Scholarship examinations of 1846/47 (-1853/54). |
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Page 16
... . ( 1. ) Shew that the equation whose roots are cos - la Cos COS , 3 2+ cos - ' a COS- 2π -1a COS 3 is x3 3 x 3 a 0 . 4 ( 2. ) An equation must have an even number 16 SCHOLARSHIP QUESTIONS . Theory of Equations and Conic Sections,
... . ( 1. ) Shew that the equation whose roots are cos - la Cos COS , 3 2+ cos - ' a COS- 2π -1a COS 3 is x3 3 x 3 a 0 . 4 ( 2. ) An equation must have an even number 16 SCHOLARSHIP QUESTIONS . Theory of Equations and Conic Sections,
Page 17
... roots , or How far is this true of irrational possible roots ? Having given none . one root of the equation x4 the equation . ― 6x2 - 48x110 is 2 + 5 solve ( 3. ) If f ( x ) be a rational and integral function of x ; Explain the ...
... roots , or How far is this true of irrational possible roots ? Having given none . one root of the equation x4 the equation . ― 6x2 - 48x110 is 2 + 5 solve ( 3. ) If f ( x ) be a rational and integral function of x ; Explain the ...
Page 18
... root of a binomial surd , one of whose terms is a rational quantity , and the other a quadratic surd . -4-10√2 Ex . ( 9. ) Solve the equations a3 + x3 a3 + a + x a = 4 ( x2 + 1 ) ( x + 2 ) = 2 m 218 218 + + n y = α m = b y : .. ( 1 ) ...
... root of a binomial surd , one of whose terms is a rational quantity , and the other a quadratic surd . -4-10√2 Ex . ( 9. ) Solve the equations a3 + x3 a3 + a + x a = 4 ( x2 + 1 ) ( x + 2 ) = 2 m 218 218 + + n y = α m = b y : .. ( 1 ) ...
Page 22
... roots . can the equation an 2 - ax2 + b = o have . wanting in an equation , it How many possible roots ( 3. ) Give Cardan's method for the solution of a cubic equation . Shew that it fails when all the roots are real , and succeeds when ...
... roots . can the equation an 2 - ax2 + b = o have . wanting in an equation , it How many possible roots ( 3. ) Give Cardan's method for the solution of a cubic equation . Shew that it fails when all the roots are real , and succeeds when ...
Page 64
... would take " such deep root therein " that they would form a portion of the mind itself . Milton and Shakespeare and Bacon would furnish us with 66 thoughts that " reach beyond eternity " and " sentiments 64 ENGLISH ESSAY .
... would take " such deep root therein " that they would form a portion of the mind itself . Milton and Shakespeare and Bacon would furnish us with 66 thoughts that " reach beyond eternity " and " sentiments 64 ENGLISH ESSAY .
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Afternoon Paper alluded Answer Aristotle axis Bacon battle of Actium Bengali body cause centre character Charles CONIC SECTIONS curve Describe DWARKA effect electric telegraph ellipse England English equation Essay Europe examination Explain expression force FOURTH CLASS France Give given Hindu College History Hooghly human hyperbola Italy Junior Scholarships king language latus rectum laws Literature Proper Macbeth Mathematics maxima and minima means mind Mixed Mathematics MOHENDRO LAUL SHOME moral Morning Paper nations nature Novum Organum object parabola parliament passage perpendicular philosophy plane poet poetry principles prose prove Question.-The reason reign rents right angles Roman roots says SECOND CLASS senary Senior Shakspeare Shew Spain straight line tangent things THIRD CLASS thou tion triangle truth velocity verse vertex words اور এই এবং করিয়া করিলেন দ্বারা পদার্থ বিদ্যার যে সমস্ত হইয়া হইয়াছে
Popular passages
Page 17 - He was a scholar, and a ripe and good one; Exceeding wise, fair spoken, and persuading : Lofty, and sour, to them that lov'd him not ; But, to those men that sought him, sweet as summer. And though he were unsatisfied in getting, (Which was a sin,) yet in bestowing, madam, He was most princely : Ever witness for him Those twins of learning, that he rais'd in you, Ipswich, and Oxford ! one of which fell with him. Unwilling to outlive the good that did it ; The other, though unfinish'd, yet so famous,...
Page 9 - Ye elves of hills, brooks, standing lakes and groves, And ye that on the sands with printless foot Do chase the ebbing Neptune and do fly him When he comes back ; you demi-puppets that By moonshine do the green sour ringlets make, Whereof the ewe not bites...
Page 8 - gainst that season comes Wherein our Saviour's birth is celebrated, The bird of dawning singeth all night long...
Page 7 - It is too full o' the milk of human kindness To catch the nearest way : thou wouldst be great; Art not without ambition — but without The illness should attend it : what thou wouldst highly That wouldst thou holily : wouldst not play false, And yet wouldst wrongly win : Thou 'dst have, great Glamis, That which cries, " Thus thou must do, if thou have it;" And that which rather thou dost fear to do Than wishest should be undone.
Page 13 - Muse, The place of fame and elegy supply: And many a holy text around she strews, That teach the rustic moralist to die. For who to dumb Forgetfulness a prey, This pleasing anxious being e'er resigned, Left the warm precincts of the cheerful day, Nor cast one longing lingering look behind?
Page 10 - He sought the storms; but, for a calm unfit, Would steer too nigh the sands, to boast his wit. Great wits are sure to madness near allied, And thin partitions do their bounds divide; Else, why should he, with wealth and honour blest, Refuse his age the needful hours of rest?
Page 28 - That to the observer doth thy history Fully unfold. Thyself and thy belongings Are not thine own so proper, as to waste Thyself upon thy virtues, they on thee. Heaven doth with us as we with torches do, Not light them for themselves ; for if our virtues Did not go forth of us, 'twere all alike As if we had them not.
Page 66 - Our revels now are ended... These our actors, As I foretold you, were all spirits, and Are melted into air, into thin air, And, like the baseless fabric of this vision, The cloud-capped towers, the gorgeous palaces, The solemn temples, the great globe itself, Yea, all which it inherit, shall dissolve, And, like this insubstantial pageant faded, Leave not a rack behind: we are such stuff As dreams are made on; and our little life Is rounded with a sleep..
Page 46 - My sentence is for open war: of wiles More unexpert, I boast not; them let those Contrive who need, or when they need, not now.
Page 8 - tis done, then 'twere well It were done quickly: if the assassination Could trammel up the consequence, and catch, With his surcease, success ; that but this blow Might be the be-all and the end-all here, 5 But here, upon this bank and shoal of time, We'd jump the life to come.