Selected And compiled Problems (W.B.J.E.E.) on Geometrical Progression

     Selected And compiled Problems (W.B.J.E.E.) on Geometrical Progression – © Anuran Chowdhury , 8.9.2011                                                

Problem 1|| log10 2, log₁₀ (2^x-1) and log₁₀ (2^x+3) are in Arithmetic Progression; then what is the value of x?

(a)   log₂ 5 (b) log ₅ 2 (c) 1 (d) 0

Solution: (a) is correct

As they are in AP .^. . log₁₀ (2^x-1)-log₁₀ 2 = log₁₀ (2^x+3)-log₁₀(2^x-1)

                                or; 2log₁₀(2^x-1)=log₁₀ 2+log₁₀ (2^x+3)

Therefore, (2^x-1)2 = 2(2^x+3)

     Or, 2^2x -2.2^x + 1 = 2.2^x +6

     Or, 2^2x-4.2^x -5 =0

     Or, (2^x-5)(2^x+1)=0

     Or, 2^x=5 or 2^x=-1 (Not Possible)

     Or, x= log₂ 5

Problem 2|| Find the sum to n terms of the series 11+102+1003+10004+…T_n

Solution : 11+102+1003+10004+…T_n

               =(10+1)+(100+2)+(1000+3)+(10000+4)+….n terms

              = (10+100+1000+10000+…n terms)+(1+2+3+4+… n terms)

              = 10(10ⁿ-1)  + n(n+1)

9                              2

 Problem 3 || Find the sum of 1+4+13+40+ … n terms

Solution : S_n = 1+ 4 + 13 + 40 + ……… T_{n  ……………(i)}

                         S_n =       1 + 4   + 13 + ………. T_{n-1 + Tn …………(ii)}

(i)-(ii) => 0= 1+3+9+… n terms - T_n

                 _or, T_n = 1(3ⁿ-1)

                            2

Put n=1,2,3 and then add respectively-

1(3-1)  +  1(3²-1)  +  1(3³-1)  +……1(3ⁿ-1)

     2              2                 2                      2

=1 {(3+3²+3³+3⁴+….3ⁿ)-(1+1+1….n)}

  2

= 3(3ⁿ   -1 ) -n

         4          2 

raga khat

Khat is a raga which is sang generally in agra-atrauli-jaipur gharana axis.But is now Ustad Bade Ghulam ali khan
Raga-Khat (A.I.R. program)

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Ustad Sharafat Hussain Khan-from our archives

Sharafat Hussain Khan was amongst the most brilliant Khayal vocalists of the post - independence era. He represented the Agra Gharana (stylistic lineage) and was unanimously regarded as the most illustrious heir to the legacy of his principal mentor, the legendary Ustad Faiyyaz Khan (1886 - 1950). Sharafat Hussain Khan was born in July 1930,  to Ustad Liaquat Hussain Khan, a court musician in the erstwhile Jaipur State, and Alla Rakhi Beghum. From his father`s side, Sharafat was a descendant of

Inayet Hussain Khan (1845 - 1936), founder of  Atrauli Gharana, and from his mother`s side, of his maternal grandfather Mehboob Khan (Daras Piya). Mehboob Khan was also of the Atrauli Gharana, but his music was greatly influenced by the Rangile Gharana of his mother`s family, founded by Ramzan Khan (1759 - 1806). In early childhood, Sharafat was trained by his father. When Sharafat was only eight years old, his prodigious talent impressed the legendary Faiyyaz Khan during one of his visits to Atrauli. The maestro, who had no sons, adopted Sharafat, and took him away forthwith to Baroda to groom him as his heir.

Sharafat was a child prodigy, who rose meteorically after his adoption by Faiyyaz Khan. As a result of incessant riyaz, Sharafat Hussain gained a deep insight into music and his voice gained a rich timber. During this time he used to accompany Ustad Faiyaz Khan on the Tanpura in many concerts and gained valuable experience in gauging the pulse of the listeners and creating the right atmosphere towards the commencement of a Mehfil. At the age of eight, he made a stunning debut at the influential Matunga Music Circle in Mumbai. This triggered off invitations to perform at the All India Music Conference at Allahabad and the All Bengal Conference in Kolkata. When he was eleven, he was hailed as the `Rising Sun` of vocalism at the Gaya Conference. By the time he was twelve, he had made his first disc with HMV/ EMI, and topped the prestigious Baroda State Music Competition.

Sharafat was only 20, when Faiyyaz Khan died. Thereafter, he started studying with his maternal uncle, Ustad Ata Hussain Khan of the allied Atrauli - Rangile lineage. Soon thereafter, he acquired a third guide - his scholarly father - in - law, Vilayat Hussain Khan of the Agra Lineage. Thus, like his foster - father, Sharafat Hussain came to represent a magnificent confluence of three intimately connected lineages - Agra, Atrauli, and Rangile.

While still in his 30s, Sharafat became amongst the busiest vocalists in India, and enjoyed a continuous run of success for two decades (1965 - 1985). Along with popularity came the honours. He was made an Honorary Fellow of the Performing Arts Academy of Uttar Pradesh (Northern Provinces) and decorated with the Padma Shri by the President of India. He also got a Tansen Award.

During the latter years of his life, Sharafat Hussain settled down in Atrauli. He preferred its quiet atmosphere and the surrounding countryside to the glamour of the big cities. There are some artists who receive appreciation and monetary gain in abundance and there are others whose merits have never been fully recognized. Sharafat Hussain belonged to the latter category.

In 1985, Sangeet Natak Akademi held a special ceremony to honour him shortly before he succumbed to lung cancer on July 7, 1985, at the age of 55.

We present you raga shuddh kalyan by Ustad sharafat hussain khan.

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Ustad Faiyyaz Khan-life of a maestro

Ustad Faiyyaz Khan "Aftab-E-Mousiqi" (1887-1950)
 Ustad Faiyaz Khan is still remembered as the ‘Mehfil ka Badshah’ by those who have been fortunate enough to hear him live, as well as those who have at least heard his recordings. On the dais he was the symbol of a dignified personality, always clad in a silk sherwani, his chest blazing with rows of sparkling gold medals and chains, and complete with an immaculate pugree. Flanked by his disciples on both sides, together with the sarangi and tabla players, he sang with a deep, masculine, jawaridar voice, all in keeping with his grand stage presence. Among the many titles and awards that he received, just the Aftab-e-Mausiqi alone testifies to the musical phenomenon that he was, and the magical and musical spell he cast over his audience whenever he performed.

Faiyaz Khan was born in 1886 at Sikandra in Agra. He belonged to a family of great musicians, going back to Haji Sujaan Khan in the court of Emperor Akbar. He was groomed mainly by his grandfather, Ghulam Abbas Khan, and granduncle, Kallan Khan. Both were very eminent singers of the Agra gharana. In his formative years, Faiyaz Khan was also deeply influenced by Zohra Bai and other contemporary ustads. Later he became the son-in-law of the great musician and composer ‘Daraspiya’ Ustad Mehboob Khan. Faiyaz Khan blended the styles of his different gurus giving the Agra gayaki a new direction. He also included many thumris, dadras, ghazals and qawalis in his repertoire.

Ustad Faiyaz Khan would render a full scale ‘Nom-Tom’ alap and follow it up with khayal compositions, thus blending dhrupad and khayal and giving his gayaki more flexibility. His bol-banawo, bant, layakari, and his inimitable style of reaching the sam are unmatched even today. He was a great composer himself, his pen name being #145;Prempiya’. His compositions in raga Jaijaiwanti, Jog etc. are treasured by Agra singers to this day. In fact, Faiyaz Khan’s Agra gayaki became so famous that most of his students and followers would actually copy him to the very last detail, imitating even his voice.

Faiyaz Khan was a reformist among traditionalists and a traditionalist among reformists, and his gayaki is still an example of the evolution of Hindustani classical music from dhrupad to khayal, thumri, dadra and ghazal. He was an architect in music with the feeling of a poet.

He was appointed court singer at Baroda in 1912. However, Faiyaz Khan also performed in various other darbars, festivals and conferences. He taught many students like Ata Hussain Khan (his brother-in-law), Latafat Hussain Khan, K. L. Saigal, Dipali Nag, Dilip Chandra Vedi, D. T. Joshi, S. N. Ratanjhankar, Swami Ballabhdas, Ramrao Naik, R. N. Chatterjee and Sharafat Hussain Khan among others.

In his last years, he suffered from tuberculosis. His demise, in November 1950, marked the end of a great era in Hindustani Classical Music.

  We present you recording in bhoop by Faiyyaz Khan sahib from our archives.

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Ustad azmat hussain khan-from our archives

Ustad Azmat Hussain Khan(1911-1975)

This year i.e.,2011 will be the birth centenary of Ustad azmat hussain khan.
We present you a recording in raga darbari sung at panjim kala academy,1970's.Ustad Azmat Hussain Khan belonged to the very prestigious families of traditional vocalists of Atrauli (said to be Jaipur) Gharana, Khurja Gharana and the Agra Gharana, which has given India such giants as Haji Ustad Altaf Hussain Khan, Ustad Allahdiya Khan, Ustad Vilayat Hussain Khan, Ustad Fayyaz Khan, Ustad Tanras Khan and many others. Like all truly great masters he contributed to and enriched his great musical heritage. Under the pen - name of Dilrang he composed more than 150 Bandishes in various Ragas such as Todi, Shree, Marwa, Puriya Dhanshri, Malkauns Kedara, Malsri, Devgiri - Bilwal, Bairagi, Bilhagda, Bhoopali, Hindoli "Chandrajog", "Devta Bhairon" (the last two are his own creations). His compositions stand out for their lyrics and beauty of form. Khan Sahab had been acknowledged as the greatest exponent of Khurja, Atrauli (Jaipur) Gharana, after Ustad Allahdiya Khan and Haji Ustad Altaf Hussain Khan. Ustad Azmat Hussain Khan, died in Bombay on 26th July 1975, after a brief illness. A great musician and a scholar, a good man and a poet, who left his mark, leaving behind a trail of disciples, friends, admirers and well wishers. The word "AZMAT" means 'greatness' in Urdu and that is how Ustad Azmat Hussain Khan, struck all those who came in touch with him.

Click to download-vilambit khayal
Click to download-drut khayal

Ustad Bade Ghulam Ali khan-from our archives

Ustad Bade Ghulam Ali khan(1902-1968)

Raga-gavati
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Raga-chayanat (calcutta,1954)
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Ustad Vilayat Hussain Khan-From our archives

Ustad Vilayat Hussain Khan(1895-1962)

Ustad Vilayat Hussain Khan Sahab was a musician who was his own example born in centuries. Agra Gharana has flowered through musicians of his caliber and Khan Sahabcarried on this tradition with great enthusiasm. Khan Sahab dedicated his life for the wide dissemination of classical music as an outstanding performer, great composer and greatest teacher. According to Dr. B. Gopal Reddy (then Union Minister of I. & B.) Khan Sahab was the non assuming reservoir, from which great many rivulets in the form of innumerable disciples flowed over the country. He wanted the rivulets to flow Perpetually both Historically and musically, Ustad Vilayat Hussain Khan, was a bridge between the last phase of the "Darbar music and the modern period. He brought Sangeet Vidya (the science of music), authentic "gayaki" and a treasure of ragas and compositions, in its purest form. Whatever he imparted from old masters, conversed it to the new generation disciples and also other needy contemporaries. Thus, his contribution to the advancement of music in the present century is monumental.

Khan Sahab inherited, imbibed and developed a Style which was both individualistic and representative of Agra Gharana. While assimilating the majority and the clear out rhythmic patterns of Dhrupad style of "Nohar Bani", he brought an easy flow KhayalSinging. This spontaneity marked by well-defined rhythmic movements and appropriate flourishes, with which he could make each word, syllable and letter of the composition dance brought a rare alliance and charm to the gayaki of this tradition, which is perhaps unrivalled. Written by Ustad Vilayat Hussain Khan and published by Sangeet Natak Academy "Sangeetagyon Ke Sansmaran" is very important book.There are a lot of recordings of him recorded at A.I.R. and many live concerts in which he sang rare ragas for the listeners.

We Present you his recorded raga gara-kanada from A.I.R. 1960's

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