CBSE Class 12 Mathematics Question Paper 65/5/3 Flashcards

Vocabulary and conceptual flashcards generated from the CBSE Class 12 Mathematics Question Paper Code 65/5/3.

Q.P. Code 65/5/3 Exam Structure

A Class 12 Mathematics examination comprising 38 compulsory questions divided into five sections (A, B, C, D, and E) with a maximum of $80$ marks and $3$ hours time allowed.

Section A Specification

Comprises 20 questions carrying $1$ mark each, consisting of 18 multiple choice questions (MCQs, Questions 1 to 18) and 2 Assertion-Reason based questions (Questions 19 and 20).

Section B Specification

Comprises 5 Very Short Answer (VSA) type questions carrying $2$ marks each (Questions 21 to 25).

Section C Specification

Comprises 6 Short Answer (SA) type questions carrying $3$ marks each (Questions 26 to 31).

Section D Specification

Comprises 4 Long Answer (LA) type questions carrying $5$ marks each (Questions 32 to 35).

Section E Specification

Comprises 3 case study based questions carrying $4$ marks each (Questions 36 to 38).

Principal Value of $\cot^{-1}\left(\frac{1}{\sqrt{3}}\right)$

The principal value of $\cot^{-1}\left(\frac{1}{\sqrt{3}}\right)$ is $\frac{\pi}{3}$.

Determinant of a $3 \times 3$ Diagonal Matrix

For a $3 \times 3$ diagonal matrix $A = [a_{ij}]$ with $a_{11} = 1$, $a_{22} = 5$, and $a_{33} = -2$, the determinant $|A|$ equals $-10$.

Determinant Property $|A| = k^n|B|$

If $A = kB$, where $A$ and $B$ are square matrices of order $n$ and $k$ is a scalar, then $|A| = k^n|B|$.

Greatest Integer Function Continuity at $x = 2$

For $f(x) = [x]$, where $f$ is the greatest integer function, $f$ is neither continuous nor differentiable at $x = 2$.

Order and Degree Sum of $\left(\frac{dy}{dx}\right)^2 = \frac{d^2y}{dx^2}$

The differential equation $\left(\frac{dy}{dx}\right)^2 = \frac{d^2y}{dx^2}$ has order $2$ and degree $1$, giving a sum of order and degree equal to $3$.

Perpendicular Vector Calculation

The problem of finding a vector of magnitude $5$ that is perpendicular to both $3\mathbf{\hat{i}} - 2\mathbf{\hat{j}} + \mathbf{\hat{k}}$ and $4\mathbf{\hat{i}} + 3\mathbf{\hat{j}} - 2\mathbf{\hat{k}}$.

Case Study 1: Student Roll Number Function

A function $f: A \rightarrow \mathbb{N}$ defined on a set $A$ of $30$ students in class XII, where $f(x)$ is given by the roll number of student $x$.

Case Study 2: Seed Germination Probabilities

A setup involving $10$ brinjal seeds, $12$ cabbage seeds, and $8$ radish seeds with germination probabilities of $25\%$, $35\%$, and $40\%$ respectively.

Case Study 3: Cuboidal Box Optimization

Optimization problem for a closed wooden cuboidal box with square base (length = breadth = $x\,\text{m}$) and height = $y\,\text{m}$ to achieve minimum surface area $S$ for a fixed volume $V$.