Day 63: CBSE Class 12 Maths

5 questions (6 parts). Try each one first, then open its answer.

Question 1
Integrals. Asked once: 2026 (same type asked 5 times)
11 $\int_{-1}^{1} (1 - |x|)\, dx$
Tap an option to check your answer.
Question 2
Integrals. Asked once: 2026 (same type asked 5 times)
28 $\int_{0}^{\pi/2} \dfrac{\sin^2 x}{1 + \sin 2x}\, dx$
Question 3
Integrals. Asked once: 2026 (same type asked 5 times)
26 $\int_{0}^{1} x \tan^{-1} x \, dx$
Question 4
Integrals. Asked once: 2026 (same type asked 5 times)
10 $\displaystyle\int \sqrt{\dfrac{1 - \cos 2x}{1 + \cos 2x}}\,dx$
Tap an option to check your answer.
Question 5 (case study, 2 parts)
Probability. Asked once: 2026 (same type asked 5 times)
An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is $\dfrac{i}{6}$ , where i = 1, 2, 3. Based on the above information, answer the following questions : A person selects a cap.
38 (i) $What is the probability that he selects a red cap ?$
38 (ii) $If he selects a green cap, what is the probability that the cap has come from Box II ?$

Question 1