List of top Questions asked in UP Board XII

If P(A) = 0.3, P(B) = 0.4, then find P(A/B) if A and B are independent events.
The order of the differential equation \( \frac{d^3y}{dx^3} + \frac{d^2y}{dx^2} + y \cos x = 0 \) is :
If \( A = \begin{bmatrix} \cos\alpha & -\sin\alpha
\sin\alpha & \cos\alpha \end{bmatrix} \) and \( A + A' = I \), then find the value of \( \alpha \).
The value of \( \int_1^{\sqrt{3}} \frac{dx}{1 + x^2} \) will be :
If three vectors \( \vec{a} \), \( \vec{b} \) and \( \vec{c} \) satisfying the condition \( \vec{a} + \vec{b} + \vec{c} = \vec{0} \). If \( |\vec{a}| = 3 \), \( |\vec{b}| = 4 \) and \( |\vec{c}| = 2 \), then find the value of \( \vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a} \).
The radius of an air bubble is increasing at the rate of \( \frac{1}{2} \) cm/s. At what rate is the volume of the bubble increasing while the radius is 1 cm?
There are 4 white and 2 black balls in a bag and in another bag 3 white and 5 black balls. Find the probability of getting both black balls if a ball is drawn from each bag.
If the Cartesian equation of a line is \( \frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2} \), then find its equation in vector form.
Find the degree of the differential equation \( xy \frac{d^2y}{dx^2} + x \left(\frac{dy}{dx}\right)^2 - y\left(\frac{dy}{dx}\right) = 2 \)
Prove that the function f(x) = |x| is continuous at x = 0.
Prove that (4, 4, 2), (3, 5, 2) and (-1, -1, 2) are vertices of a right angle triangle.
The value of \( \int_{0}^{\pi/2} \frac{dx}{1 + \sqrt{\tan x}} \) will be
Explain with reason:
(i) Cr2+ is a reducing agent while Mn3+ is an oxidising agent, while both have d4 configuration.
The resistance of a column formed by a \(0.10\ \mathrm{mol\ L^{-1}}\) concentrated solution is \(6.5\times10^{3}\ \Omega\). Its diameter is \(1\ \text{cm}\) and length is \(50\ \text{cm}\). Calculate its resistivity, conductivity and molar conductivity.
Calculate molality of a solution of 5.0 g of ethanoic acid (\(CH_3COOH\)) in 150.0 g of benzene.

Give the structures of A, B, and C in the following reaction sequences: 
(i) \(\mathrm{CH_3CH_2I} \xrightarrow[\ ]{\mathrm{NaCN}} A \xrightarrow[\ ]{\;\;HO^-\;/\;H_2O\;\;} B \xrightarrow[\;Br_2/NaOH\;]{} C\)
(ii) \(\mathrm{C_6H_5N_2^+Cl^-} \xrightarrow[\ ]{\mathrm{CuCN}} A \xrightarrow[\ ]{\;H_3O^+\;} B \xrightarrow[\ \Delta\ ]{\;NH_3\;} C\)
(iii) \(\mathrm{CH_3CH_2Br} \xrightarrow[\ ]{\mathrm{KCN}} A \xrightarrow[\ ]{\mathrm{LiAlH_4}} B \xrightarrow[\;273\,K\;]{\;HNO_2\;} C\)
 

Write IUPAC names of the following compounds:

 

What is elevation of boiling point? A liquid has boiling point 353.23 K. The boiling point of solution becomes 354.11 K after dissolving 1.8 g non-volatile solute of molar mass 58 g mol$^{-1}$ to 90 g liquid. Calculate boiling point elevation constant for the liquid.
The colour of dilute solutions of [Fe(CN)$_6$]$^{4-}$ and [Fe(H$_2$O)$_6$]$^{2+}$ are different. Explain.

Describe the method of preparation of potassium permanganate. How does acidic potassium permanganate react with the following? Give ionic equations: (i) H$_2$S  (ii) Fe  (iii) iodide ion.
 

Write the products of the following reactions:

A first order reaction completes 20% in 10 minutes. Calculate the time taken for 75% completion.
 

Methyl amine gives precipitate of hydrated ferric oxide on reaction with ferric chloride in water.
Gabriel-Pthalimide synthesis is given priority in the synthesis of primary amines.
Aniline does not show Friedel-Crafts reaction.