Day 134: 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)
27 (b) $\int_{0}^{5} (|x - 1| + |x - 2| + |x - 5|)\,dx$
Question 2
Integrals. Asked once: 2025 (same type asked 5 times)
30 (b) $\int_{0}^{\frac{\pi}{2}} \frac{5\sin x + 3\cos x}{\sin x + \cos x}\,dx$
Question 3
Integrals. Asked once: 2026 (same type asked 5 times)
26 (b) $\int \tan^{-1} \left(\dfrac{1 - x}{1 + x}\right) dx$
Question 4
Integrals. Asked once: 2026 (same type asked 5 times)
1 $\displaystyle\int \dfrac{dx}{1 + \cos x}$
Tap an option to check your answer.
Question 5 (case study, 4 parts)
Probability. Asked once: 2026 (same type asked 5 times)
There are three types of vaccines $A_1$ , $A_2$ , $A_3$ , available in the market to protect the population of the country from spread of certain infection. According to a survey conducted, it was found that 25% of the population was given Vaccine $A_1$ , 35% of the population was given Vaccine $A_2$ and 40% of the population was given Vaccine $A_3$ . The survey also stated that the probabilities that Vaccines $A_1$ , $A_2$ and $A_3$ would protect against the infection were 60%, 55% and 50% respectively. Based on the above information, answer the following questions : Find the probability that :
37 (i) $A_2$
37 (ii) $If a person is chosen randomly, he/she will be protected from the infection.$
37 (iii) (a) $A_1$
37 (iii) (b) $A_3$

Question 1