List of top Questions asked in CBSE CLASS XII- 2025

Find \( \int \frac{3x + 1}{(x - 2)^2 (x + 2)} \, dx \)
Show that of all rectangles with a fixed perimeter, the square has the greatest area.
Differentiate \( \log(x^2 + \csc^2 x) \) with respect to \( x \).
If \( A = \begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix} \), then find the value of \( K \) if \( A^2 = 6A + K I_2 \), where \( I_2 \) is the identity matrix.
If A and B are two events such that $P(B) = \frac{1}{5}$, $P(A | B) = \frac{2}{3}$ and $P(A \cup B) = \frac{3}{5}$, then $P(A)$ is :
Edge of a variable cube increases at the rate of 5 cm/s. The rate at which the surface area of the cube increases when the edge is 2 cm long is :
If $f(x) = 3x - b$, $x>1$ ; $f(x) = 11$, $x = 1$ ; $f(x) = -3x - 2b$, $x<1$ is continuous at $x = 1$, then the values of $a$ and $b$ are :
If $f(x) = 2x^8$, then the correct statement is :
Solve the differential equation \((x^2 + y^2) \, dx + xy \, dy = 0\), \(y(1) = 1\).
(a) Find \[ \int \frac{x}{(x - 1)(x^2 + 4)} \, dx \]
Show that the derivative of \( \tan^{-1} (\sec x + \tan x) \) with respect to \( x \) is equal to \( \frac{1}{2} \) for \( \left( -\frac{\pi}{2}<x<\frac{\pi}{2} \right) \).
In a Linear Programming Program (LPP) for objective function \( Z = 14x - 10y \) subject to the constraints: \[ x + y \leq 8, \quad 3x - 2y \geq -6, \quad x, y \geq 0 \] shade the feasible region and mark the corner points in a neatly drawn graph.
If \[ \begin{bmatrix} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{bmatrix} A = \begin{bmatrix} 2 & -5 \\ -17 \end{bmatrix} \] then find matrix \( A \).
If \( P(A) = \frac{1}{5}, P(B) = \frac{3}{5} \) and \( P(A \cap B) = \frac{2}{5} \), then \( P(A' \cup B') \) is :
A student tries to tie ropes, parallel to each other from one end of the wall to the other. If one rope is along the vector \( \hat{i} + 15 \hat{j} + 6 \hat{k} \) and the other is along the vector \( 2 \hat{i} + 10 \hat{j} + 6 \hat{k} \), then the value of \( \lambda \) is :
\[ \int \frac{a^x}{\sqrt{1 - a^2 x}} \, dx \] is equal to :
\[ \int \frac{e^{9 \log x} - e^{8 \log x}}{e^{6 \log x}} \, dx \] is equal to :
If \( f(x) = -2x^8 \), then the correct statement is :
If \( R \) be a relation defined as \( a \, R \, b \) iff \( |a - b|>0 \), \( a, b \in \mathbb{R} \), then \( R \) is :
If \( f(x) = \begin{cases} \frac{\sin^2 ax}{x^2}, & \text{if } x \neq 0 \\ 1, & \text{if } x = 0 \end{cases} \) is continuous at \( x = 0 \), then the value of 'a' is :
Arrange the following compounds as asked:
(a) In decreasing order of pKb values
C2H5NH2, (C2H5)2NH, C6H5NHCH3, C6H5NH2
(b) In increasing order of boiling point
C2H5OH, C2H5NH2, (CH3)2NH
(c) In increasing order of solubility in water
C6H5NH2, (C2H5)2NH, C2H5NH2

An aromatic compound ‘A’ with molecular formula C8H8O gives positive 2,4-DNP test. It gives yellow precipitate of compound ‘B’ on treatment with sodium hypoiodite. Compound ‘A’ does not react with Tollen’s or Fehling’s reagent; on drastic oxidation with KMnO4 it forms a carboxylic acid ‘C’. Elucidate the structures of A, B, and C. Also give their IUPAC names.

The reaction between A2 (g) and B2 (g) was carried out in a sealed isothermal container. The rate law for the reaction was found to be:

Rate = \( k[\text{A}_2][\text{B}_2] \)

If 1 mole of A2 (g) was added to the reaction chamber and the temperature was kept constant, then predict the change in rate of the reaction and the rate constant.

Name and define the cell which was used for providing electric power in the Apollo space programme. Also write its one advantage.

Name the type of isomerism exhibited and draw isomers:

(I) [Co(NH3)6][Cr(CN)6]

(II) [Co(en)3]3+

(III) [Co(NH3)3(NO2)3]