List of top Questions asked in UP Board XII- 2025

What is the reason that made M. Hamel declare that the lesson which he was going to teach on that fateful day, was to be the last lesson?

If \( E_1 \) and \( E_2 \) are mutually exclusive events, then prove that \( P(E_1) + P(E_2) = P(E_1 \cup E_2) + P(E_1 \cap E_2) \).

Write \( \cot^{-1}\left\{\frac{1}{\sqrt{x^2-1}}\right\}; x>1 \) in the simplest form.

Compound of which transition metal ion is colourless?

What is the role of technology in Globalisation ?

Explain with reason:
(i) Cr^{2+} is a reducing agent while Mn^{3+} is an oxidising agent, while both have \(d^4\) configuration.}

Voltage (V) equation in an alternating current circuit is represented by \( V = 40 \sin(100 \pi t) \) volt. Here t is in second. Draw the time-voltage graph for one cycle with proper scale.

Transform any one of the following as directed:
(i) Nainital is not so hot as Agra. (Into Comparative degree)

What is antitoxin?

Describe exponential growth.

The voltage and current of an ac circuit are represented as \( V = 100 \sin(100t) \) volt and \( i = 100 \sin(100t + \frac{\pi}{3}) \) mA respectively. The power dissipated in the circuit is:

Answer the following questions in about 40 words each:
b.What complaint did Rajkumar Shukla file when he came to the Congress Session?

Mention any two causes of Globalization.

Equation of electric field of a plane electromagnetic wave is given as:
\[ E_z = 60 \sin(500x + 1.5 \times 10^{11} t) \, \text{V/m}. \] Write the equation for the magnetic field of the wave.

Find the Cartesian equation of a line which passes through point (3, -2, -5) and is parallel to the vector \( (3\hat{i} + 2\hat{j} - 2\hat{k}) \).

Magnetic moment of a bivalent ion in aqueous solution will be, if its atomic number is 25:

Suppose you are Amit and while playing you used abusive terms to your friend, Vikas. Now, write a letter of apology to him assuring that you will never do it again.

Who guided the model of shock therapy?

The probability of solving a question by the three students A, B, C are respectively \( \frac{3}{10}, \frac{1}{5} \) and \( \frac{1}{10} \). Find the probability of solving the question.

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 \( x\frac{dy}{dx} = \frac{y^2}{1 - y \log x} \).