List of top Questions asked in UP Board XII

Explain the following:
(i) Lanthanoid contraction
(ii) Oxidation states in Lanthanoids and Actinoids
Find the unit vector perpendicular to each of the vectors \( (\vec{a} + \vec{b}) \) and \( (\vec{a} - \vec{b}) \) where \( \vec{a} = \hat{i} + \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} + 2\hat{j} + 3\hat{k} \).
(a) A person with narrow religious views is called
The degree of differential equation \[ 9 \frac{d^2y}{dx^2} = \left\{ 1 + \left(\frac{dy}{dx}\right)^2 \right\}^{\tfrac{3}{2}} \] is
If \( y = x^{x^{x^{.... \text{ad inf}}}} \), then prove that \( x\frac{dy}{dx} = \frac{y^2}{1 - y \log x} \).
Integrate: \( \int \left(\frac{2 + \sin 2x}{1 + \cos 2x}\right) e^x dx \)
If \( y = e^{\tan^{-1}x} \), prove that \( (1 + x^2)\frac{d^2y}{dx^2} + (2x - 1)\frac{dy}{dx} = 0 \).
The value of expression \( \hat{i} \cdot \hat{i} - \hat{j} \cdot \hat{j} + \hat{k} \times \hat{k} \) is
100 ml of 10 M HCl is mixed with 75 ml of 10 M Na$_2$CO$_3$. The resulting solution would be –
Find the principal value of \( \sec^{-1}(-\sqrt{2}) \).
Answer the following questions in about 40 words each:
(a) Where did the squatters living in the periphery of Delhi come from?
Write IUPAC names of the following compounds:
(i)\; \includegraphics[height=10pt]{dummy} (ring with –CHO and adjacent –CH$_3$)
(ii)\; (CH$_3$)$_2$CHCOCH(CH$_3$)$_2$
(iii)\; CH$_3$CH(OCH$_3$)CHO
(iv)\; HOOC–(CH$_2$)$_4$–COOH
(v)\; \includegraphics[height=10pt]{dummy} (benzene–CH$_2$COOH)
Differentiate \( \tan^{-1}\left(\frac{\sin x}{1 + \cos x}\right) \) with respect to x.
If the function f: N \(\rightarrow\) N, is defined by f(x) = x - 1 for all x > 2 and f(1) = f(2) = 1, then f is
A cell in which the following reaction occurs:
\[ \text{Zn}_{(s)} + \text{Cu}^{2+}_{(aq)} \rightarrow \text{Zn}^{2+}_{(aq)} + \text{Cu}_{(s)} \] has standard electrode potential \(E^\circ_{\text{cell}} = 1.1~\text{V}\) at \(298~\text{K}\). Calculate the standard Gibbs energy and the equilibrium constant of the cell reaction.
If elasticity is equal to 3 and Average Revenue is Rs. 30, then Marginal Revenue will be
Profits of the last three years were Rs. 6,000, Rs. 13,000 and Rs. 8,000 respectively. Goodwill at two years' purchase of the average net profit will be.
Answer the following questions in about 40 words each:
(a) What made the writer forget all about M. Hamel's ruler?
Give the name of two water-soluble vitamins and diseases due to deficiency of them.
Write any two characteristics of partnership.
What is gene therapy? Illustrate this using the example of adenosine deaminase (AD deficiency.
Differentiate between co-dominance and incomplete dominance.
Find the angle between the pair of lines:
\( \vec{r} = 3\hat{i} + \hat{j} - 2\hat{k} + \lambda(\hat{i} - \hat{j} - 2\hat{k}) \) and
\( \vec{r} = 2\hat{i} - \hat{j} - 56\hat{k} + \mu(3\hat{i} - 5\hat{j} - 4\hat{k}) \).
A charge \( q \) enters with speed \( v \) in the direction of magnetic field \( B \). The force on the charge in magnetic field will be:
The angle between polarization plane and direction of propagation of electromagnetic waves is :