Monday, July 29
Thursday, July 25
Solution of Baap of Challenger
There are how many integers "n" in between 1 and 10^7, including both, such that last 7 digits of n and n^3 are
the same? (If n or n^3 has fewer than 7 digits,
then add 0s in the left and then compare the last 7 digits.)
a. 10 b. 15 c. 20 d.
None of These
Sol [b]
If last 7 digits of n and n^3 are the same it means n^3 - n
is divisible 10^7
i.e (n-1)*n*(n+1) is divisible by 10^7 [n^3 - n=(n-1)*n*(n+1)]
It shows (n-1)*n*(n+1) is divisible by both 2^7 & 5^y
Case I: (n-1)*n*(n+1) is divisible by 2^7
Sub-case a : If n is even than both (n-1) & (n+1)are odd so n should be
divisible by 2^7
=> n is multiple of 2^7.......................(i)
=>n = 2^7, 2*2^7,.........,5^7*2^7
Sub-case b : If n is odd than (n-1)*(n+1) should be
divisible by 2^7
Since the gap between n-1 and n+1 is 2 so one of them is divisible by 4 and
other is by only 2
Sub-case b1 : Let n-1 is divisible by 2 but 4 , then n+1 is
divisible by 2^6 => (n+1) is multiple of 2^6
=> n = 2^6 -1 , 2*2^6 -1, 5^7*2^6 -1 .....5^7*2*2^6 - 1
Sub-case b2: Let n+1 is divisible by 2 but 4 , then n-1 is
divisible by 2^6 => (n-1) is multiple of 2^6
=> n = 1, 2^6 +1 , 2*2^6 +1, 5^7*2^6 +1 .....
Sub-case b3 : Let n-1 is divisible by 2^7 => (n-1)
is multiple of 2^7
Sub-case b4 : Let n+1 is divisible by 2^7 => (n+1)
is multiple of 2^7
So we
can say we are getting 5 different remainders for "n" when divided by
2^7 which are 0, 1, 2^6-1, 2^6+1 & 2^7 -1
Case II: (n-1)*n*(n+1) is divisible by 5^7
Sub-case (i) : n-1 divisible by 5^7 => n = k*5^7 +1
Sub-case (ii) : n divisible by 5^7 => n = k*5^7
Sub-case (iii) : n+1 divisible by 5^7 => n = k*5^7 -1
So we
can say we are getting 3 different remainders for "n" when divided by
5^7 which are 0, 1, -1
There are three possible values of remainders by 5^7 and five possible values by
2^7 . Then by the CRT (Chinese Remainder Theorem) there are 15 possible values
of remainder by 10^7.
Hence there are 15 required solutions of n in between 1 to 10^7.
Saturday, July 20
Mumbai's bar dancers will only get partial relief from the Supreme Court's recent ruling
#LAV
Mumbai's bar dancers will only get partial relief from the Supreme Court's recent ruling.
The Supreme Court’s 16 July ruling upholding the 2006 judgment of the Bombay High Court that upturned the Maharashtra government’s ban on dance bars is, at best, a pyrrhic “victory” for the women who danced in these bars. In 2005, when the ban was instituted, an estimated 75,000 women lost their main source of livelihood. Hence, it is presumed that following the Supreme Court’s ruling these women will once again have recourse to a livelihood option. However, a closer reading of the judgment coupled with the competitive “moral” politics of Maharashtra suggests that the “victory” is only partial.
The Bombay High Court struck down the Maharashtra government’s amendment to the Bombay Police Act, 1951 banning all forms of dancing in bars that were lower than three star status, to be against the constitutional provisions in Articles 14 and 19(1)(g). By amending Section 33 (A) of the law, the Maharashtra government had created two categories for the same activities. Women could not perform in licensed bars outside hotels that were three star or higher, or in private clubs. The justification for the ban was that these performances resulted in depravity, lowering public morality and exploited the women. Yet, no such value judgment was made on the same or similar performances in the higher class establishments. Therefore, it comes as no surprise that the Supreme Court has confirmed what the Bombay High Court concluded, namely, that such a law is discriminatory and goes against the Constitution.
Now that the ban has been struck down, will dance bars reopen and the women find work again? In the year following the ban, which was incidentally supported by virtually all political parties in Maharashtra, and the Bombay High Court judgment, hundreds of bars were forced to close. Apart from the women dancers, the entire industry consisting of support staff, waiters, managers, and others who provided services to these bars was put out of work. And as the Maharashtra government managed to get a stay from the Supreme Court on the Bombay High Court ruling, the ban prevailed.
Despite the Court ruling, it is unlikely that things will return to pre-ban days. Although many dance bars metamorphosed as “live music” bars, they will now have to apply for fresh licences if they want to introduce dance performances. It is unlikely that these will be granted in a hurry. The Maharashtra government has already indicated that it might go back to Court. It has to maintain the appearance of being concerned about “public morality”, the apparent reason it went in for the ban, because it cannot afford to yield this high moral ground to its competitors, especially the Shiv Sena but also its ally the Nationalist Congress Party.
The Supreme Court has asked the Maharashtra government to implement the rules formulated by its own committee prior to the ban. These rules include restrictions on what the women can wear while dancing, a fenced-off area where they dance, not more than eight women dancing at one time, not permitting the “showering” of money on dancers and registering the names and addresses of the dancers. In their anxiety to restart, bar owners are already promising to implement all this and more.
None of these so-called “rules”, however, will alter the daily reality that bar dancers have had to live with all these years. For instance, there is no guarantee that these women will work under better conditions. In the past, many did not get paid and depended entirely on the money “showered” on them by the clientele. If these tips are now to be collected by the bar’s management, it is anybody’s guess how much will finally get to the women. Even at the best of times, the bar dancers had no security and could be turned away on any given day. That insecurity will continue. And finally, only a small number of those who lost their jobs in 2005 are likely to be re-employed as they are now older and do not fit the profile of the bar dancer.
The Court’s intervention apart, what remains untouched is the “popular” conception of what is moral and immoral. The ban on dance bars exposed how lawmakers fell over each other in declaring the immorality of women dancing in bars even as they swore concern about the exploitation of women. At no point did any of them notice the hypocrisy of pushing ahead with policies that make women more vulnerable to exploitation while denying them agency and the right of choice.
Mumbai's bar dancers will only get partial relief from the Supreme Court's recent ruling.
The Supreme Court’s 16 July ruling upholding the 2006 judgment of the Bombay High Court that upturned the Maharashtra government’s ban on dance bars is, at best, a pyrrhic “victory” for the women who danced in these bars. In 2005, when the ban was instituted, an estimated 75,000 women lost their main source of livelihood. Hence, it is presumed that following the Supreme Court’s ruling these women will once again have recourse to a livelihood option. However, a closer reading of the judgment coupled with the competitive “moral” politics of Maharashtra suggests that the “victory” is only partial.
The Bombay High Court struck down the Maharashtra government’s amendment to the Bombay Police Act, 1951 banning all forms of dancing in bars that were lower than three star status, to be against the constitutional provisions in Articles 14 and 19(1)(g). By amending Section 33 (A) of the law, the Maharashtra government had created two categories for the same activities. Women could not perform in licensed bars outside hotels that were three star or higher, or in private clubs. The justification for the ban was that these performances resulted in depravity, lowering public morality and exploited the women. Yet, no such value judgment was made on the same or similar performances in the higher class establishments. Therefore, it comes as no surprise that the Supreme Court has confirmed what the Bombay High Court concluded, namely, that such a law is discriminatory and goes against the Constitution.
Now that the ban has been struck down, will dance bars reopen and the women find work again? In the year following the ban, which was incidentally supported by virtually all political parties in Maharashtra, and the Bombay High Court judgment, hundreds of bars were forced to close. Apart from the women dancers, the entire industry consisting of support staff, waiters, managers, and others who provided services to these bars was put out of work. And as the Maharashtra government managed to get a stay from the Supreme Court on the Bombay High Court ruling, the ban prevailed.
Despite the Court ruling, it is unlikely that things will return to pre-ban days. Although many dance bars metamorphosed as “live music” bars, they will now have to apply for fresh licences if they want to introduce dance performances. It is unlikely that these will be granted in a hurry. The Maharashtra government has already indicated that it might go back to Court. It has to maintain the appearance of being concerned about “public morality”, the apparent reason it went in for the ban, because it cannot afford to yield this high moral ground to its competitors, especially the Shiv Sena but also its ally the Nationalist Congress Party.
The Supreme Court has asked the Maharashtra government to implement the rules formulated by its own committee prior to the ban. These rules include restrictions on what the women can wear while dancing, a fenced-off area where they dance, not more than eight women dancing at one time, not permitting the “showering” of money on dancers and registering the names and addresses of the dancers. In their anxiety to restart, bar owners are already promising to implement all this and more.
None of these so-called “rules”, however, will alter the daily reality that bar dancers have had to live with all these years. For instance, there is no guarantee that these women will work under better conditions. In the past, many did not get paid and depended entirely on the money “showered” on them by the clientele. If these tips are now to be collected by the bar’s management, it is anybody’s guess how much will finally get to the women. Even at the best of times, the bar dancers had no security and could be turned away on any given day. That insecurity will continue. And finally, only a small number of those who lost their jobs in 2005 are likely to be re-employed as they are now older and do not fit the profile of the bar dancer.
The Court’s intervention apart, what remains untouched is the “popular” conception of what is moral and immoral. The ban on dance bars exposed how lawmakers fell over each other in declaring the immorality of women dancing in bars even as they swore concern about the exploitation of women. At no point did any of them notice the hypocrisy of pushing ahead with policies that make women more vulnerable to exploitation while denying them agency and the right of choice.
Friday, July 19
Happy Birthday Gregor Johann Mendel - "Father of Modern Genetics"
Happy Birthday Gregor Johann Mendel - "Father of Modern Genetics"
Wednesday, July 17
Maths By Amiya, Questions & Solutions Link
Maths By Amiya, Questions & Solutions Link
Click on the links: To Download CTRL+S or from File TabYou Can also ask to share the doc to keep the file in your Google Drive.
350 & Rest - https://docs.google.com/file/d/0B65FQ9DyYQ_rUXZSRXk2cF8yXzA/edit
VA 20 Question
Maths By Amiya,PnC Ques 11-20
Maths By Amiya,PnC Ques+Sol 11-20
Maths By Amiya,PnC Ques 1-10
Maths By Amiya,PnC Ques+ Sol/Ans 1-10
Maths By Amiya,Number System Ques 1-30
Maths By Amiya,Number System Ques+ Sol/Ans 1-30
Maths By Amiya,QUESTIONS 246-350
Maths By Amiya,QUESTIONS + Solutions 246-350
Maths By Amiya,DI+ LR QUESTIONS 261-280
Maths By Amiya,DI+ LR SOLUTIONS 261-280
Maths By Amiya,QUESTIONS 181-245
Maths By Amiya,QUESTIONS & Solutions 181 -245 :
Maths By Amiya,QUESTIONS 121-180
Maths By Amiya, QUESTIONS & Solutions 121 -180 :
Maths By Amiya,QUESTIONS 61-120
Maths By Amiya,QUESTIONS & Solutions 61--120
Maths By Amiya, QUESTIONS & Solutions 1-60
Maths By Amiya,QUESTIONS & Solutions 1-60
"The Geometrical Album of Maths By Amiya, A compiled PDF"
Compiled PDF Link : http://goo.gl/f5TL6a 
To Download :- CTRL+S or from file tab
Use SHIFT+ CTRL+ MINUS to rotate the file.
On the request of aspirants, sharing all images of Geometrical Album in one place.
TnC:
1. Please Study and Study
2. Do not Use it for revenue generation
3. Do not violate the IPR (Intellectual Property Rights)
©AMIYA KUMAR
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Friday, July 12
Happy Birth Day "Malala Yousafzai"
Malala Yousafzai (Born 12 July 1997) is a Pakistani school pupil and education activist from the town of Mingora in the Swat District of Pakistan's Khyber Pakhtunkhwa province, and the youngest nominee for the Nobel Peace Prize in history.
She is known for her education and women's rights activism in the Swat Valley, where the Taliban had at times banned girls from attending school. In early 2009, at the age of 11/12, Yousafzai wrote a blog under a pseudonym for the BBC detailing her life under Taliban rule, their attempts to take control of the valley, and her views on promoting education for girls. The following summer, a New York Times documentary was filmed about her life as the Pakistani military intervened in the region, culminating in the Second Battle of Swat. Yousafzai began to rise in prominence, giving interviews in print and on television and taking a position as chairperson of the District Child Assembly Swat. She has since been nominated for the International Children's Peace Prize by Desmond Tutu and the Nobel Peace Prize. She is the winner of Pakistan's first National Youth Peace Prize.
On 9 October 2012, Yousafzai was shot in the head and neck in an assassination attempt by Taliban gunmen while returning home on a school bus. In the days immediately following the attack, she remained unconscious and in critical condition, but later her condition improved enough for her to be sent to a hospital in the United Kingdom for intensive rehabilitation. On 12 October, a group of 50 Islamic clerics in Pakistan issued a fatwā against those who tried to kill her, but the Taliban reiterated its intent to kill Yousafzai and her father, Ziauddin. Former British Prime Minister and current U.N. Special Envoy for Global Education Gordon Brown launched a United Nations petition in Yousafzai's name, using the slogan "I am Malala" and demanding that all children worldwide be in school by the end of 2015. Brown said he would hand the petition to Pakistan's President Asif Ali Zardari in November. U.N. Secretary-General Ban Ki-Moon has announced that 10 November will be celebrated as Malala Day. In the April 29th issue of Time magazine, Malala was featured as one of "The 100 Most Influential People In The World". Her picture was featured on the front cover of the magazine and was listed in the Icon section. Malala's section was written by former first daughter of the USA, Chelsea Clinton.
Courtesy: Wiki
Friday, July 5
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