৪০ দিনে ৪৭তম বিসিএস প্রস্তুতি - Archived

“Novum Organum” was written by Francis bacon.
Source:https://www.britannica.com/topic/Novum-Organum

Christopher Marlowe, (baptized Feb. 26, 1564, Canterbury, Kent, Eng.—died May 30, 1593, Deptford, near London), Elizabethan poet and Shakespeare’s most important predecessor in English drama, who is noted especially for his establishment of dramatic blank verse.
Source: https://www.britannica.com/biography/Christopher-Marlowe

Utopia (or Kingdom of Nowhere) is a famous book of Thomas More. The book was originally written in Latin in 1516.
Source: An ABC of English Literature - Dr M Mofizar Rahman

The later, or “new,” Arcadia is an epic novel whose theoretical concerns include the dualities of contemplation and action, reason and passion, and theory and practice.
https://www.britannica.com/topic/Arcadia-by-Sidney

Jacobean age, (from Latin Jacobus, “James”), period of visual and literary arts during the reign of James I of England (1603–25). The distinctions between the early Jacobean and the preceding Elizabethan styles are subtle ones, often merely a question of degree, for although the dynasty changed, there was no distinct stylistic transition.
https://www.britannica.com/art/Jacobean-age

The Rape of the Lock, mock-epic poem in heroic couplets by Alexander Pope. The first version, published in 1712, consisted of two cantos; the final version, published in 1714, was expanded to five cantos. Alexander Pope, (born May 21, 1688, London, England—died May 30, 1744, Twickenham, near London), poet and satirist of the English Augustan period, best known for his poems An Essay on Criticism (1711), The Rape of the Lock (1712–14), The Dunciad (1728), and An Essay on Man (1733–34). He is one of the most epigrammatic of all English authors.
Source: britannica.com

The Definition of Love BY ANDREW MARVEL
My love is of a birth as rare
As ’tis for object strange and high;
It was begotten by Despair
Upon Impossibility.
Magnanimous Despair alone
Could show me so divine a thing
Where feeble Hope could ne’er have flown,
But vainly flapp’d its tinsel wing
Source: https://www.poetryfoundation.org/poems/44679/the-definition-of-love

Comedy of humours, a dramatic genre most closely associated with the English playwright Ben Jonson from the late 16th century. The term derives from the Latin humor (more properly umor), meaning “liquid,” and its use in the medieval and Renaissance medical theory that the human body held a balance of four liquids, or humours: blood, phlegm, yellow bile (choler), and black bile (melancholy). When properly balanced, these humours were thought to give the individual a healthy mind in a healthy body.
ENCYCLOPÆDIA BRITANNICA

To Daffodils
by Robert Herrick
Fair Daffodils, we weep to see
You haste away so soon;
As yet the early-rising sun
Has not attain’d his noon.
Themes:
-The short-lived nature of life, the fleeting passage of time.
-Like the flowers we humans have a very short life in this world.
-Beauty is not going to stay forever.
Message:
Life is short, and world is beautiful, love is splendid and we must use the short time we live to make the most of it. This is shown in the words “haste”, “run”, “short” and “quick”
https://karinacognomen.com/2009/11/14/short-analysis-of-robert-herricks-to-daffodils/

১২ তম পদ
= ‍a+(12-1)d = 77
a+11d = 77
প্রথম ২৩টি পদের সমষ্টি
S = n/2{2a+(n-1)d}
= 23/2{2a+(23-1)d}
= 23/2{2a+22d}
= 23(a+11d)
= 23 x 77
= 1771

³√5 . ³√5
= 5^1/3 . 5^1/3
= 5(^1/3 + ^1/3)
= 5^2/3
= ³√5²
= 3√25

log_x 1/16 = -2
বা, x^-2 = 1/16
বা, 1/x² = 1/16
বা, x² = 16
বা, x =√16
বা, x = 4

2^x+2^1-x =3
⇒ 2^x+2/2^x =3
⇒(2^x.2^x+2)/2^x =3
⇒(a²+2)/a = 3 [2^x = a ধরে]
⇒ a²-3a+2=0
⇒(a-2)(a-1) =0
⇒a=2
⇒2^x=2
∴x=1
আবার, a=1
2^x=2⁰
∴x=0
x =(0,1)

আমরা জানি, n তম পদ = a + (n - 1)d
প্রশ্নমতে, 52 = a + (6 - 1)×10
বা, a = 52 - 50 = 2
সুতরাং 15 তম পদ
= a + (n - 1)d
= 2 + (15 - 1)×10
= 142

ধরি, a^x = b
বা, log a^x = logb
বা, xloga = logb
বা, x = logb/loga
অনুরূপভাবে, y = logc/logb এবং z = loga/logc
তাহলে, xyz = logb/loga. logc/logb. loga/logc
xyz = 1
a^xyz = a¹

4^x+1 = 32^x-2 
⇒2^2(x+1) = 2^5(x-2) 
⇒2x + 2 = 5x -10
⇒ 3x = 12
∴x=4

প্রথম পদ a = 1
n তম পদ = 99
s_n=2500
আমরা জানি, a + (n-1)d = 99 (n-1)d = 98 ..........(1)
আবার, s_n = n/2{2a + (n-1)d}
2500 = n/2(2+98)
n = 50
d = 2

√(2ⁿ) = 64
⇒ 2ⁿ = 64²
⇒ 2ⁿ = 2¹²
∴ n = 12

log₅5√5
= log₅(5.5^1/2)
= log₅5^3/2 
= 3/2 log₅5
= 3/2 .1
= 3/2

3^x + 3^x + 3^x
= 3^x(1+1+1)
= 3^x.3
= 3^x+1

{(a^-1)^-1}^-1
= {(1/a)^-1}^-1
= a^-1
= 1/a

প্রথম পদ a এবং সাধারণ অনুপাত r হলে
n তম পদ = arⁿ⁻¹
∴ তৃতীয় পদ ar³⁻¹ = ar² = 20 ------- (i)
∴ ষষ্ঠ পদ ar⁶⁻¹ = ar⁵ = 160 ------- (ii)
এখন, (ii) ÷ (i) ⇒ r³ = 8
⇒ r³ = 2³
∴ r = 2 r এর মান (i) নং এ বসিয়ে পাই প্রথম পদ-
a.2² = 20
∴ a = 5

(a^-1 + b^-1)^-1
= (1/a + 1/b)^-1
= {(a+b) / ab}^-1
= ab / (a+b)

a ≠ 0 হলেই শুধুমাত্র a⁰ = 1 হয়।

3log2 + log5 = log2³ + log5 = log(2³ × 5) = log40

c^z = a ⇒ (b^y)^z = a
⇒ (a^x)^yz = a
⇒ a^xyz = a
∴ xyz = 1.

X^(x√x) = (X√X)^x
X^(x√x) = (X¹X^1/2)x
X^(x√x) = (X^3/2)x
((X^x)^√x) = (X^x)^3/2
√x = 3/2
X = (3/2)²
X = 9/4

প্রশ্নমতে,
log_a400 = 4
a4 = 400
a² = 20
a = 2√5

ধরি, ধারাটির n তম পদ 383
এখানে a = 5, d = 8 - 5 = 3
আমরা জানি, ধারাটির n তম পদ = a + (n - 1)d
বা, 383 = 5 + (n - 1)×3
∴ n = 127

দেওয়া আছে,
m তম পদ = n
বা, a + (m - 1)d = n ............ (1)
এবং n তম পদ = m
বা, a + (n - 1)d = m ;............ (2)
(2) - (1) থেকে পাই,
d(n - 1 - m + 1) = m - n
বা, d(n - m) = -(n - m)
∴ d = -1 ∴
ধারাটির (m + n) তম পদ
= a + (m + n - 1)d
= a + (m - 1)d + nd
= n + n(-1)
= n - n
= 0

a^x=y
বা, log_aa^x = log_ay
বা, xlog_aa = log_ay
সুতরাং, x= log_ay 

এখানে, a=2, d=4-2 =6-4=2
n তম পদ = a+(n-1)d
= 2+(n-1)2
= 2+2n-2
= 2n
সুতরাং, d:n = 2:2n

{n(n+1)/2}² 
= {6(6+1)/2}²
=(6.7/2)²
= (21)² 
= 441

১ থেকে ১০০ পর্যন্ত সংখ্যাগুলোর ই যোগফল,
১০০×(১০০+১)/২ = ১০০×১০১/২ = ৫০×১০০
= ৫০৫০

সাধারণভাবে হিসাব করলেই সহজে উত্তর পাওয়া যাবে।
5×3=15
15×3=45  

Daniel Defoe published Robinson Crusoe on April 25, 1719. An interesting fact is that the original title was 374 characters long: The Life and Strange Surprizing Adventures of Robinson Crusoe, Of York, Mariner: Who lived Eight and Twenty Years, all alone in an un-inhabited Island on the Coast of America, near the Mouth of the Great River of Oroonoque; Having been cast on Shore by Shipwreck, wherein all the Men perished but himself. With An Account how he was at last as strangely deliver'd by Pyrates.
https://americanliterature.com/author/daniel-defoe/book/robinson-crusoe/summary

Paradise Lost is an epic poem in blank verse by the 17th-century English poet John Milton.
The poem concerns the biblical story of the Fall of Man: the temptation of Adam and Eve by the fallen angel Satan and their expulsion from the Garden of Eden.
Milton's purpose, as stated in Book I, is to "justify the ways of God to men

Delight in Disorder
BY ROBERT HERRICK
A sweet disorder in the dress
Kindles in clothes a wantonness;
A lawn about the shoulders thrown
Into a fine distraction;

Piers Plowman, in full The Vision of Piers Plowman, Middle English alliterative poem presumed to have been written by William Langland. Three versions of Piers Plowman are extant: A, the poem’s short early form, dating from the 1360s; B, a major revision and extension of A made in the late 1370s; and C, a less “literary” version of B dating from the 1380s and apparently intended to focus the work’s doctrinal issues. Some scholars think that version C may not be entirely attributable to Langland.
Source: https://www.britannica.com/topic/Piers-Plowman

Famous plays of Fielding: Rape Upon Rape, The Modern Husband, The Temple Beau, The Tragedy of Tragedies etc. Henry Fielding is the 'Father of Modern English Novel'. He is famous for Picaresque Novel. His pen name is Captain Hercules Vinegar. His Novels are Tom Jones, Amelia, Joseph Andrews.
Source: Live MCQ lecture and Britannica.

George Farquhar:
- The recruiting officer
- The Beaux's Stratagem

Shakespeare who had started writing in the Elizabethan Period wrote twelve serious plays in Jacobean period. Those plays are:
1. Measure for Measure (1604)
2. Othello (1604)
3. Macbeth (1605)
4. King Lear (1605)
5. Antony and Cleopatra (1606)
6. Coriolanus (1606)
7 Timon of Athens (unfinished-1608)
8. Pericles (in part-1608)
9. Cymbeline (1609)
10. The Winter's Tale
11. The Tempest (1611)
12. Henry VIII (in part-1613)
(Dr M Mofizur Rahman)

Nicholas Udall wrote the first English Comedy named Ralph Roister Doister.
(Dr M Mofizur Rahman)