Day 239: CBSE Class 12 Maths

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

Question 1
Vector Algebra. Asked once: 2024 (same type asked 4 times)
Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
20 $(\vec{b} \cdot \vec{c})\, \vec{a}$
Tap an option to check your answer.
Question 2
Integrals. Asked once: 2024 (same type asked 4 times)
23 (b) $\int_0^{\frac{\pi^2}{4}} \frac{\sin \sqrt{x}}{\sqrt{x}} \; dx$
Question 3
Integrals. Asked once: 2024 (same type asked 4 times)
28 $\displaystyle\int \dfrac{2x + 3}{x^{2}(x + 3)}\,dx$
Question 4
Integrals. Asked once: 2022 (same type asked 4 times)
6 (b) $\int \frac{1}{x (x^2 + 4)} \, dx$
Question 5 (case study, 4 parts)
Probability. Asked once: 2023 (same type asked 4 times)
An octagonal prism is a three-dimensional polyhedron bounded by two octagonal bases and eight rectangular side faces. It has 24 edges and 16 vertices. The prism is rolled along the rectangular faces and number on the bottom face (touching the ground) is noted. Let X denote the number obtained on the bottom face and the following table give the probability distribution of X.
X : 1 2 3 4 5 6 7 8
P(X) : p 2p 2p p 2p $p^2$ $2p^2$ $7p^2 + p$
36 (i) $Find the value of p.$
36 (ii) $Find P(X > 6).$
36 (iii) (a) $Find P(X = 3m), where m is a natural number.$
36 (iii) (b) $Find the mean E(X).$

Question 1