Day 250: CBSE Class 12 Maths

5 questions (8 parts). Try each one first, then open its answer.

Question 1
Integrals. Asked once: 2025 (same type asked 5 times)
14 $\int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha}\, dx$
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Question 2 (case study, 4 parts)
Probability. Asked once: 2024 (same type asked 5 times)
A departmental store sends bills to charge its customers once a month. Past experience shows that 70% of its customers pay their first month bill in time. The store also found that the customer who pays the bill in time has the probability of 0.8 of paying in time next month and the customer who doesn't pay in time has the probability of 0.4 of paying in time the next month. Based on the above information, answer the following questions :
38 (i) $\mathrm{E}_1$
38 (ii) $P(\mathrm{A}|\mathrm{E}_1)$
38 (iii) (a) $Find the probability of customer paying second month's bill in time.$
38 (iii) (b) $Find the probability of customer paying first month's bill in time if it is found that customer has paid the second month's bill in time.$
Question 3
Probability. Asked once: 2024 (same type asked 5 times)
18 $P(A/B) = P(B/A) \ne 0$
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Question 4
Probability. Asked once: 2023 (same type asked 5 times)
18 $Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is$
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Question 5
Continuity and Differentiability. Asked once: 2024 (same type asked 4 times)
22 (a) $f(x) = |\tan 2x|$

Question 1