Education Is The Key To SuccessSSC Part 1 and 2

Friday 21 October 2022

Unit.3 -Practicing Positive Work Ethics - King Bruce And The Spider (Poem) - Reading Comprehension- Words/Meaning, About Poet, Central Idea and Summary

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Unit-3 - Practicing Positive Work Ethics
Reading Comprehension
King Bruce And The Spider (Poem)
English For Class X (2022 and Onward

Words/Meaning

S.NO.	Words	Meanings
1.	Braced his mind	Determined, Decided
2.	Bravo	Well done
3.	Clue	A thread (according to the poem)
4.	Ceiling	Lower roof
5.	Cobweb	Fine network of single thread made by a spider, Spider's home
6.	Crown	King's head-wear
7.	Deed	Action
8.	Delicate thread	Of fine texture
9.	Despair	Disappointment, Hopelessness
10.	In a low despair	Downhearted, Discourage
11.	To divine	Of God, Workout an answer
12.	Dizzy	Giddy, Having a feeling that everything is turning round
13.	Dome	Rounded roof
14.	Down in came with the slippery sprawl	Came slipping down along the wall and hung in an awkward position
15.	Endeavour	An attempt
16.	Entirely	Completely
17.	Fine	Delicate
18.	To fling oneself down	To throw oneself violently on a bed or on the floor, Fall down.
19.	Glad	Happy
20.	Grieved	Sad
21.	Gossips tell the tale	People talk about it
22.	Head grew steady	Came to its senses, gained balanced (according to poem)
23.	The last pinch	The last little bit of distance
24.	Lonely	Alone
25.	Monarch	King
26.	To mount	To Climb, Ascend
27.	Native cot	His own home, (In this poem) the spider's web
28.	Ponder	Think
29.	Pondered	Thought
30.	Sink	Go into water
31.	To strive	To struggle, to try hard
32.	Utter	To speak
33.	To toil	To work hard, Labour
34.	Tread	To walk
35.	To tumble	To fall over
36.	Utter	Say
37.	Verses	Poems
38.	Wear	To put on
39.	Wretched	Sad

About Poetess
Eliza Cook (1818-1889)

This poem is written by Eliza Cook (1818-1889). Born in London she was the youngest of eleven children. She was entirely self-educated and wrote verses from the age of fourteen. Her first volume being published at seventeen. In 1849, she edited and published "Eliza Cook's Journal." Her work is simple and highly moral. In this poem, she teaches the reader what she always practiced in her own life: to keep on trying and never to be discouraged.

Central Idea

Reference
This poem is written by Eliza cook (1818-1889).
Central Idea
If a man fails in his struggle, he should not lose his hope. He should try again and again till he succeed.

The central idea of this poem is that we should cultivate a strong will – power and a hopeful attitude to life, be bold through thick and thin.

Those who go on trying for their goal, they succeed in life. One should never lose hope, efforts never go waste.

Theme

“Where there is a will, there is a way.”
OR
“The world is his who has patients and industry.”

Summary

The poem King Bruce and the Spider is written by Eliza Cook. It tells us how to rise again after after defeat and achieve success in our life. King Bruce,though a king, was beginning to lose hope, and became disappointed after defeated from his enemies. He had tried many times and do everything to make his people happy but he couldn't succeed. He was hopeless and also very upset. After deep thinking he decided that he would give up.
Just then,a spider dropped down with its fine silky thread, the king stopped thinking in the middle and looked at it to see what it would do. Spider was very far from its cobweb and was hanging by a rope. The king could not work out how it would reach its home.It began to go up with strong endeavour but soon slipped down and became close to the ground as it was before.
It did not stop even a second for complaint and ran up again, but due to weakness it fell still lower than ever. Once it felt better it travelled higher and that time it covered a half yard higher. Its rope was delicate and the journey was tiring. It tried again and again, went up sometimes slowly and sometimes fast, but every time it slipped down and in this way it made nine brave attempts.
The king thought that it was her foolish attempt, falling again and again after struggle. The spider would now give up and not try anymore. But the spider went up again and this time it was just one foot away from its home, this was an anxious moment and it made king hopeful if the spider would lose or win. It kept moving up inch by inch, At last it ran boldly and thus succeeded in reaching its home.
The king cried out with pleasure and realized that those who try, succeed; like the spider did. He also could succeed, if he tried. Than the king changed his mind and tried again and succeeded.
The moral of the story is that after watching the struggle of a spider, King Bruce thought that this spider made so many attempted to reached at her home and failed but it did not lose hope and succeed in last. King Bruce got motivation from the spider and tried again with the hope that he would not give up till he would achieved success and he succeeded.

King Bruce learns from a spider the lesson of success. He wanted to do a great deed for his people. However, he failed each time. He had given up all hope. He saw a spider that made nine attempts to reach its home. It was not successful in its nine attempts. King Bruce thought that it would give up its attempts. The spider made one further attempt and this time it succeeded. King Bruce also decided to try again and succeeded in his mission.

The poetess has expressed the true sense of life in this poem. Solution to the problems of life and key to the success are being preached in this poem in a dramatic style. This poem tells the story of the king Bruce of Scotland. Once he was defeated by the English men. He took refuge in a cave. Due to his repeated failures, he was very grieve.
King Bruce mentally accepted his defeat from the English men. One day, he was pondering at the point of his defeat, he watched a spider who was trying to reach to her cobweb. Thread was the only pathway for the spider to reach her destination. Spider started her voyage with great anxiety and force. But the spider come down to the initial stage where it had started her journey. King Bruce was showing security on the foolish attempts to reach the destination that spider will not try again.
However the spider succeeded in the 10th attempt to reach its cobweb. After the success to spider the King Bruce sounded in a optimistic order. “All honour to those who tries persistently.” King Bruce resolute in heart to try once more in order to get the win over on his enemies.” At last he succeeded.

Poetry With Urdu Translation
King Bruce and the Spider

King Bruce of Scotland flung himself down
In a lonely mood to think,
Tis true he was monarch and wore a crown
But his heart was beginning to sink.

کنگ بروس اور مکڑی

سکاٹ لینڈ کے بادشاہ بروس نے خود کو جھکا لیا۔
تنہائی کی حالت میں غور و فکر کے لۓ
، یہ سچ ہے کہ وہ بادشاہ تھا اور اس نے تاج پہنا تھا۔
لیکن اس کا دل ڈوبا جا رہا تھا۔

For he had been trying to do a great deed,
To make his people glad;
He had tired and tried, but couldn’t succeed,
So became quite sad.

کیونکہ وہ ایک عظیم کام کرنے کی کوشش کر رہا تھا
، اپنے لوگوں (قوم) کو خوش کرنے کے لیے۔
اس نے بار بار کر کوشش کی لیکن کامیاب نہ ہو سکا
اس لۓ وہ بالکل غمگین تھا۔

He flung himself down in a low despair,
As grieved as man could be,
And after a while, as he pondered there
“I’ll give it all up” said he.

اس نے مایوسی کے عالم میں اپنے آپ کو جھکا لیا
، وہ اتنا افسردہ تھا جتنا کہ کوئی ہو سکتا ہے
، اور تھوڑی دیر کے بعد جیسے وہ وہاں سوچ رہا تھا۔
"میں یہ سب چھوڑ دوں گا" اس نے کہا۔

Now just at the moment a spider dropped,
With it’s silken filmy clue,
And the king in the midst of his thinking stopped.
To see what the spider would do.

ابھی اسی لمحے مکڑی گر گئی
، اس کے ریشمی جالے کے ساتھ
، اور بادشاہ اپنی سوچ کے دوران رک گیا۔
یہ دیکھنے کے لیے کہ اب مکڑی کیا کرتی ہے۔

Twas a long way up to the ceiling dome,
And it hung by a rope so fine,
That how it would get to its cobweb home
King Bruce could not divine.

چھت کے گنبد تک پہنچنے کے لۓ کافی لمبا راستہ تھا
، اور وہ ایک پتلے دھاگے سے لٹک رہی تھی
، کہ یہ اپنے جالے کے گھر تک کیسے پہنچے گی۔
بادشاہ بروس کچھ نہیں سمجھ سکا۔

It soon began to cling and crawl
Straight up with strong endeavour;
But down it came with a slippery sprawl,
As near to the ground as ever.

اس نے جلد ہی لپیٹنا اور رینگنا شروع کر دیا,
سیدھا اوپر بڑی کوشش کے ساتھ؛
لیکن وہ پھسل کے نیچے گری
، ہمیشہ کی طرح زمین کے قریب۔

Up, up it ran, not a second, could stay,
To utter the least complaint,
Till it fell still lower and there it lay
A little dizzy and faint.

وہ اوپر کی جانب دوڑی، ایک لمحے کے لۓ بھی نہیں رکی
، شکایت کرنے کے لیے
، یہاں تک کہ وہ نیچے گری اور وہیں پڑی رہی۔
تھوڑی بد حواس اور بیہوش۔

Its head grew steady again it went,
And traveled a half yard higher,
Twas a delicate thread it had to tread.
And a road where it feet would tire.

جب وہ ہوش میں آئی تو دوبارہ چل پڑی.
اور آدھا گز اوپر سفر کیا
، یہ ایک نازک دھاگہ تھا جس پر اسے چلنا تھا۔
اور ایک ایسا رستہ تھا جس پر اس کے پاؤں تھک سکتے تھے۔

Again it fell and swung below,
But again it quickly mounted,
Till up and down, now fast, now slow
Nine brave attempts were counted.

وہ پھر گری اور دھاگے سے جھولتی رہی
، لیکن جلد ہی وہ پھر تیزی سے اوپر چڑھنے لگی
، اس طرح اوپر نیچے کبھی تیز کبھی آہستہ
اس کی نو بہادر کوششیں شمار کی گئیں۔

“Sure” cried the King, “that foolish thing
Will strive no more to climb,
When it toils so hard to reach and cling,
And tumbles every time”.

"یقینا" بادشاہ چیخا، "یہ احمقانہ چیز:؛
اوپر چڑھنے کی مزید کوشش نہیں کریں گی,
جبکہ اس نے اوپر پہنچنے اور چمٹنے کی بھر پور کوشش کی ہے,
اور ہر بار ڈگمگا کر گرتی ہے۔"

But up the insect went one more,
Ah me! It is an anxious minute,
He’s only a foot from his cobweb door!
Oh, say will he lose or win it?

لیکن یہ کیڑا اٹھا اور ایک دفعہ پھر چل پڑا,
آہ میرے لۓ یہ ایک لمحہ فکریہ ہے,
اب وہ اپنے جالے کے دروازے سے صرف ایک فٹ کے فاصلے پر تھی,
! اب بولو وہ ہار جاۓ گی یا جیت جاۓ گی؟

Steadily, steadily, inch by inch,
Higher and higher he got,
And a bold little runs at the very last pinch,
Put him into his native cot.

مستقل مزاجی سے، انچ انچ کر کے,
وہ اوپر سے اوپر ہوتی گئی,
اور آخری لمحے میں اس نے بہادرانہ دوڑ لگائی,
اور اپنے گھر یعنی جالے میں چلی گئی۔

“Bravo! Bravo!” the King cried out,
“All honour to those who try!
The spider up there defied despair;
He conquered, and why should not I”?

"شاباش! شاباش!" بادشاہ چلایا،
"جو لوگ کوشش کرتے ہیں، وہ قابل عزت ہیں!
اوپر جو مکڑی ہے، اس نے مایوسی کا مقابلہ کیا۔
وہ فاتح بن گئی، اور میں کیوں نہ (فاتح) نہ بن سکوں گا؟"

And Bruce of Scotland braced his mind,
And gossips tell the tale,
That he tried once more as he tried before,
And that time did not fail.

اسکاٹ لینڈ کے بروس نےپکا ارادہ کر لیا,
اور لوگ داستان بیان کرتے ہیں,
کہ اس نے پہلے کی طرح ایک بار پھر کوشش کی,
اور اس دفعہ وہ ناکام نہیں ہوا۔

Wednesday 19 October 2022

English Vocabulary - Words Start from Letter 'A'

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English Vocabulary
Words Start from Letter 'A'

ABANDON: To give up completely, Cease to support.
Sentence:
*Her natural mother had abandoned her at an early age.
*He had clearly abandoned all preferences of trying to success.
*Abandoned the sinking ship.
Synonyms: Forgo, Forsake, Relinquish.
ABASH: To lose self confidence, To confuse, Put to Shame or ashamed.
Sentence:
* Abashed before the assembled dignitaries.
Synonyms: Disconcert, Discomfit, Discompose, Fluster.
Antonym: (adj.) Self-possessed.
ABDICATE: To give up claim to.
Sentence:
* He abdicated as general manager after six month jobs.
* Harry looked slightly abashed.
* Abdicated the throne.
Synonyms: Abandon, Quit, Renounce, Relinquish, Resign, Retire.
ABET: To encourage, or support.
Sentence:
* Treacherously abetted the enemy.
Synonyms: Assist, Aid, Incite, Spur.
Antonym: Deter.
ABRIDGE: To reduced, To shorten.
Sentence:
*He was asked to abridged his story for TV drama.
*Abridged his lengthy speech.
Synonyms: Curtail (a right or privileged), Diminish, Lessen, Truncate, Retrench.
Antonym: Amplify, Elongate, Protract.
ABROGATE: To abolish or Render, Void.
Sentence:
*A treaty abrogated by mutual consent.
Synonyms: Annul, Cancel, Nullify, Rescind, Void.
ABSTEMIOUS: Moderate in the use of food and drink.
Sentence:
*He is abstemious in his habits.
Synonyms: Temperate.
ACADEMIC:Pertaining to school.
Sentence:
*Theoretical academic interests.
*An academic discussion, with no practical implications
Synonyms: Educational, Scholastic.
ACCEDE: To agree to.
Sentence:
*Accede to a request.
*The authority did not accede to the striker's demand.
Synonym: Accept, Assent.
Antonym: Demur.
ACCELERATE: To quicken, Speed tip.
Sentence:
*Took an accelerated course in order to graduate early.
Synonym: Expedite (adj. Expeditious).
Antonym: Retard.
ACCOLADE: An award or salute.
Sentence:
*A tremendous accolade for a returning hero.
Synonyms: Tribute, Ovation, Title, Privileged, Honour.
ACCORD: Agreement or harmony.
Sentence:
*In full accord with his view.
*Opposition group refused to sign the accord.
Synonyms: Concord, Treaty, concurrence Grant, Award.
Antonyms: Dissension, Discord
ACRIMONIOUS: Sharp or harsh in language or temper.
Sentence:
*stung by the acrimonious remark.
* An acrimonious dispute about wages.
Synonym: Caustic, Acerbic, Pungent, Tart, Mordant, Acrid, (Noun) Asperity.
Antonyms: Suave, Affable.
ACUMEN: keenness of mind or insight.
Sentence:
* Showing exceptional business acumen.
Synonym: Perspicacity, Discernment, Perception, Awareness.
Antonym: Obtuseness.
ADMONISH (Noun: ADMONITION): To warn or find fault gently.
Sentence:
*Admonishing the unruly child.
*She admonish him to play online games not more than one hour.
Synonym: Chide, Caution, Reprimand, Reprehend, Reproach, Archaic.
ADVERSARY (Adj: ADVERSE): An opponent.
Sentence:
*His adversary in a bitter debate.
*David beat his old adversary in the quarter-final.
Synonym: Antagonist.
Antonyms: Confederate, Ally, Accomplice.
ADVERSITY: Misfortune.
Sentence:
*Calm in the face of adversity.
Synonym: Affliction, Mischance, Reverse.
AESTHETIC: Pertaining to the beautiful.
Sentence:
*interested in aesthetic values rather than in purely practical affairs.
*The Nature's painting gives great aesthetic pleasure.
AFFABLE: Sociable, Courageous, and agreeable in manner a much admirable.
Sentence:
*Affable gentlemen.
Synonyms: Civil, Complaisant, Benign,Gracious,Genial, Urbane, Cordial.
Antonyms: Curt, Brusque, Rude, Boorish, Surly.
AFFLUENT: Prosperous, Flourishing, Copious.
Sentence:
*A large bequest from an affluent grandfather.
Synonyms: Opulent, Profuse, wealthy.
Antonyms: Destitute, Impecunious.
AGGRESSIVE (Noun: AGGRESSION): An unprovoked attack, self-assertive, Attacking, Offensive.
Sentence:
*Annoyed people by his aggressive attitude.
Synonyms: Officious, Obtrusive.
Antonyms: Meek, Humble, Retiring, Diffident.
ALACRITY: Eagerness, Cheerful promptness.
Sentence:
*Responded to the flattering offer with alacrity.
Synonyms: Celerity, Briskness, Energy, Animation.
Antonyms: Apathy, Nonchalance, Sluggishness, Lethargy, Phlegmatic.
ALIENATE: To estrage.
Sentence:
*Alienated by his gruff manner.
ALLAY: To calm, To lessen in severity.
Sentence:
*At ease now that his fears have been allayed.
Synonyms: Appease, Alleviate, Pacify, Assuage, Abate, Mitigate, Propitiate, Mollify, Placate.
Antonyms: Intensify, Aggravate.
ALLUDE (Noun: ALLUSION): To refer to indirectly.
Sentence:
*Alluded quite subtly to his friend's misfortune.
Synonyms: Insinuate, Intimate, Imply.
Antonyms: Refer, Cite.
ALLURE: To tempt by flattery or an attractive offer.
Sentence:
*Allured by the prospect of a new job.
Synonyms: Lure, Decoy, Inveigle, Entice, Seduce, Wheedle, Beguile, Cajole.
Antonyms: Repel.
AMBIGUOUS: Uncertain, Vague, Capable of being inter, In more than one way.
Sentence:
*Puzzled by the ambiguous statement.
Synonyms: Hazy, Obscure, Equivocal, Dubious, Nebulous.
Antonyms: Explicit, Unquestionable.
AMENABLE: Obedient, wiling to submit.
Sentence:
*Amenable to the suggestion.
Synonyms: Tractable, Docile, Responsive.
Antonyms: Intractable, Refractory, Recalcitrant.
AMIABLE: Good-nature, Friendly.
Sentence:
*Attracted friends by his amiable position.
Synonyms: Complaisant
ANACHRONISM: A thing placed or occurring out of the normal time.
Sentences:
* A machine gun at the battle of Yorktown would be anachronism.
ANALOGY (Adj: ANALOGOUS): A relation between two things shown in the resemblance not of the things themselves but of their characteristics.
Sentence:
* He indicated the point of analogy between the two situations.
Synonyms: Correspondence, Affinity
Antonyms: Anomaly ( a deviation from the general rule.)
ANARCHY: State of confusion or lawlessness.
Sentence:
* A country brought to utter anarchy by civil war.
Synonyms: Chaos, Pandemonium.
ANIMUS: A feeling of hatred.
Sentence:
* Felt no animus, even against the enemy.
Synonyms: Enmity. Rancor, Malevolence, Animosity
Antonyms: Amity.
ANNALS: A historical records.
Sentence:
*In the annals of literature
ANONYMOUS: Of unknown authorship.
Sentence:
* An anonymous publication.
ANTHOLOGY: A collection of choice literally works.
Sentence:
* An anthology of modern poetry.
ANTITHESIS (Adj: ANTITHETICAL): Contrast, The direct opposite.
Sentence:
* His selfish attitude seemed to me the antithesis of patriotism.
APATHY (Adj: APATHETIC): Lack of feeling, emotion or intense.
Sentence:
* Attributed failure to apathy, rather than lack of patriotism.
Synonyms: Torpor, Lethargy, Sluggishness, Langour, Lassitude, Dispassion, (verb) Languish
Antonyms: Zeal, Animation
APPREHENSIVE (Verb: APPREHEND): Fearful.
Sentence:
*Being unprepared, John is apprehensive of the examination.
APPRISE: To inform.
Sentence:
* Apprised lieutenants of the new situation.
APPROBATION: Approval. Praise.
Sentence:
* A plan that meet with hearty approbation.
Synonyms: Sanction, Commendation.
Antonym: Disapprobation.
APT: (Noun: APTITUDE, APTNESS):
(1) Like, inclined or disposed.
Sentence:
* Apt to succeed.
Synonyms: Prone.
(2) Fit, Suitable.
Sentence:
* An apt remark.
Synonyms: Appropriate, Felicitous
(3) Skillful, Expert
Sentence
* Apt at woodcarving
Synonyms: Deft, Dexterous, Adept.
Antonym: Inept
ARBITER: A person who has authority to decide matters in dispute
Sentence:
* A fair decision rendered by the arbiter.
Synonyms: mediator, arbitrator
ARCHETYPE: An original pattern.
Sentence:
* Copies reproduced from the archetype.
Synonym: prototype
Antonyms: Stereotype, facsimile, replica
ARID: Dry; barren
Sentence:
* The arid desert land.
Synonyms: jejune, parched
Antonyms: arable, fertile
ARISTOCRACY: Government by the best people; a privileged class
Sentence:
* Special privileges enjoyed by the aristocracy.
Synonym: oligarchy Antonym: democracy war
ARMISTICE: A temporary suspension of hostilities.
Sentence:
* The armistice halted the war.
Synonym: truce
ARTFUL: Sly; crafty
Sentence:
* Attained his mean objective by artful measures.
Synonyms: cunning, wily, adroit, ingenious, guileful
Antonyms: guileless, ingenuous, artless
ARTICULATE:
(1) (Verb): To speak clearly or distinctly,
Sentence:
* Articulated slowly so that he could not be misunderstood.
(2) (Adj.): Capable of speech; distinct, clear
Sentence:
* An articulate man, always ready to give his views.
ASCETIC: Rigorously self-denying
Sentence:
* Pursued the ascetic life of a monk.
Synonyms: austere, abstinent
Antonyms: wanton, self-indulgent
ASKANCE: With distrust
Sentence:
* Looked askance at the forged signature.
ASSEVERATE: To declare positively; to confirm
Sentence:
* Asseverated his views with conviction.
Synonyms: assert, avouch, aver, avow, allege
Antonyms: gainsay, controvert, recant, rescind, abjure, disavow
ASSIDUOUS: Industrious
Sentence:
* An assiduous worker, toiling long hours.
Synonyms: sedulous, attentive: diligent, indefatigable
Antonyms: indolent, slothful
ASYLUM: A place offering shelter and retreat
Sentence:
* Found asylum from persecution.
Synonyms: sanctuary, refuge
ATHEIST: One who denies that God exists.
Sentence:
* The atheist declared, "There is no God."
Synonyms: infidel, agnostic, skeptic
ATTRIBUTE:
(1) (verb): Assign.
Sentence:
* Attributed his success to bard work.
Synonym: ascribe
(2) (noun): An inherent quality
Sentence:
* Generosity was his outstanding attribute.
AUGMENT: To increase or enlarge
Sentence:
* An army augmented by numerous enlistments.
Synonyms: enhance, amplify
Antonyms: abate, curtail
AUSPICIOUS: Indicating a happy outcome.
Sentence:
* The prospect for this project appears auspicious.
Synonyms: propitious, fortunate
Antonyms: ominous, foreboding
AUTHENTIC: Genuine
Sentence:
* Proved to be an authentic document.
Synonyms: veritable, bona fide
Antonyms: apocryphal, counterfeit, spurious, bogus
AUTOCRATIC: Despotic (Relating to ruler who has absolute power, Take no account of the other people wishes or opinion, domineering.)
Sentence:
* Feared by the masses as an autocratic ruler.
Synonym: tyrannical
Antonym: benevolent
AVARICE: Excessive greed
Sentence:
* A fortune accumulated by avarice and miserliness.
Synonyms: covetousness, cupidity, avidity
Antonym: magnanimity
AWRY: Unsymmetrical; not straight
Sentence:
* The picture, hanging awry on the wall.
Synonym: askew

Adj.= Adjective

Tuesday 18 October 2022

Unit 1: Real And Complex Numbers - Mathematics For Class IX (Science Group) - Solved Exercise 1.5

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Unit 1: Real And Complex Numbers
Exercise 1.1

EXAMPLES FROM TEXT BOOK

Example 1:
Recognize real and imaginary parts for the given complex number.
z = 3 - 2i
Solution:
Here, Re(z) = a = 3 and
Im(z)= b = -2

Unit 1: Real And Complex Numbers - Mathematics For Class IX (Science Group) - Explanation Of Exercise 1.5

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Unit 1: Real And Complex Numbers
Explanation Of Exercise 1.5

Definition of Complex Number

A number which consists of an imaginary part is called complex number. it is denoted by z.
e.g. z = a + ib
Where a and b are real numbers and i is an imaginary unit or part indication which is called iota and its value is, i = √-1. So i² = -1.
Thus, in a complex number we have both components (a + ib) so:

a = real part and
b = imaginary part

The complex number a+ ib can be written in order pair form (a, b) such as:

5+ 8i = (5, 8)
3 + 4i = (3, 4)

Explanation:
Imaginary Number:
We know that the square of real number is non-negative. So the solution of the equation x² + 1 = 0 does not exist in R. To overcome this inadequacy of real number, mathematicians introduced a new number √-1, imaginary unit and denoted it by the letter i (iota) having the property that i² = -1. Obviously i is not real number. It is a new mathematical entity that enables us to find the solution of every algebraic equation of the type x² + a = 0 where a > 0. Numbers like √-1 = i, √-5 = √5i, √-49 = 7i are called pure imaginary number.

Recognize 'a' as real part and 'b' as imaginary part of z = a + ib

In the complex number z = a + ib, "a" is the real part of complex number and "b" is the imaginary part of complex number.

The real part number is denoted by Re(z)
Its imaginary part is denote Im(z)

Conjugate Of A Complex Number

If we have a complex number (x + iy) then (x - iy) is called the conjugate of the given complex number .Conjugate of z is denoted by z i.e.,

If z = a + ib,
then z = a - ib

If z = (a, b)
then z = (a, - b)

if z = a - ib,
then z = a + ib

If z = (a, - b),
then z =(a, b)

In conjugate we just change the sign of imaginary part.

The Condition Of Equality Of Complex Numbers:

Two complex numbers are said to be equal if and only if, they have same real parts and same imaginary parts. i.e.
∀a, b, c, d ∈R, such that:
a + ib = c + id, iff a = c and b = d.

Sunday 16 October 2022

Sabaq No. 36: Mir Taqi Mir ki Gazalein (Hisa-e-Nazam) - الفاظ و معنی اور درسی کتاب کی مشق - Gulzaar E Urdu - Compulsory (NEW BOOK - 2022 and onward) - Class XI (1st year) For All Groups

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سبق نمبر 36: میر تقی میر کی غزلیں (حصہ نظم)
الفاظ و معنی اور درسی کتاب کی مشق

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Sabaq No. 35: Khawaja Mir Dard ki Gazalein(Hisa-e-Nazam) - الفاظ و معنی اور درسی کتاب کی مشق - Gulzaar E Urdu - Compulsory (NEW BOOK - 2022 and onward) - Class XI (1st year) For All Groups

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سبق نمبر 35: خواجہ میر درد کی غزلیں (حصہ نظم)
الفاظ و معنی اور درسی کتاب کی مشق

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سوال نمبر 7: غزل سے کیا مراد ہے؟
جواب: غزل:

Thursday 13 October 2022

Words Start from Letter 'D' - Scrabble Valid Words From All Dictionaries

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Scrabble Valid Words From All Dictionaries
Words Start from Letter 'D'

2 Letters Word

3 Letters Word

Dab:
Dad:
Dae:
Dag:
Dah:
Dai:
Dak:
Dal:
Dam:
Dan:
Dap:
Das:
Daw:
Day:
Deb:
Dee:
Def:
Deg:
Dei:
Del:
Den:
Der:
Dev:
Dew:
Dex:
Dey:
Dhu:
Dib:
Did:
Die:
Dif:
Dig:
Dim:
Din:
Dip:
Dis:
Dit:
Div:
Dob:
Doc:
Dod:
Doe:
Dof:
Dog:
Doh:
Dol:
Dom:
Don:
Doo:
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Dor:
Dos:
Dot:
Dow:
Dox:
Doy:
Dry:
Dso:
Dub:
Dud:
Due:
Dug:
Duh:
Dui:
Dum:
Dun:
Duo:
Dup:
Dur:
Dux:
Dye:
Dzo:

4 Letters Word

Daub(s):
Doab(s):
Dojo:
Done:

5 Letters Word

Donee:
Droid:
Duans:

6 Letters Word

Dallop:
Dilute:

7 Letters Word

Darning:
Debouch:

8 Letters Word

9 Letters Word

10Letters Word

11 Letters Word

12 Letters Word

Tuesday 11 October 2022

UNIT 03: INPUT/OUTPUT HANDLING IN C++ - Lab Activities - Computer Science For Class X

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Computer Science For Class X
Unit 03: Input / Output Handling In C++
Lab Activities

Q.1: Develop programs for manipulating the following formulas.

Title	Formula	Description
Calculating speed of an object	s=d/t	Speed = distance / time
Newton's second law of motion	F=ma	Force = mass x acceleration
Calculating acceleration	a = (v_f-v_i) / t	Acceleration is equal to (final velocity - initial velocity) / time
Area of triangle	a = ¹/₂bh	Area = ¹/₂ (base)(height)
Convert the Celsius to Fahrenheit	F = (c*1.8) + 32	-

Ans: (i) Calculating speed of an object

#include<iostream>
#include <conio.h>
#include <stdio.h>
using namespace std;
int main()
{
float speed;
float d;
float t;
cout << "\n \t Enter distance = ";
cin >> d;
cout << "\n\t Enter time = ";
cin >> t;
speed = d/t;
cout << "\n\t The speed of the object is = " << speed <<" m/s";
return 0;
}

(ii) Newton's second law of motion

#include <iostream>
#include <conio.h>
#include <stdio.h>
using namespace std;
int main()
{
float f;
float m;
float a;
cout << "\n \t Enter mass = ";
cin >> m;
cout << "\n\t Enter acceleration = ";
cin >> a;
f = m*a;
cout << "\n\t The value of F is = " << f <<" N";
return 0;
}

(iii) Calculating acceleration

#include <iostream>
#include <conio.h>
#include <stdio.h>
using namespace std;
int main()
{
float in_velocity;
float acceleration;
float f_velocity;
float time;
cout << "\n \t Enter the initial velocity of an object in m/s = ";
cin >> in_velocity;
cout << "\n\t Enter the final velocity of an object in m/s = ";
cin >> f_velocity;
cout << "\n \t Enter the time in seconds = ";
cin >> time;
acceleration = (f_velocity - in_velocity)/ time;
cout << "\n\t The Acceleration of the object is = " << acceleration <<" m/s²";
return 0;
}

(iv) Area of triangle

#include <iostream>
#include <conio.h>
#include <stdio.h>
using namespace std;
int main()
{
float base;
float height;
float area;
cout << "\n \t Enter the base of triangle = ";
cin >> base;
cout << "\n\t Enter the height of triangle = ";
cin >> height;
area = (base * height);
cout << "\n\t The area of the triangle is = " << area<<" s²";
return 0;
}

(v) Convert the Celsius to Fahrenheit

#include <iostream>
#include <conio.h>
#include <stdio.h>
using namespace std;
int main()
{
float celsius;
float fahrenheit;
cout << "\n \t Enter the temperature in Celsius = ";
cin >> celsius;
fahrenheit = (celsius * 1.8) + 32;
cout << "\n\t The temperature in Fahrenheit is = " << fahrenheit<<" F";
return 0;
}

Q.2: Write a program to calculate the volume of a box.
Ans: VOLUME OF A BOX:

#include<iostream>
#include<conio.h>
#include<stdio.h>
using namespace std;
int main()
{
float length;
float height;
float volume;
float width;
cout << "\n \t Enter the length of box = ";
cin >> length;
cout << "\n \t Enter the height of box = ";
cin >> height;
cout << "\n \t Enter the width of box = ";
cin >> width;
volume = (length*height*width);
cout << "\n \t The volume of the box is = " <<volume;
return 0;
}

Q.3: Write a program of marksheet, take input of five subjects, print its total and percentage also.
Ans: Marks Sheet

#include<iostream>
#include<conio.h>
#include<stdio.h>
using namespace std;
int main()
{
int phy, eng, comp, chem, urdu;
int obt_marks, per;

cout << "\n \t Enter Chemistry Marks = ";
cin >> chem;
cout << "\n \t Enter Physics Marks = ";
cin >> phy;
cout << "\n \t Enter Computer Marks = ";
cin >> comp;
cout << "\n \t Enter English Marks = ";
cin >> eng;
cout << "\n \t Enter Urdu Marks = ";
cin >> urdu;
obt_marks = chem + phy + comp + eng + urdu;
per = (obt_marks*100) /500;
cout << "\n \t The total marks are = " << obt_marks;
cout << "\n \t The percentage is = " << per <<"%\n";
return 0;
}

Q.4: Write a code to calculate mathematical expression of a² + 2ab +b².
Ans: Mathematical Expression:

#include<iostream>
#include<conio.h>
#include<stdio.h>
using namespace std;
int main()
{
float sol;
int a, b;
cout << "\n\t Program to calculate expression a² + 2ab +b²";
cout << "\n\t Enter the value of a. \t";
cin >> a;
cout << "\n\t Enter the value of b. \t";
cin >> b;
sol = (a*a) + 2*(a*b) + (b*b);
cout << "\n\t The solution of expression a² + 2ab +b² for given a and b is. \t" << sol;
return 0;
}

Q.5: list out errors from the C++ program and remove those errors, write the output.
#include<iostream.h>
using namespace std
int main (void);
{
int x;
cout << "\n Enter the value of x........";
cin >> x
cout << "\n The square of x......." << a*a;
return 0;
}
Ans: List of errors:

#include<iostream.h>
using namespace std
int main (void);
{
int x;
cout << "\n Enter the value of x........";
cin >> x
cout << "\n The square of x......." << a*a;
return 0;
}

Line No.	Error
1.	iostream.h
2.	Terminator (;) missing after std
3.	Terminator (;) present after main function
7.	Terminator (;) missing after cin function
8.	Wrong variable used in square expression (a)

Correct Program:

#include<iostream>
using namespace std;
int main (void)
{
int x;
cout << "\n Enter the value of x .....";
cin >> x;
cout << "\n The square of x ....." << x*x;
return 0;
}

OUTPUT:
Enter the value of x ..... 5
The square of x ..... 25

Words Start from Letter 'C' - Scrabble Valid Words From All Dictionaries