CBSE Class 12 Maths Board Paper 2026

4 Class 12 questions like these, with worked solutions

Written and checked by us, not taken from the CBSE paper. Try each one, then tap "Worked solution" to see every step and its marks.

1. Inverse Trigonometric Functions · 2 marks

   Find the domain of $f(x)={\cos }^{-1}(2x-3)+\sqrt{x-1}$.

   Worked solution

   $-1\le 2x-3\le 1\Rightarrow 1\le x\le 2$; and $x\ge 1$ M1
   Domain $=[1,2]$ A1

2. Matrices · 2 marks

   Construct the $2\times 3$ matrix $A=[a_{ij}]$ whose elements are given by $a_{ij}=\{\begin{array}{ll}ij,& i\ge j\\ i-j,& i<j\end{array}$.

   Worked solution

   $a_{11}=1,a_{12}=-1,a_{13}=-2,a_{21}=2,a_{22}=4,a_{23}=-1$ M1
   $A=\left[\begin{array}{ccc}1& -1& -2\\ 2& 4& -1\end{array}\right]$ A1

3. Application of Derivatives · 2 marks

   The height of a closed cylindrical container is always twice its radius. If the radius is increasing at $0.1$ cm/s, find the rate at which its volume is increasing when the radius is $3$ cm.

   Worked solution

   $V=\pi r^2(2r)=2\pi r^3\Rightarrow {\displaystyle \frac{dV}{dt}}=6\pi r^2{\displaystyle \frac{dr}{dt}}$ M1
   $=6\pi (9)(0.1)=5.4\pi {\text{cm}}^3/\text{s}$ A1

4. Application of Integrals · 2 marks

   Using integration, find the area of the region bounded by the line $x+2y=8$, the $x$-axis and the lines $x=2$ and $x=6$.

   Worked solution

   Area $={\displaystyle {\int }_2^6{\displaystyle \frac{8-x}{2}}dx={\displaystyle \frac{1}{2}}{[8x-{\displaystyle \frac{x^2}{2}}]}_2^6}$ M1
   $={\displaystyle \frac{1}{2}}(30-14)=8$ sq units A1

More on these topics: Inverse Trigonometric Functions · Matrices · Application of Derivatives · Application of Integrals

Marks often lost in these chapters

Check your answers to the questions above, and this paper's questions on the same chapters, for these slips.

• Inverse Trigonometric Functions: Writing ${\sin }^{-1}(\sin {\displaystyle \frac{2\pi }{3}})={\displaystyle \frac{2\pi }{3}}$ — the answer must lie in the principal range. Also: Giving ${\cos }^{-1}(-x)$ a negative value: ${\cos }^{-1}$ is never negative. More on one page
• Matrices: Writing $(AB{)}^T=A^T{B}^T$ — the order must reverse. Also: Expanding $(A+B{)}^2$ as $A^2+2AB+B^2$ or cancelling: $AB=AC$ does not give $B=C$ unless $A$ is invertible. More on one page
• Application of Derivatives: Substituting the particular value before differentiating in a rate problem. Also: Forgetting end points when finding absolute extrema; confusing a local maximum with the absolute maximum. More on one page
• Application of Integrals: Reporting a negative or zero “area” because part of the curve is below the axis. Also: Forgetting to double when using symmetry — or doubling a region that is not symmetric. More on one page

What the paper covers

The unit weightage, with each unit's chapters, is on the Class 12 Maths papers page. We haven't mapped this paper question by question yet.

Our worked solutions to the 2026 paper

Written and checked by us (not CBSE's), done by hand the no-calculator way. CBSE prints several sets of each paper; we solved one set of each.

• Mathematics (041), set 65/1/1: all 38 questions worked step by step, with the step marks from CBSE's marking scheme.

Formula booklet

CBSE Mathematics (Class 10 and Class 12) · CBSE · No official formula booklet

CBSE does not publish a formula booklet and none is given in the exam: formulas must be learnt. Use our one-page sheets to revise them.

More Class 12 papers

• Sample paper 2026-27
• Sample paper 2025-26
• Board paper 2025
• Sample paper 2024-25
• All 13 Class 12 papers