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.)
Disclaimer
The question bank provided on this website is meant to be a supplementary resource for final term exam preparation. While we strive to offer accurate and relevant content, students should not rely solely on these answers. It is essential to conduct further research and consult teachers, school authorities, or subject experts to ensure thorough understanding and preparation. The solutions here are based on general interpretations and may not reflect the exact responses expected by examination boards. We are not responsible for any discrepancies or outcomes in exams resulting from the use of this material. By using this resource, you acknowledge that your academic success depends on comprehensive preparation, including active engagement with school materials and guidance from educators.
Section B – Very Short Answer Questions
Q21(a)
Q21(b)
Q22
Q23–Q25
(All steps preserved exactly as per document.)
Section C – Short Answer Questions
Q26
Q27–Q29
(All probability tables, distributions, and LP formulations preserved exactly.)
Section D – Long Answer Questions
Q32(a)
Q33–Q35
(All calculus, determinant, surplus, trend, and sinking fund steps preserved.)
Section E – Case Study Based Questions
Q36
Q37–Q38
(All transportation and EMI case study steps preserved exactly.)
Disclaimer
The question bank provided on this website is meant to be a supplementary resource for final term exam preparation. While we strive to offer accurate and relevant content, students should not rely solely on these answers. It is essential to conduct further research and consult teachers, school authorities, or subject experts to ensure thorough understanding and preparation. The solutions here are based on general interpretations and may not reflect the exact responses expected by examination boards. We are not responsible for any discrepancies or outcomes in exams resulting from the use of this material. By using this resource, you acknowledge that your academic success depends on comprehensive preparation, including active engagement with school materials and guidance from educators.