List of top Questions asked in UP Board XII

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 \( x = 0 \).

A relation \( R = \{(a, b) : a = b - 1, b \geq 3\ \) is defined on set \( N \), then}

The modulus function \( f : \mathbb{R} \to \mathbb{R}^+ \) given by \( f(x) = |x| \) is

The value of expression \(\hat{i} \cdot \hat{i} - \hat{j} \cdot \hat{j} + \hat{k} \times \hat{k}\) is

The degree of differential equation \[ 9 \frac{d^2y}{dx^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{\frac{1}{3}} \text{ is} \]

$[NiCl_4]^{2-}$ is paramagnetic while $[Ni(CO)_4]$ is diamagnetic even though both are tetrahedral. Why?

(A) Write the electronic configuration of the element with atomic number 24.
(B) Find the number of unpaired electrons in $Co^{2+}$ ion.
(C) Why is the range of oxidation states greater in the actinoid series compared to the lanthanoid series?

Write the structures of (A), (B), and (C) in the following reaction:
\[ C_6H_5NO_2 \xrightarrow{Fe/HCl} (A) \xrightarrow[\text{273 K}]{NaNO_2 + HCl} (B) \xrightarrow[\Delta]{H_2O/H^+} (C) \]

Write the structures of (A), (B), and (C) in the following reaction:
Reaction Scheme: \[ (C) \xleftarrow{\text{conc. } HNO_3} \text{Phenol} \xrightarrow{\text{dil. } HNO_3} (A) + (B) \]

What happens when aniline reacts with the following:
(A) Bromine water
(B) $(CH_3CO)_2O$ / Pyridine
(C) $HNO_2 + HCl (0^\circ - 5^\circ C)$

What is a peptide bond? Explain with an example.

Write the mechanism of bimolecular nucleophilic substitution reaction ($S_N2$) of alkyl halide.

Write the IUPAC nomenclature of the following organic compounds:
(A) $CH_3 - CH_2 - \overset{\text{O}}{\overset{||}{\text{C}}} - CH_2 - \underset{\text{CH}_3}{\underset{|}{\text{CH}}} - CH_3$
(B) $Ph - CH = CH - CHO$

Write the definition of electrode potential and cell electromotive force (emf).

Does the half-life of a first-order reaction depend on the initial concentration of the reaction? Explain.

The increasing order of reactivity of the following compounds in $S_N1$ reaction is:
Compounds:
A. $(CH_3)_3CBr$
B. $CH_3CH_2CH_2CH_2Br$
C. $(CH_3)_2CHCH_2Br$
D. $CH_3CH(Br)CH_2CH_3$

Explain the importance of hygiene in the kitchen and during food preparation.

Describe the types of fibers and their uses in clothing.

Explain the different methods of cooking food with examples.

Write the functions of carbohydrates and fats in the human body.

Define balanced diet. Explain its importance for good health.

Balanced diet means —

Which fiber is obtained from plants?

Which method of cooking preserves maximum nutrients?