Indian Navy 10+2 B.Tech Cadet JEE Main 2023 Mixed — practice questions

Explore 2 free JEE Main 2023 Mixed questions in Indian Navy 10+2 B.Tech Cadet Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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JEE Main 2023 Mixed questions and exercises with answers

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lim_(x→0) (e^x - 1)/sin x =Read the answer and worked solution →Two cards drawn from a deck of 52 (without replacement). P(both aces):Read the answer and worked solution →

Worked practice questions

lim_(x→0) (e^x - 1)/sin x =

1
-1
0
∞

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Correct answer: A. 1

**Use Taylor:** e^x - 1 ≈ x for small x; sin x ≈ x. Ratio → 1. Also L'Hôpital: e^x / cos x → 1/1 = 1.

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Two cards drawn from a deck of 52 (without replacement). P(both aces):

1/4
1/52
1/16
C(4,2)/C(52,2) = 6/1326 = 1/221

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Correct answer: D. C(4,2)/C(52,2) = 6/1326 = 1/221

P(both aces) = (4/52)(3/51) = 12/2652 = 1/221 ≈ 0.0045.