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🚀𝖩𝗈𝗂𝗇 𝗎𝗌 𝖿𝗈𝗋 𝖽𝖺𝗂𝗅𝗒 𝗂𝗇𝗌𝗂𝗀𝗁𝗍𝗌, 𝗌𝗍𝗎𝖽𝗒 𝗍𝗂𝗉𝗌, 𝖺𝗇𝖽 𝗋𝖾𝗌𝗈𝗎𝗋𝖼𝖾𝗌 𝗍𝗁𝖺𝗍 𝖾𝗆𝗉𝗈𝗐𝖾𝗋 𝗅𝖾𝖺𝗋𝗇𝖾𝗋𝗌 𝗈𝖿 𝖺𝗅𝗅 𝖺𝗀𝖾𝗌.

✅𝖶𝗁𝖾𝗍𝗁𝖾𝗋 𝗒𝗈𝗎'𝗋𝖾 𝗅𝗈𝗈𝗄𝗂𝗇𝗀 𝖿𝗈𝗋 𝖺𝖼𝖺𝖽𝖾𝗆𝗂𝖼 𝗌𝗎𝗉𝗉𝗈𝗋𝗍, 𝗌𝗄𝗂𝗅𝗅 𝖽𝖾𝗏𝖾𝗅𝗈𝗉𝗆𝖾𝗇𝗍, 𝗈𝗋 𝗂𝗇𝗌𝗉𝗂𝗋𝗂𝗇𝗀 𝖼𝗈𝗇𝗍𝖾𝗇𝗍, 𝗐𝖾 𝗉𝗋𝗈𝗏𝗂𝖽𝖾 𝖺 𝗏𝗂𝖻𝗋𝖺𝗇𝗍 𝖼𝗈𝗆𝗆𝗎𝗇𝗂𝗍𝗒 𝗐𝗁𝖾𝗋𝖾 𝗄𝗇𝗈𝗐𝗅𝖾𝖽𝗀𝖾 𝗍𝗁𝗋𝗂𝗏𝖾𝗌.

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➤Answer: B) Present Continuous
Explanation: Present Continuous (is/am/are + V-ing) describes ongoing actions.


14. "She has lived here for 5 years." Which tense is this?
A) Present Perfect
B) Past Perfect
C) Simple Past
D) Future Simple

➤Answer: A) Present Perfect
Explanation: Has/have + V3 emphasizes actions started in the past and continuing to the present.


15. Which signal word fits Simple Past?
A) Now
B) Yesterday
C) Already
D) Tomorrow

➤Answer: B) Yesterday
Explanation: Simple Past uses time markers like yesterday, last week, ago.


16. Passive form of "We were playing football."
A) Football was played by us.
B) Football was being played by us.
C) Football had been played by us.
D) Football is played by us.

➤Answer: B) Football was being played by us.
Explanation: Past Continuous (Active: was/were + V-ing) becomes was/were + being + V3 in passive.


17. Which writing type uses sensory details?
A) Expository
B) Descriptive
C) Persuasive
D) Narrative

➤Answer: B) Descriptive
Explanation: Descriptive writing evokes images using the five senses.


18. Reported speech for: "Will you help me?" she asked.
A) She asked if I would help her.
B) She asked if I will help her.
C) She asked if I helped her.
D) She asked if I had helped her.

➤Answer: A) She asked if I would help her.
Explanation: "Will" changes to "would" in reported questions.


19. "If I were you, I would apologize." This is a:
A) Type 1
B) Type 2
C) Type 3
D) Zero

➤Answer: B) Type 2
Explanation: Hypothetical advice uses Past Simple + would + V1.


20. Which tense is used for scheduled future events?
A) Future Simple (will)
B) Present Simple
C) Future Continuous
D) Present Perfect

➤Answer: B) Present Simple
Explanation: Timetables (e.g., "The train leaves at 6 PM") use Present Simple.

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Crypto
🇬🇧ENGLISH

♻️20 multiple-choice questions based on the Active/Passive Voice, Types of Writing, Direct/Reported Speech, Conditionals, and Tenses.


1. What is the passive form of: "Rohit takes tea."?
A) Tea is taken by Rohit.
B) Tea was taken by Rohit.
C) Tea has been taken by Rohit.
D) Tea will be taken by Rohit.

➤Answer: A) Tea is taken by Rohit.
Explanation: The sentence is in Simple Present Tense (Active: S + V1 + s/es + O), so its passive form is S + is/am/are + V3 + by + O.


2. Which sentence is in the active voice?
A) A letter is being written by me.
B) The clothes were washed by us.
C) Maddie will have reached the station.
D) The door was shut by him.

➤Answer: C) Maddie will have reached the station.
Explanation: Only option C follows the active voice structure (S + will + have + V3 + O). The others are passive.


3. How is the imperative sentence "Shut the door" converted to passive?
A) The door must be shut.
B) Let the door be shut.
C) The door is shut by you.
D) The door was shut.

➤Answer: B) Let the door be shut.
Explanation: Imperative sentences in passive use "Let + O + be + V3".


4. Which type of writing aims to "expose" facts without personal opinions?
A) Persuasive
B) Descriptive
C) Expository
D) Narrative

➤Answer: C) Expository
Explanation: Expository writing explains facts logically (e.g., textbooks, news articles).


5. "The pumpkin pie recipe uses five ingredients." This is an example of:
A) Descriptive writing
B) Narrative writing
C) Expository writing
D) Persuasive writing

➤Answer: C) Expository writing
Explanation: The sentence informs/explains a process (recipe) without persuasion or storytelling.


6. Which type of writing would include dialogue and characters?
A) Persuasive
B) Narrative
C) Expository
D) Descriptive

➤Answer: B) Narrative
Explanation: Narratives tell stories with characters, plots, and dialogue (e.g., novels).


7. Convert to reported speech: "I am tired," she said.
A) She said she was tired.
B) She said she is tired.
C) She said she had been tired.
D) She said she will be tired.

➤Answer: A) She said she was tired.
Explanation: Present Simple ("am") changes to Past Simple ("was") in reported speech.


8. What changes in reported speech for "tomorrow"?
A) Yesterday
B) The next day
C) Today
D) That day

➤Answer: B) The next day
Explanation: Time expressions shift (e.g., "tomorrow" → "the next day").


9. Which modal verb does NOT change in reported speech?
A) Will
B) Can
C) Must
D) Might

➤Answer: D) Might
Explanation: Modals like might, could, would, should remain unchanged.


10. "If you heat ice, it melts." This is a:
A) Type 1 Conditional
B) Type 2 Conditional
C) Zero Conditional
D) Mixed Conditional

➤Answer: C) Zero Conditional
Explanation: Zero Conditional expresses general truths (If + Present, Present).


11. Which conditional type describes hypothetical situations?
A) Type 1
B) Type 2
C) Type 3
D) Zero

➤Answer: B) Type 2
Explanation: Type 2 uses Past Simple + would + V1 for unreal scenarios (e.g., "If I were rich...").


12. "If I had studied, I would have passed." This is a:
A) Type 1
B) Type 2
C) Type 3
D) Zero

➤Answer: C) Type 3
Explanation: Type 3 refers to unreal past conditions (Past Perfect + would have + V3).


13. Which tense is used for actions happening now?
A) Simple Present
B) Present Continuous
C) Present Perfect
D) Past Simple

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖺) 48.2 𝗄𝗆 𝖺𝗍 39° 𝖶 𝗈𝖿 𝖭
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖦𝗂𝗏𝖾𝗇 𝖽𝗂𝗋𝖾𝖼𝗍𝗅𝗒 𝗂𝗇 𝗍𝗁𝖾 𝖯𝖣𝖥'𝗌 𝖾𝗑𝖺𝗆𝗉𝗅𝖾 𝗌𝗈𝗅𝗎𝗍𝗂𝗈𝗇.


25. 𝖳𝗁𝖾 𝗉𝗋𝗈𝗃𝖾𝖼𝗍𝗂𝗈𝗇 𝗈𝖿 𝗏𝖾𝖼𝗍𝗈𝗋 𝖠 𝗈𝗇𝗍𝗈 𝖡 𝗂𝗌:
𝖺) 𝖠 𝗌𝗂𝗇 θ
𝖻) 𝖠 𝖼𝗈𝗌 θ
𝖼) 𝖠 + 𝖡
𝖽) 𝖠 / 𝖡

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖻) 𝖠 𝖼𝗈𝗌 θ
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖯𝗋𝗈𝗃𝖾𝖼𝗍𝗂𝗈𝗇 = |𝖠|𝖼𝗈𝗌θ 𝗂𝗇 𝖽𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇 𝗈𝖿 𝖡.


26. 𝖣𝗈𝗍 𝗉𝗋𝗈𝖽𝗎𝖼𝗍 𝗈𝖿 𝗎𝗇𝗂𝗍 𝗏𝖾𝖼𝗍𝗈𝗋𝗌 𝗂‌ · 𝗃‌ 𝗂𝗌:
𝖺) 1
𝖻) –1
𝖼) 0
𝖽) 𝗂

𝖠𝗇𝗌𝗐𝖾𝗋: 𝖼) 0
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖳𝗁𝖾𝗒 𝖺𝗋𝖾 𝗉𝖾𝗋𝗉𝖾𝗇𝖽𝗂𝖼𝗎𝗅𝖺𝗋; 𝗁𝖾𝗇𝖼𝖾 𝖽𝗈𝗍 𝗉𝗋𝗈𝖽𝗎𝖼𝗍 𝗂𝗌 𝗓𝖾𝗋𝗈.


27. 𝖵𝖾𝖼𝗍𝗈𝗋 𝗋𝖾𝗌𝗈𝗅𝗎𝗍𝗂𝗈𝗇 𝗌𝗉𝗅𝗂𝗍𝗌 𝖺 𝗏𝖾𝖼𝗍𝗈𝗋 𝗂𝗇𝗍𝗈:
𝖺) 𝖳𝗐𝗈 𝗉𝖾𝗋𝗉𝖾𝗇𝖽𝗂𝖼𝗎𝗅𝖺𝗋 𝖼𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝗌
𝖻) 𝖳𝗐𝗈 𝗌𝖼𝖺𝗅𝖺𝗋𝗌
𝖼) 𝖮𝗉𝗉𝗈𝗌𝗂𝗍𝖾 𝗏𝖾𝖼𝗍𝗈𝗋𝗌
𝖽) 𝖱𝖺𝗇𝖽𝗈𝗆 𝖽𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇𝗌

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖺) 𝖳𝗐𝗈 𝗉𝖾𝗋𝗉𝖾𝗇𝖽𝗂𝖼𝗎𝗅𝖺𝗋 𝖼𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝗌
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖴𝗌𝗎𝖺𝗅𝗅𝗒 𝖺𝗅𝗈𝗇𝗀 𝗑 𝖺𝗇𝖽 𝗒 𝖺𝗑𝖾𝗌.


28. 𝖠 𝗏𝖾𝖼𝗍𝗈𝗋 𝖠 𝗁𝖺𝗌 𝖺𝗇𝗀𝗅𝖾 θ 𝗐𝗂𝗍𝗁 𝗑-𝖺𝗑𝗂𝗌. 𝖠𝗑 = 𝖠 𝖼𝗈𝗌θ. 𝖶𝗁𝖺𝗍 𝗂𝗌 𝖠𝗒?
𝖺) 𝖠 𝗌𝗂𝗇θ
𝖻) 𝖠 𝖼𝗈𝗌θ
𝖼) 𝖠 𝗍𝖺𝗇θ
𝖽) 𝖠 / 𝗌𝗂𝗇θ

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖺) 𝖠 𝗌𝗂𝗇θ
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠𝗒 = 𝖠 𝗌𝗂𝗇θ 𝖿𝗋𝗈𝗆 𝗋𝗂𝗀𝗁𝗍 𝗍𝗋𝗂𝖺𝗇𝗀𝗅𝖾 𝗍𝗋𝗂𝗀𝗈𝗇𝗈𝗆𝖾𝗍𝗋𝗒.


29. 𝖠 𝗏𝖾𝖼𝗍𝗈𝗋 𝗐𝗂𝗍𝗁 𝗈𝗇𝗅𝗒 𝗄‌ 𝖼𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍 𝗅𝗂𝖾𝗌 𝖺𝗅𝗈𝗇𝗀:
𝖺) 𝗑-𝖺𝗑𝗂𝗌
𝖻) 𝗒-𝖺𝗑𝗂𝗌
𝖼) 𝗓-𝖺𝗑𝗂𝗌
𝖽) 𝗑𝗒-𝗉𝗅𝖺𝗇𝖾

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖼) 𝗓-𝖺𝗑𝗂𝗌
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝗄‌ 𝗂𝗌 𝗍𝗁𝖾 𝗎𝗇𝗂𝗍 𝗏𝖾𝖼𝗍𝗈𝗋 𝗂𝗇 𝗍𝗁𝖾 𝗓 𝖽𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇.


30. 𝖳𝗁𝖾 𝗌𝖼𝖺𝗅𝖺𝗋 𝗍𝗋𝗂𝗉𝗅𝖾 𝗉𝗋𝗈𝖽𝗎𝖼𝗍 𝖠 · (𝖡 × 𝖢) 𝗋𝖾𝗌𝗎𝗅𝗍𝗌 𝗂𝗇:
𝖺) 𝖲𝖼𝖺𝗅𝖺𝗋
𝖻) 𝖵𝖾𝖼𝗍𝗈𝗋
𝖼) 𝖬𝖺𝗍𝗋𝗂𝗑
𝖽) 𝖳𝖾𝗇𝗌𝗈𝗋

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖺) 𝖲𝖼𝖺𝗅𝖺𝗋
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖨𝗍 𝗂𝗌 𝖺 𝗌𝖼𝖺𝗅𝖺𝗋 𝗋𝖾𝗉𝗋𝖾𝗌𝖾𝗇𝗍𝗂𝗇𝗀 𝗍𝗁𝖾 𝗏𝗈𝗅𝗎𝗆𝖾 𝗈𝖿 𝗍𝗁𝖾 𝗉𝖺𝗋𝖺𝗅𝗅𝖾𝗅𝖾𝗉𝗂𝗉𝖾𝖽 𝖿𝗈𝗋𝗆𝖾𝖽.

📌𝖳𝗈 𝗃𝗈𝗂𝗇 𝗍𝗁𝖾 𝗉𝗋𝗂𝗏𝖺𝗍𝖾 𝖼𝗅𝖺𝗌𝗌 𝖿𝗈 𝖿𝗋𝖾𝖾👇

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11. 𝖶𝗁𝖺𝗍 𝗂𝗌 𝗍𝗁𝖾 𝗎𝗇𝗂𝗍 𝗏𝖾𝖼𝗍𝗈𝗋 𝖺𝗅𝗈𝗇𝗀 𝖠 = 3𝗂 + 4𝗃?
𝖺) 𝗂 + 𝗃
𝖻) (3/5)𝗂 + (4/5)𝗃
𝖼) 3𝗂 + 4𝗃
𝖽) 5𝗂 + 5𝗃

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖻) (3/5)𝗂 + (4/5)𝗃
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖬𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾 = √(3² + 4²) = 5. 𝖴𝗇𝗂𝗍 𝗏𝖾𝖼𝗍𝗈𝗋 = 𝖠 / |𝖠| = (3/5)𝗂 + (4/5)𝗃.


12. 𝖨𝖿 𝖠 = 5𝗆 𝖤𝖺𝗌𝗍, 𝖡 = 5𝗆 𝖶𝖾𝗌𝗍, 𝗐𝗁𝖺𝗍 𝗂𝗌 𝖠 + 𝖡?
𝖺) 10𝗆 𝖤𝖺𝗌𝗍
𝖻) 0
𝖼) 5𝗆
𝖽) 5𝗆 𝖭𝗈𝗋𝗍𝗁

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖻) 0
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖳𝗁𝖾𝗒 𝖼𝖺𝗇𝖼𝖾𝗅 𝖾𝖺𝖼𝗁 𝗈𝗍𝗁𝖾𝗋 𝖻𝖾𝖼𝖺𝗎𝗌𝖾 𝗍𝗁𝖾𝗒 𝖺𝗋𝖾 𝖾𝗊𝗎𝖺𝗅 𝖺𝗇𝖽 𝗈𝗉𝗉𝗈𝗌𝗂𝗍𝖾 𝗏𝖾𝖼𝗍𝗈𝗋𝗌.


13. 𝖵𝖾𝖼𝗍𝗈𝗋 𝖠 = 4𝗂 + 3𝗃. 𝖥𝗂𝗇𝖽 𝗂𝗍𝗌 𝗆𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾.
𝖺) 5
𝖻) 7
𝖼) 1
𝖽) 6

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖺) 5
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖬𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾 = √(4² + 3²) = √25 = 5


14. 𝖶𝗁𝗂𝖼𝗁 𝗂𝗌 𝖺 𝖼𝗈𝗋𝗋𝖾𝖼𝗍 𝗋𝖾𝗉𝗋𝖾𝗌𝖾𝗇𝗍𝖺𝗍𝗂𝗈𝗇 𝗈𝖿 𝗏𝖾𝖼𝗍𝗈𝗋 𝗂𝗇 3𝖣?
𝖺) 𝖠𝗂
𝖻) 𝖠𝗑𝗂 + 𝖠𝗒𝗃 + 𝖠𝗓𝗄
𝖼) 𝖠 + 𝖡
𝖽) 𝖠𝖡𝖼𝗈𝗌θ

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖻) 𝖠𝗑𝗂 + 𝖠𝗒𝗃 + 𝖠𝗓𝗄
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖳𝗁𝗂𝗌 𝗂𝗌 𝗍𝗁𝖾 𝗌𝗍𝖺𝗇𝖽𝖺𝗋𝖽 𝗎𝗇𝗂𝗍 𝗏𝖾𝖼𝗍𝗈𝗋 𝖿𝗈𝗋𝗆 𝗂𝗇 3𝖣 𝗌𝗉𝖺𝖼𝖾.


15. 𝖨𝖿 𝖠 𝖺𝗇𝖽 𝖡 𝖺𝗋𝖾 𝗉𝖾𝗋𝗉𝖾𝗇𝖽𝗂𝖼𝗎𝗅𝖺𝗋, 𝖠 · 𝖡 𝖾𝗊𝗎𝖺𝗅𝗌:
𝖺) 0
𝖻) 1
𝖼) 𝖠 + 𝖡
𝖽) 𝖠𝖡

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖺) 0
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖣𝗈𝗍 𝗉𝗋𝗈𝖽𝗎𝖼𝗍 𝗂𝗌 𝗓𝖾𝗋𝗈 𝗐𝗁𝖾𝗇 𝗏𝖾𝖼𝗍𝗈𝗋𝗌 𝖺𝗋𝖾 𝖺𝗍 90°.


16. 𝖳𝗁𝖾 𝖼𝗋𝗈𝗌𝗌 𝗉𝗋𝗈𝖽𝗎𝖼𝗍 𝗈𝖿 𝗍𝗐𝗈 𝗏𝖾𝖼𝗍𝗈𝗋𝗌 𝗋𝖾𝗌𝗎𝗅𝗍𝗌 𝗂𝗇 𝖺 𝗏𝖾𝖼𝗍𝗈𝗋:
𝖺) 𝖢𝗈𝗅𝗅𝗂𝗇𝖾𝖺𝗋 𝗐𝗂𝗍𝗁 𝖠
𝖻) 𝖢𝗈𝗅𝗅𝗂𝗇𝖾𝖺𝗋 𝗐𝗂𝗍𝗁 𝖡
𝖼) 𝖯𝖾𝗋𝗉𝖾𝗇𝖽𝗂𝖼𝗎𝗅𝖺𝗋 𝗍𝗈 𝖻𝗈𝗍𝗁 𝖠 𝖺𝗇𝖽 𝖡
𝖽) 𝖤𝗊𝗎𝖺𝗅 𝗍𝗈 𝖠

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖼) 𝖯𝖾𝗋𝗉𝖾𝗇𝖽𝗂𝖼𝗎𝗅𝖺𝗋 𝗍𝗈 𝖻𝗈𝗍𝗁 𝖠 𝖺𝗇𝖽 𝖡
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖢𝗋𝗈𝗌𝗌 𝗉𝗋𝗈𝖽𝗎𝖼𝗍 𝗒𝗂𝖾𝗅𝖽𝗌 𝖺 𝗏𝖾𝖼𝗍𝗈𝗋 𝗈𝗋𝗍𝗁𝗈𝗀𝗈𝗇𝖺𝗅 𝗍𝗈 𝖻𝗈𝗍𝗁 𝗂𝗇𝗉𝗎𝗍𝗌.


17. 𝖠 × 𝖠 𝖾𝗊𝗎𝖺𝗅𝗌:
𝖺) 𝖠
𝖻) 𝖠²
𝖼) 0
𝖽) |𝖠|

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖼) 0
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖢𝗋𝗈𝗌𝗌 𝗉𝗋𝗈𝖽𝗎𝖼𝗍 𝗈𝖿 𝖺 𝗏𝖾𝖼𝗍𝗈𝗋 𝗐𝗂𝗍𝗁 𝗂𝗍𝗌𝖾𝗅𝖿 𝗂𝗌 𝖺𝗅𝗐𝖺𝗒𝗌 𝗓𝖾𝗋𝗈.


18. 𝖶𝗁𝗂𝖼𝗁 𝗈𝗇𝖾 𝗂𝗌 𝗍𝗋𝗎𝖾 𝖺𝖻𝗈𝗎𝗍 𝗌𝖼𝖺𝗅𝖺𝗋-𝗏𝖾𝖼𝗍𝗈𝗋 𝗆𝗎𝗅𝗍𝗂𝗉𝗅𝗂𝖼𝖺𝗍𝗂𝗈𝗇?
𝖺) 𝖢𝗁𝖺𝗇𝗀𝖾𝗌 𝖽𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇
𝖻) 𝖢𝗁𝖺𝗇𝗀𝖾𝗌 𝗆𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾
𝖼) 𝖢𝗈𝗇𝗏𝖾𝗋𝗍𝗌 𝗏𝖾𝖼𝗍𝗈𝗋 𝗍𝗈 𝗌𝖼𝖺𝗅𝖺𝗋
𝖽) 𝖨𝗌 𝖺𝗅𝗐𝖺𝗒𝗌 𝗓𝖾𝗋𝗈

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖻) 𝖢𝗁𝖺𝗇𝗀𝖾𝗌 𝗆𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖲𝖼𝖺𝗅𝖺𝗋 𝗆𝗎𝗅𝗍𝗂𝗉𝗅𝗂𝖼𝖺𝗍𝗂𝗈𝗇 𝗌𝖼𝖺𝗅𝖾𝗌 𝗍𝗁𝖾 𝗆𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾, 𝗇𝗈𝗍 𝖽𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇.


19. 𝖶𝗁𝖺𝗍 𝖽𝗈𝖾𝗌 𝗂‌ × 𝗃‌ 𝖾𝗊𝗎𝖺𝗅?
𝖺) 𝗂‌
𝖻) 𝗃‌
𝖼) 𝗄‌
𝖽) 0

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖼) 𝗄‌
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖥𝗈𝗅𝗅𝗈𝗐𝗌 𝗋𝗂𝗀𝗁𝗍-𝗁𝖺𝗇𝖽 𝗋𝗎𝗅𝖾: 𝗂‌ × 𝗃‌ = 𝗄‌.


20. 𝖶𝗁𝖺𝗍 𝗂𝗌 (𝖠 × 𝖡) · (𝖡 × 𝖠)?
𝖺) 0
𝖻) –|𝖠 × 𝖡|²
𝖼) |𝖠||𝖡|
𝖽) 𝖠 · 𝖡

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖻) –|𝖠 × 𝖡|²
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠 × 𝖡 = –(𝖡 × 𝖠); 𝗌𝗈 𝖽𝗈𝗍𝗍𝗂𝗇𝗀 𝗍𝗁𝖾 𝗋𝖾𝗌𝗎𝗅𝗍 𝗐𝗂𝗍𝗁 𝗂𝗍𝗌 𝗇𝖾𝗀𝖺𝗍𝗂𝗏𝖾 𝗒𝗂𝖾𝗅𝖽𝗌 –𝗆𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾 𝗌𝗊𝗎𝖺𝗋𝖾𝖽.


21. 𝖳𝗐𝗈 𝗏𝖾𝖼𝗍𝗈𝗋𝗌 𝖺𝗋𝖾 𝖾𝗊𝗎𝖺𝗅 𝗂𝖿 𝗍𝗁𝖾𝗒 𝗁𝖺𝗏𝖾:
𝖺) 𝖲𝖺𝗆𝖾 𝗅𝖾𝗇𝗀𝗍𝗁 𝗈𝗇𝗅𝗒
𝖻) 𝖲𝖺𝗆𝖾 𝖽𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇 𝗈𝗇𝗅𝗒
𝖼) 𝖲𝖺𝗆𝖾 𝗆𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾 𝖺𝗇𝖽 𝖽𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇
𝖽) 𝖣𝗂𝖿𝖿𝖾𝗋𝖾𝗇𝗍 𝖽𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇𝗌

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖼) 𝖲𝖺𝗆𝖾 𝗆𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾 𝖺𝗇𝖽 𝖽𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖤𝗊𝗎𝖺𝗅 𝗏𝖾𝖼𝗍𝗈𝗋𝗌 𝗆𝗎𝗌𝗍 𝗁𝖺𝗏𝖾 𝖻𝗈𝗍𝗁 𝗍𝗁𝖾 𝗌𝖺𝗆𝖾 𝗆𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾 𝖺𝗇𝖽 𝖽𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇.


22. 𝖨𝖿 𝖠 = 2𝗂 – 3𝗃 𝖺𝗇𝖽 𝖡 = –2𝗂 + 3𝗃, 𝗐𝗁𝖺𝗍 𝗂𝗌 𝖠 + 𝖡?
𝖺) 4𝗂 – 6𝗃
𝖻) 0
𝖼) –4𝗂 + 6𝗃
𝖽) 2𝗂 + 3𝗃

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖻) 0
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠 𝖺𝗇𝖽 𝖡 𝖺𝗋𝖾 𝗇𝖾𝗀𝖺𝗍𝗂𝗏𝖾𝗌 𝗈𝖿 𝖾𝖺𝖼𝗁 𝗈𝗍𝗁𝖾𝗋.


23. 𝖨𝖿 𝖠 = 4𝗂, 𝖡 = 3𝗃, 𝗐𝗁𝖺𝗍 𝗂𝗌 𝖠 × 𝖡?
𝖺) 12𝗄
𝖻) 7𝗄
𝖼) 1𝗄
𝖽) 0

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖺) 12𝗄
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝗂 × 𝗃 = 𝗄; 𝖠 × 𝖡 = 4𝗂 × 3𝗃 = 12𝗄.


24. 𝖠 𝖼𝖺𝗋 𝗆𝗈𝗏𝖾𝗌 20 𝗄𝗆 𝖭𝗈𝗋𝗍𝗁 𝖺𝗇𝖽 35 𝗄𝗆 𝖺𝗍 60° 𝖶𝖾𝗌𝗍 𝗈𝖿 𝖭𝗈𝗋𝗍𝗁. 𝖱𝖾𝗌𝗎𝗅𝗍𝖺𝗇𝗍 𝖽𝗂𝗌𝗉𝗅𝖺𝖼𝖾𝗆𝖾𝗇𝗍?
𝖺) 48.2 𝗄𝗆 𝖺𝗍 39° 𝖶 𝗈𝖿 𝖭
𝖻) 30 𝗄𝗆
𝖼) 55 𝗄𝗆
𝖽) 20 𝗄𝗆 𝖺𝗍 60°

𝖢𝗋𝗒𝗉𝗍𝗈
⚛️𝖯𝖧𝖸𝖲𝖨𝖢𝖲

♻️30 𝗆𝗎𝗅𝗍𝗂𝗉𝗅𝖾 𝖼𝗁𝗈𝗂𝖼𝖾 𝗊𝗎𝖾𝗌𝗍𝗂𝗈𝗇𝗌 𝖿𝗋𝗈𝗆 𝗍𝗁𝖾 "𝖵𝖾𝖼𝗍𝗈𝗋𝗌"

1. 𝖶𝗁𝗂𝖼𝗁 𝗈𝖿 𝗍𝗁𝖾 𝖿𝗈𝗅𝗅𝗈𝗐𝗂𝗇𝗀 𝗂𝗌 𝖺 𝗌𝖼𝖺𝗅𝖺𝗋 𝗊𝗎𝖺𝗇𝗍𝗂𝗍𝗒?
𝖺) 𝖵𝖾𝗅𝗈𝖼𝗂𝗍𝗒
𝖻) 𝖥𝗈𝗋𝖼𝖾
𝖼) 𝖬𝖺𝗌𝗌
𝖽) 𝖠𝖼𝖼𝖾𝗅𝖾𝗋𝖺𝗍𝗂𝗈𝗇

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖼) 𝖬𝖺𝗌𝗌
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖲𝖼𝖺𝗅𝖺𝗋𝗌 𝗁𝖺𝗏𝖾 𝗈𝗇𝗅𝗒 𝗆𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾. 𝖬𝖺𝗌𝗌 𝗂𝗌 𝖺 𝗌𝖼𝖺𝗅𝖺𝗋, 𝗐𝗁𝗂𝗅𝖾 𝗍𝗁𝖾 𝗋𝖾𝗌𝗍 𝖺𝗋𝖾 𝗏𝖾𝖼𝗍𝗈𝗋𝗌.


2. 𝖶𝗁𝖺𝗍 𝖽𝗈𝖾𝗌 𝖺 𝗉𝗈𝗌𝗂𝗍𝗂𝗈𝗇 𝗏𝖾𝖼𝗍𝗈𝗋 𝗋𝖾𝗉𝗋𝖾𝗌𝖾𝗇𝗍?
𝖺) 𝖲𝗉𝖾𝖾𝖽
𝖻) 𝖣𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇 𝗈𝖿 𝗆𝗈𝗍𝗂𝗈𝗇
𝖼) 𝖣𝗂𝗌𝗉𝗅𝖺𝖼𝖾𝗆𝖾𝗇𝗍 𝖿𝗋𝗈𝗆 𝗍𝗁𝖾 𝗈𝗋𝗂𝗀𝗂𝗇
𝖽) 𝖬𝖺𝗌𝗌

𝖠𝗇𝗌𝗐𝖾𝗋: 𝖼) 𝖣𝗂𝗌𝗉𝗅𝖺𝖼𝖾𝗆𝖾𝗇𝗍 𝖿𝗋𝗈𝗆 𝗍𝗁𝖾 𝗈𝗋𝗂𝗀𝗂𝗇
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠 𝗉𝗈𝗌𝗂𝗍𝗂𝗈𝗇 𝗏𝖾𝖼𝗍𝗈𝗋 𝗉𝗈𝗂𝗇𝗍𝗌 𝖿𝗋𝗈𝗆 𝗍𝗁𝖾 𝗈𝗋𝗂𝗀𝗂𝗇 𝗍𝗈 𝗍𝗁𝖾 𝗅𝗈𝖼𝖺𝗍𝗂𝗈𝗇 𝗈𝖿 𝖺 𝗉𝗈𝗂𝗇𝗍 𝗂𝗇 𝗌𝗉𝖺𝖼𝖾.


3. 𝖵𝖾𝖼𝗍𝗈𝗋 𝖺𝖽𝖽𝗂𝗍𝗂𝗈𝗇 𝗂𝗌 𝖼𝗈𝗆𝗆𝗎𝗍𝖺𝗍𝗂𝗏𝖾. 𝖳𝗁𝗂𝗌 𝗆𝖾𝖺𝗇𝗌:
𝖺) 𝖠 + 𝖡 = 𝖠 – 𝖡
𝖻) 𝖠 + 𝖡 = 𝖡 + 𝖠
𝖼) 𝖠 + 𝖡 = –(𝖡 + 𝖠)
𝖽) 𝖭𝗈𝗇𝖾 𝗈𝖿 𝗍𝗁𝖾 𝖺𝖻𝗈𝗏𝖾

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖻) 𝖠 + 𝖡 = 𝖡 + 𝖠
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖢𝗈𝗆𝗆𝗎𝗍𝖺𝗍𝗂𝗏𝖾 𝗉𝗋𝗈𝗉𝖾𝗋𝗍𝗒 𝖺𝗅𝗅𝗈𝗐𝗌 𝖼𝗁𝖺𝗇𝗀𝗂𝗇𝗀 𝗍𝗁𝖾 𝗈𝗋𝖽𝖾𝗋 𝗈𝖿 𝖺𝖽𝖽𝗂𝗍𝗂𝗈𝗇 𝗐𝗂𝗍𝗁𝗈𝗎𝗍 𝖼𝗁𝖺𝗇𝗀𝗂𝗇𝗀 𝗍𝗁𝖾 𝗋𝖾𝗌𝗎𝗅𝗍.


4. 𝖳𝗐𝗈 𝗏𝖾𝖼𝗍𝗈𝗋𝗌 𝖺𝗍 𝗋𝗂𝗀𝗁𝗍 𝖺𝗇𝗀𝗅𝖾𝗌: 𝖠 = 8𝗆 𝖤𝖺𝗌𝗍, 𝖡 = 6𝗆 𝖭𝗈𝗋𝗍𝗁. 𝖥𝗂𝗇𝖽 𝗆𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾 𝗈𝖿 𝗋𝖾𝗌𝗎𝗅𝗍𝖺𝗇𝗍.
𝖺) 10𝗆
𝖻) 14𝗆
𝖼) 2𝗆
𝖽) 12𝗆

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖺) 10𝗆
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖴𝗌𝖾 𝖯𝗒𝗍𝗁𝖺𝗀𝗈𝗋𝖺𝗌: √(8² + 6²) = √(64 + 36) = √100 = 10𝗆.


5. 𝖳𝗁𝖾 𝗎𝗇𝗂𝗍 𝗏𝖾𝖼𝗍𝗈𝗋 𝗁𝖺𝗌 𝖺 𝗆𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾 𝗈𝖿:
𝖺) 0
𝖻) 1
𝖼) 𝖠
𝖽) 𝖨𝗇𝖿𝗂𝗇𝗂𝗍𝗒

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖻) 1
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖴𝗇𝗂𝗍 𝗏𝖾𝖼𝗍𝗈𝗋𝗌 𝗁𝖺𝗏𝖾 𝗆𝖺𝗀𝗇𝗂𝗍𝗎𝖽𝖾 1 𝖺𝗇𝖽 𝗂𝗇𝖽𝗂𝖼𝖺𝗍𝖾 𝖽𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇.


6. 𝖶𝗁𝗂𝖼𝗁 𝖾𝗑𝗉𝗋𝖾𝗌𝗌𝗂𝗈𝗇 𝗋𝖾𝗉𝗋𝖾𝗌𝖾𝗇𝗍𝗌 𝗍𝗁𝖾 𝗌𝖼𝖺𝗅𝖺𝗋 (𝖽𝗈𝗍) 𝗉𝗋𝗈𝖽𝗎𝖼𝗍?
𝖺) 𝖠 × 𝖡
𝖻) 𝖠 · 𝖡
𝖼) 𝖠 + 𝖡
𝖽) 𝖠 – 𝖡

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖻) 𝖠 · 𝖡
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖳𝗁𝖾 𝖽𝗈𝗍 𝗉𝗋𝗈𝖽𝗎𝖼𝗍 𝗒𝗂𝖾𝗅𝖽𝗌 𝖺 𝗌𝖼𝖺𝗅𝖺𝗋 𝖺𝗇𝖽 𝗂𝗌 𝗀𝗂𝗏𝖾𝗇 𝖻𝗒 𝖠·𝖡 = 𝖠𝖡𝖼𝗈𝗌(θ).


7. 𝖶𝗁𝗂𝖼𝗁 𝗈𝖿 𝗍𝗁𝖾 𝖿𝗈𝗅𝗅𝗈𝗐𝗂𝗇𝗀 𝗂𝗌 𝗇𝗈𝗍 𝖺 𝗉𝗋𝗈𝗉𝖾𝗋𝗍𝗒 𝗈𝖿 𝗍𝗁𝖾 𝗌𝖼𝖺𝗅𝖺𝗋 𝗉𝗋𝗈𝖽𝗎𝖼𝗍?
𝖺) 𝖢𝗈𝗆𝗆𝗎𝗍𝖺𝗍𝗂𝗏𝖾
𝖻) 𝖣𝗂𝗌𝗍𝗋𝗂𝖻𝗎𝗍𝗂𝗏𝖾
𝖼) 𝖭𝗈𝗇-𝖺𝗌𝗌𝗈𝖼𝗂𝖺𝗍𝗂𝗏𝖾
𝖽) 𝖯𝗋𝗈𝖽𝗎𝖼𝖾𝗌 𝖺 𝗏𝖾𝖼𝗍𝗈𝗋

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖽) 𝖯𝗋𝗈𝖽𝗎𝖼𝖾𝗌 𝖺 𝗏𝖾𝖼𝗍𝗈𝗋
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖲𝖼𝖺𝗅𝖺𝗋 𝗉𝗋𝗈𝖽𝗎𝖼𝗍 𝗀𝗂𝗏𝖾𝗌 𝖺 𝗌𝖼𝖺𝗅𝖺𝗋, 𝗇𝗈𝗍 𝖺 𝗏𝖾𝖼𝗍𝗈𝗋.


8. 𝖶𝗁𝗂𝖼𝗁 𝗉𝗋𝗈𝗉𝖾𝗋𝗍𝗒 𝗂𝗌 𝗎𝗇𝗂𝗊𝗎𝖾 𝗍𝗈 𝖼𝗋𝗈𝗌𝗌 𝗉𝗋𝗈𝖽𝗎𝖼𝗍?
𝖺) 𝖢𝗈𝗆𝗆𝗎𝗍𝖺𝗍𝗂𝗏𝖾
𝖻) 𝖯𝗋𝗈𝖽𝗎𝖼𝖾𝗌 𝗌𝖼𝖺𝗅𝖺𝗋
𝖼) 𝖭𝗈𝗇-𝖼𝗈𝗆𝗆𝗎𝗍𝖺𝗍𝗂𝗏𝖾
𝖽) 𝖦𝗂𝗏𝖾𝗌 𝖽𝗂𝗋𝖾𝖼𝗍𝗂𝗈𝗇𝗅𝖾𝗌𝗌 𝗋𝖾𝗌𝗎𝗅𝗍

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖼) 𝖭𝗈𝗇-𝖼𝗈𝗆𝗆𝗎𝗍𝖺𝗍𝗂𝗏𝖾
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠 × 𝖡 = –𝖡 × 𝖠, 𝗐𝗁𝗂𝖼𝗁 𝗂𝗌 𝗎𝗇𝗂𝗊𝗎𝖾 𝗍𝗈 𝗏𝖾𝖼𝗍𝗈𝗋 (𝖼𝗋𝗈𝗌𝗌) 𝗉𝗋𝗈𝖽𝗎𝖼𝗍.


9. 𝖠 · 𝖡 = 0 𝗂𝗆𝗉𝗅𝗂𝖾𝗌:
𝖺) 𝖠 𝗂𝗌 𝗉𝖺𝗋𝖺𝗅𝗅𝖾𝗅 𝗍𝗈 𝖡
𝖻) 𝖠 𝗂𝗌 𝗉𝖾𝗋𝗉𝖾𝗇𝖽𝗂𝖼𝗎𝗅𝖺𝗋 𝗍𝗈 𝖡
𝖼) 𝖠 = 𝖡
𝖽) 𝖠 𝖺𝗇𝖽 𝖡 𝖺𝗋𝖾 𝗌𝖼𝖺𝗅𝖺𝗋𝗌

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖻) 𝖠 𝗂𝗌 𝗉𝖾𝗋𝗉𝖾𝗇𝖽𝗂𝖼𝗎𝗅𝖺𝗋 𝗍𝗈 𝖡
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖣𝗈𝗍 𝗉𝗋𝗈𝖽𝗎𝖼𝗍 = 0 𝗐𝗁𝖾𝗇 𝖼𝗈𝗌θ = 0 ⇒ θ = 90°.


10. 𝖢𝗋𝗈𝗌𝗌 𝗉𝗋𝗈𝖽𝗎𝖼𝗍 𝗈𝖿 𝗉𝖺𝗋𝖺𝗅𝗅𝖾𝗅 𝗏𝖾𝖼𝗍𝗈𝗋𝗌 𝗂𝗌:
𝖺) 𝖬𝖺𝗑𝗂𝗆𝗎𝗆
𝖻) 𝖹𝖾𝗋𝗈
𝖼) 𝖭𝖾𝗀𝖺𝗍𝗂𝗏𝖾
𝖽) 𝖴𝗇𝖽𝖾𝖿𝗂𝗇𝖾𝖽

➢𝖠𝗇𝗌𝗐𝖾𝗋: 𝖻) 𝖹𝖾𝗋𝗈
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝗌𝗂𝗇(0°) = 0 ⇒ 𝖼𝗋𝗈𝗌𝗌 𝗉𝗋𝗈𝖽𝗎𝖼𝗍 𝗂𝗌 𝗓𝖾𝗋𝗈 𝖿𝗈𝗋 𝗉𝖺𝗋𝖺𝗅𝗅𝖾𝗅 𝗏𝖾𝖼𝗍𝗈𝗋𝗌.

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖼)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝗑² = 9 → 𝗑 = ±3.


27. 𝖶𝗁𝖺𝗍 𝗂𝗌 𝗍𝗁𝖾 𝗋𝖾𝗌𝗎𝗅𝗍 𝗈𝖿 (𝖠 ∪ 𝖡)’?
(𝖺) 𝖠 ∩ 𝖡
(𝖻) 𝖠’ ∩ 𝖡’
(𝖼) 𝖠’ ∪ 𝖡’
(𝖽) 𝖠 ∪ 𝖡

𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖡𝗒 𝖣𝖾 𝖬𝗈𝗋𝗀𝖺𝗇’𝗌 𝗅𝖺𝗐.


28. 𝖳𝗁𝖾 𝗌𝖾𝗍 {ϕ} 𝖼𝗈𝗇𝗍𝖺𝗂𝗇𝗌 𝗁𝗈𝗐 𝗆𝖺𝗇𝗒 𝖾𝗅𝖾𝗆𝖾𝗇𝗍𝗌?
(𝖺) 0
(𝖻) 1
(𝖼) 𝖴𝗇𝖽𝖾𝖿𝗂𝗇𝖾𝖽
(𝖽) 𝖨𝗇𝖿𝗂𝗇𝗂𝗍𝖾

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖨𝗍 𝖼𝗈𝗇𝗍𝖺𝗂𝗇𝗌 𝗈𝗇𝖾 𝖾𝗅𝖾𝗆𝖾𝗇𝗍 — 𝗍𝗁𝖾 𝖾𝗆𝗉𝗍𝗒 𝗌𝖾𝗍.


29. 𝖶𝗁𝗂𝖼𝗁 𝗂𝗌 𝗍𝗁𝖾 𝖼𝗈𝗋𝗋𝖾𝖼𝗍 𝗂𝖽𝖾𝗇𝗍𝗂𝗍𝗒: 𝖠 – (𝖠 ∩ 𝖡) = ?
(𝖺) 𝖠 ∩ 𝖡
(𝖻) 𝖠 ∪ 𝖡
(𝖼) 𝖠 – 𝖡
(𝖽) 𝖡 – 𝖠

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖼)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖱𝖾𝗆𝗈𝗏𝗂𝗇𝗀 𝖼𝗈𝗆𝗆𝗈𝗇 𝖾𝗅𝖾𝗆𝖾𝗇𝗍𝗌 𝗀𝗂𝗏𝖾𝗌 𝖠 – 𝖡.


30. 𝗇(𝖠 ∆ 𝖡) = ?
(𝖺) 𝗇(𝖠) + 𝗇(𝖡) – 𝗇(𝖠 ∩ 𝖡)
(𝖻) 𝗇(𝖠 ∩ 𝖡)
(𝖼) 𝗇(𝖠) + 𝗇(𝖡) – 2𝗇(𝖠 ∩ 𝖡)
(𝖽) 𝗇(𝖠) ∪ 𝗇(𝖡)

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖼)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖡𝗒 𝖿𝗈𝗋𝗆𝗎𝗅𝖺 𝖿𝗈𝗋 𝗌𝗒𝗆𝗆𝖾𝗍𝗋𝗂𝖼 𝖽𝗂𝖿𝖿𝖾𝗋𝖾𝗇𝖼𝖾.

📌𝖳𝗈 𝗃𝗈𝗂𝗇 𝗍𝗁𝖾 𝗉𝗋𝗂𝗏𝖺𝗍𝖾 𝖼𝗅𝖺𝗌𝗌 𝖿𝗈𝗋 𝖿𝗋𝖾𝖾👇
https://t.me/harme_students2017/472

11. 𝖨𝖿 𝖠 = {2, 4, 6}, 𝗍𝗁𝖾𝗇 𝗍𝗁𝖾 𝖼𝗈𝗆𝗉𝗅𝖾𝗆𝖾𝗇𝗍 𝗈𝖿 𝖠 𝗂𝗇 𝖴 = {1, 2, 3, 4, 5, 6} 𝗂𝗌:
(𝖺) {1, 2, 3}
(𝖻) {1, 3, 5}
(𝖼) {4, 6}
(𝖽) {2, 4, 6}

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖢𝗈𝗆𝗉𝗅𝖾𝗆𝖾𝗇𝗍 = 𝖾𝗅𝖾𝗆𝖾𝗇𝗍𝗌 𝗂𝗇 𝖴 𝖻𝗎𝗍 𝗇𝗈𝗍 𝗂𝗇 𝖠 → {1, 3, 5}.


12. 𝖶𝗁𝖺𝗍 𝗂𝗌 𝗍𝗁𝖾 𝗌𝗒𝗆𝗆𝖾𝗍𝗋𝗂𝖼 𝖽𝗂𝖿𝖿𝖾𝗋𝖾𝗇𝖼𝖾 𝗈𝖿 𝖠 = {1, 2, 3} 𝖺𝗇𝖽 𝖡 = {2, 3, 4}?
(𝖺) {2, 3}
(𝖻) {1, 4}
(𝖼) {1, 2, 3, 4}
(𝖽) {1, 2, 4}

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠 ∆ 𝖡 = (𝖠 – 𝖡) ∪ (𝖡 – 𝖠) = {1} ∪ {4} = {1, 4}.

13. 𝖨𝖿 𝖠 = {𝗑 ∈ 𝖭 | 𝗑 < 5}, 𝗍𝗁𝖾𝗇 𝖠 =
(𝖺) {0, 1, 2, 3, 4}
(𝖻) {1, 2, 3, 4}
(𝖼) {2, 3, 4, 5}
(𝖽) {1, 2, 3, 4, 5}

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖭𝖺𝗍𝗎𝗋𝖺𝗅 𝗇𝗎𝗆𝖻𝖾𝗋𝗌 𝗌𝗍𝖺𝗋𝗍 𝖿𝗋𝗈𝗆 1, 𝗌𝗈 𝗑 < 5 𝗀𝗂𝗏𝖾𝗌 {1, 2, 3, 4}.


14. 𝖨𝖿 𝖠 = {1, 3}, 𝖡 = {2, 3}, 𝗍𝗁𝖾𝗇 𝖠 ∩ 𝖡 = ?
(𝖺) {3}
(𝖻) {1, 2, 3}
(𝖼) ϕ
(𝖽) {1, 3}

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖺)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖮𝗇𝗅𝗒 3 𝗂𝗌 𝖼𝗈𝗆𝗆𝗈𝗇.


15. 𝖳𝗁𝖾 𝗇𝗎𝗆𝖻𝖾𝗋 𝗈𝖿 𝗌𝗎𝖻𝗌𝖾𝗍𝗌 𝗈𝖿 {𝖺, 𝖻, 𝖼, 𝖽} 𝗂𝗌:
(𝖺) 8
(𝖻) 16
(𝖼) 4
(𝖽) 24

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 2⁴ = 16 𝗌𝗎𝖻𝗌𝖾𝗍𝗌.


16. 𝖨𝖿 𝗇(𝖠) = 10, 𝗇(𝖡) = 15, 𝖺𝗇𝖽 𝗇(𝖠 ∩ 𝖡) = 5, 𝗍𝗁𝖾𝗇 𝗇(𝖠 ∪ 𝖡) = ?
(𝖺) 30
(𝖻) 20
(𝖼) 25
(𝖽) 15

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖴𝗌𝖾 𝖿𝗈𝗋𝗆𝗎𝗅𝖺: 𝗇(𝖠 ∪ 𝖡) = 𝗇(𝖠) + 𝗇(𝖡) – 𝗇(𝖠 ∩ 𝖡) = 10 + 15 – 5 = 20.


17. 𝖶𝗁𝗂𝖼𝗁 𝗈𝖿 𝗍𝗁𝖾 𝖿𝗈𝗅𝗅𝗈𝗐𝗂𝗇𝗀 𝗂𝗌 𝖺 𝗌𝗂𝗇𝗀𝗅𝖾𝗍𝗈𝗇 𝗌𝖾𝗍?
(𝖺) {1, 2, 3}
(𝖻) {𝗑 | 𝗑 𝗂𝗌 𝖺𝗇 𝖾𝗏𝖾𝗇 𝗉𝗋𝗂𝗆𝖾}
(𝖼) ϕ
(𝖽) {𝗑 | 𝗑² = 4}

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖮𝗇𝗅𝗒 𝖾𝗏𝖾𝗇 𝗉𝗋𝗂𝗆𝖾 𝗂𝗌 2 → 𝗌𝗂𝗇𝗀𝗅𝖾𝗍𝗈𝗇 {2}.


18. 𝖨𝖿 𝖠 = {1, 2, 3}, 𝖡 = {3, 4, 5}, 𝗍𝗁𝖾𝗇 𝖠 – 𝖡 = ?
(𝖺) {1, 2}
(𝖻) {3}
(𝖼) {1, 2, 4}
(𝖽) {1, 2, 5}

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖺)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖤𝗅𝖾𝗆𝖾𝗇𝗍𝗌 𝗂𝗇 𝖠 𝖻𝗎𝗍 𝗇𝗈𝗍 𝗂𝗇 𝖡.


19. 𝖨𝖿 𝖠 𝖺𝗇𝖽 𝖡 𝖺𝗋𝖾 𝖽𝗂𝗌𝗃𝗈𝗂𝗇𝗍, 𝗍𝗁𝖾𝗇 𝖠 ∩ 𝖡 = ?
(𝖺) 𝖠
(𝖻) 𝖡
(𝖼) ϕ
(𝖽) 𝖠 ∪ 𝖡

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖼)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖣𝗂𝗌𝗃𝗈𝗂𝗇𝗍 𝗆𝖾𝖺𝗇𝗌 𝗇𝗈 𝖼𝗈𝗆𝗆𝗈𝗇 𝖾𝗅𝖾𝗆𝖾𝗇𝗍𝗌 → 𝗂𝗇𝗍𝖾𝗋𝗌𝖾𝖼𝗍𝗂𝗈𝗇 𝗂𝗌 𝖾𝗆𝗉𝗍𝗒.


20. 𝖶𝗁𝗂𝖼𝗁 𝗈𝖿 𝗍𝗁𝖾 𝖿𝗈𝗅𝗅𝗈𝗐𝗂𝗇𝗀 𝗂𝗌 𝗇𝗈𝗍 𝖺 𝗌𝖾𝗍?
(𝖺) 𝖲𝖾𝗍 𝗈𝖿 𝖺𝗅𝗅 𝗏𝗈𝗐𝖾𝗅𝗌
(𝖻) 𝖲𝖾𝗍 𝗈𝖿 𝗉𝗋𝗂𝗆𝖾 𝗇𝗎𝗆𝖻𝖾𝗋𝗌 𝗅𝖾𝗌𝗌 𝗍𝗁𝖺𝗇 10
(𝖼) 𝖲𝖾𝗍 𝗈𝖿 𝖼𝗅𝖾𝗏𝖾𝗋 𝗌𝗍𝗎𝖽𝖾𝗇𝗍𝗌
(𝖽) 𝖲𝖾𝗍 𝗈𝖿 𝖾𝗏𝖾𝗇 𝗇𝖺𝗍𝗎𝗋𝖺𝗅 𝗇𝗎𝗆𝖻𝖾𝗋𝗌

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖼)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: “𝖢𝗅𝖾𝗏𝖾𝗋” 𝗂𝗌 𝗌𝗎𝖻𝗃𝖾𝖼𝗍𝗂𝗏𝖾, 𝗌𝗈 𝗇𝗈𝗍 𝗐𝖾𝗅𝗅-𝖽𝖾𝖿𝗂𝗇𝖾𝖽.


21. 𝖠 𝗌𝖾𝗍 𝗐𝗁𝗂𝖼𝗁 𝖼𝗈𝗇𝗍𝖺𝗂𝗇𝗌 𝗂𝗍𝗌𝖾𝗅𝖿 𝖺𝗌 𝖺𝗇 𝖾𝗅𝖾𝗆𝖾𝗇𝗍 𝗂𝗌:
(𝖺) 𝖴𝗇𝗂𝗏𝖾𝗋𝗌𝖺𝗅 𝗌𝖾𝗍
(𝖻) 𝖨𝗆𝗉𝗋𝗈𝗉𝖾𝗋 𝗌𝖾𝗍
(𝖼) 𝖭𝗈𝗍 𝗉𝗈𝗌𝗌𝗂𝖻𝗅𝖾 𝗂𝗇 𝗌𝗍𝖺𝗇𝖽𝖺𝗋𝖽 𝗌𝖾𝗍 𝗍𝗁𝖾𝗈𝗋𝗒
(𝖽) 𝖯𝗈𝗐𝖾𝗋 𝗌𝖾𝗍

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖼)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖨𝗇 𝗌𝗍𝖺𝗇𝖽𝖺𝗋𝖽 (𝖹𝖥𝖢) 𝗌𝖾𝗍 𝗍𝗁𝖾𝗈𝗋𝗒, 𝗌𝖾𝗍𝗌 𝖼𝖺𝗇'𝗍 𝖼𝗈𝗇𝗍𝖺𝗂𝗇 𝗍𝗁𝖾𝗆𝗌𝖾𝗅𝗏𝖾𝗌.


22. 𝖶𝗁𝗂𝖼𝗁 𝗈𝖿 𝗍𝗁𝖾 𝖿𝗈𝗅𝗅𝗈𝗐𝗂𝗇𝗀 𝗌𝖾𝗍𝗌 𝗂𝗌 𝖿𝗂𝗇𝗂𝗍𝖾?
(𝖺) 𝖲𝖾𝗍 𝗈𝖿 𝖺𝗅𝗅 𝗋𝖾𝖺𝗅 𝗇𝗎𝗆𝖻𝖾𝗋𝗌
(𝖻) 𝖲𝖾𝗍 𝗈𝖿 𝖺𝗅𝗅 𝗂𝗇𝗍𝖾𝗀𝖾𝗋𝗌
(𝖼) 𝖲𝖾𝗍 𝗈𝖿 𝖺𝗅𝗅 𝖾𝗏𝖾𝗇 𝗇𝖺𝗍𝗎𝗋𝖺𝗅 𝗇𝗎𝗆𝖻𝖾𝗋𝗌
(𝖽) 𝖲𝖾𝗍 𝗈𝖿 𝖽𝖺𝗒𝗌 𝗂𝗇 𝖺 𝗐𝖾𝖾𝗄

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖽)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖧𝖺𝗌 𝖾𝗑𝖺𝖼𝗍𝗅𝗒 7 𝖾𝗅𝖾𝗆𝖾𝗇𝗍𝗌.


23. 𝖳𝗁𝖾 𝖼𝗈𝗆𝗉𝗅𝖾𝗆𝖾𝗇𝗍 𝗈𝖿 𝗍𝗁𝖾 𝗎𝗇𝗂𝗏𝖾𝗋𝗌𝖺𝗅 𝗌𝖾𝗍 𝗂𝗌:
(𝖺) 𝖠
(𝖻) ϕ
(𝖼) 𝖴
(𝖽) 𝖠’

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖴 – 𝖴 = ϕ.


24. 𝖶𝗁𝗂𝖼𝗁 𝗈𝖿 𝗍𝗁𝖾 𝖿𝗈𝗅𝗅𝗈𝗐𝗂𝗇𝗀 𝗌𝖾𝗍𝗌 𝖺𝗋𝖾 𝖾𝗊𝗎𝖺𝗅?
𝖠 = {1, 2, 3}, 𝖡 = {3, 2, 1}
(𝖺) 𝖠 = 𝖡
(𝖻) 𝖠 ⊆ 𝖡
(𝖼) 𝖠 ≠ 𝖡
(𝖽) 𝖡 ⊂ 𝖠

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖺)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖲𝖾𝗍𝗌 𝖺𝗋𝖾 𝗎𝗇𝗈𝗋𝖽𝖾𝗋𝖾𝖽, 𝗌𝗈 𝖠 = 𝖡.


25. 𝖨𝖿 𝖠 ⊆ 𝖡 𝖺𝗇𝖽 𝖡 ⊆ 𝖠, 𝗍𝗁𝖾𝗇:
(𝖺) 𝖠 = ϕ
(𝖻) 𝖠 = 𝖡
(𝖼) 𝖡 = 𝖴
(𝖽) 𝖠 ⊂ 𝖡

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖡𝗈𝗍𝗁 𝗌𝗎𝖻𝗌𝖾𝗍𝗌 𝗈𝖿 𝖾𝖺𝖼𝗁 𝗈𝗍𝗁𝖾𝗋 𝗂𝗆𝗉𝗅𝗂𝖾𝗌 𝖾𝗊𝗎𝖺𝗅𝗂𝗍𝗒.


26. 𝖨𝖿 𝖠 = {𝗑 ∈ 𝖹 | 𝗑² = 9}, 𝗍𝗁𝖾𝗇 𝖠 =
(𝖺) {3}
(𝖻) {–3}
(𝖼) {–3, 3}
(𝖽) {9}

𝖢𝗋𝗒𝗉𝗍𝗈
📐𝖬𝖠𝖳𝖧𝖤𝖬𝖠𝖳𝖨𝖢𝖲

♻️30 𝗆𝗎𝗅𝗍𝗂𝗉𝗅𝖾 𝖼𝗁𝗈𝗂𝖼𝖾 𝗊𝗎𝖾𝗌𝗍𝗂𝗈𝗇𝗌 𝗈𝗇 𝖲𝖾𝗍 𝖳𝗁𝖾𝗈𝗋𝗒:

1. 𝖶𝗁𝗂𝖼𝗁 𝗈𝖿 𝗍𝗁𝖾 𝖿𝗈𝗅𝗅𝗈𝗐𝗂𝗇𝗀 𝗂𝗌 𝖺 𝗇𝗎𝗅𝗅 𝗌𝖾𝗍?
(𝖺) {𝗑 : 𝗑 𝗂𝗌 𝖺 𝗋𝖾𝖺𝗅 𝗇𝗎𝗆𝖻𝖾𝗋 𝖺𝗇𝖽 𝗑 > 2 𝖺𝗇𝖽 𝗑 < 2}
(𝖻) {𝗑 : 𝗑 𝗂𝗌 𝖺 𝗋𝖾𝖺𝗅 𝗇𝗎𝗆𝖻𝖾𝗋 𝖺𝗇𝖽 𝗑 = 0}
(𝖼) {ϕ}
(𝖽) {𝗑 : 𝗑 𝗂𝗌 𝖺 𝗇𝖺𝗍𝗎𝗋𝖺𝗅 𝗇𝗎𝗆𝖻𝖾𝗋 𝖺𝗇𝖽 𝗑 = 1}

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖺)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖭𝗈 𝗇𝗎𝗆𝖻𝖾𝗋 𝗂𝗌 𝖻𝗈𝗍𝗁 𝗀𝗋𝖾𝖺𝗍𝖾𝗋 𝗍𝗁𝖺𝗇 2 𝖺𝗇𝖽 𝗅𝖾𝗌𝗌 𝗍𝗁𝖺𝗇 2, 𝗌𝗈 𝗍𝗁𝖾 𝗌𝖾𝗍 𝗂𝗌 𝖾𝗆𝗉𝗍𝗒.


2. 𝖳𝗁𝖾 𝗌𝖾𝗍 𝖠 = {1, 2, 3} 𝗁𝖺𝗌 𝗁𝗈𝗐 𝗆𝖺𝗇𝗒 𝗉𝗋𝗈𝗉𝖾𝗋 𝗌𝗎𝖻𝗌𝖾𝗍𝗌?
(𝖺) 8
(𝖻) 6
(𝖼) 7
(𝖽) 4

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖼)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖳𝗈𝗍𝖺𝗅 𝗌𝗎𝖻𝗌𝖾𝗍𝗌 = 2³ = 8; 𝗉𝗋𝗈𝗉𝖾𝗋 𝗌𝗎𝖻𝗌𝖾𝗍𝗌 = 8 – 1 = 7.


3. 𝖨𝖿 𝖠 = {2, 4, 6}, 𝖡 = {4, 6, 8}, 𝗐𝗁𝖺𝗍 𝗂𝗌 𝖠 ∩ 𝖡?
(𝖺) {2, 4, 6}
(𝖻) {4, 6}
(𝖼) {2}
(𝖽) {8}

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠 ∩ 𝖡 𝗂𝗇𝖼𝗅𝗎𝖽𝖾𝗌 𝖾𝗅𝖾𝗆𝖾𝗇𝗍𝗌 𝖼𝗈𝗆𝗆𝗈𝗇 𝗍𝗈 𝖻𝗈𝗍𝗁 𝗌𝖾𝗍𝗌: {4, 6}.


4. 𝖶𝗁𝗂𝖼𝗁 𝗈𝖿 𝗍𝗁𝖾 𝖿𝗈𝗅𝗅𝗈𝗐𝗂𝗇𝗀 𝗂𝗌 𝗍𝗁𝖾 𝗎𝗇𝗂𝗏𝖾𝗋𝗌𝖺𝗅 𝗌𝖾𝗍 𝖿𝗈𝗋 𝖠 = {1, 2, 3} 𝖺𝗇𝖽 𝖡 = {2, 3, 4}?
(𝖺) {1, 2, 3}
(𝖻) {2, 3}
(𝖼) {1, 2, 3, 4}
(𝖽) {1, 2, 4}

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖼)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖴𝗇𝗂𝗏𝖾𝗋𝗌𝖺𝗅 𝗌𝖾𝗍 𝗆𝗎𝗌𝗍 𝖼𝗈𝗇𝗍𝖺𝗂𝗇 𝖺𝗅𝗅 𝖾𝗅𝖾𝗆𝖾𝗇𝗍𝗌 𝗈𝖿 𝖠 𝖺𝗇𝖽 𝖡.


5. 𝖳𝗁𝖾 𝗉𝗈𝗐𝖾𝗋 𝗌𝖾𝗍 𝗈𝖿 𝖠 = {1, 2} 𝗂𝗌:
(𝖺) {1, 2}
(𝖻) {{1}, {2}, {1, 2}}
(𝖼) {ϕ, {1}, {2}, {1, 2}}
(𝖽) {{1, 2}}

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖼)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖯𝗈𝗐𝖾𝗋 𝗌𝖾𝗍 𝗂𝗇𝖼𝗅𝗎𝖽𝖾𝗌 𝖺𝗅𝗅 𝗌𝗎𝖻𝗌𝖾𝗍𝗌 𝗂𝗇𝖼𝗅𝗎𝖽𝗂𝗇𝗀 𝗍𝗁𝖾 𝖾𝗆𝗉𝗍𝗒 𝗌𝖾𝗍.


6. 𝖨𝖿 𝖠 = {1, 2, 3, 4}, 𝖡 = {2, 4}, 𝗍𝗁𝖾𝗇 𝖡 𝗂𝗌:
(𝖺) 𝖤𝗊𝗎𝖺𝗅 𝗍𝗈 𝖠
(𝖻) 𝖯𝗋𝗈𝗉𝖾𝗋 𝗌𝗎𝖻𝗌𝖾𝗍 𝗈𝖿 𝖠
(𝖼) 𝖲𝗎𝗉𝖾𝗋𝗌𝖾𝗍 𝗈𝖿 𝖠
(𝖽) 𝖣𝗂𝗌𝗃𝗈𝗂𝗇𝗍 𝖿𝗋𝗈𝗆 𝖠

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠𝗅𝗅 𝖾𝗅𝖾𝗆𝖾𝗇𝗍𝗌 𝗈𝖿 𝖡 𝖺𝗋𝖾 𝗂𝗇 𝖠, 𝖺𝗇𝖽 𝖡 ≠ 𝖠.


7. 𝖭𝗎𝗆𝖻𝖾𝗋 𝗈𝖿 𝖾𝗅𝖾𝗆𝖾𝗇𝗍𝗌 𝗂𝗇 𝖯(𝖠) 𝗂𝖿 𝖠 𝗁𝖺𝗌 5 𝖾𝗅𝖾𝗆𝖾𝗇𝗍𝗌:
(𝖺) 10
(𝖻) 25
(𝖼) 32
(𝖽) 5

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖼)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖯𝗈𝗐𝖾𝗋 𝗌𝖾𝗍 𝗈𝖿 𝖺 𝗌𝖾𝗍 𝗐𝗂𝗍𝗁 𝗇 𝖾𝗅𝖾𝗆𝖾𝗇𝗍𝗌 = 2ⁿ = 2⁵ = 32.


8. 𝖠 ∩ ϕ 𝖾𝗊𝗎𝖺𝗅𝗌:
(𝖺) 𝖠
(𝖻) ϕ
(𝖼) 𝖴
(𝖽) 𝖠 ∪ ϕ

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖻)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖭𝗈 𝖾𝗅𝖾𝗆𝖾𝗇𝗍𝗌 𝖺𝗋𝖾 𝖼𝗈𝗆𝗆𝗈𝗇 𝖻𝖾𝗍𝗐𝖾𝖾𝗇 𝖺𝗇𝗒 𝗌𝖾𝗍 𝖺𝗇𝖽 𝗍𝗁𝖾 𝖾𝗆𝗉𝗍𝗒 𝗌𝖾𝗍.


9. 𝖠 ∪ 𝖠 𝖾𝗊𝗎𝖺𝗅𝗌:
(𝖺) 𝖠
(𝖻) ϕ
(𝖼) 𝖴
(𝖽) 2𝖠

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖺)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖴𝗇𝗂𝗈𝗇 𝗐𝗂𝗍𝗁 𝗂𝗍𝗌𝖾𝗅𝖿 𝗀𝗂𝗏𝖾𝗌 𝗍𝗁𝖾 𝗌𝖺𝗆𝖾 𝗌𝖾𝗍.


10. 𝖶𝗁𝗂𝖼𝗁 𝗅𝖺𝗐 𝗂𝗌 𝗌𝗁𝗈𝗐𝗇 𝖻𝗒 𝖠 ∪ 𝖡 = 𝖡 ∪ 𝖠?
(𝖺) 𝖠𝗌𝗌𝗈𝖼𝗂𝖺𝗍𝗂𝗏𝖾
(𝖻) 𝖣𝗂𝗌𝗍𝗋𝗂𝖻𝗎𝗍𝗂𝗏𝖾
(𝖼) 𝖢𝗈𝗆𝗆𝗎𝗍𝖺𝗍𝗂𝗏𝖾
(𝖽) 𝖨𝖽𝖾𝗆𝗉𝗈𝗍𝖾𝗇𝗍

➲𝖠𝗇𝗌𝗐𝖾𝗋: (𝖼)
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖮𝗋𝖽𝖾𝗋 𝖽𝗈𝖾𝗌𝗇'𝗍 𝖺𝖿𝖿𝖾𝖼𝗍 𝗎𝗇𝗂𝗈𝗇 (𝖼𝗈𝗆𝗆𝗎𝗍𝖺𝗍𝗂𝗏𝖾).

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖠
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖲𝗂𝗆𝗉𝗅𝖾 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾𝗌 𝗎𝗌𝖾 𝖺 𝗌𝗂𝗇𝗀𝗅𝖾 𝖻𝗂𝖼𝗈𝗇𝗏𝖾𝗑 𝗅𝖾𝗇𝗌 𝖿𝗈𝗋 𝖻𝖺𝗌𝗂𝖼 𝗆𝖺𝗀𝗇𝗂𝖿𝗂𝖼𝖺𝗍𝗂𝗈𝗇.


27. 𝖶𝗁𝗂𝖼𝗁 𝗍𝗈𝗈𝗅 𝗂𝗌 𝗎𝗌𝖾𝖽 𝖿𝗈𝗋 𝗏𝗂𝗌𝗎𝖺𝗅𝗂𝗓𝗂𝗇𝗀 𝗌𝗉𝖺𝗍𝗂𝖺𝗅 𝖽𝖺𝗍𝖺?
𝖠) 𝖬𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾
𝖡) 𝖦𝖨𝖲
𝖢) 𝖯𝖾𝗍𝗋𝗂 𝖽𝗂𝗌𝗁
𝖣) 𝖣𝗂𝗌𝗌𝖾𝖼𝗍𝗂𝗇𝗀 𝗄𝗂𝗍

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖡
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖦𝖨𝖲 (𝖦𝖾𝗈𝗀𝗋𝖺𝗉𝗁𝗂𝖼𝖺𝗅 𝖨𝗇𝖿𝗈𝗋𝗆𝖺𝗍𝗂𝗈𝗇 𝖲𝗒𝗌𝗍𝖾𝗆) 𝗁𝖾𝗅𝗉𝗌 𝖽𝗂𝗌𝗉𝗅𝖺𝗒 𝗌𝗉𝖺𝗍𝗂𝖺𝗅 𝖽𝖺𝗍𝖺.


28. 𝖶𝗁𝗂𝖼𝗁 𝗈𝖿 𝗍𝗁𝖾 𝖿𝗈𝗅𝗅𝗈𝗐𝗂𝗇𝗀 𝗍𝗈𝗈𝗅𝗌 𝗂𝗌 𝗎𝗌𝖾𝖽 𝗂𝗇 𝗍𝗁𝖾 𝖿𝗂𝖾𝗅𝖽?
𝖠) 𝖢𝖾𝗇𝗍𝗋𝗂𝖿𝗎𝗀𝖾
𝖡) 𝖶𝖺𝗍𝖾𝗋 𝖻𝖺𝗍𝗁
𝖢) 𝖠𝗅𝗍𝗂𝗆𝖾𝗍𝖾𝗋
𝖣) 𝖬𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠𝗅𝗍𝗂𝗆𝖾𝗍𝖾𝗋𝗌 𝖺𝗋𝖾 𝗎𝗌𝖾𝖽 𝗂𝗇 𝖿𝗂𝖾𝗅𝖽𝗐𝗈𝗋𝗄 𝗍𝗈 𝗆𝖾𝖺𝗌𝗎𝗋𝖾 𝖾𝗅𝖾𝗏𝖺𝗍𝗂𝗈𝗇.


29. 𝖶𝗁𝗂𝖼𝗁 𝗉𝖺𝗋𝗍 𝗈𝖿 𝖺 𝖼𝗈𝗆𝗉𝗈𝗎𝗇𝖽 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾 𝗁𝖾𝗅𝗉𝗌 𝗐𝗂𝗍𝗁 𝗋𝖾𝗌𝗈𝗅𝗎𝗍𝗂𝗈𝗇?
𝖠) 𝖲𝗍𝖺𝗀𝖾
𝖡) 𝖠𝗋𝗆
𝖢) 𝖮𝖻𝗃𝖾𝖼𝗍𝗂𝗏𝖾 𝗅𝖾𝗇𝗌
𝖣) 𝖬𝗂𝗋𝗋𝗈𝗋

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖮𝖻𝗃𝖾𝖼𝗍𝗂𝗏𝖾 𝗅𝖾𝗇𝗌𝖾𝗌 𝖽𝖾𝗍𝖾𝗋𝗆𝗂𝗇𝖾 𝗍𝗁𝖾 𝗋𝖾𝗌𝗈𝗅𝗎𝗍𝗂𝗈𝗇 𝖺𝗇𝖽 𝗆𝖺𝗀𝗇𝗂𝖿𝗂𝖼𝖺𝗍𝗂𝗈𝗇 𝗉𝗈𝗐𝖾𝗋.


30. 𝖶𝗁𝖺𝗍 𝗂𝗌 𝗍𝗁𝖾 𝗉𝗎𝗋𝗉𝗈𝗌𝖾 𝗈𝖿 𝗉𝗎𝖻𝗅𝗂𝗌𝗁𝗂𝗇𝗀 𝗌𝖼𝗂𝖾𝗇𝗍𝗂𝖿𝗂𝖼 𝖿𝗂𝗇𝖽𝗂𝗇𝗀𝗌?
𝖠) 𝖯𝖾𝗋𝗌𝗈𝗇𝖺𝗅 𝖿𝖺𝗆𝖾
𝖡) 𝖠𝗏𝗈𝗂𝖽𝗂𝗇𝗀 𝖿𝗎𝗍𝗎𝗋𝖾 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍𝗌
𝖢) 𝖲𝗁𝖺𝗋𝗂𝗇𝗀 𝗐𝗂𝗍𝗁 𝗈𝗍𝗁𝖾𝗋𝗌 𝖺𝗇𝖽 𝖺𝗏𝗈𝗂𝖽𝗂𝗇𝗀 𝗋𝖾𝗉𝖾𝗍𝗂𝗍𝗂𝗈𝗇
𝖣) 𝖥𝗈𝗋 𝗀𝗋𝖺𝖽𝗂𝗇𝗀

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖯𝗎𝖻𝗅𝗂𝗌𝗁𝗂𝗇𝗀 𝗁𝖾𝗅𝗉𝗌 𝖼𝗈𝗆𝗆𝗎𝗇𝗂𝖼𝖺𝗍𝖾 𝖿𝗂𝗇𝖽𝗂𝗇𝗀𝗌 𝖺𝗇𝖽 𝗉𝗋𝖾𝗏𝖾𝗇𝗍𝗌 𝗋𝖾𝖽𝗎𝗇𝖽𝖺𝗇𝗍 𝗋𝖾𝗌𝖾𝖺𝗋𝖼𝗁.

📌𝖳𝗈 𝗃𝗈𝗂𝗇 𝗍𝗁𝖾 𝗉𝗋𝗂𝗏𝖺𝗍𝖾 𝖼𝗅𝖺𝗌𝗌 𝖿𝗈𝗋 𝖿𝗋𝖾𝖾👇
https://t.me/harme_students2017/472

𝖡) 𝖤𝗋𝗋𝗈𝗋𝗌 𝗂𝗇 𝗉𝗋𝗈𝖼𝖾𝖽𝗎𝗋𝖾
𝖢) 𝖮𝖽𝖽 𝗋𝖾𝗌𝗎𝗅𝗍𝗌 𝗇𝗈𝗍 𝖿𝗂𝗍𝗍𝗂𝗇𝗀 𝗍𝗁𝖾 𝗉𝖺𝗍𝗍𝖾𝗋𝗇
𝖣) 𝖠𝗅𝗐𝖺𝗒𝗌 𝖺𝖼𝖼𝗎𝗋𝖺𝗍𝖾

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠𝗇𝗈𝗆𝖺𝗅𝗈𝗎𝗌 𝗋𝖾𝗌𝗎𝗅𝗍𝗌 𝖽𝖾𝗏𝗂𝖺𝗍𝖾 𝖿𝗋𝗈𝗆 𝗍𝗁𝖾 𝗀𝖾𝗇𝖾𝗋𝖺𝗅 𝗍𝗋𝖾𝗇𝖽 𝖺𝗇𝖽 𝗋𝖾𝗊𝗎𝗂𝗋𝖾 𝖿𝗎𝗋𝗍𝗁𝖾𝗋 𝖼𝗁𝖾𝖼𝗄𝗂𝗇𝗀.


17. 𝖵𝖺𝗅𝗂𝖽𝗂𝗍𝗒 𝗂𝗇 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍𝗌 𝗂𝗌 𝖾𝗇𝗌𝗎𝗋𝖾𝖽 𝖻𝗒:
𝖠) 𝖢𝗁𝖺𝗇𝗀𝗂𝗇𝗀 𝗆𝗎𝗅𝗍𝗂𝗉𝗅𝖾 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾𝗌
𝖡) 𝖢𝗈𝗇𝗍𝗋𝗈𝗅𝗅𝗂𝗇𝗀 𝖺𝗅𝗅 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾𝗌 𝖾𝗑𝖼𝖾𝗉𝗍 𝗈𝗇𝖾
𝖢) 𝖨𝗀𝗇𝗈𝗋𝗂𝗇𝗀 𝖼𝗈𝗇𝖿𝗅𝗂𝖼𝗍𝗂𝗇𝗀 𝖽𝖺𝗍𝖺
𝖣) 𝖬𝖺𝗄𝗂𝗇𝗀 𝗊𝗎𝗂𝖼𝗄 𝖺𝗌𝗌𝗎𝗆𝗉𝗍𝗂𝗈𝗇𝗌

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖡
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖵𝖺𝗅𝗂𝖽 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍𝗌 𝗍𝖾𝗌𝗍 𝗈𝗇𝗅𝗒 𝗈𝗇𝖾 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾 𝖺𝗍 𝖺 𝗍𝗂𝗆𝖾, 𝖼𝗈𝗇𝗍𝗋𝗈𝗅𝗅𝗂𝗇𝗀 𝗍𝗁𝖾 𝗋𝖾𝗌𝗍.


18. 𝖣𝖺𝗍𝖺 𝖺𝗇𝖺𝗅𝗒𝗌𝗂𝗌 𝗂𝗇𝗏𝗈𝗅𝗏𝖾𝗌:
𝖠) 𝖦𝗎𝖾𝗌𝗌𝗐𝗈𝗋𝗄
𝖡) 𝖱𝖺𝗇𝖽𝗈𝗆 𝗂𝗇𝗍𝖾𝗋𝗉𝗋𝖾𝗍𝖺𝗍𝗂𝗈𝗇
𝖢) 𝖲𝗒𝗌𝗍𝖾𝗆𝖺𝗍𝗂𝖼 𝗌𝗍𝗎𝖽𝗒 𝗈𝖿 𝗈𝗋𝗀𝖺𝗇𝗂𝗓𝖾𝖽 𝖽𝖺𝗍𝖺
𝖣) 𝖠𝗌𝗌𝗎𝗆𝗉𝗍𝗂𝗈𝗇𝗌

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠𝗇𝖺𝗅𝗒𝗌𝗂𝗌 𝗂𝗇𝗏𝗈𝗅𝗏𝖾𝗌 𝗋𝖾𝗏𝗂𝖾𝗐𝗂𝗇𝗀 𝗈𝗋𝗀𝖺𝗇𝗂𝗓𝖾𝖽 𝖽𝖺𝗍𝖺 𝖿𝗈𝗋 𝖾𝗌𝗌𝖾𝗇𝗍𝗂𝖺𝗅 𝗂𝗇𝗌𝗂𝗀𝗁𝗍𝗌.


19. 𝖶𝗁𝖺𝗍 𝖿𝗈𝗅𝗅𝗈𝗐𝗌 𝖺𝖿𝗍𝖾𝗋 𝖽𝖺𝗍𝖺 𝖺𝗇𝖺𝗅𝗒𝗌𝗂𝗌 𝗂𝗇 𝗍𝗁𝖾 𝗌𝖼𝗂𝖾𝗇𝗍𝗂𝖿𝗂𝖼 𝗆𝖾𝗍𝗁𝗈𝖽?
𝖠) 𝖬𝗈𝗋𝖾 𝗈𝖻𝗌𝖾𝗋𝗏𝖺𝗍𝗂𝗈𝗇
𝖡) 𝖢𝗈𝗇𝖼𝗅𝗎𝗌𝗂𝗈𝗇
𝖢) 𝖥𝗈𝗋𝗆𝗂𝗇𝗀 𝖺 𝗇𝖾𝗐 𝗁𝗒𝗉𝗈𝗍𝗁𝖾𝗌𝗂𝗌
𝖣) 𝖲𝗍𝖺𝗋𝗍𝗂𝗇𝗀 𝗈𝗏𝖾𝗋

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖡
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖢𝗈𝗇𝖼𝗅𝗎𝗌𝗂𝗈𝗇𝗌 𝖺𝗋𝖾 𝖽𝗋𝖺𝗐𝗇 𝖺𝖿𝗍𝖾𝗋 𝖺𝗇𝖺𝗅𝗒𝗓𝗂𝗇𝗀 𝗍𝗁𝖾 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍𝖺𝗅 𝖽𝖺𝗍𝖺.


20. 𝖠 𝗐𝖾𝗅𝗅-𝗍𝖾𝗌𝗍𝖾𝖽 𝗁𝗒𝗉𝗈𝗍𝗁𝖾𝗌𝗂𝗌 𝖻𝖾𝖼𝗈𝗆𝖾𝗌:
𝖠) 𝖠𝗇 𝖾𝗋𝗋𝗈𝗋
𝖡) 𝖠𝗇 𝖺𝗇𝗈𝗆𝖺𝗅𝗒
𝖢) 𝖠 𝗍𝗁𝖾𝗈𝗋𝗒
𝖣) 𝖠 𝗐𝗂𝗅𝖽 𝗀𝗎𝖾𝗌𝗌

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠 𝗁𝗒𝗉𝗈𝗍𝗁𝖾𝗌𝗂𝗌 𝖻𝖾𝖼𝗈𝗆𝖾𝗌 𝖺 𝗍𝗁𝖾𝗈𝗋𝗒 𝗐𝗁𝖾𝗇 𝗌𝗎𝗉𝗉𝗈𝗋𝗍𝖾𝖽 𝖻𝗒 𝖼𝗈𝗇𝗌𝗂𝗌𝗍𝖾𝗇𝗍 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍𝖺𝗅 𝗋𝖾𝗌𝗎𝗅𝗍𝗌.


21. 𝖠 𝗌𝖼𝗂𝖾𝗇𝗍𝗂𝖿𝗂𝖼 𝗆𝗈𝖽𝖾𝗅 𝗂𝗌:
𝖠) 𝖠 𝖿𝖺𝗌𝗁𝗂𝗈𝗇 𝗍𝖾𝗋𝗆
𝖡) 𝖠 𝗉𝗋𝗈𝗏𝖾𝗇 𝗅𝖺𝗐
𝖢) 𝖠 𝗌𝗂𝗆𝗉𝗅𝗂𝖿𝗂𝖾𝖽 𝗋𝖾𝗉𝗋𝖾𝗌𝖾𝗇𝗍𝖺𝗍𝗂𝗈𝗇
𝖣) 𝖠 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖬𝗈𝖽𝖾𝗅𝗌 𝖺𝗋𝖾 𝖺𝗇𝖺𝗅𝗈𝗀𝗂𝖾𝗌 𝗎𝗌𝖾𝖽 𝗍𝗈 𝗌𝗂𝗆𝗉𝗅𝗂𝖿𝗒 𝖺𝗇𝖽 𝗋𝖾𝗉𝗋𝖾𝗌𝖾𝗇𝗍 𝗌𝖼𝗂𝖾𝗇𝗍𝗂𝖿𝗂𝖼 𝗂𝖽𝖾𝖺𝗌.


22. 𝖶𝗁𝗂𝖼𝗁 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾 𝖼𝖺𝗇 𝗆𝖺𝗀𝗇𝗂𝖿𝗒 𝗎𝗉 𝗍𝗈 1500𝗑?
𝖠) 𝖣𝗂𝗌𝗌𝖾𝖼𝗍𝗂𝗇𝗀 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾
𝖡) 𝖫𝗂𝗀𝗁𝗍 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾
𝖢) 𝖤𝗅𝖾𝖼𝗍𝗋𝗈𝗇 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾
𝖣) 𝖯𝗁𝖺𝗌𝖾 𝖼𝗈𝗇𝗍𝗋𝖺𝗌𝗍 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖡
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖫𝗂𝗀𝗁𝗍 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾𝗌 𝖼𝖺𝗇 𝗆𝖺𝗀𝗇𝗂𝖿𝗒 𝗎𝗉 𝗍𝗈 1500 𝗍𝗂𝗆𝖾𝗌.


23. 𝖶𝗁𝗂𝖼𝗁 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾 𝗌𝗁𝗈𝗐𝗌 𝗍𝗁𝖾 𝗌𝗎𝗋𝖿𝖺𝖼𝖾 𝗈𝖿 𝖺𝗇 𝗈𝖻𝗃𝖾𝖼𝗍 𝗂𝗇 3𝖣 𝖽𝖾𝗍𝖺𝗂𝗅?
𝖠) 𝖳𝖤𝖬
𝖡) 𝖫𝗂𝗀𝗁𝗍 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾
𝖢) 𝖲𝖤𝖬
𝖣) 𝖯𝗁𝖺𝗌𝖾 𝖼𝗈𝗇𝗍𝗋𝖺𝗌𝗍

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖲𝖼𝖺𝗇𝗇𝗂𝗇𝗀 𝖾𝗅𝖾𝖼𝗍𝗋𝗈𝗇 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾𝗌 𝗌𝗁𝗈𝗐 𝗌𝗎𝗋𝖿𝖺𝖼𝖾 𝖽𝖾𝗍𝖺𝗂𝗅𝗌 𝗂𝗇 𝗍𝗁𝗋𝖾𝖾 𝖽𝗂𝗆𝖾𝗇𝗌𝗂𝗈𝗇𝗌.


24. 𝖶𝗁𝗂𝖼𝗁 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾 𝗋𝖾𝗏𝖾𝖺𝗅𝗌 𝖿𝗂𝗇𝖾 𝗂𝗇𝗍𝖾𝗋𝗇𝖺𝗅 𝗌𝗍𝗋𝗎𝖼𝗍𝗎𝗋𝖾𝗌?
𝖠) 𝖲𝖤𝖬
𝖡) 𝖳𝖤𝖬
𝖢) 𝖧𝖺𝗇𝖽 𝗅𝖾𝗇𝗌
𝖣) 𝖣𝗂𝗌𝗌𝖾𝖼𝗍𝗂𝗇𝗀 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖡
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖳𝗋𝖺𝗇𝗌𝗆𝗂𝗌𝗌𝗂𝗈𝗇 𝖾𝗅𝖾𝖼𝗍𝗋𝗈𝗇 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾𝗌 𝗌𝗁𝗈𝗐 𝖽𝖾𝗍𝖺𝗂𝗅𝖾𝖽 𝗂𝗇𝗍𝖾𝗋𝗇𝖺𝗅 𝗌𝗍𝗋𝗎𝖼𝗍𝗎𝗋𝖾𝗌.


25. 𝖶𝗁𝗂𝖼𝗁 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾 𝗂𝗌 𝖻𝗂𝗇𝗈𝖼𝗎𝗅𝖺𝗋 𝖺𝗇𝖽 𝗎𝗌𝖾𝖽 𝖿𝗈𝗋 𝖽𝗂𝗌𝗌𝖾𝖼𝗍𝗂𝗇𝗀?
𝖠) 𝖢𝗈𝗆𝗉𝗈𝗎𝗇𝖽 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾
𝖡) 𝖲𝖤𝖬
𝖢) 𝖣𝗂𝗌𝗌𝖾𝖼𝗍𝗂𝗇𝗀 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾
𝖣) 𝖯𝗁𝖺𝗌𝖾 𝖼𝗈𝗇𝗍𝗋𝖺𝗌𝗍 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖣𝗂𝗌𝗌𝖾𝖼𝗍𝗂𝗇𝗀 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾𝗌 𝗁𝖺𝗏𝖾 𝗍𝗐𝗈 𝗈𝖼𝗎𝗅𝖺𝗋 𝗅𝖾𝗇𝗌𝖾𝗌 𝖺𝗇𝖽 𝖺𝗋𝖾 𝗎𝗌𝖾𝖽 𝗂𝗇 𝖻𝗂𝗈𝗅𝗈𝗀𝗒 𝗅𝖺𝖻𝗌.


26. 𝖠 𝖻𝗂𝖼𝗈𝗇𝗏𝖾𝗑 𝗅𝖾𝗇𝗌 𝗂𝗌 𝗎𝗌𝖾𝖽 𝗂𝗇 𝖺:
𝖠) 𝖲𝗂𝗆𝗉𝗅𝖾 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾
𝖡) 𝖲𝖤𝖬
𝖢) 𝖨𝗇𝗍𝖾𝗋𝖿𝖾𝗋𝖾𝗇𝖼𝖾 𝗆𝗂𝖼𝗋𝗈𝗌𝖼𝗈𝗉𝖾
𝖣) 𝖳𝖤𝖬

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖣
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖨𝗇𝖽𝖾𝗉𝖾𝗇𝖽𝖾𝗇𝗍 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾𝗌 𝖺𝗋𝖾 𝖽𝖾𝗅𝗂𝖻𝖾𝗋𝖺𝗍𝖾𝗅𝗒 𝖼𝗁𝖺𝗇𝗀𝖾𝖽 𝗍𝗈 𝗌𝗍𝗎𝖽𝗒 𝗍𝗁𝖾𝗂𝗋 𝖾𝖿𝖿𝖾𝖼𝗍.


10. 𝖶𝗁𝗂𝖼𝗁 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾 𝖽𝖾𝗉𝖾𝗇𝖽𝗌 𝗈𝗇 𝗍𝗁𝖾 𝗂𝗇𝖽𝖾𝗉𝖾𝗇𝖽𝖾𝗇𝗍 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾?
𝖠) 𝖢𝗈𝗇𝗍𝗋𝗈𝗅𝗅𝖾𝖽
𝖡) 𝖢𝗈𝗇𝖿𝗈𝗎𝗇𝖽𝗂𝗇𝗀
𝖢) 𝖣𝖾𝗉𝖾𝗇𝖽𝖾𝗇𝗍
𝖣) 𝖲𝗍𝖺𝖻𝗅𝖾

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖳𝗁𝖾 𝖽𝖾𝗉𝖾𝗇𝖽𝖾𝗇𝗍 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾 𝖼𝗁𝖺𝗇𝗀𝖾𝗌 𝗂𝗇 𝗋𝖾𝗌𝗉𝗈𝗇𝗌𝖾 𝗍𝗈 𝗍𝗁𝖾 𝗂𝗇𝖽𝖾𝗉𝖾𝗇𝖽𝖾𝗇𝗍 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾.


11. 𝖶𝗁𝖺𝗍 𝖺𝗋𝖾 𝖼𝗈𝗇𝗍𝗋𝗈𝗅𝗅𝖾𝖽 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾𝗌?
𝖠) 𝖵𝖺𝗋𝗂𝖺𝖻𝗅𝖾𝗌 𝗍𝗁𝖺𝗍 𝖿𝗅𝗎𝖼𝗍𝗎𝖺𝗍𝖾 𝗇𝖺𝗍𝗎𝗋𝖺𝗅𝗅𝗒
𝖡) 𝖵𝖺𝗋𝗂𝖺𝖻𝗅𝖾𝗌 𝗂𝗇𝗍𝖾𝗇𝗍𝗂𝗈𝗇𝖺𝗅𝗅𝗒 𝗄𝖾𝗉𝗍 𝖼𝗈𝗇𝗌𝗍𝖺𝗇𝗍
𝖢) 𝖴𝗇𝗉𝗋𝖾𝖽𝗂𝖼𝗍𝖺𝖻𝗅𝖾 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾𝗌
𝖣) 𝖨𝗇𝖽𝖾𝗉𝖾𝗇𝖽𝖾𝗇𝗍 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾𝗌

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖡
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖢𝗈𝗇𝗍𝗋𝗈𝗅𝗅𝖾𝖽 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾𝗌 𝖺𝗋𝖾 𝗄𝖾𝗉𝗍 𝖼𝗈𝗇𝗌𝗍𝖺𝗇𝗍 𝗍𝗈 𝖾𝗇𝗌𝗎𝗋𝖾 𝖺 𝗏𝖺𝗅𝗂𝖽 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍.


12. 𝖶𝗁𝖺𝗍 𝗂𝗌 𝗍𝗁𝖾 𝗉𝗎𝗋𝗉𝗈𝗌𝖾 𝗈𝖿 𝖺 𝖼𝗈𝗇𝗍𝗋𝗈𝗅 𝗀𝗋𝗈𝗎𝗉 𝗂𝗇 𝖺𝗇 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍?
𝖠) 𝖳𝗈 𝖼𝗈𝗇𝖿𝗂𝗋𝗆 𝖺𝗅𝗅 𝗋𝖾𝗌𝗎𝗅𝗍𝗌
𝖡) 𝖳𝗈 𝖾𝗑𝗉𝗈𝗌𝖾 𝗌𝗎𝖻𝗃𝖾𝖼𝗍𝗌 𝗍𝗈 𝖺𝗅𝗅 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾𝗌
𝖢) 𝖳𝗈 𝗉𝗋𝗈𝗏𝗂𝖽𝖾 𝖺 𝖼𝗈𝗆𝗉𝖺𝗋𝗂𝗌𝗈𝗇
𝖣) 𝖳𝗈 𝖺𝖼𝗍 𝖺𝗌 𝗍𝗁𝖾 𝗆𝖺𝗂𝗇 𝗍𝖾𝗌𝗍 𝗀𝗋𝗈𝗎𝗉

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖳𝗁𝖾 𝖼𝗈𝗇𝗍𝗋𝗈𝗅 𝗀𝗋𝗈𝗎𝗉 𝗁𝖾𝗅𝗉𝗌 𝖼𝗈𝗆𝗉𝖺𝗋𝖾 𝖼𝗁𝖺𝗇𝗀𝖾𝗌 𝗌𝖾𝖾𝗇 𝗂𝗇 𝗍𝗁𝖾 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍𝖺𝗅 𝗀𝗋𝗈𝗎𝗉.


13. 𝖶𝗁𝖺𝗍 𝖼𝖺𝗎𝗌𝖾𝗌 𝗅𝗂𝗆𝖾𝗐𝖺𝗍𝖾𝗋 𝗍𝗈 𝗍𝗎𝗋𝗇 𝗆𝗂𝗅𝗄𝗒 𝗂𝗇 𝖺 𝗀𝖾𝗋𝗆𝗂𝗇𝖺𝗍𝗂𝗈𝗇 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍?
𝖠) 𝖫𝗂𝗀𝗁𝗍
𝖡) 𝖶𝖺𝗍𝖾𝗋
𝖢) 𝖢𝖮₂
𝖣) 𝖮𝗑𝗒𝗀𝖾𝗇

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖢𝖮₂ 𝗋𝖾𝗅𝖾𝖺𝗌𝖾𝖽 𝖽𝗎𝗋𝗂𝗇𝗀 𝗌𝖾𝖾𝖽 𝗋𝖾𝗌𝗉𝗂𝗋𝖺𝗍𝗂𝗈𝗇 𝗋𝖾𝖺𝖼𝗍𝗌 𝗐𝗂𝗍𝗁 𝗅𝗂𝗆𝖾𝗐𝖺𝗍𝖾𝗋, 𝗆𝖺𝗄𝗂𝗇𝗀 𝗂𝗍 𝗆𝗂𝗅𝗄𝗒.


14. 𝖶𝗁𝗂𝖼𝗁 𝗍𝗈𝗈𝗅 𝗉𝗋𝗈𝗏𝗂𝖽𝖾𝗌 𝗍𝗁𝖾 𝗆𝗈𝗌𝗍 𝖺𝖼𝖼𝗎𝗋𝖺𝗍𝖾 𝗍𝗂𝗆𝖾 𝗆𝖾𝖺𝗌𝗎𝗋𝖾𝗆𝖾𝗇𝗍?
𝖠) 𝖢𝗅𝗈𝖼𝗄
𝖡) 𝖶𝗋𝗂𝗌𝗍𝗐𝖺𝗍𝖼𝗁
𝖢) 𝖲𝗍𝗈𝗉-𝖼𝗅𝗈𝖼𝗄
𝖣) 𝖢𝖺𝗅𝖾𝗇𝖽𝖺𝗋

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠 𝗌𝗍𝗈𝗉-𝖼𝗅𝗈𝖼𝗄 𝗂𝗌 𝗉𝗋𝖾𝖼𝗂𝗌𝖾 𝖺𝗇𝖽 𝗌𝗎𝗂𝗍𝖺𝖻𝗅𝖾 𝖿𝗈𝗋 𝗆𝖾𝖺𝗌𝗎𝗋𝗂𝗇𝗀 𝗌𝗁𝗈𝗋𝗍 𝗍𝗂𝗆𝖾 𝗂𝗇𝗍𝖾𝗋𝗏𝖺𝗅𝗌.


15. 𝖶𝗁𝖺𝗍 𝖾𝗇𝗌𝗎𝗋𝖾𝗌 𝗍𝗁𝖾 𝖽𝖾𝗉𝖾𝗇𝖽𝖺𝖻𝗂𝗅𝗂𝗍𝗒 𝗈𝖿 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍𝖺𝗅 𝗋𝖾𝗌𝗎𝗅𝗍𝗌?
𝖠) 𝖠𝖼𝖼𝗎𝗋𝖺𝖼𝗒
𝖡) 𝖵𝖺𝗅𝗂𝖽𝗂𝗍𝗒
𝖢) 𝖱𝖾𝗅𝗂𝖺𝖻𝗂𝗅𝗂𝗍𝗒
𝖣) 𝖱𝖺𝗇𝖽𝗈𝗆𝗇𝖾𝗌𝗌

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖱𝖾𝗅𝗂𝖺𝖻𝗂𝗅𝗂𝗍𝗒 𝗂𝗇𝖽𝗂𝖼𝖺𝗍𝖾𝗌 𝗁𝗈𝗐 𝗋𝖾𝗉𝖾𝖺𝗍𝖺𝖻𝗅𝖾 𝖺𝗇𝖽 𝖼𝗈𝗇𝗌𝗂𝗌𝗍𝖾𝗇𝗍 𝗋𝖾𝗌𝗎𝗅𝗍𝗌 𝖺𝗋𝖾.


16. 𝖠𝗇𝗈𝗆𝖺𝗅𝗈𝗎𝗌 𝗋𝖾𝗌𝗎𝗅𝗍𝗌 𝖺𝗋𝖾:
𝖠) 𝖢𝗈𝗇𝗌𝗂𝗌𝗍𝖾𝗇𝗍 𝗐𝗂𝗍𝗁 𝖽𝖺𝗍𝖺

𝖢𝗋𝗒𝗉𝗍𝗈
🦠𝖡𝖨𝖮𝖫𝖮𝖦𝖸

♻️30 𝗆𝗎𝗅𝗍𝗂𝗉𝗅𝖾 𝖼𝗁𝗈𝗂𝖼𝖾 𝗊𝗎𝖾𝗌𝗍𝗂𝗈𝗇𝗌 𝖻𝖺𝗌𝖾𝖽 𝗈𝗇 𝗍𝗁𝖾 𝖴𝗇𝗂𝗍 1 𝖡𝗂𝗈𝗅𝗈𝗀𝗒.

1. 𝖶𝗁𝖺𝗍 𝖽𝗈𝖾𝗌 𝗍𝗁𝖾 𝗐𝗈𝗋𝖽 "𝖡𝗂𝗈𝗅𝗈𝗀𝗒" 𝗅𝗂𝗍𝖾𝗋𝖺𝗅𝗅𝗒 𝗆𝖾𝖺𝗇?
𝖠) 𝖲𝗍𝗎𝖽𝗒 𝗈𝖿 𝖼𝗁𝖾𝗆𝗂𝖼𝖺𝗅𝗌
𝖡) 𝖲𝗍𝗎𝖽𝗒 𝗈𝖿 𝗍𝗁𝖾 𝖻𝗈𝖽𝗒
𝖢) 𝖲𝗍𝗎𝖽𝗒 𝗈𝖿 𝗅𝗂𝖿𝖾
𝖣) 𝖲𝗍𝗎𝖽𝗒 𝗈𝖿 𝖤𝖺𝗋𝗍𝗁

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: "𝖡𝗂𝗈𝗅𝗈𝗀𝗒" 𝗂𝗌 𝖽𝖾𝗋𝗂𝗏𝖾𝖽 𝖿𝗋𝗈𝗆 𝖦𝗋𝖾𝖾𝗄: "𝖻𝗂𝗈𝗌" (𝗅𝗂𝖿𝖾) 𝖺𝗇𝖽 "𝗅𝗈𝗀𝗈𝗌" (𝗌𝗍𝗎𝖽𝗒), 𝗆𝖾𝖺𝗇𝗂𝗇𝗀 𝗍𝗁𝖾 𝗌𝗍𝗎𝖽𝗒 𝗈𝖿 𝗅𝗂𝖿𝖾.


2. 𝖶𝗁𝗂𝖼𝗁 𝗈𝖿 𝗍𝗁𝖾 𝖿𝗈𝗅𝗅𝗈𝗐𝗂𝗇𝗀 𝗂𝗌 𝖺 𝖼𝗁𝖺𝗋𝖺𝖼𝗍𝖾𝗋𝗂𝗌𝗍𝗂𝖼 𝗈𝖿 𝗌𝖼𝗂𝖾𝗇𝖼𝖾?
𝖠) 𝖨𝗍 𝗂𝗌 𝖺 𝖿𝗂𝗑𝖾𝖽 𝖻𝗈𝖽𝗒 𝗈𝖿 𝖿𝖺𝖼𝗍𝗌
𝖡) 𝖨𝗍 𝖺𝗏𝗈𝗂𝖽𝗌 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍𝗌
𝖢) 𝖨𝗍 𝗂𝗌 𝖻𝖺𝗌𝖾𝖽 𝗈𝗇 𝗍𝗁𝖾 𝗌𝖼𝗂𝖾𝗇𝗍𝗂𝖿𝗂𝖼 𝗆𝖾𝗍𝗁𝗈𝖽
𝖣) 𝖨𝗍 𝗂𝗌 𝗉𝗎𝗋𝖾𝗅𝗒 𝗍𝗁𝖾𝗈𝗋𝖾𝗍𝗂𝖼𝖺𝗅

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖲𝖼𝗂𝖾𝗇𝖼𝖾 𝗂𝗌 𝖺 𝗌𝗒𝗌𝗍𝖾𝗆 𝗈𝖿 𝖺𝖼𝗊𝗎𝗂𝗋𝗂𝗇𝗀 𝗄𝗇𝗈𝗐𝗅𝖾𝖽𝗀𝖾 𝗎𝗌𝗂𝗇𝗀 𝗅𝗈𝗀𝗂𝖼𝖺𝗅 𝗌𝗍𝖾𝗉𝗌 𝗄𝗇𝗈𝗐𝗇 𝖺𝗌 𝗍𝗁𝖾 𝗌𝖼𝗂𝖾𝗇𝗍𝗂𝖿𝗂𝖼 𝗆𝖾𝗍𝗁𝗈𝖽.


3. 𝖶𝗁𝖺𝗍 𝗂𝗌 𝖺𝗇 𝗈𝗋𝗀𝖺𝗇𝗂𝗌𝗆?
𝖠) 𝖠 𝗍𝗒𝗉𝖾 𝗈𝖿 𝗍𝗈𝗈𝗅
𝖡) 𝖠 𝖼𝗁𝖾𝗆𝗂𝖼𝖺𝗅 𝗋𝖾𝖺𝖼𝗍𝗂𝗈𝗇
𝖢) 𝖠 𝗅𝗂𝗏𝗂𝗇𝗀 𝖻𝖾𝗂𝗇𝗀 𝗆𝖺𝖽𝖾 𝗈𝖿 𝗈𝗇𝖾 𝗈𝗋 𝗆𝗈𝗋𝖾 𝖼𝖾𝗅𝗅𝗌
𝖣) 𝖠 𝖻𝗂𝗈𝗅𝗈𝗀𝗂𝖼𝖺𝗅 𝗆𝖾𝗍𝗁𝗈𝖽

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠𝗇 𝗈𝗋𝗀𝖺𝗇𝗂𝗌𝗆 𝗂𝗌 𝖺𝗇𝗒 𝗅𝗂𝗏𝗂𝗇𝗀 𝖻𝖾𝗂𝗇𝗀 𝖼𝗈𝗆𝗉𝗈𝗌𝖾𝖽 𝗈𝖿 𝗈𝗇𝖾 𝗈𝗋 𝗆𝖺𝗇𝗒 𝖼𝖾𝗅𝗅𝗌.


4. 𝖶𝗁𝖺𝗍 𝗍𝗒𝗉𝖾 𝗈𝖿 𝗌𝖼𝗂𝖾𝗇𝖼𝖾 𝗂𝗌 𝗎𝗌𝖾𝖽 𝗍𝗈 𝗆𝖾𝖾𝗍 𝗁𝗎𝗆𝖺𝗇 𝗇𝖾𝖾𝖽𝗌?
𝖠) 𝖳𝗁𝖾𝗈𝗋𝖾𝗍𝗂𝖼𝖺𝗅 𝗌𝖼𝗂𝖾𝗇𝖼𝖾
𝖡) 𝖤𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍𝖺𝗅 𝗌𝖼𝗂𝖾𝗇𝖼𝖾
𝖢) 𝖠𝗉𝗉𝗅𝗂𝖾𝖽 𝗌𝖼𝗂𝖾𝗇𝖼𝖾
𝖣) 𝖠𝖻𝗌𝗈𝗅𝗎𝗍𝖾 𝗌𝖼𝗂𝖾𝗇𝖼𝖾

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠𝗉𝗉𝗅𝗂𝖾𝖽 𝗌𝖼𝗂𝖾𝗇𝖼𝖾 𝗂𝗌 𝗎𝗌𝖾𝖽 𝗍𝗈 𝖺𝖽𝖽𝗋𝖾𝗌𝗌 𝗁𝗎𝗆𝖺𝗇 𝗇𝖾𝖾𝖽𝗌 𝗌𝗎𝖼𝗁 𝖺𝗌 𝖼𝗎𝗋𝗂𝗇𝗀 𝖽𝗂𝗌𝖾𝖺𝗌𝖾𝗌 𝖺𝗇𝖽 𝗋𝖾𝗌𝗈𝗎𝗋𝖼𝖾 𝗆𝖺𝗇𝖺𝗀𝖾𝗆𝖾𝗇𝗍.


5. 𝖶𝗁𝖺𝗍 𝗂𝗌 𝗍𝗁𝖾 𝖿𝗂𝗋𝗌𝗍 𝗌𝗍𝖾𝗉 𝗂𝗇 𝗍𝗁𝖾 𝗌𝖼𝗂𝖾𝗇𝗍𝗂𝖿𝗂𝖼 𝗆𝖾𝗍𝗁𝗈𝖽?
𝖠) 𝖯𝗋𝖾𝖽𝗂𝖼𝗍𝗂𝗈𝗇
𝖡) 𝖧𝗒𝗉𝗈𝗍𝗁𝖾𝗌𝗂𝗌
𝖢) 𝖮𝖻𝗌𝖾𝗋𝗏𝖺𝗍𝗂𝗈𝗇
𝖣) 𝖤𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖮𝖻𝗌𝖾𝗋𝗏𝖺𝗍𝗂𝗈𝗇 𝗂𝗌 𝗍𝗁𝖾 𝗂𝗇𝗂𝗍𝗂𝖺𝗅 𝗌𝗍𝖾𝗉 𝗐𝗁𝖾𝗋𝖾 𝗉𝗁𝖾𝗇𝗈𝗆𝖾𝗇𝖺 𝖺𝗋𝖾 𝖽𝗂𝗋𝖾𝖼𝗍𝗅𝗒 𝗈𝗋 𝗂𝗇𝖽𝗂𝗋𝖾𝖼𝗍𝗅𝗒 𝖾𝗑𝖺𝗆𝗂𝗇𝖾𝖽.


6. 𝖶𝗁𝖺𝗍 𝗂𝗌 𝖺 𝗁𝗒𝗉𝗈𝗍𝗁𝖾𝗌𝗂𝗌?
𝖠) 𝖠 𝖼𝗈𝗇𝖿𝗂𝗋𝗆𝖾𝖽 𝗍𝗁𝖾𝗈𝗋𝗒
𝖡) 𝖠 𝗐𝗂𝗅𝖽 𝗀𝗎𝖾𝗌𝗌
𝖢) 𝖠 𝗍𝖾𝗇𝗍𝖺𝗍𝗂𝗏𝖾 𝖾𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇 𝖻𝖺𝗌𝖾𝖽 𝗈𝗇 𝗈𝖻𝗌𝖾𝗋𝗏𝖺𝗍𝗂𝗈𝗇
𝖣) 𝖠 𝗉𝗋𝗈𝗏𝖾𝗇 𝖼𝗈𝗇𝖼𝗅𝗎𝗌𝗂𝗈𝗇

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖢
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖠 𝗁𝗒𝗉𝗈𝗍𝗁𝖾𝗌𝗂𝗌 𝗂𝗌 𝖺𝗇 𝗂𝗇𝗍𝖾𝗅𝗅𝗂𝗀𝖾𝗇𝗍, 𝗍𝖾𝗌𝗍𝖺𝖻𝗅𝖾 𝗀𝗎𝖾𝗌𝗌 𝖻𝖺𝗌𝖾𝖽 𝗈𝗇 𝗀𝖺𝗍𝗁𝖾𝗋𝖾𝖽 𝗂𝗇𝖿𝗈𝗋𝗆𝖺𝗍𝗂𝗈𝗇.


7. 𝖶𝗁𝗂𝖼𝗁 𝗍𝗒𝗉𝖾 𝗈𝖿 𝗋𝖾𝖺𝗌𝗈𝗇𝗂𝗇𝗀 𝗆𝗈𝗏𝖾𝗌 𝖿𝗋𝗈𝗆 𝗌𝗉𝖾𝖼𝗂𝖿𝗂𝖼 𝗈𝖻𝗌𝖾𝗋𝗏𝖺𝗍𝗂𝗈𝗇𝗌 𝗍𝗈 𝗀𝖾𝗇𝖾𝗋𝖺𝗅 𝖼𝗈𝗇𝖼𝗅𝗎𝗌𝗂𝗈𝗇𝗌?
𝖠) 𝖣𝖾𝖽𝗎𝖼𝗍𝗂𝗏𝖾 𝗋𝖾𝖺𝗌𝗈𝗇𝗂𝗇𝗀
𝖡) 𝖨𝗇𝖽𝗎𝖼𝗍𝗂𝗏𝖾 𝗋𝖾𝖺𝗌𝗈𝗇𝗂𝗇𝗀
𝖢) 𝖱𝖺𝗇𝖽𝗈𝗆 𝗋𝖾𝖺𝗌𝗈𝗇𝗂𝗇𝗀
𝖣) 𝖨𝗇𝗍𝗋𝗈𝗌𝗉𝖾𝖼𝗍𝗂𝗏𝖾 𝗋𝖾𝖺𝗌𝗈𝗇𝗂𝗇𝗀

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖡
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖨𝗇𝖽𝗎𝖼𝗍𝗂𝗏𝖾 𝗋𝖾𝖺𝗌𝗈𝗇𝗂𝗇𝗀 𝗀𝖾𝗇𝖾𝗋𝖺𝗅𝗂𝗓𝖾𝗌 𝖿𝗋𝗈𝗆 𝗌𝗉𝖾𝖼𝗂𝖿𝗂𝖼 𝖾𝗑𝖺𝗆𝗉𝗅𝖾𝗌.


8. 𝖶𝗁𝗂𝖼𝗁 𝗍𝗒𝗉𝖾 𝗈𝖿 𝗋𝖾𝖺𝗌𝗈𝗇𝗂𝗇𝗀 𝖻𝖾𝗀𝗂𝗇𝗌 𝗐𝗂𝗍𝗁 𝖺 𝗀𝖾𝗇𝖾𝗋𝖺𝗅 𝗂𝖽𝖾𝖺 𝖺𝗇𝖽 𝗍𝖾𝗌𝗍𝗌 𝗂𝗍 𝗍𝗁𝗋𝗈𝗎𝗀𝗁 𝗌𝗉𝖾𝖼𝗂𝖿𝗂𝖼 𝖼𝖺𝗌𝖾𝗌?
𝖠) 𝖣𝖾𝖽𝗎𝖼𝗍𝗂𝗏𝖾 𝗋𝖾𝖺𝗌𝗈𝗇𝗂𝗇𝗀
𝖡) 𝖨𝗇𝖽𝗎𝖼𝗍𝗂𝗏𝖾 𝗋𝖾𝖺𝗌𝗈𝗇𝗂𝗇𝗀
𝖢) 𝖢𝗋𝖾𝖺𝗍𝗂𝗏𝖾 𝗋𝖾𝖺𝗌𝗈𝗇𝗂𝗇𝗀
𝖣) 𝖱𝖾𝖿𝗅𝖾𝖼𝗍𝗂𝗏𝖾 𝗋𝖾𝖺𝗌𝗈𝗇𝗂𝗇𝗀

➲𝖠𝗇𝗌𝗐𝖾𝗋: 𝖠
𝖤𝗑𝗉𝗅𝖺𝗇𝖺𝗍𝗂𝗈𝗇: 𝖣𝖾𝖽𝗎𝖼𝗍𝗂𝗏𝖾 𝗋𝖾𝖺𝗌𝗈𝗇𝗂𝗇𝗀 𝗆𝗈𝗏𝖾𝗌 𝖿𝗋𝗈𝗆 𝗀𝖾𝗇𝖾𝗋𝖺𝗅 𝗉𝗋𝖾𝗆𝗂𝗌𝖾𝗌 𝗍𝗈 𝗌𝗉𝖾𝖼𝗂𝖿𝗂𝖼 𝖼𝗈𝗇𝖼𝗅𝗎𝗌𝗂𝗈𝗇𝗌.


9. 𝖶𝗁𝖺𝗍 𝗂𝗌 𝖺𝗇 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍𝖺𝗅 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾 𝗍𝗁𝖺𝗍 𝗂𝗌 𝖼𝗁𝖺𝗇𝗀𝖾𝖽 𝖽𝗎𝗋𝗂𝗇𝗀 𝖺𝗇 𝖾𝗑𝗉𝖾𝗋𝗂𝗆𝖾𝗇𝗍?
𝖠) 𝖢𝗈𝗇𝗍𝗋𝗈𝗅𝗅𝖾𝖽 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾
𝖡) 𝖢𝗈𝗇𝖿𝗈𝗎𝗇𝖽𝗂𝗇𝗀 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾
𝖢) 𝖣𝖾𝗉𝖾𝗇𝖽𝖾𝗇𝗍 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾
𝖣) 𝖨𝗇𝖽𝖾𝗉𝖾𝗇𝖽𝖾𝗇𝗍 𝗏𝖺𝗋𝗂𝖺𝖻𝗅𝖾

16. Which sub-discipline is most closely linked to biology?
A) Urban geography
B) Geomorphology
C) Biogeography
D) Political geography

➲Answer: C
Explanation: Biogeography studies plant and animal distributions, linking it with biology.


17. What science is meteorology linked with in geography?
A) Biogeography
B) Climatology
C) Soil Geography
D) Population Geography

➲Answer: B
Explanation: Meteorology relates closely to climatology in geography.


18. What does geomorphology study?
A) Human settlements
B) Political systems
C) Landforms and earth’s surface changes
D) Climate zones

➲Answer: C
Explanation: Geomorphology focuses on the formation and changes of landforms.


19. The “anthroposphere” relates to:
A) Oceans
B) The human-made environment
C) Earth's mantle
D) Plant ecosystems

➲Answer: B
Explanation: The anthroposphere includes human-altered or human-made features.


20. A formal region is defined by:
A) Functional linkages
B) Unique climate
C) Homogeneity in specific characteristics
D) Cultural traditions only

➲Answer: C
Explanation: A formal region has uniform characteristics like climate or language.


21. Urban geography studies:
A) Ocean currents
B) Agricultural land use
C) Towns and cities
D) Weather patterns

➲Answer: C
Explanation: Urban geography focuses on the growth and organization of urban areas.


22. Possibilism supports the idea that:
A) Nature controls humans completely
B) Only the environment changes humans
C) Humans can alter and benefit from nature
D) Climate is the sole influence on culture

➲Answer: C
Explanation: Possibilism holds that humans can shape the environment using technology and knowledge.


23. Geography was once considered:
A) A theoretical science only
B) Unscientific and solely descriptive
C) A branch of chemistry
D) Limited to cartography

➲Answer: B
Explanation: Before the quantitative revolution, geography was often viewed as purely descriptive.


24. Historical geography studies:
A) The internal structure of the earth
B) Past geographic conditions and changes
C) Future economic plans
D) Animal populations

➲Answer: B
Explanation: Historical geography examines how places have changed over time.


25. Which is not a theme of geography?
A) Movement
B) Climate
C) Region
D) Location

➲Answer: B
Explanation: While important, climate is a topic within geography, not one of its five core themes.


26. The site of a place refers to:
A) Its economic value
B) Its exact coordinates
C) Its physical characteristics
D) Its population density

➲Answer: C
Explanation: Site refers to the actual physical features of a location.


27. What approach is used to study global climate patterns?
A) Regional
B) Topical
C) Cultural
D) Political

➲Answer: B
Explanation: The topical approach analyzes specific phenomena like climate globally.


28. Which of the following is not a sphere studied in geography?
A) Lithosphere
B) Stratosphere
C) Biosphere
D) Hydrosphere

➲Answer: B
Explanation: Geography focuses on the troposphere, not the stratosphere.


29. Who are considered pioneers in geographic thought?
A) Karl Marx and Darwin
B) Humboldt and Ritter
C) Febvre and Yeates
D) Demolins and Febvre

➲Answer: B
Explanation: Humboldt and Ritter are regarded as foundational figures in geography.


30. What was a key outcome of the quantitative revolution?
A) Abandoning regional studies
B) Increased use of computers and models
C) Emphasis on descriptive narratives
D) Separation of physical and human geography

➲Answer: B
Explanation: The revolution led to statistical modeling and the use of computers in geographic research.

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🌍GEOGRAPHY

♻️30 multiple-choice questions based on the "Unit 1 Geography".


1. Who is known for defining geography as the “description of the earth”?
A) Hartshorne
B) Yeates
C) Eratosthenes
D) Ritter

➲Answer: C
Explanation: Eratosthenes is credited with one of the earliest definitions of geography as the description of the earth.


2. Which branch of geography studies natural features like landforms and climate?
A) Human Geography
B) Economic Geography
C) Political Geography
D) Physical Geography

➲Answer: D
Explanation: Physical Geography studies natural aspects like climate, soil, and landforms.


3. What does climatology focus on?
A) Economic interactions
B) Human settlements
C) Distribution of landforms
D) Variation and distribution of climate

➲Answer: D
Explanation: Climatology studies factors that create and affect climate.


4. Which branch studies population distribution and structure?
A) Cultural Geography
B) Population Geography
C) Political Geography
D) Urban Geography

➲Answer: B
Explanation: Population Geography focuses on population data such as growth and structure.


5. What is the primary concern of political geography?
A) Ocean currents
B) Soil characteristics
C) Power and decision-making systems
D) Animal habitats

➲Answer: C
Explanation: Political geography studies how people use political systems to exercise power.


6. What does “place” refer to in geography?
A) A method of research
B) Human-environment interaction
C) A location’s physical and human aspects
D) Political borders

➲Answer: C
Explanation: “Place” describes the physical and human characteristics of a location.


7. What term defines geography as a study of spatial distribution of phenomena?
A) General geography
B) Environmental studies
C) Spatial science
D) Socio-geography

➲Answer: C
Explanation: Geography is often defined as a spatial science due to its focus on spatial patterns.


8. What kind of region is defined by functional interrelationships?
A) Cultural region
B) Formal region
C) Functional or nodal region
D) Physical region

➲Answer: C
Explanation: Functional regions are defined by interactions or connections, like trade or transport.


9. The topical approach in geography focuses on:
A) One place and its features
B) Universal laws of nature
C) Specific themes across multiple places
D) Cultural differences

➲Answer: C
Explanation: The topical/systematic approach studies specific phenomena across different locations.


10. Which is an example of a regional approach?
A) The geography of migration
B) The geography of agriculture
C) The geography of Africa
D) The geography of population

➲Answer: C
Explanation: The regional approach focuses on particular geographic areas like continents.


11. What is “human-environment interaction”?
A) Mapping cities
B) Describing economic activities
C) How humans depend on and affect the environment
D) Analyzing climate zones

➲Answer: C
Explanation: This theme addresses dependency, adaptation, and modification of the environment by humans.


12. Who postulated environmental possibilism?
A) Darwin
B) Humboldt
C) Febvre
D) Ritter

➲Answer: C
Explanation: Febvre is associated with introducing the concept of environmental possibilism.


13. What is environmental determinism?
A) The belief that humans dominate nature
B) Nature has no effect on humans
C) The environment shapes human life
D) Humans adapt nature freely

➲Answer: C
Explanation: Determinism emphasizes the environment’s influence over human activity.


14. Which revolution introduced statistical methods to geography?
A) Cultural revolution
B) Industrial revolution
C) Agricultural revolution
D) Quantitative revolution

➲Answer: D
Explanation: The Quantitative Revolution introduced statistical and mathematical methods into geography.


15. Applied geography is primarily concerned with:
A) Philosophical questions
B) Physical theory
C) Solving real-world problems
D) Artistic mapping

➲Answer: C
Explanation: Applied geography uses geographic knowledge to solve socio-economic and environmental problems.

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