Day 197: 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 4 times)
32 (a) $\displaystyle\int \dfrac{x^2 + 1}{(x^2 + 2)(2x^2 + 1)}\, dx$
Question 2
Integrals. Asked once: 2024 (same type asked 4 times)
25 $\displaystyle\int \dfrac{1}{x(x^{2} - 1)}\,dx$
Question 3 (case study, 4 parts)
Probability. Asked once: 2024 (same type asked 4 times)
Self-study helps students to build confidence in learning. It boosts the self-esteem of the learners. Recent surveys suggested that close to 50% learners were self-taught using internet resources and upskilled themselves. A student may spend 1 hour to 6 hours in a day in upskilling self. The probability distribution of the number of hours spent by a student is given below : $P(X = x) = \begin{cases} kx^2, & \text{for } x = 1, 2, 3 \\ 2kx, & \text{for } x = 4, 5, 6 \\ 0, & \text{otherwise} \end{cases}$ where x denotes the number of hours. Based on the above information, answer the following questions :
36 (i) $Express the probability distribution given above in the form of a probability distribution table.$
36 (ii) $Find the value of k.$
36 (iii) (a) $Find the mean number of hours spent by the student.$
36 (iii) (b) $P(1 < X < 6)$
Question 4
Probability. Asked once: 2024 (same type asked 4 times)
31 (b) $A biased die is twice as likely to show an even number as an odd number. If such a die is thrown twice, find the probability distribution of the number of sixes. Also, find the mean of the distribution.$
Question 5
Three Dimensional Geometry. Asked once: 2023 (same type asked 4 times)
4 $(2, -1, 0)$
Tap an option to check your answer.

Question 1

Question 2

Question 3 (case study, 4 parts)

Question 4

Question 5