Mathbee · CBSE Class 12 Maths

CBSE Board Paper 2026 80 Marks · 38 Questions

CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2 — Step-by-Step Solutions & Marking Scheme

Select any question below to view the complete worked solution and official CBSE stepwise marking breakdown.

Question 11M · Applications Of Derivatives

For \(f(x)=-|x+1|+5\), which statement is true?

Question 21M · Continuity And Differentiability

Let \(f(x)=|x|/x\) for \(x\ne0\), with \(f(0)=0\). Which statement is incorrect?

Question 31M · Inverse Trigonometric Functions

Evaluate \(\cos^{-1}(\cos(7\pi/6))\).

Question 41M · Determinants

If \(\begin{vmatrix}3x&x+2\\3(x-1)&x-2\end{vmatrix}=\begin{vmatrix}1&5\\3&3\end{vmatrix}\), find x.

Question 51M · Matrices

For a square matrix A, which statement is not generally true?

Question 61M · Matrices

If \(A=\begin{bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{bmatrix}\) satisfies \(A^T+A=I\), which listed…

Question 71M · Inverse Trigonometric Functions

Evaluate \(\tan^{-1}\sqrt3-\sec^{-1}(-2)\).

Question 81M · Continuity And Differentiability

Differentiate \(\cos^{-1}(e^x)\) with respect to x.

Question 91M · Integrals

If \(\int_0^1(9x^2-4x-2k)\,dx=0\), find k.

Question 101M · Determinants

For order-three matrices with \(\det A=4\), \(\det B=7\), find \(\det(2AB)\).

Question 111M · Applications Of Derivatives

Find a circle’s radius when the nonzero rates of change of area and diameter are numerically equal.

Question 121M · Vector Algebra

If \((3,-2,4)\) and \((\lambda,1,0)\) are perpendicular, find \(\lambda\).

Question 131M · Integrals

Evaluate \(\int [\sin(\ln x)+\cos(\ln x)]\,dx\).

Question 141M · Continuity And Differentiability

If y=√(y+cos x), find dy/dx where 1−2y≠0.

Question 151M · Matrices

If \(A=\begin{bmatrix}1&-2&3\\3&2&-1\end{bmatrix}\), \(B=\begin{bmatrix}2&3\\-1&2\\4&-5\end{bmatrix}\), and \(C=AB\)…

Question 161M · Probability

For independent events A and B, which statement is not generally correct?

Question 171M · Integrals

If \(\int_0^4 dx/(x+\sqrt{x})=k\log3\), find k.

Question 181M · Probability

If P(B)=3/5, P(A | B)=1/2 and P(A∪B)=4/5, find P(A).

Question 191M · Relations And Functions

Assertion A. On the set of all books in a school library, let R relate books with equal page counts and S relate two…

Question 201M · Vector Algebra

Assertion A. Points A=(6,−7,0), B=(16,−19,−4), C=(1,−1,2) are collinear. Reason R. Three points are collinear when C…

Question 212M · Matrices

For x>0, solve x[[2x,2],[3,x]]+2[[8,5x],[4,0]]=2[[x²+8,24],[10,8]].

Question 222M · Relations And Functions

Thumb pins on a graph sheet are related when their distance is less than 3 cm. Determine whether this defines an…

Question 232M · Probability

Two cards are drawn uniformly without replacement from cards numbered 1 through 22. Find the probability that both…

Question 242M · Linear Programming

Shade the feasible region for 2x+y≥8, x+2y≥10 and x,y≥0, and list its corner points.

Question 252M · Continuity And Differentiability

Find a,b for continuity of f(x)=2 for x≤3, ax+b for 3<x<5, and 5 for x≥5. OR If \(2y^3+y=2x\), prove…

Question 263M · Matrices

Express \(A=\begin{bmatrix}2&4\\5&6\end{bmatrix}\) as a sum of a symmetric and a skew-symmetric matrix. OR Using…

Question 273M · Continuity And Differentiability

For \(y=(x+\sqrt{x^2-a^2})^n\), show \(y\prime=ny/\sqrt{x^2-a^2}\) on regular real branches where the power is defined…

Question 283M · Applications Of Derivatives

Find the sum of maximum and minimum values of sin x(1+cos x) on [0,π].

Question 293M · Linear Programming

Minimize \(Z=4x+y\) subject to \(x+y\ge3\), \(x+2y\ge4\), \(x,y\ge0\), graphically.

Question 303M · Three Dimensional Geometry

Find the line through (1,−1,2) parallel to the x-axis and its shortest distance to r=(2,1,−1)+t(3,−5,2). OR For…

Question 313M · Relations And Functions

On positive natural numbers, \(R=\{(x,y):x+2y=25\}\). Find its domain and range and decide whether it is an…

Question 325M · Integrals

Evaluate \(\int_0^{\pi/2}\frac{\sin^2 x}{1+\sin x\cos x}\,dx\).

Question 335M · Vector Algebra

Nonzero vectors α,β,γ satisfy α×β=γ and β×γ=α. Show they are mutually perpendicular, norm β=1, and norm α=norm γ. Find…

Question 345M · Differential Equations

Solve (x+y)dy+(x−y)dx=0 with y(1)=1.

Question 355M · Applications Of Integrals

Using integration, find the area enclosed by \(y=x^2\) and \(y=2\). OR Using integration, find the area inside…

Question 364M · Applications Of Derivatives

A window consists of a rectangle of length x and breadth y metres, surmounted by an equilateral triangle on its…

Question 374M · Probability

Companies X,Y,Z have selection probabilities 1/3,2/9,4/9. Their conditional probabilities of poor construction quality…

Question 384M · Three Dimensional Geometry

A cuboid swimming pool has breadth line \((-x+2)/(-5)=y=z-3\). Students A and B swim along its length. Student A…