Day 222: CBSE Class 12 Maths

5 questions (11 parts). Try each one first, then open its answer.

Question 1
Integrals. Asked once: 2025 (same type asked 5 times)
28 $\int \frac{\cos x\, dx}{1 + \cos x + \sin x}$
Question 2 (case study, 4 parts)
Probability. Asked once: 2025 (same type asked 5 times)
Some students are having a misconception while comparing decimals. For example, a student may mention that $78{\cdot}56 > 78{\cdot}9$ as 7856 > 789. In order to assess this concept, a decimal comparison test was administered to the students of class VI through the following question : In the recently held Sports Day in the school, 5 students participated in a javelin throw competition. The distances to which they have thrown the javelin are shown below in the table :
Name of student Distance of javelin (in meters)
Ajay $47{\cdot}7$
Bijoy $47{\cdot}07$
Kartik $43{\cdot}09$
Dinesh $43{\cdot}9$
Devesh $45{\cdot}2$
The students were asked to identify who has thrown the javelin the farthest. Based on the test attempted by the students, the teacher concludes that 40% of the students have the misconception in the concept of decimal comparison and the rest do not have the misconception. 80% of the students having misconception answered Bijoy as the correct answer in the paper. 90% of the students who are identified with not having misconception, did not answer Bijoy as their answer. On the basis of the above information, answer the following questions :
36 (i) $What is the probability of a student not having misconception but still answers Bijoy in the test ?$
36 (ii) $What is the probability that a randomly selected student answers Bijoy as his answer in the test ?$
36 (iii) (a) $What is the probability that a student who answered as Bijoy is having misconception ?$
36 (iii) (b) $What is the probability that a student who answered as Bijoy is amongst students who do not have the misconception ?$
Question 3
Probability. Asked once: 2025 (same type asked 5 times)
7 $P(E) > 0$
Tap an option to check your answer.
Question 4 (case study, 4 parts)
Probability. Asked once: 2024 (same type asked 5 times)
Rohit, Jaspreet and Alia appeared for an interview for three vacancies in the same post. The probability of Rohit's selection is $\dfrac{1}{5}$ , Jaspreet's selection is $\dfrac{1}{3}$ and Alia's selection is $\dfrac{1}{4}$ . The event of selection is independent of each other. Based on the above information, answer the following questions :
38 (i) $What is the probability that at least one of them is selected ?$
38 (ii) $P(G\,|\,\overline{H})$
38 (iii) (a) $Find the probability that exactly one of them is selected.$
38 (iii) (b) $Find the probability that exactly two of them are selected.$
Question 5
Continuity and Differentiability. Asked once: 2023 (same type asked 4 times)
9 $f(x) = \begin{cases} k(3x^2 - 5x), & x \le 0 \\ \cos x, & x > 0 \end{cases}$
Tap an option to check your answer.

Name of student	Distance of javelin (in meters)
Ajay	$47{\cdot}7$
Bijoy	$47{\cdot}07$
Kartik	$43{\cdot}09$
Dinesh	$43{\cdot}9$
Devesh	$45{\cdot}2$

Question 1

Question 2 (case study, 4 parts)

Question 3

Question 4 (case study, 4 parts)

Question 5