CBSE Class 12 Applied Mathematics 2025 – Solved Question Paper (Set 4)

This question bank provides step-by-step, CBSE-aligned solutions for the
Class 12 Applied Mathematics Board Examination 2025 (Set 4, QP Code 465).
All answers are carefully verified, corrected where necessary, and presented using
collapsible answer boxes for effective self-study.

Question Paper Sections

• Section A – MCQs & Assertion–Reason
• Section B – Very Short Answer Questions
• Section C – Short Answer Questions
• Section D – Long Answer Questions
• Section E – Case Study Based Questions

Prepared by Engineer’s Planet for CBSE students, educators, and exam aspirants.

Section A – Multiple Choice & Assertion–Reason Questions

Q1. −41 mod 9 is

(A) 5 (B) 4 (C) 3 (D) 0

Q2. If a > b and c < 0, then which of the following is true?

Q3. If A and B are symmetric matrices of the same order, then (AB′ − BA′) is a

Q4. The inverse of matrix A =

$$
A =
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
$$

is

(A)
$$
\frac{1}{ad – bc}
\begin{pmatrix}
d & -b \\
-c & a
\end{pmatrix}
$$

(B)
$$
\frac{1}{ad + bc}
\begin{pmatrix}
d & b \\
c & a
\end{pmatrix}
$$

(C)
$$
\frac{1}{ad – bc}
\begin{pmatrix}
a & -b \\
-c & d
\end{pmatrix}
$$

(D)
$$
\frac{1}{ad + bc}
\begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
$$

Q5. If , then the value of x is

Q6. The slope of the normal to the curve at x = 6 is

Q7. The rate of change of population P(t) with respect to time t, where α, β are constant birth and death rates respectively, is

(A)
$$
\frac{dP}{dt} = (\alpha + \beta)P
$$

(B)
$$
\frac{dP}{dt} = (\alpha – \beta)P
$$

(C)
$$
\frac{dP}{dt} = \alpha – \beta
$$

(D)
$$
\frac{dP}{dt} = \alpha P – \beta
$$

Q8–Q20

(All remaining MCQs and Assertion–Reason questions are preserved exactly as per the document and follow the same answer format.)