List of top Questions asked in CBSE CLASS XII

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 :

For the reaction:
2H$_2$O$_2$ $\xrightarrow{I^-}$ 2H$_2$O + O$_2$
Given mechanism:
(I) H$_2$O$_2$ + I$^-$ → H$_2$O + IO$^-$ (slow)
(II) H$_2$O$_2$ + IO$^-$ → H$_2$O + I$^-$ + O$_2$ (fast)
(1) Write rate law for the reaction.
(2) Write the overall order and molecularity of the reaction.

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.

Give explanation for each of the following observations:

(a) With the same d-orbital configuration (d⁴), Mn³⁺ ion is an oxidizing agent whereas Cr²⁺ ion is a reducing agent.

(b) Actinoid contraction is greater from element to element than that among lanthanoids.

(c) Transition metals form a large number of interstitial compounds with H, B, C, and N.

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.

Identify and draw the main products formed in the following chemical reactions:

Out of Ti³⁺, Cr³⁺, Fe²⁺ and Ni²⁺ ions, the one which is the most stable ion in aqueous solution is:

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]

Give explanation for each of the following observations:

(a) Mn³⁺ is an oxidizing agent, whereas Cr²⁺ is a reducing agent (both d⁴ configuration).

(b) Actinoid contraction is greater than lanthanoid contraction.

(c) Transition metals form interstitial compounds with H, B, C, N.

Complete the following reactions by writing the structural formulae of ‘A’ and ‘B’:

(i) \( \text{CH}_3\text{CH} = \text{CH}_2 \)
\( \xrightarrow{\text{HBr, Peroxide}} \) ‘A’ \( \xrightarrow{\text{aq. KOH}} \) ‘B’

(ii) \( \text{CH}_3\text{CH}_2\text{CH(Cl)CH}_3 \)
\( \xrightarrow{\text{alc. KOH}, \Delta} \) ‘A’ \( \xrightarrow{\text{HBr}} \) ‘B’

(iii) ‘A’ \( \xrightarrow{\text{Mg}} \) \( \text{CH}_3\text{CH}_2\text{CH}_2\text{MgCl} \) \( \xrightarrow{\text{H}_2\text{O, H}^+} \) ‘B’ (Main product)