started walking at the rate of 5kmph and ram went back to pick up shyam.All three reached the destination simaltaneously.The number of the hours required for the trip was .... ?? how to solve this? it is XAT 2013 question .
Let A be the Origin and B be the point of final destination..Thus, AB= 100 km..Now, Let at C Hari get off from the car after "t" hrs..Then, AC= 25t km..
Now, In that time, Shyam wud had reached point D..Thus, AD= 5t km..
Let, Ram meet Shyam a point E after he dropped Hari off..Thus, DC=AC-AD= 20t km.
Thus, time taken to reach E= 20t/30 hr=> 2/3t hr...Thus, DE= 10/3t km..Thereby EC= DC-DE= 50/3t km..
Given,
2*EC + CB/25 = CB/5
=>(2*50/3t + 100 - 25t)/25 = (100-25t)/5
=>4/3t - t + 4 = 20 - 5t
=>t/3 + 5t = 16 => t= 3hr..
Thus, Total time of the Journey= 25/5 + 75/25 = 8hr..
at the centre of a city's municipal park,there is a large circular pool.A fish is released in the water at the edge of the pool.The fish swims north for 300 feet before it hits the edge of the pool.It then returns east and swims for 400 feet before hitting the edge again.What is the area of the pool ?
I marked as "cannot be answered from the given data " which was wrong answer. answer was 62,500pi.
one more question from XAT.at the centre of a city's municipal park,there is a large circular pool.A fish is released in the water at the edge of the pool.The fish swims north for 300 feet before it hits the edge of the pool.It then returns east and swims for 400 feet before hitting the edge again.What is the area of the pool ?I marked as none of these which was wrong answer. answer was 62,500pi.
The two chords of length 300ft and 400 ft are mutually perpendicular to each other..Thus, the mid-point of both the chords will touch the center of the pond..
