List of top Questions asked in UP Board XII- 2026

Find the angle between the vectors \(-2\hat{i} + \hat{j} + 3\hat{k}\) and \(3\hat{i} - 2\hat{j} + \hat{k}\).

If \( P(A) = 0.12, P(B) = 0.15 \) and \( P(B/A) = 0.18 \), then find the value of \( P(A \cap B) \).

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

The value of \( \displaystyle \int_{0}^{\pi/2} \frac{dx}{1 + \sqrt{\tan x}} \) will be

Differentiate between a strike and a lockout.

What is alienation?

What is rural society?

Identify two negative social effects of Green Revolution.

How did planters live?

Define Nation.

What is class system?

State the main features of Panchayati Raj System.

Give two characteristics of modernization.

Why is it difficult to define a nation?

What is meant by prejudices?

Discuss the impact of liberalization on Indian society.

What are the reasons of higher birth rate in India?

$[NiCl_4]^{2-}$ 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:
\[ C_6H_5NO_2 \xrightarrow{Fe/HCl} (A) \xrightarrow[\text{273 K}]{NaNO_2 + HCl} (B) \xrightarrow[\Delta]{H_2O/H^+} (C) \]