Day 262: CBSE Class 12 Maths

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

Question 1
Differential Equations. Asked once: 2024 (same type asked 5 times)
14 $\dfrac{d^4y}{dx^4} - \sin\left(\dfrac{d^2y}{dx^2}\right) = 5$
Tap an option to check your answer.
Question 2
Integrals. Asked once: 2022 (same type asked 5 times)
8 (b) $\displaystyle\int_1^4 \{|x| + |3 - x|\} \, dx$
Question 3
Integrals. Asked once: 2023 (same type asked 5 times)
30 (b) $\int \frac{\sin^{-1} x}{(1 - x^2)^{3/2}} \, dx$
Question 4
Integrals. Asked once: 2024 (same type asked 5 times)
29 (b) $\int\limits_{0}^{\pi/4} \dfrac{1}{\sin x + \cos x}\, dx$
Question 5 (case study, 4 parts)
Probability. Asked once: 2023 (same type asked 5 times)
A building contractor undertakes a job to construct 4 flats on a plot along with parking area. Due to strike the probability of many construction workers not being present for the job is $0{\cdot}65$ . The probability that many are not present and still the work gets completed on time is $0{\cdot}35$ . The probability that work will be completed on time when all workers are present is $0{\cdot}80$ . Let : $E_1$ : represent the event when many workers were not present for the job; $E_2$ : represent the event when all workers were present; and E : represent completing the construction work on time. Based on the above information, answer the following questions :
37 (i) $What is the probability that all the workers are present for the job ?$
37 (ii) $What is the probability that construction will be completed on time ?$
37 (iii) (a) $What is the probability that many workers are not present given that the construction work is completed on time ?$
37 (iii) (b) $What is the probability that all workers were present given that the construction job was completed on time ?$

Question 1

Question 2

Question 3

Question 4

Question 5 (case study, 4 parts)