अंग्रेजी भाषा दक्षता परीक्षा IELTS, PTE, TOEFL र Duolingo तयारी
अंग्रेजी भाषा दक्षता परीक्षा – IELTS, PTE, TOEFL र Duolingo
IELTS / PTE / TOEFL / Duolingo · IELTS / PTE / TOEFL / Duolingo
२,३३० प्रश्न उपलब्ध। मोड छान्नुहोस्:
English Test: प्रश्न र उत्तर
सही लागेको विकल्पमा थिच्नुहोस्। सही भए हरियो, गलत भए रातो देखिन्छ; ३ सेकेन्डपछि सही उत्तर र व्याख्या देखिन्छ।
सही: ० / ०
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A coin is tossed 4 times. What is the probability of getting at least one tail?
सही उत्तर: घ) 15/16
P(no tails) = (1/2)^4 = 1/16, so P(at least one tail) = 1 − 1/16 = 15/16. 1/16 is the complement itself.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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A card is drawn from a standard 52-card deck. What is the probability that it is a king or a heart?
सही उत्तर: ग) 4/13
P(king) + P(heart) − P(king of hearts) = 4/52 + 13/52 − 1/52 = 16/52 = 4/13. 17/52 double-counts the king of hearts.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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A bag has 4 red and 6 blue balls. Two balls are drawn without replacement. What is the probability that both are red?
सही उत्तर: ख) 2/15
(4/10) × (3/9) = 12/90 = 2/15. 4/25 = (4/10)² assumes replacement.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Two fair dice are rolled. What is the probability that the sum is 7?
सही उत्तर: क) 1/6
Six of the 36 outcomes give 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), so 6/36 = 1/6. 1/9 (4/36) is the probability of a sum of 5 (or, separately, of 9).
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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A fair coin is tossed 3 times. What is the probability of getting exactly 2 heads?
सही उत्तर: घ) 3/8
There are 8 equally likely outcomes, and exactly 2 heads occurs in 3 (HHT, HTH, THH): 3/8. 1/4 would be (1/2)² ignoring the third toss and arrangements.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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How many distinct arrangements are there of the letters of the word LEVEL?
सही उत्तर: ग) 30
5 letters with L twice and E twice: 5!/(2!·2!) = 30. 120 ignores the repeated letters.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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How many different committees of 3 can be chosen from 8 people?
सही उत्तर: ख) 56
C(8, 3) = 8!/(3!5!) = 56. 336 is the number of ordered selections (permutations), which overcounts by 3! = 6.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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In how many ways can 5 different books be arranged on a shelf?
सही उत्तर: क) 120
5! = 5 × 4 × 3 × 2 × 1 = 120. 3125 = 5^5 would allow books to repeat.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Which set of side lengths CANNOT form a triangle?
सही उत्तर: घ) 3, 4, 8
Triangle inequality: the sum of any two sides must exceed the third. 3 + 4 = 7 < 8, so 3, 4, 8 fails; 6 + 7 = 13 > 12, so 6, 7, 12 works.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
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Two similar triangles have corresponding sides in the ratio 2 : 3. What is the ratio of their areas?
सही उत्तर: ग) 4 : 9
Areas of similar figures scale with the square of the side ratio: 2² : 3² = 4 : 9. 8 : 27 is the ratio of volumes of similar solids.
💬 टिप्पणी / गल्ती रिपोर्ट (०)
यी अभ्यास प्रश्न हुन्, आधिकारिक प्रश्न होइनन्। पाठ्यक्रम, विज्ञापन र नतिजाका लागि सम्बन्धित निकायको आधिकारिक वेबसाइट हेर्नुहोस्। उत्तरमा गल्ती भेटे प्रश्नमुनिको "टिप्पणी / गल्ती रिपोर्ट" मा लेख्नुहोस्।
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