List of top Questions asked in CBSE CLASS XII- 2026

If \(\vec{AB} = \hat{j} + \hat{k}\) and \(\vec{AC} = 3\hat{i} - \hat{j} + 4\hat{k}\) represent two vectors along the sides \(AB\) and \(AC\) of \(\Delta ABC\), prove that the median vector satisfies \(\vec{AB} + \vec{AC} = 2\vec{AD}\), where \(D\) is the midpoint of \(BC\). Hence, find the length of the median \(AD\).

If the volume of a solid hemisphere increases at a uniform rate, prove that its surface area varies inversely as its radius.

If $e^{x + y} = 3x$, then $\frac{dy}{dx}$ is equal to:

Assertion (A): $|\vec{a} \times \vec{b}|^2 + (\vec{a} \cdot \vec{b})^2 = |\vec{a}|^2|\vec{b}|^2$.
Reason (R): $|\vec{a} \times \vec{b}| = (\vec{a} \cdot \vec{b})\tan\theta$, where $\theta$ is the angle between vectors $\vec{a}$ and $\vec{b}$ ($\theta \neq \frac{\pi}{2}$).

Assertion (A): A line can have direction cosines $\langle 1, 1, 1 \rangle$.
Reason (R): $\cos\theta = 1$ is possible for $\theta = 0$.

For two events $A$ and $B$ such that $P(A) \neq 0$ and $P(B) \neq 1$, the conditional probability $P(A'/B')$ is equal to:

If $A$ and $B$ are square matrices of the same order, then which of the following statements is/are always true?
(i) $(A + B)(A - B) = A^2 - B^2$
(ii) $AB = BA$
(iii) $(A + B)^2 = A^2 + AB + BA + B^2$
(iv) $AB = 0 \implies A = 0$ or $B = 0$

A relation $R$ on the set $A = \{1, 2, 3\}$ defined as $R = \{(1, 2), (2, 1), (2, 2)\}$ is:

For a square matrix $A$ of order $n$, the inverse matrix $(3A)^{-1}$ is equal to:

For a feasible region bounded by the corner points $(0,3)$, $(3,2)$, and $(5,0)$ in the first quadrant, the non-trivial constraints of the linear programming problem are:

If $|\vec{a}| = 5$ and $-2 \le \lambda \le 1$, then the sum of the greatest and the smallest value of $|\lambda \vec{a}|$ is:

In a linear programming problem, the linear function which has to be maximized or minimized is called:

The direction cosines of the line given by $x = y = 1 - z$ are:

The integrating factor of the differential equation $2x \frac{dy}{dx} - y = 3$ is:

A vector of magnitude 3 making equal angles with the $x$ and $y$ axes and perpendicular to the $z$ axis is:

The indefinite integral $\int \frac{1}{1 + \cos x} \, dx$ is equal to:

The general solution of the differential equation $x \, dy - y \, dx = 0$ is:

For the function $f(x) = x + \frac{1}{x}$ ($x \neq 0$), which of the following statements is true?

Which of the following expressions will give the area of the region bounded by the curve $y = x^2$ and the line $y = 16$?

According to Werner's theory, the primary valencies of the central metal atom :

In the given political outline map of India, four states have been marked as A, B, C and D. Identify these on the basis of the information given below and write their correct names in your answer book along with their respective serial number of the information used and the concerned alphabet as per format that follows:

Study the given cartoon carefully and answer the questions that follow:

Read the passage given below carefully and answer the questions that follow:
The South Asian Association for Regional Co-operation (SAARC) is a major regional initiative by the South Asian states to evolve co-operation through multilateral means. It began in 1985. Unfortunately due to persisting political differences, SAARC has not had much success. SAARC members signed the South Asian Free Trade Agreement (SAFTA) in 2002 which promised the formation of a free trade zone for the whole of South Asia.

In the given political outline map of India, four States have been marked as and . Identify these States on the basis of the information given below and write their correct names in your answer-book along with the respective serial number of the information used and the concerned alphabets given in the map as per the following format:

Read the following passage carefully and answer the questions based on it:
‘‘After the Chinese revolution, India was one of the first countries to recognise the communist government. Nehru felt strongly for this neighbour and helped the new government in international fora. A joint enunciation of peaceful coexistence was signed by Indian Prime Minister and the Chinese premier in 1954. But two developments strained this relationship. China annexed Tibet and removed a historical buffer between the two countries. A little earlier, a boundary dispute had surfaced between India and China.’’